var bibbase_data = {"data":"<img src=\"//bibbase.org/img/ajax-loader.gif\" id=\"spinner\"\n  style=\"display: none;\" alt=\"Loading..\" />\n\n<div id=\"bibbase\">\n\n  <script type=\"text/javascript\">\n    var bibbase = {\n      params: {\"bib\":\"https://bibbase.org/f/J9gZq33SPmmZsfyhm/pub_list.bib\",\"filter\":\"keywords:pubs\",\"theme\":\"default\",\"jsonp\":\"1\",\"token\":\"f59280376ccfb7587fdcc22b5b0cea15\",\"host\":\"bibbase.org\"},\n      data: [{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This is seen in leaves, flowers, fungi, corals, and marine invertebrates. We investigate this morphology from the perspective of non-Euclidean plate theory. We identify a novel type of defect, a branch-point of the normal map, that allows for the generation of such complex wrinkling patterns in thin elastic hyperbolic surfaces, even in the absence of stretching. We argue that branch points are the natural defects in hyperbolic sheets, they carry a topological charge which gives them a degree of robustness, and they can influence the overall morphology of a hyperbolic surface without concentrating elastic energy. We develop a theory for branch points and investigate their role in determining the mechanical response of hyperbolic sheets to weak external forces.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Yamamoto\"],\"firstnames\":[\"Kenneth\",\"K.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Shearman\"],\"firstnames\":[\"Toby\",\"L.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Struckmeyer\"],\"firstnames\":[\"Erik\",\"J.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Gemmer\"],\"firstnames\":[\"John\",\"A.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]}],\"da\":\"2021/07/13\",\"date-added\":\"2021-07-18 21:03:52 -0700\",\"date-modified\":\"2021-07-18 21:04:38 -0700\",\"doi\":\"10.1140/epje/s10189-021-00099-6\",\"id\":\"Yamamoto:2021wk\",\"isbn\":\"1292-895X\",\"journal\":\"The European Physical Journal E\",\"keywords\":\"pubs\",\"number\":\"7\",\"pages\":\"95\",\"title\":\"Nature's forms are frilly, flexible, and functional\",\"ty\":\"JOUR\",\"url\":\"https://doi.org/10.1140/epje/s10189-021-00099-6\",\"url_arxiv\":\"https://arxiv.org/abs/2103.10509\",\"volume\":\"44\",\"year\":\"2021\",\"bdsk-url-1\":\"https://doi.org/10.1140/epje/s10189-021-00099-6\",\"bibtex\":\"@article{Yamamoto:2021wk,\\n\\tabstract = {A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This is seen in leaves, flowers, fungi, corals, and marine invertebrates. We investigate this morphology from the perspective of non-Euclidean plate theory. We identify a novel type of defect, a branch-point of the normal map, that allows for the generation of such complex wrinkling patterns in thin elastic hyperbolic surfaces, even in the absence of stretching. We argue that branch points are the natural defects in hyperbolic sheets, they carry a topological charge which gives them a degree of robustness, and they can influence the overall morphology of a hyperbolic surface without concentrating elastic energy. We develop a theory for branch points and investigate their role in determining the mechanical response of hyperbolic sheets to weak external forces.},\\n\\tauthor = {Yamamoto, Kenneth K. and Shearman, Toby L. and Struckmeyer, Erik J. and Gemmer, John A. and Venkataramani, Shankar C.},\\n\\tda = {2021/07/13},\\n\\tdate-added = {2021-07-18 21:03:52 -0700},\\n\\tdate-modified = {2021-07-18 21:04:38 -0700},\\n\\tdoi = {10.1140/epje/s10189-021-00099-6},\\n\\tid = {Yamamoto2021},\\n\\tisbn = {1292-895X},\\n\\tjournal = {The European Physical Journal E},\\n\\tkeywords = {pubs},\\n\\tnumber = {7},\\n\\tpages = {95},\\n\\ttitle = {Nature's forms are frilly, flexible, and functional},\\n\\tty = {JOUR},\\n\\turl = {https://doi.org/10.1140/epje/s10189-021-00099-6},\\n\\turl_arxiv = {https://arxiv.org/abs/2103.10509},\\n\\tvolume = {44},\\n\\tyear = {2021},\\n\\tBdsk-Url-1 = {https://doi.org/10.1140/epje/s10189-021-00099-6}}\\n\\n\",\"author_short\":[\"Yamamoto, K. K.\",\"Shearman, T. L.\",\"Struckmeyer, E. J.\",\"Gemmer, J. A.\",\"Venkataramani, S. C.\"],\"key\":\"Yamamoto:2021wk\",\"bibbaseid\":\"yamamoto-shearman-struckmeyer-gemmer-venkataramani-naturesformsarefrillyflexibleandfunctional-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://doi.org/10.1140/epje/s10189-021-00099-6\",\" arxiv\":\"https://arxiv.org/abs/2103.10509\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":14,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We argue that a natural explanation for a variety of robust galaxy scaling relations comes from the perspective of pattern formation and self-organization as a result of symmetry breaking. We propose a simple Lagrangian model that combines a conventional model for normal matter in a galaxy with a conventional model for stripe pattern formation in systems that break continuous translation invariance. We show that the energy stored in the pattern field acts as an effective dark matter. Our theory reproduces the gross features of elliptic galaxies as well as disk galaxies (HSB and LSB) including their detailed rotation curves, the radial acceleration relation, and the Freeman law. We investigate the stability of disk galaxies in the context of our model and obtain scaling relations for the central dispersion for elliptical galaxies. A natural interpretation of our results is that (1) `dark matter'is potentially a collective, emergent phenomenon and not necessarily an as yet undiscovered particle, and (2) MOND is an effective theory for the description of a self-organized complex system rather than a fundamental description of nature that modifies Newton's second law.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Newell\"],\"firstnames\":[\"Alan\",\"C.\"],\"suffixes\":[]}],\"da\":\"2021/06/18\",\"date-added\":\"2021-07-18 20:58:08 -0700\",\"date-modified\":\"2021-07-18 20:59:43 -0700\",\"doi\":\"10.1140/epjs/s11734-021-00196-9\",\"id\":\"Venkataramani:2021tn\",\"isbn\":\"1951-6401\",\"journal\":\"The European Physical Journal Special Topics\",\"keywords\":\"pubs\",\"title\":\"Pattern dark matter and galaxy scaling relations\",\"ty\":\"JOUR\",\"url\":\"https://doi.org/10.1140/epjs/s11734-021-00196-9\",\"url_arxiv\":\"https://arxiv.org/abs/2101.08372\",\"year\":\"2021\",\"bdsk-url-1\":\"https://doi.org/10.1140/epjs/s11734-021-00196-9\",\"bibtex\":\"@article{Venkataramani:2021tn,\\n\\tabstract = {We argue that a natural explanation for a variety of robust galaxy scaling relations comes from the perspective of pattern formation and self-organization as a result of symmetry breaking. We propose a simple Lagrangian model that combines a conventional model for normal matter in a galaxy with a conventional model for stripe pattern formation in systems that break continuous translation invariance. We show that the energy stored in the pattern field acts as an effective dark matter. Our theory reproduces the gross features of elliptic galaxies as well as disk galaxies (HSB and LSB) including their detailed rotation curves, the radial acceleration relation, and the Freeman law. We investigate the stability of disk galaxies in the context of our model and obtain scaling relations for the central dispersion for elliptical galaxies. A natural interpretation of our results is that (1) `dark matter'is potentially a collective, emergent phenomenon and not necessarily an as yet undiscovered particle, and (2) MOND is an effective theory for the description of a self-organized complex system rather than a fundamental description of nature that modifies Newton's second law.},\\n\\tauthor = {Venkataramani, Shankar C. and Newell, Alan C.},\\n\\tda = {2021/06/18},\\n\\tdate-added = {2021-07-18 20:58:08 -0700},\\n\\tdate-modified = {2021-07-18 20:59:43 -0700},\\n\\tdoi = {10.1140/epjs/s11734-021-00196-9},\\n\\tid = {Venkataramani2021},\\n\\tisbn = {1951-6401},\\n\\tjournal = {The European Physical Journal Special Topics},\\n\\tkeywords = {pubs},\\n\\ttitle = {Pattern dark matter and galaxy scaling relations},\\n\\tty = {JOUR},\\n\\turl = {https://doi.org/10.1140/epjs/s11734-021-00196-9},\\n\\turl_arxiv = {https://arxiv.org/abs/2101.08372},\\n\\tyear = {2021},\\n\\tBdsk-Url-1 = {https://doi.org/10.1140/epjs/s11734-021-00196-9}}\\n\\n\",\"author_short\":[\"Venkataramani, S. C.\",\"Newell, A. C.\"],\"key\":\"Venkataramani:2021tn\",\"bibbaseid\":\"venkataramani-newell-patterndarkmatterandgalaxyscalingrelations-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://doi.org/10.1140/epjs/s11734-021-00196-9\",\" arxiv\":\"https://arxiv.org/abs/2101.08372\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":12,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they appear as `unphysical' singularities, with non-integrable energy densities in coarse-grained macroscopic models. We develop a principled approach for enriching coarse-grained theories with enough of the `micro-physics' to obtain thermodynamically consistent, well-set models that allow for the investigations of dynamics and interactions of defects in extended systems. We also develop associated numerical methods that are applicable to computing energy driven behaviors of defects across the amorphous-soft-crystalline materials spectrum. Our methods can handle order parameters that have a head-tail symmetry, i.e. director fields, in systems with a continuous translation symmetry, as in nematic liquid crystals, and in systems where the translation symmetry is broken, as in smectics and convection patterns. We illustrate our methods with explicit computations.\",\"author\":[{\"firstnames\":[\"Chiqun\"],\"propositions\":[],\"lastnames\":[\"Zhang\"],\"suffixes\":[]},{\"firstnames\":[\"Amit\"],\"propositions\":[],\"lastnames\":[\"Acharya\"],\"suffixes\":[]},{\"firstnames\":[\"Alan\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Newell\"],\"suffixes\":[]},{\"firstnames\":[\"Shankar\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"suffixes\":[]}],\"date-added\":\"2021-05-29 14:50:02 -0700\",\"date-modified\":\"2021-05-29 14:50:42 -0700\",\"doi\":\"https://doi.org/10.1016/j.physd.2020.132828\",\"issn\":\"0167-2789\",\"journal\":\"Physica D: Nonlinear Phenomena\",\"keywords\":\"pubs,Defects in materials, Non-orientability, Effective theories, Liquid crystals, Pattern formation, Computation of defects\",\"pages\":\"132828\",\"title\":\"Computing with non-orientable defects: Nematics, smectics and natural patterns\",\"url\":\"https://www.sciencedirect.com/science/article/pii/S0167278920308290\",\"volume\":\"417\",\"year\":\"2021\",\"bdsk-url-1\":\"https://www.sciencedirect.com/science/article/pii/S0167278920308290\",\"bdsk-url-2\":\"https://doi.org/10.1016/j.physd.2020.132828\",\"bibtex\":\"@article{Zhang20211Computing,\\n\\tabstract = {Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they appear as `unphysical' singularities, with non-integrable energy densities in coarse-grained macroscopic models. We develop a principled approach for enriching coarse-grained theories with enough of the `micro-physics' to obtain thermodynamically consistent, well-set models that allow for the investigations of dynamics and interactions of defects in extended systems. We also develop associated numerical methods that are applicable to computing energy driven behaviors of defects across the amorphous-soft-crystalline materials spectrum. Our methods can handle order parameters that have a head-tail symmetry, i.e. director fields, in systems with a continuous translation symmetry, as in nematic liquid crystals, and in systems where the translation symmetry is broken, as in smectics and convection patterns. We illustrate our methods with explicit computations.},\\n\\tauthor = {Chiqun Zhang and Amit Acharya and Alan C. Newell and Shankar C. Venkataramani},\\n\\tdate-added = {2021-05-29 14:50:02 -0700},\\n\\tdate-modified = {2021-05-29 14:50:42 -0700},\\n\\tdoi = {https://doi.org/10.1016/j.physd.2020.132828},\\n\\tissn = {0167-2789},\\n\\tjournal = {Physica D: Nonlinear Phenomena},\\n\\tkeywords = {pubs,Defects in materials, Non-orientability, Effective theories, Liquid crystals, Pattern formation, Computation of defects},\\n\\tpages = {132828},\\n\\ttitle = {Computing with non-orientable defects: Nematics, smectics and natural patterns},\\n\\turl = {https://www.sciencedirect.com/science/article/pii/S0167278920308290},\\n\\tvolume = {417},\\n\\tyear = {2021},\\n\\tBdsk-Url-1 = {https://www.sciencedirect.com/science/article/pii/S0167278920308290},\\n\\tBdsk-Url-2 = {https://doi.org/10.1016/j.physd.2020.132828}}\\n\\n\",\"author_short\":[\"Zhang, C.\",\"Acharya, A.\",\"Newell, A. C.\",\"Venkataramani, S. C.\"],\"key\":\"Zhang20211Computing\",\"id\":\"Zhang20211Computing\",\"bibbaseid\":\"zhang-acharya-newell-venkataramani-computingwithnonorientabledefectsnematicssmecticsandnaturalpatterns-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://www.sciencedirect.com/science/article/pii/S0167278920308290\"},\"keyword\":[\"pubs\",\"Defects in materials\",\"Non-orientability\",\"Effective theories\",\"Liquid crystals\",\"Pattern formation\",\"Computation of defects\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":7,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Jaramillo\"],\"firstnames\":[\"Gabriela\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]}],\"date-added\":\"2021-05-29 14:38:32 -0700\",\"date-modified\":\"2021-05-29 14:39:29 -0700\",\"doi\":\"10.1137/19M1306907\",\"eprint\":\"https://doi.org/10.1137/19M1306907\",\"journal\":\"Multiscale Modeling & Simulation\",\"keywords\":\"pubs\",\"number\":\"2\",\"pages\":\"886-920\",\"title\":\"A Modified Split Bregman Algorithm for Computing Microstructures Through Young Measures\",\"url\":\"https://doi.org/10.1137/19M1306907\",\"url_arxiv\":\"https://arxiv.org/abs/1912.03360\",\"volume\":\"19\",\"year\":\"2021\",\"bdsk-url-1\":\"https://doi.org/10.1137/19M1306907\",\"bibtex\":\"@article{jaramillo2019microstructure,\\n\\tauthor = {Jaramillo, Gabriela and Venkataramani, Shankar C.},\\n\\tdate-added = {2021-05-29 14:38:32 -0700},\\n\\tdate-modified = {2021-05-29 14:39:29 -0700},\\n\\tdoi = {10.1137/19M1306907},\\n\\teprint = {https://doi.org/10.1137/19M1306907},\\n\\tjournal = {Multiscale Modeling \\\\& Simulation},\\n\\tkeywords = {pubs},\\n\\tnumber = {2},\\n\\tpages = {886-920},\\n\\ttitle = {A Modified Split Bregman Algorithm for Computing Microstructures Through Young Measures},\\n\\turl = {https://doi.org/10.1137/19M1306907},\\n\\turl_arxiv = {https://arxiv.org/abs/1912.03360},\\n\\tvolume = {19},\\n\\tyear = {2021},\\n\\tBdsk-Url-1 = {https://doi.org/10.1137/19M1306907}}\\n\\n\",\"author_short\":[\"Jaramillo, G.\",\"Venkataramani, S. C.\"],\"key\":\"jaramillo2019microstructure\",\"id\":\"jaramillo2019microstructure\",\"bibbaseid\":\"jaramillo-venkataramani-amodifiedsplitbregmanalgorithmforcomputingmicrostructuresthroughyoungmeasures-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://doi.org/10.1137/19M1306907\",\" arxiv\":\"https://arxiv.org/abs/1912.03360\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":5,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Shearman\"],\"firstnames\":[\"Toby\",\"L\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C\"],\"suffixes\":[]}],\"date-added\":\"2021-05-23 19:13:38 -0700\",\"date-modified\":\"2021-05-23 19:14:52 -0700\",\"journal\":\"Journal of Nonlinear Science\",\"keywords\":\"pubs\",\"number\":\"1\",\"pages\":\"1–60\",\"publisher\":\"Springer\",\"title\":\"Distributed Branch Points and the Shape of Elastic Surfaces with Constant Negative Curvature\",\"url_arxiv\":\"https://arxiv.org/abs/2006.14461\",\"volume\":\"31\",\"year\":\"2021\",\"bibtex\":\"@article{shearman2021distributed,\\n\\tauthor = {Shearman, Toby L and Venkataramani, Shankar C},\\n\\tdate-added = {2021-05-23 19:13:38 -0700},\\n\\tdate-modified = {2021-05-23 19:14:52 -0700},\\n\\tjournal = {Journal of Nonlinear Science},\\n\\tkeywords = {pubs},\\n\\tnumber = {1},\\n\\tpages = {1--60},\\n\\tpublisher = {Springer},\\n\\ttitle = {Distributed Branch Points and the Shape of Elastic Surfaces with Constant Negative Curvature},\\n\\turl_arxiv = {https://arxiv.org/abs/2006.14461},\\n\\tvolume = {31},\\n\\tyear = {2021}}\\n\\n\",\"author_short\":[\"Shearman, T. L\",\"Venkataramani, S. C\"],\"key\":\"shearman2021distributed\",\"id\":\"shearman2021distributed\",\"bibbaseid\":\"shearman-venkataramani-distributedbranchpointsandtheshapeofelasticsurfaceswithconstantnegativecurvature-2021\",\"role\":\"author\",\"urls\":{\" arxiv\":\"https://arxiv.org/abs/2006.14461\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":4,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"Galaxies are built by complex physical processes with significant inherent stochasticity. It is therefore surprising that the inferred dark matter distributions in galaxies are correlated with the observed baryon distributions leading to various `Baryon-Halo conspiracies'. The fact that no dark matter candidate has been definitively identified invites a search for alternative explanations for such correlations and we present an approach motivated by the behaviors of self organized patterns. We propose a nonlocal relativistic Lagrangian theory for a `pattern field' which acts as an `effective dark matter', built on the idea that defects in this pattern field couple to the baryonic matter distribution. The model applies to rotation supported systems and, for them, we compute galactic rotation curves, obtain a radial acceleration relation with two branches, and deduce the Freeman limit for central surface brightness.\",\"author\":[{\"firstnames\":[\"Shankar\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"suffixes\":[]},{\"firstnames\":[\"Alan\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Newell\"],\"suffixes\":[]}],\"date-added\":\"2021-05-23 19:11:31 -0700\",\"date-modified\":\"2021-05-23 19:17:57 -0700\",\"doi\":\"https://doi.org/10.1016/j.physletb.2020.136060\",\"issn\":\"0370-2693\",\"journal\":\"Physics Letters B\",\"keywords\":\"pubs,Self-organized patterns, Symmetry breaking, Defects, Dark matter, Galaxy scaling relations\",\"pages\":\"136060\",\"title\":\"Disk galaxies and their dark halos as self-organized patterns\",\"url\":\"https://www.sciencedirect.com/science/article/pii/S0370269320308637\",\"url_arxiv\":\"https://arxiv.org/abs/1910.14649\",\"volume\":\"813\",\"year\":\"2021\",\"bdsk-url-1\":\"https://www.sciencedirect.com/science/article/pii/S0370269320308637\",\"bdsk-url-2\":\"https://doi.org/10.1016/j.physletb.2020.136060\",\"bibtex\":\"@article{PatternDM,\\n\\tabstract = {Galaxies are built by complex physical processes with significant inherent stochasticity. It is therefore surprising that the inferred dark matter distributions in galaxies are correlated with the observed baryon distributions leading to various `Baryon-Halo conspiracies'. The fact that no dark matter candidate has been definitively identified invites a search for alternative explanations for such correlations and we present an approach motivated by the behaviors of self organized patterns. We propose a nonlocal relativistic Lagrangian theory for a `pattern field' which acts as an `effective dark matter', built on the idea that defects in this pattern field couple to the baryonic matter distribution. The model applies to rotation supported systems and, for them, we compute galactic rotation curves, obtain a radial acceleration relation with two branches, and deduce the Freeman limit for central surface brightness.},\\n\\tauthor = {Shankar C. Venkataramani and Alan C. Newell},\\n\\tdate-added = {2021-05-23 19:11:31 -0700},\\n\\tdate-modified = {2021-05-23 19:17:57 -0700},\\n\\tdoi = {https://doi.org/10.1016/j.physletb.2020.136060},\\n\\tissn = {0370-2693},\\n\\tjournal = {Physics Letters B},\\n\\tkeywords = {pubs,Self-organized patterns, Symmetry breaking, Defects, Dark matter, Galaxy scaling relations},\\n\\tpages = {136060},\\n\\ttitle = {Disk galaxies and their dark halos as self-organized patterns},\\n\\turl = {https://www.sciencedirect.com/science/article/pii/S0370269320308637},\\n\\turl_arxiv = {https://arxiv.org/abs/1910.14649},\\n\\tvolume = {813},\\n\\tyear = {2021},\\n\\tBdsk-Url-1 = {https://www.sciencedirect.com/science/article/pii/S0370269320308637},\\n\\tBdsk-Url-2 = {https://doi.org/10.1016/j.physletb.2020.136060}}\\n\\n\",\"author_short\":[\"Venkataramani, S. C.\",\"Newell, A. C.\"],\"key\":\"PatternDM\",\"id\":\"PatternDM\",\"bibbaseid\":\"venkataramani-newell-diskgalaxiesandtheirdarkhalosasselforganizedpatterns-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://www.sciencedirect.com/science/article/pii/S0370269320308637\",\" arxiv\":\"https://arxiv.org/abs/1910.14649\"},\"keyword\":[\"pubs\",\"Self-organized patterns\",\"Symmetry breaking\",\"Defects\",\"Dark matter\",\"Galaxy scaling relations\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":6,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"Growth and other dynamical processes in soft materials can create novel types of mesoscopic defects including discontinuities for the second and higher derivatives of the deformation, and terminating defects for these discontinuities. These higher-order defects move ``easily\\\", and can thus confer a great degree of flexibility to the material. We develop a general continuum mechanical framework from which we can derive the dynamics of higher order defects in a thermodynamically consistent manner. We illustrate our framework by obtaining the explicit dynamical equations for the next higher order defects in an elastic body beyond dislocations, phase boundaries, and disclinations, namely, surfaces of inflection and branch lines.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Acharya\"],\"firstnames\":[\"Amit\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]}],\"da\":\"2020/04/16\",\"date-added\":\"2020-05-25 22:56:27 -0700\",\"date-modified\":\"2020-05-25 23:08:19 -0700\",\"doi\":\"10.1186/s41313-020-00018-w\",\"id\":\"Acharya2020mechanics\",\"isbn\":\"2509-8012\",\"journal\":\"Materials Theory\",\"keywords\":\"pubs\",\"number\":\"1\",\"pages\":\"2\",\"title\":\"Mechanics of moving defects in growing sheets: 3-d, small deformation theory\",\"ty\":\"JOUR\",\"url\":\"https://doi.org/10.1186/s41313-020-00018-w\",\"url_arxiv\":\"https://arxiv.org/abs/1906.08122\",\"volume\":\"4\",\"year\":\"2020\",\"bdsk-url-1\":\"https://doi.org/10.1186/s41313-020-00018-w\",\"bibtex\":\"@article{Acharya2020mechanics,\\n\\tabstract = {Growth and other dynamical processes in soft materials can create novel types of mesoscopic defects including discontinuities for the second and higher derivatives of the deformation, and terminating defects for these discontinuities. These higher-order defects move ``easily\\\", and can thus confer a great degree of flexibility to the material. We develop a general continuum mechanical framework from which we can derive the dynamics of higher order defects in a thermodynamically consistent manner. We illustrate our framework by obtaining the explicit dynamical equations for the next higher order defects in an elastic body beyond dislocations, phase boundaries, and disclinations, namely, surfaces of inflection and branch lines.},\\n\\tauthor = {Acharya, Amit and Venkataramani, Shankar C.},\\n\\tda = {2020/04/16},\\n\\tdate-added = {2020-05-25 22:56:27 -0700},\\n\\tdate-modified = {2020-05-25 23:08:19 -0700},\\n\\tdoi = {10.1186/s41313-020-00018-w},\\n\\tid = {Acharya2020},\\n\\tisbn = {2509-8012},\\n\\tjournal = {Materials Theory},\\n\\tkeywords = {pubs},\\n\\tnumber = {1},\\n\\tpages = {2},\\n\\ttitle = {Mechanics of moving defects in growing sheets: 3-d, small deformation theory},\\n\\tty = {JOUR},\\n\\turl = {https://doi.org/10.1186/s41313-020-00018-w},\\n\\turl_arxiv = {https://arxiv.org/abs/1906.08122},\\n\\tvolume = {4},\\n\\tyear = {2020},\\n\\tBdsk-Url-1 = {https://doi.org/10.1186/s41313-020-00018-w}}\\n\\n\",\"author_short\":[\"Acharya, A.\",\"Venkataramani, S. C.\"],\"key\":\"Acharya2020mechanics\",\"bibbaseid\":\"acharya-venkataramani-mechanicsofmovingdefectsingrowingsheets3dsmalldeformationtheory-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://doi.org/10.1186/s41313-020-00018-w\",\" arxiv\":\"https://arxiv.org/abs/1906.08122\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":4,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"abstract\":\"We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known that the graph evolution condenses, that is a.s. in the limit graph there will be a single random node with infinite degree, while all others have finite degree. In this note, we establish a.s. law of large numbers type limits and fluctuation results, as $}{$n$\\\\$uparrow $\\\\$infty $}{$, for the counts of the number of nodes with degree $}{$k$\\\\$ge 1$}{$at time $}{$n$\\\\$ge 1$}{$. These limits rigorously verify and extend a physical picture of Krapivisky et al. (Phys Rev Lett 85:4629–4632, 2000 $[$16$]$) on how the condensation arises with respect to the degree distribution.\",\"address\":\"Cham\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Sethuraman\"],\"firstnames\":[\"Sunder\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]}],\"booktitle\":\"Probability and Analysis in Interacting Physical Systems\",\"da\":\"2019//\",\"date-added\":\"2019-11-04 23:11:43 -0700\",\"date-modified\":\"2019-11-04 23:14:02 -0700\",\"editor\":[{\"propositions\":[],\"lastnames\":[\"Friz\"],\"firstnames\":[\"Peter\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"König\"],\"firstnames\":[\"Wolfgang\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Mukherjee\"],\"firstnames\":[\"Chiranjib\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Olla\"],\"firstnames\":[\"Stefano\"],\"suffixes\":[]}],\"id\":\"Sethuraman2019growth\",\"isbn\":\"978-3-030-15338-0\",\"keywords\":\"pubs\",\"pages\":\"243–265\",\"publisher\":\"Springer International Publishing\",\"title\":\"On the Growth of a Superlinear Preferential Attachment Scheme\",\"ty\":\"CONF\",\"url\":\"https://link.springer.com/chapter/10.1007/978-3-030-15338-0_9\",\"url_arxiv\":\"https://arxiv.org/abs/1704.05568\",\"year\":\"2019\",\"bdsk-url-1\":\"https://link.springer.com/chapter/10.1007/978-3-030-15338-0_9\",\"bibtex\":\"@inproceedings{Sethuraman2019growth,\\n\\tabstract = {We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known that the graph evolution condenses, that is a.s. in the limit graph there will be a single random node with infinite degree, while all others have finite degree. In this note, we establish a.s. law of large numbers type limits and fluctuation results, as {\\\\$}{\\\\$}n{$\\\\backslash$}uparrow {$\\\\backslash$}infty {\\\\$}{\\\\$}, for the counts of the number of nodes with degree {\\\\$}{\\\\$}k{$\\\\backslash$}ge 1{\\\\$}{\\\\$}at time {\\\\$}{\\\\$}n{$\\\\backslash$}ge 1{\\\\$}{\\\\$}. These limits rigorously verify and extend a physical picture of Krapivisky et al. (Phys Rev Lett 85:4629--4632, 2000 {$[$}16{$]$}) on how the condensation arises with respect to the degree distribution.},\\n\\taddress = {Cham},\\n\\tauthor = {Sethuraman, Sunder and Venkataramani, Shankar C.},\\n\\tbooktitle = {Probability and Analysis in Interacting Physical Systems},\\n\\tda = {2019//},\\n\\tdate-added = {2019-11-04 23:11:43 -0700},\\n\\tdate-modified = {2019-11-04 23:14:02 -0700},\\n\\teditor = {Friz, Peter and K{\\\\\\\"o}nig, Wolfgang and Mukherjee, Chiranjib and Olla, Stefano},\\n\\tid = {10.1007/978-3-030-15338-0{\\\\_}9},\\n\\tisbn = {978-3-030-15338-0},\\n\\tkeywords = {pubs},\\n\\tpages = {243--265},\\n\\tpublisher = {Springer International Publishing},\\n\\ttitle = {On the Growth of a Superlinear Preferential Attachment Scheme},\\n\\tty = {CONF},\\n\\turl = {https://link.springer.com/chapter/10.1007/978-3-030-15338-0_9},\\n\\turl_arxiv = {https://arxiv.org/abs/1704.05568},\\n\\tyear = {2019},\\n\\tBdsk-Url-1 = {https://link.springer.com/chapter/10.1007/978-3-030-15338-0_9}}\\n\\n\",\"author_short\":[\"Sethuraman, S.\",\"Venkataramani, S. C.\"],\"editor_short\":[\"Friz, P.\",\"König, W.\",\"Mukherjee, C.\",\"Olla, S.\"],\"key\":\"Sethuraman2019growth\",\"bibbaseid\":\"sethuraman-venkataramani-onthegrowthofasuperlinearpreferentialattachmentscheme-2019\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://link.springer.com/chapter/10.1007/978-3-030-15338-0_9\",\" arxiv\":\"https://arxiv.org/abs/1704.05568\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"In this essay we explore analogies between macroscopic patterns, which result from a sequence of phase transitions/instabilities starting from a homogeneous state, and similar phenomena in cosmology, where a sequence of phase transitions in the early universe is believed to have separated the fundamental forces from each other, and also shaped the structure and distribution of matter in the universe. We discuss three distinct aspects of this analogy: (i) Defects and topological charges in macroscopic patterns are analogous to spins and charges of quarks and leptons; (ii) Defects in generic 3+1 stripe patterns carry an energy density that accounts for phenomena that are currently attributed to dark matter; (iii) Space-time patterns of interacting nonlinear waves display behaviors reminiscent of quantum phenomena including inflation, entanglement and dark energy. Résumé Dans cet article, nous explorons plusieurs analogies entre la formation de structures périodiques macroscopiques, qui résultent de la succession de transitions de phase ou d'instabilités, et certains phénomènes similaires en cosmologie, où une suite de transitions de phase dans l'univers primordial aurait donné lieu à la séparation des forces fondamentales et à la formation des structures. Nous considérons trois analogies différentes : (i) les défauts et charges topologiques dans les structures macroscopiques sont analogues aux spins et charges des quarks et des leptons ; (ii) les défauts dans les structures périodiques génériques (en dimensions 3+1) ont une densité d'énergie qui donne lieu à certains phénomènes attribués à la présence de matière noire ; (iii) les structures spatio-temporelles résultant de l'interaction d'ondes non linéaires ont des comportements qui rappellent certains phénomènes quantiques, tels que l'inflation cosmique, l'enchevêtrement quantique et l'énergie noire.\",\"author\":[{\"firstnames\":[\"Alan\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Newell\"],\"suffixes\":[]},{\"firstnames\":[\"Shankar\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"suffixes\":[]}],\"date-added\":\"2019-11-04 23:01:37 -0700\",\"date-modified\":\"2019-11-04 23:03:49 -0700\",\"doi\":\"https://doi.org/10.1016/j.crme.2019.03.004\",\"issn\":\"1631-0721\",\"journal\":\"Comptes Rendus Mécanique\",\"keywords\":\"pubs,Pattern formation, Cosmology, Phase transitions, Formation de motifs, Cosmologie, Transition de phase\",\"note\":\"Patterns and dynamics: homage to Pierre Coullet / Formes et dynamique: hommage à Pierre Coullet\",\"number\":\"4\",\"pages\":\"318 - 331\",\"title\":\"Pattern universes\",\"url_arxiv\":\"https://arxiv.org/abs/1811.10546\",\"url_journal\":\"http://www.sciencedirect.com/science/article/pii/S1631072119300464\",\"volume\":\"347\",\"year\":\"2019\",\"bdsk-url-1\":\"http://www.sciencedirect.com/science/article/pii/S1631072119300464\",\"bdsk-url-2\":\"https://doi.org/10.1016/j.crme.2019.03.004\",\"bibtex\":\"@article{NV19,\\n\\tabstract = {In this essay we explore analogies between macroscopic patterns, which result from a sequence of phase transitions/instabilities starting from a homogeneous state, and similar phenomena in cosmology, where a sequence of phase transitions in the early universe is believed to have separated the fundamental forces from each other, and also shaped the structure and distribution of matter in the universe. We discuss three distinct aspects of this analogy: (i) Defects and topological charges in macroscopic patterns are analogous to spins and charges of quarks and leptons; (ii) Defects in generic 3+1 stripe patterns carry an energy density that accounts for phenomena that are currently attributed to dark matter; (iii) Space-time patterns of interacting nonlinear waves display behaviors reminiscent of quantum phenomena including inflation, entanglement and dark energy.\\nR{\\\\'e}sum{\\\\'e}\\nDans cet article, nous explorons plusieurs analogies entre la formation de structures p{\\\\'e}riodiques macroscopiques, qui r{\\\\'e}sultent de la succession de transitions de phase ou d'instabilit{\\\\'e}s, et certains ph{\\\\'e}nom{\\\\`e}nes similaires en cosmologie, o{\\\\`u} une suite de transitions de phase dans l'univers primordial aurait donn{\\\\'e} lieu {\\\\`a} la s{\\\\'e}paration des forces fondamentales et {\\\\`a} la formation des structures. Nous consid{\\\\'e}rons trois analogies diff{\\\\'e}rentes : (i) les d{\\\\'e}fauts et charges topologiques dans les structures macroscopiques sont analogues aux spins et charges des quarks et des leptons ; (ii) les d{\\\\'e}fauts dans les structures p{\\\\'e}riodiques g{\\\\'e}n{\\\\'e}riques (en dimensions 3+1) ont une densit{\\\\'e} d'{\\\\'e}nergie qui donne lieu {\\\\`a} certains ph{\\\\'e}nom{\\\\`e}nes attribu{\\\\'e}s {\\\\`a} la pr{\\\\'e}sence de mati{\\\\`e}re noire ; (iii) les structures spatio-temporelles r{\\\\'e}sultant de l'interaction d'ondes non lin{\\\\'e}aires ont des comportements qui rappellent certains ph{\\\\'e}nom{\\\\`e}nes quantiques, tels que l'inflation cosmique, l'enchev{\\\\^e}trement quantique et l'{\\\\'e}nergie noire.},\\n\\tauthor = {Alan C. Newell and Shankar C. Venkataramani},\\n\\tdate-added = {2019-11-04 23:01:37 -0700},\\n\\tdate-modified = {2019-11-04 23:03:49 -0700},\\n\\tdoi = {https://doi.org/10.1016/j.crme.2019.03.004},\\n\\tissn = {1631-0721},\\n\\tjournal = {Comptes Rendus M{\\\\'e}canique},\\n\\tkeywords = {pubs,Pattern formation, Cosmology, Phase transitions, Formation de motifs, Cosmologie, Transition de phase},\\n\\tnote = {Patterns and dynamics: homage to Pierre Coullet / Formes et dynamique: hommage {\\\\`a} Pierre Coullet},\\n\\tnumber = {4},\\n\\tpages = {318 - 331},\\n\\ttitle = {Pattern universes},\\n\\turl_arxiv = {https://arxiv.org/abs/1811.10546},\\n\\turl_journal = {http://www.sciencedirect.com/science/article/pii/S1631072119300464},\\n\\tvolume = {347},\\n\\tyear = {2019},\\n\\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S1631072119300464},\\n\\tBdsk-Url-2 = {https://doi.org/10.1016/j.crme.2019.03.004}}\\n\\n\",\"author_short\":[\"Newell, A. C.\",\"Venkataramani, S. C.\"],\"key\":\"NV19\",\"id\":\"NV19\",\"bibbaseid\":\"newell-venkataramani-patternuniverses-2019\",\"role\":\"author\",\"urls\":{\" arxiv\":\"https://arxiv.org/abs/1811.10546\",\" journal\":\"http://www.sciencedirect.com/science/article/pii/S1631072119300464\"},\"keyword\":[\"pubs\",\"Pattern formation\",\"Cosmology\",\"Phase transitions\",\"Formation de motifs\",\"Cosmologie\",\"Transition de phase\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":3,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We propose a time dependent Eulerian model for sea surface entrainment, buoyancy transport and droplet dynamics of ocean oil. The model captures the microscale vertical oil mass exchanges in the neighborhood of the sea surface. This model is in turn part of an oil fate model designed to capture oil dynamics at large spatio-temporal scales typical of environmental studies. The adiabatic dynamics of the droplets are upscaled by a combination of filtering and stochastic parametrization. The upscaling addresses the computational burden of resolving the microscale. The upscaled droplet dynamics are tested against data and the mass exchange mechanism is incorporated into a nearshore oil transport model in order to highlight the importance of incorporating vertical mass exchanges and droplet distribution dynamics in predicting the distributing of shoaling oil.\",\"author\":[{\"firstnames\":[\"Jorge\"],\"propositions\":[],\"lastnames\":[\"Ramírez\"],\"suffixes\":[]},{\"firstnames\":[\"Saeed\"],\"propositions\":[],\"lastnames\":[\"Moghimi\"],\"suffixes\":[]},{\"firstnames\":[\"Juan\",\"M.\"],\"propositions\":[],\"lastnames\":[\"Restrepo\"],\"suffixes\":[]},{\"firstnames\":[\"Shankar\"],\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"suffixes\":[]}],\"date-added\":\"2019-03-20 20:59:16 -0700\",\"date-modified\":\"2019-03-20 21:42:06 -0700\",\"doi\":\"https://doi.org/10.1016/j.ocemod.2018.06.004\",\"issn\":\"1463-5003\",\"journal\":\"Ocean Modelling\",\"keywords\":\"Oil spill; Oil fate model; Oil entrainment; Ocean oil transport; Ocean pollution; pubs\",\"month\":\"September\",\"pages\":\"1 - 12\",\"title\":\"Modelling the mass exchange dynamics of oceanic surface and subsurface oil\",\"url\":\"http://www.sciencedirect.com/science/article/pii/S1463500318302087\",\"url_arxiv\":\"https://arxiv.org/abs/1703.05361\",\"volume\":\"129\",\"year\":\"2018\",\"bdsk-url-1\":\"http://www.sciencedirect.com/science/article/pii/S1463500318302087\",\"bdsk-url-2\":\"https://doi.org/10.1016/j.ocemod.2018.06.004\",\"bibtex\":\"@article{2018b,\\n\\tabstract = {We propose a time dependent Eulerian model for sea surface entrainment, buoyancy transport and droplet dynamics of ocean oil. The model captures the microscale vertical oil mass exchanges in the neighborhood of the sea surface. This model is in turn part of an oil fate model designed to capture oil dynamics at large spatio-temporal scales typical of environmental studies. The adiabatic dynamics of the droplets are upscaled by a combination of filtering and stochastic parametrization. The upscaling addresses the computational burden of resolving the microscale. The upscaled droplet dynamics are tested against data and the mass exchange mechanism is incorporated into a nearshore oil transport model in order to highlight the importance of incorporating vertical mass exchanges and droplet distribution dynamics in predicting the distributing of shoaling oil.},\\n\\tauthor = {Jorge Ram\\\\'{i}rez and Saeed Moghimi and Juan M. Restrepo and Shankar Venkataramani},\\n\\tdate-added = {2019-03-20 20:59:16 -0700},\\n\\tdate-modified = {2019-03-20 21:42:06 -0700},\\n\\tdoi = {https://doi.org/10.1016/j.ocemod.2018.06.004},\\n\\tissn = {1463-5003},\\n\\tjournal = {Ocean Modelling},\\n\\tkeywords = {Oil spill; Oil fate model; Oil entrainment; Ocean oil transport; Ocean pollution; pubs},\\n\\tmonth = {September},\\n\\tpages = {1 - 12},\\n\\ttitle = {Modelling the mass exchange dynamics of oceanic surface and subsurface oil},\\n\\turl = {http://www.sciencedirect.com/science/article/pii/S1463500318302087},\\n\\turl_arxiv = {https://arxiv.org/abs/1703.05361},\\n\\tvolume = {129},\\n\\tyear = {2018},\\n\\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S1463500318302087},\\n\\tBdsk-Url-2 = {https://doi.org/10.1016/j.ocemod.2018.06.004}}\\n\\n\",\"author_short\":[\"Ramírez, J.\",\"Moghimi, S.\",\"Restrepo, J. M.\",\"Venkataramani, S.\"],\"key\":\"2018b\",\"id\":\"2018b\",\"bibbaseid\":\"ramirez-moghimi-restrepo-venkataramani-modellingthemassexchangedynamicsofoceanicsurfaceandsubsurfaceoil-2018\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://www.sciencedirect.com/science/article/pii/S1463500318302087\",\" arxiv\":\"https://arxiv.org/abs/1703.05361\"},\"keyword\":[\"Oil spill; Oil fate model; Oil entrainment; Ocean oil transport; Ocean pollution; pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]}],\"date-added\":\"2019-03-20 20:33:42 -0700\",\"date-modified\":\"2019-03-20 20:35:03 -0700\",\"doi\":\"10.1073/pnas.1820937116\",\"eprint\":\"https://www.pnas.org/content/116/5/1477.full.pdf\",\"issn\":\"0027-8424\",\"journal\":\"Proceedings of the National Academy of Sciences\",\"keywords\":\"pubs\",\"month\":\"January\",\"number\":\"5\",\"pages\":\"1477–1479\",\"publisher\":\"National Academy of Sciences\",\"title\":\"Buckling sheets open a door to understanding self-organization in soft matter\",\"url\":\"https://www.pnas.org/content/116/5/1477\",\"url_arxiv\":\"https://arxiv.org/abs/1901.03032\",\"volume\":\"116\",\"year\":\"2019\",\"bdsk-url-1\":\"https://www.pnas.org/content/116/5/1477\",\"bdsk-url-2\":\"https://doi.org/10.1073/pnas.1820937116\",\"bibtex\":\"@article{2019a,\\n\\tauthor = {Venkataramani, Shankar C.},\\n\\tdate-added = {2019-03-20 20:33:42 -0700},\\n\\tdate-modified = {2019-03-20 20:35:03 -0700},\\n\\tdoi = {10.1073/pnas.1820937116},\\n\\teprint = {https://www.pnas.org/content/116/5/1477.full.pdf},\\n\\tissn = {0027-8424},\\n\\tjournal = {Proceedings of the National Academy of Sciences},\\n\\tkeywords = {pubs},\\n\\tmonth = {January},\\n\\tnumber = {5},\\n\\tpages = {1477--1479},\\n\\tpublisher = {National Academy of Sciences},\\n\\ttitle = {Buckling sheets open a door to understanding self-organization in soft matter},\\n\\turl = {https://www.pnas.org/content/116/5/1477},\\n\\turl_arxiv = {https://arxiv.org/abs/1901.03032},\\n\\tvolume = {116},\\n\\tyear = {2019},\\n\\tBdsk-Url-1 = {https://www.pnas.org/content/116/5/1477},\\n\\tBdsk-Url-2 = {https://doi.org/10.1073/pnas.1820937116}}\\n\\n\",\"author_short\":[\"Venkataramani, S. C.\"],\"key\":\"2019a\",\"id\":\"2019a\",\"bibbaseid\":\"venkataramani-bucklingsheetsopenadoortounderstandingselforganizationinsoftmatter-2019\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://www.pnas.org/content/116/5/1477\",\" arxiv\":\"https://arxiv.org/abs/1901.03032\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We analyze the effect of adding a weak, localized, inhomogeneity to a two dimensional array of oscillators with nonlocal coupling. We propose and also justify a model for the phase dynamics in this system. Our model is a generalization of a viscous eikonal equation that is known to describe the phase modulation of traveling waves in reaction–diffusion systems. We show the existence of a branch of target pattern solutions that bifurcates from the spatially homogeneous state when , the strength of the inhomogeneity, is nonzero and we also show that these target patterns have an asymptotic wavenumber that is small beyond all orders in . The strategy of our proof is to pose a good ansatz for an approximate form of the solution and use the implicit function theorem to prove the existence of a solution in its vicinity. The analysis presents two challenges. First, the linearization about the homogeneous state is a convolution operator of diffusive type and hence not invertible on the usual Sobolev spaces. Second, a regular perturbation expansion in does not provide a good ansatz for applying the implicit function theorem since the nonlinearities play a major role in determining the relevant approximation, which also needs to be `correct' to all orders in . We overcome these two points by proving Fredholm properties for the linearization in appropriate Kondratiev spaces and using a refined ansatz for the approximate solution which was obtained using matched asymptotics.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Jaramillo\"],\"firstnames\":[\"Gabriela\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C\"],\"suffixes\":[]}],\"da\":\"2018/07/27\",\"date-added\":\"2019-03-20 14:49:42 -0700\",\"date-modified\":\"2019-03-20 15:07:42 -0700\",\"doi\":\"10.1088/1361-6544/aac9a6\",\"isbn\":\"0951-7715; 1361-6544\",\"journal\":\"Nonlinearity\",\"keywords\":\"pubs\",\"number\":\"9\",\"pages\":\"4162-4201\",\"publisher\":\"IOP Publishing\",\"title\":\"Target patterns in a 2D array of oscillators with nonlocal coupling\",\"ty\":\"JOUR\",\"url_arxiv\":\"https://arxiv.org/abs/1706.00524\",\"url_journal\":\"https://iopscience.iop.org/article/10.1088/1361-6544/aac9a6/pdf\",\"volume\":\"31\",\"year\":\"2018\",\"bdsk-url-1\":\"http://dx.doi.org/10.1088/1361-6544/aac9a6\",\"bibtex\":\"@article{jaramillo2018target,\\n\\tabstract = {We analyze the effect of adding a weak, localized, inhomogeneity to a two dimensional array of oscillators with nonlocal coupling. We propose and also justify a model for the phase dynamics in this system. Our model is a generalization of a viscous eikonal equation that is known to describe the phase modulation of traveling waves in reaction--diffusion systems. We show the existence of a branch of target pattern solutions that bifurcates from the spatially homogeneous state when , the strength of the inhomogeneity, is nonzero and we also show that these target patterns have an asymptotic wavenumber that is small beyond all orders in . The strategy of our proof is to pose a good ansatz for an approximate form of the solution and use the implicit function theorem to prove the existence of a solution in its vicinity. The analysis presents two challenges. First, the linearization about the homogeneous state is a convolution operator of diffusive type and hence not invertible on the usual Sobolev spaces. Second, a regular perturbation expansion in  does not provide a good ansatz for applying the implicit function theorem since the nonlinearities play a major role in determining the relevant approximation, which also needs to be `correct' to all orders in . We overcome these two points by proving Fredholm properties for the linearization in appropriate Kondratiev spaces and using a refined ansatz for the approximate solution which was obtained using matched asymptotics.},\\n\\tauthor = {Jaramillo, Gabriela and Venkataramani, Shankar C},\\n\\tda = {2018/07/27},\\n\\tdate-added = {2019-03-20 14:49:42 -0700},\\n\\tdate-modified = {2019-03-20 15:07:42 -0700},\\n\\tdoi = {10.1088/1361-6544/aac9a6},\\n\\tisbn = {0951-7715; 1361-6544},\\n\\tjournal = {Nonlinearity},\\n\\tkeywords = {pubs},\\n\\tnumber = {9},\\n\\tpages = {4162-4201},\\n\\tpublisher = {IOP Publishing},\\n\\ttitle = {Target patterns in a 2D array of oscillators with nonlocal coupling},\\n\\tty = {JOUR},\\n\\turl_arxiv = {https://arxiv.org/abs/1706.00524},\\n\\turl_journal = {https://iopscience.iop.org/article/10.1088/1361-6544/aac9a6/pdf},\\n\\tvolume = {31},\\n\\tyear = {2018},\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.1088/1361-6544/aac9a6}}\\n\\n\",\"author_short\":[\"Jaramillo, G.\",\"Venkataramani, S. C\"],\"key\":\"jaramillo2018target\",\"id\":\"jaramillo2018target\",\"bibbaseid\":\"jaramillo-venkataramani-targetpatternsina2darrayofoscillatorswithnonlocalcoupling-2018\",\"role\":\"author\",\"urls\":{\" arxiv\":\"https://arxiv.org/abs/1706.00524\",\" journal\":\"https://iopscience.iop.org/article/10.1088/1361-6544/aac9a6/pdf\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We connect the theories of the deformation of elastic surfaces and phase surfaces arising in the description of almost periodic patterns. In particular, we show striking parallels between expansions for the energy of elastic surfaces in powers of the thickness h and the free energy averaged over a period of an almost periodic pattern expanded in powers of ϵ, the inverse aspect ratio of the pattern field. In both cases, the resulting energy can be expressed in terms of the first and second fundamental forms of the surfaces involved, the elastic surface in the former case and the phase surface in the latter. We discuss various results that are obtained by exploiting this analogy and also address some of the outstanding questions. One common result of particular interest concerns the condensation of the Gaussian curvature onto isolated point defects in two dimensions and onto loop filaments in three dimensions. We also lay out an ambitious and somewhat speculative program to build a multi-scale model of the universe inspired by patterns, in which the short (spatial and temporal) scale structure on the Planck scales is given by a nearly periodic microstructure, and macroscopic/slowly varying/averaged behaviors on scales much larger than the Planck scale leads to a hierarchy of structures and features including analogues of quarks, leptons, dark matter, dark energy and inflationary cosmology. \",\"author\":[{\"firstnames\":[\"Alan\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Newell\"],\"suffixes\":[]},{\"firstnames\":[\"Shankar\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"suffixes\":[]}],\"date-added\":\"2017-10-15 18:02:26 +0000\",\"date-modified\":\"2017-10-15 18:15:10 +0000\",\"doi\":\"http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full\",\"journal\":\"Studies in Applied Mathematics\",\"keywords\":\"pubs\",\"number\":\"2\",\"pages\":\"322–368\",\"title\":\"Elastic sheets, phase surfaces and pattern universes\",\"url_arxiv\":\"arxiv.org/abs/1612.01007\",\"url_journal\":\"http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full\",\"volume\":\"139\",\"year\":\"2017\",\"bdsk-url-1\":\"http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full\",\"bibtex\":\"@article{pattern-universe,\\n\\tabstract = {We connect the theories of the deformation of elastic surfaces and phase surfaces arising in the description of almost periodic patterns. In particular, we show striking parallels between expansions for the energy of elastic surfaces in powers of the thickness h and the free energy averaged over a period of an almost periodic pattern expanded in powers of ϵ, the inverse aspect ratio of the pattern field. In both cases, the resulting energy can be expressed in terms of the first and second fundamental forms of the surfaces involved, the elastic surface in the former case and the phase surface in the latter. We discuss various results that are obtained by exploiting this analogy and also address some of the outstanding questions. One common result of particular interest concerns the condensation of the Gaussian curvature onto isolated point defects in two dimensions and onto loop filaments in three dimensions. \\n\\nWe also lay out an ambitious and somewhat speculative program to build a multi-scale model of the universe inspired by patterns, in which the short (spatial and temporal) scale structure on the Planck scales is given by a nearly periodic microstructure, and macroscopic/slowly varying/averaged behaviors on scales much larger than the Planck scale leads to a hierarchy of structures and features including analogues of quarks, leptons, dark matter, dark energy and inflationary cosmology.\\n},\\n\\tauthor = {Alan C. Newell and Shankar C. Venkataramani},\\n\\tdate-added = {2017-10-15 18:02:26 +0000},\\n\\tdate-modified = {2017-10-15 18:15:10 +0000},\\n\\tdoi = {http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full},\\n\\tjournal = {Studies in Applied Mathematics},\\n\\tkeywords = {pubs},\\n\\tnumber = {2},\\n\\tpages = {322--368},\\n\\ttitle = {Elastic sheets, phase surfaces and pattern universes},\\n\\turl_arxiv = {arxiv.org/abs/1612.01007},\\n\\turl_journal = {http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full},\\n\\tvolume = {139},\\n\\tyear = {2017},\\n\\tBdsk-Url-1 = {http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full}}\\n\\n\",\"author_short\":[\"Newell, A. C.\",\"Venkataramani, S. C.\"],\"key\":\"pattern-universe\",\"id\":\"pattern-universe\",\"bibbaseid\":\"newell-venkataramani-elasticsheetsphasesurfacesandpatternuniverses-2017\",\"role\":\"author\",\"urls\":{\" arxiv\":\"https://bibbase.org/f/J9gZq33SPmmZsfyhm/arxiv.org/abs/1612.01007\",\" journal\":\"http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal'model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Raman\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Restrepo\"],\"firstnames\":[\"Juan\",\"M.\"],\"suffixes\":[]}],\"da\":\"2017//\",\"date-added\":\"2017-05-01 21:34:13 +0000\",\"date-modified\":\"2017-05-02 18:16:58 +0000\",\"doi\":\"10.1007/s10955-017-1761-7\",\"id\":\"Venkataramani:2017aa\",\"isbn\":\"1572-9613\",\"journal\":\"Journal of Statistical Physics\",\"keywords\":\"pubs\",\"number\":\"3\",\"pages\":\"892–933\",\"title\":\"Dimension Reduction for Systems with Slow Relaxation\",\"ty\":\"JOUR\",\"url_arxiv\":\"http://arxiv.org/abs/1609.09222\",\"url_journal\":\"http://dx.doi.org/10.1007/s10955-017-1761-7\",\"volume\":\"167\",\"year\":\"2017\",\"bdsk-url-1\":\"http://dx.doi.org/10.1007/s10955-017-1761-7\",\"bibtex\":\"@article{Venkataramani:2017aa,\\n\\tabstract = {We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal'model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.},\\n\\tauthor = {Venkataramani, Shankar C. and Venkataramani, Raman C. and Restrepo, Juan M.},\\n\\tda = {2017//},\\n\\tdate-added = {2017-05-01 21:34:13 +0000},\\n\\tdate-modified = {2017-05-02 18:16:58 +0000},\\n\\tdoi = {10.1007/s10955-017-1761-7},\\n\\tid = {Venkataramani2017},\\n\\tisbn = {1572-9613},\\n\\tjournal = {Journal of Statistical Physics},\\n\\tkeywords = {pubs},\\n\\tnumber = {3},\\n\\tpages = {892--933},\\n\\ttitle = {Dimension Reduction for Systems with Slow Relaxation},\\n\\tty = {JOUR},\\n\\turl_arxiv = {http://arxiv.org/abs/1609.09222},\\n\\turl_journal = {http://dx.doi.org/10.1007/s10955-017-1761-7},\\n\\tvolume = {167},\\n\\tyear = {2017},\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.1007/s10955-017-1761-7}}\\n\\n\",\"author_short\":[\"Venkataramani, S. C.\",\"Venkataramani, R. C.\",\"Restrepo, J. M.\"],\"key\":\"Venkataramani:2017aa\",\"bibbaseid\":\"venkataramani-venkataramani-restrepo-dimensionreductionforsystemswithslowrelaxation-2017\",\"role\":\"author\",\"urls\":{\" arxiv\":\"http://arxiv.org/abs/1609.09222\",\" journal\":\"http://dx.doi.org/10.1007/s10955-017-1761-7\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"Abstract We show that modifying a Bayesian data assimilation scheme by incorporating kinematically-consistent displacement corrections produces a scheme that is demonstrably better at estimating partially observed state vectors in a setting where feature information is important. While the displacement transformation is generic, here we implement it within an ensemble Kalman Filter framework and demonstrate its effectiveness in tracking stochastically perturbed vortices. \",\"author\":[{\"firstnames\":[\"W.\",\"Steven\"],\"propositions\":[],\"lastnames\":[\"Rosenthal\"],\"suffixes\":[]},{\"firstnames\":[\"Shankar\"],\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"suffixes\":[]},{\"firstnames\":[\"Arthur\",\"J.\"],\"propositions\":[],\"lastnames\":[\"Mariano\"],\"suffixes\":[]},{\"firstnames\":[\"Juan\",\"M.\"],\"propositions\":[],\"lastnames\":[\"Restrepo\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:07:29 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"http://dx.doi.org/10.1016/j.jcp.2016.10.025\",\"issn\":\"0021-9991\",\"journal\":\"Journal of Computational Physics\",\"keywords\":\"Displacement assimilation; Data assimilation; Uncertainty quantification; Ensemble Kalman Filter; Vortex dynamics; pubs\",\"pages\":\"594 - 614\",\"title\":\"Displacement data assimilation\",\"url_arxiv\":\"https://arxiv.org/abs/1602.02209\",\"url_journal\":\"http://www.sciencedirect.com/science/article/pii/S002199911630523X\",\"volume\":\"330\",\"year\":\"2017\",\"bdsk-url-1\":\"http://dx.doi.org/10.1016/j.jcp.2016.10.025\",\"bdsk-url-2\":\"http://www.sciencedirect.com/science/article/pii/S002199911630523X\",\"bibtex\":\"@article{Rosenthal_Displacement_2017,\\n\\tabstract = {Abstract We show that modifying a Bayesian data assimilation scheme by incorporating kinematically-consistent displacement corrections produces a scheme that is demonstrably better at estimating partially observed state vectors in a setting where feature information is important. While the displacement transformation is generic, here we implement it within an ensemble Kalman Filter framework and demonstrate its effectiveness in tracking stochastically perturbed vortices. },\\n\\tauthor = {W. Steven Rosenthal and Shankar Venkataramani and Arthur J. Mariano and Juan M. Restrepo},\\n\\tdate-added = {2017-01-29 16:07:29 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {http://dx.doi.org/10.1016/j.jcp.2016.10.025},\\n\\tissn = {0021-9991},\\n\\tjournal = {Journal of Computational Physics},\\n\\tkeywords = {Displacement assimilation; Data assimilation; Uncertainty quantification; Ensemble Kalman Filter; Vortex dynamics; pubs},\\n\\tpages = {594 - 614},\\n\\ttitle = {Displacement data assimilation},\\n\\turl_arxiv = {https://arxiv.org/abs/1602.02209},\\n\\turl_journal = {http://www.sciencedirect.com/science/article/pii/S002199911630523X},\\n\\tvolume = {330},\\n\\tyear = {2017},\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.1016/j.jcp.2016.10.025},\\n\\tBdsk-Url-2 = {http://www.sciencedirect.com/science/article/pii/S002199911630523X}}\\n\\n\",\"author_short\":[\"Rosenthal, W. S.\",\"Venkataramani, S.\",\"Mariano, A. J.\",\"Restrepo, J. M.\"],\"key\":\"Rosenthal_Displacement_2017\",\"id\":\"Rosenthal_Displacement_2017\",\"bibbaseid\":\"rosenthal-venkataramani-mariano-restrepo-displacementdataassimilation-2017\",\"role\":\"author\",\"urls\":{\" arxiv\":\"https://arxiv.org/abs/1602.02209\",\" journal\":\"http://www.sciencedirect.com/science/article/pii/S002199911630523X\"},\"keyword\":[\"Displacement assimilation; Data assimilation; Uncertainty quantification; Ensemble Kalman Filter; Vortex dynamics; pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"incollection\",\"type\":\"incollection\",\"annote\":\"doi:10.1142/9789812811516_0014\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Ott\"],\"firstnames\":[\"Edward\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]}],\"booktitle\":\"Proceedings of the 5th Experimental Chaos Conference\",\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2021-05-23 18:55:49 -0700\",\"doi\":\"doi:10.1142/9789812811516_0014\",\"isbn\":\"978-981-02-4561-0\",\"keywords\":\"pubs\",\"m1\":\"0\",\"m3\":\"doi:10.1142/9789812811516_0014\",\"month\":\"2016/11/23\",\"pages\":\"143-153\",\"publisher\":\"World Scientific\",\"title\":\"Continuum Coupled Maps: A model for patterns in vibrated sand\",\"ty\":\"CHAP\",\"url\":\"http://dx.doi.org/10.1142/9789812811516_0014\",\"year\":\"2001\",\"year1\":\"2001/04/01\",\"bdsk-url-1\":\"http://dx.doi.org/10.1142/9789812811516_0014\",\"bdsk-url-2\":\"http://dx.doi.org/10.1142/9789812811516%7B%5C_%7D0014\",\"bibtex\":\"@incollection{OTT:2001aa,\\n\\tannote = {doi:10.1142/9789812811516{\\\\_}0014},\\n\\tauthor = {Ott, Edward and Venkataramani, Shankar C.},\\n\\tbooktitle = {Proceedings of the 5th Experimental Chaos Conference},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2021-05-23 18:55:49 -0700},\\n\\tdoi = {doi:10.1142/9789812811516{\\\\_}0014},\\n\\tisbn = {978-981-02-4561-0},\\n\\tkeywords = {pubs},\\n\\tm1 = {0},\\n\\tm3 = {doi:10.1142/9789812811516{\\\\_}0014},\\n\\tmonth = {2016/11/23},\\n\\tpages = {143-153},\\n\\tpublisher = {World Scientific},\\n\\ttitle = {Continuum Coupled Maps: A model for patterns in vibrated sand},\\n\\tty = {CHAP},\\n\\turl = {http://dx.doi.org/10.1142/9789812811516_0014},\\n\\tyear = {2001},\\n\\tyear1 = {2001/04/01},\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.1142/9789812811516_0014},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1142/9789812811516%7B%5C_%7D0014}}\\n\\n\",\"author_short\":[\"Ott, E.\",\"Venkataramani, S. C.\"],\"key\":\"OTT:2001aa\",\"id\":\"OTT:2001aa\",\"bibbaseid\":\"ott-venkataramani-continuumcoupledmapsamodelforpatternsinvibratedsand-2001\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://dx.doi.org/10.1142/9789812811516_0014\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"Abstract We develop a stochastic parametrization, based on a `simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the ``missing physics'' to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Restrepo\"],\"firstnames\":[\"Juan\",\"M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\"],\"suffixes\":[]}],\"date\":\"2016/12//\",\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"http://dx.doi.org/10.1016/j.advwatres.2016.11.002\",\"isbn\":\"0309-1708\",\"journal\":\"Advances in Water Resources\",\"keywords\":\"Longshore currents; Stochastic parametrization; Parameter sensitivity; Consistently of model sensitivity; Data assimilation;; pubs\",\"month\":\"12\",\"pages\":\"186–197\",\"title\":\"Stochastic longshore current dynamics\",\"ty\":\"JOUR\",\"url_arxiv\":\"https://arxiv.org/abs/1612.01046\",\"url_journal\":\"http://www.sciencedirect.com/science/article/pii/S0309170816306157\",\"volume\":\"98\",\"year\":\"2016\",\"bdsk-url-1\":\"http://www.sciencedirect.com/science/article/pii/S0309170816306157\",\"bdsk-url-2\":\"http://dx.doi.org/10.1016/j.advwatres.2016.11.002\",\"bibtex\":\"@article{AdWR_2016,\\n\\tabstract = {Abstract We develop a stochastic parametrization, based on a `simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the ``missing physics'' to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation.  We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.},\\n\\tauthor = {Restrepo, Juan M. and Venkataramani, Shankar},\\n\\tdate = {2016/12//},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {http://dx.doi.org/10.1016/j.advwatres.2016.11.002},\\n\\tisbn = {0309-1708},\\n\\tjournal = {Advances in Water Resources},\\n\\tkeywords = {Longshore currents; Stochastic parametrization; Parameter sensitivity; Consistently of model sensitivity; Data assimilation;; pubs},\\n\\tmonth = {12},\\n\\tpages = {186--197},\\n\\ttitle = {Stochastic longshore current dynamics},\\n\\tty = {JOUR},\\n\\turl_arxiv = {https://arxiv.org/abs/1612.01046},\\n\\turl_journal = {http://www.sciencedirect.com/science/article/pii/S0309170816306157},\\n\\tvolume = {98},\\n\\tyear = {2016},\\n\\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0309170816306157},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1016/j.advwatres.2016.11.002}}\\n\\n\",\"author_short\":[\"Restrepo, J. M.\",\"Venkataramani, S.\"],\"key\":\"AdWR_2016\",\"id\":\"AdWR_2016\",\"bibbaseid\":\"restrepo-venkataramani-stochasticlongshorecurrentdynamics-2016\",\"role\":\"author\",\"urls\":{\" arxiv\":\"https://arxiv.org/abs/1612.01046\",\" journal\":\"http://www.sciencedirect.com/science/article/pii/S0309170816306157\"},\"keyword\":[\"Longshore currents; Stochastic parametrization; Parameter sensitivity; Consistently of model sensitivity; Data assimilation;; pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"The edges of torn plastic sheets and growing leaves often display hierarchical buckling patterns. We show that this complex morphology i) emerges even in zero strain configurations, and ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. We identify the key role of branch point (or ``monkey saddle'') singularities in generating complex wrinkling patterns in isometric immersions, and show how they arise naturally from minimizing the elastic energy.\",\"author\":[{\"firstnames\":[],\"propositions\":[],\"lastnames\":[\"Gemmer, John\"],\"suffixes\":[]},{\"firstnames\":[],\"propositions\":[],\"lastnames\":[\"Sharon, Eran\"],\"suffixes\":[]},{\"firstnames\":[],\"propositions\":[],\"lastnames\":[\"Shearman, Toby\"],\"suffixes\":[]},{\"firstnames\":[],\"propositions\":[],\"lastnames\":[\"Venkataramani, Shankar C.\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.1209/0295-5075/114/24003\",\"journal\":\"Europhys. Lett.\",\"keywords\":\"pubs\",\"number\":\"2\",\"pages\":\"24003\",\"title\":\"Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets\",\"url_arxiv\":\"https://arxiv.org/abs/1601.06863\",\"url_journal\":\"http://dx.doi.org/10.1209/0295-5075/114/24003\",\"volume\":\"114\",\"year\":\"2016\",\"bdsk-url-1\":\"http://dx.doi.org/10.1209/0295-5075/114/24003\",\"bibtex\":\"@article{GSSV2016,\\n\\tabstract = {The edges of torn plastic sheets and growing leaves often display hierarchical buckling\\n patterns. We show that this complex morphology i) emerges even in zero strain configurations, and ii) is driven by a competition between the two principal curvatures, rather than between bending  and stretching.   We identify the key role of branch point (or ``monkey saddle'') singularities in generating complex wrinkling patterns in isometric immersions, and show how they arise naturally from minimizing the elastic energy.},\\n\\tauthor = {{Gemmer, John} and {Sharon, Eran} and {Shearman, Toby} and {Venkataramani, Shankar C.}},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.1209/0295-5075/114/24003},\\n\\tjournal = {Europhys. Lett.},\\n\\tkeywords = {pubs},\\n\\tnumber = 2,\\n\\tpages = {24003},\\n\\ttitle = {Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets},\\n\\turl_arxiv = {https://arxiv.org/abs/1601.06863},\\n\\turl_journal = {http://dx.doi.org/10.1209/0295-5075/114/24003},\\n\\tvolume = 114,\\n\\tyear = 2016,\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.1209/0295-5075/114/24003}}\\n\\n\",\"author_short\":[\"Gemmer, John\",\"Sharon, Eran\",\"Shearman, Toby\",\"Venkataramani, Shankar C.\"],\"key\":\"GSSV2016\",\"id\":\"GSSV2016\",\"bibbaseid\":\"gemmer-sharon-shearman-venkataramani-isometricimmersionsenergyminimizationandselfsimilarbucklinginnoneuclideanelasticsheets-2016\",\"role\":\"author\",\"urls\":{\" arxiv\":\"https://arxiv.org/abs/1601.06863\",\" journal\":\"http://dx.doi.org/10.1209/0295-5075/114/24003\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We introduce a model for the dynamics of oil in suspension, appropriate for shallow waters, including the nearshore environment. This model is capable of oil mass conservation and does so by evolving the oil on the sea surface as well as the oil in the subsurface. The shallower portion of the continental shelf poses compounding unique modeling challenges. Many of these relate to the complex nature of advection and dispersion of oil in an environment in which wind, waves, as well as currents all play a role, as does the complex bathymetry and the nearshore geography. In this study we present an overview of the model as well as derive the most fundamental of processes, namely, the shallow water advectiion and dispersion processes. With regard to this basic transport, we superate several fundamental challenges associated with creating a transport model for oil and other buoyant pollutants, capable of capturing the dynamics at the large spatio-temporal scales demanded by environmental and hazard mitigation studies. Some of the strategies are related to dimension reduction and upscaling, and leave discussion of these to companion papers. Here we focus on wave-filtering, ensemble and depth-averaging. Integral to the model is the proposal of an ocean dynamics model that is consistent with the transport. This ocean dynamics model is detailed here. The ocean/oil transport model is applied to a couple of physically-inspired oil-spill problems in demonstrate its specialized capabilities.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Restrepo\"],\"firstnames\":[\"Juan\",\"M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ramírez\"],\"firstnames\":[\"Jorge\",\"M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.3390/jmse3041504\",\"issn\":\"2077-1312\",\"journal\":\"Journal of Marine Science and Engineering\",\"keywords\":\"pubs\",\"number\":\"4\",\"pages\":\"1504\",\"title\":\"An Oil Fate Model for Shallow-Waters\",\"url_journal\":\"http://www.mdpi.com/2077-1312/3/4/1504\",\"volume\":\"3\",\"year\":\"2015\",\"bdsk-url-1\":\"http://www.mdpi.com/2077-1312/3/4/1504\",\"bdsk-url-2\":\"http://dx.doi.org/10.3390/jmse3041504\",\"bibtex\":\"@article{jmse3041504,\\n\\tabstract = {We introduce a model for the dynamics of oil in suspension, appropriate for shallow waters, including the nearshore environment. This model is capable of oil mass conservation and does so by evolving the oil on the sea surface as well as the oil in the subsurface. The shallower portion of the continental shelf poses compounding unique modeling challenges. Many of these relate to the complex nature of advection and dispersion of oil in an environment in which wind, waves, as well as currents all play a role, as does the complex bathymetry and the nearshore geography. In this study we present an overview of the model as well as derive the most fundamental of processes, namely, the shallow water advectiion and dispersion processes. With regard to this basic transport, we superate several fundamental challenges associated with creating a transport model for oil and other buoyant pollutants, capable of capturing the dynamics at the large spatio-temporal scales demanded by environmental and hazard mitigation studies. Some of the strategies are related to dimension reduction and upscaling, and leave discussion of these to companion papers. Here we focus on wave-filtering, ensemble and depth-averaging. Integral to the model is the proposal of an ocean dynamics model that is consistent with the transport. This ocean dynamics model is detailed here. The ocean/oil transport model is applied to a couple of physically-inspired oil-spill problems in demonstrate its specialized capabilities.},\\n\\tauthor = {Restrepo, Juan M. and Ram\\\\'{i}rez, Jorge M. and Venkataramani, Shankar},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.3390/jmse3041504},\\n\\tissn = {2077-1312},\\n\\tjournal = {Journal of Marine Science and Engineering},\\n\\tkeywords = {pubs},\\n\\tnumber = {4},\\n\\tpages = {1504},\\n\\ttitle = {An Oil Fate Model for Shallow-Waters},\\n\\turl_journal = {http://www.mdpi.com/2077-1312/3/4/1504},\\n\\tvolume = {3},\\n\\tyear = {2015},\\n\\tBdsk-Url-1 = {http://www.mdpi.com/2077-1312/3/4/1504},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.3390/jmse3041504}}\\n\\n\",\"author_short\":[\"Restrepo, J. M.\",\"Ramírez, J. M.\",\"Venkataramani, S.\"],\"key\":\"jmse3041504\",\"id\":\"jmse3041504\",\"bibbaseid\":\"restrepo-ramirez-venkataramani-anoilfatemodelforshallowwaters-2015\",\"role\":\"author\",\"urls\":{\" journal\":\"http://www.mdpi.com/2077-1312/3/4/1504\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We consider a general class of preferential attachment schemes evolving by a reinforcement rule with respect to certain sublinear weights. In these schemes, which grow a random network, the sequence of degree distributions is an object of interest which sheds light on the evolving structures. In this article, we use a fluid limit approach to prove a functional law of large numbers for the degree structure in this class, starting from a variety of initial conditions. The method appears robust and applies in particular to `non-tree' evolutions where cycles may develop in the network. A main part of the argument is to analyze an infinite system of coupled ODEs, corresponding to a rate formulation of the law of large numbers limit, in terms of $C_0$-semigroup/dynamical systems methods. These results also resolve a question in Chung, Handjani and Jungreis (2003). \",\"author\":[{\"propositions\":[],\"lastnames\":[\"Choi\"],\"firstnames\":[\"Jihyeok\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Sethuraman\"],\"firstnames\":[\"Sunder\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.1002/rsa.20615\",\"issn\":\"1098-2418\",\"journal\":\"Random Structures and Algorithms\",\"keywords\":\"pubs\",\"number\":\"4\",\"pages\":\"703-731\",\"title\":\"A scaling limit for the degree distribution in sublinear preferential attachment schemes\",\"url_arxiv\":\"http://arxiv.org/abs/1402.4088\",\"url_journal\":\"http://onlinelibrary.wiley.com/doi/10.1002/rsa.20615/full\",\"volume\":\"48\",\"year\":\"2016\",\"bdsk-url-1\":\"http://dx.doi.org/10.1002/rsa.20615\",\"bibtex\":\"@article{pref-attach,\\n\\tabstract = {We consider a general class of preferential attachment schemes evolving by a reinforcement rule with respect to certain sublinear weights. In these schemes, which grow a random network, the sequence of degree distributions is an object of interest which sheds light on the evolving structures. In this article, we use a fluid limit approach to prove a functional law of large numbers for the degree structure in this class, starting from a variety of initial conditions. The method appears robust and applies in particular to `non-tree' evolutions where cycles may develop in the network. A main part of the argument is to analyze an infinite system of coupled ODEs, corresponding to a rate formulation of the law of large numbers limit, in terms of $C_0$-semigroup/dynamical systems methods. These results also resolve a question in Chung, Handjani and Jungreis (2003). },\\n\\tauthor = {Choi, Jihyeok and Sethuraman, Sunder and Venkataramani, Shankar C.},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.1002/rsa.20615},\\n\\tissn = {1098-2418},\\n\\tjournal = {Random Structures and Algorithms},\\n\\tkeywords = {pubs},\\n\\tnumber = {4},\\n\\tpages = {703-731},\\n\\ttitle = {A scaling limit for the degree distribution in sublinear preferential attachment schemes},\\n\\turl_arxiv = {http://arxiv.org/abs/1402.4088},\\n\\turl_journal = {http://onlinelibrary.wiley.com/doi/10.1002/rsa.20615/full},\\n\\tvolume = {48},\\n\\tyear = {2016},\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.1002/rsa.20615}}\\n\\n\",\"author_short\":[\"Choi, J.\",\"Sethuraman, S.\",\"Venkataramani, S. 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Moreover, we show how this method can be extended from free space to describe propagation behavior through nonimaging first-order optical systems by combining our coordinate transform approach with ray transfer matrix methods. Our framework includes several classes of interesting beams that are important in applications as special cases. Among these are, for example, the Bessel&#x2013;Gauss and the Airy&#x2013;Gauss beams, which are of strong interest to researchers and practitioners in various fields.\",\"author\":[{\"firstnames\":[\"T.\"],\"propositions\":[],\"lastnames\":[\"Graf\"],\"suffixes\":[]},{\"firstnames\":[\"D.\",\"N.\"],\"propositions\":[],\"lastnames\":[\"Christodoulides\"],\"suffixes\":[]},{\"firstnames\":[\"M.\",\"S.\"],\"propositions\":[],\"lastnames\":[\"Mills\"],\"suffixes\":[]},{\"firstnames\":[\"J.\",\"V.\"],\"propositions\":[],\"lastnames\":[\"Moloney\"],\"suffixes\":[]},{\"firstnames\":[\"S.\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"suffixes\":[]},{\"firstnames\":[\"E.\",\"M.\"],\"propositions\":[],\"lastnames\":[\"Wright\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.1364/JOSAA.29.001860\",\"journal\":\"J. Opt. Soc. Am. A\",\"keywords\":\"Mathematical methods in physics; Matrix methods in paraxial optics; Lasers and laser optics; Diffraction theory; Dispersion; Nonimaging optical systems; pubs\",\"month\":\"Sep\",\"number\":\"9\",\"pages\":\"1860–1869\",\"publisher\":\"OSA\",\"title\":\"Propagation of Gaussian-apodized paraxial beams through first-order optical systems via complex coordinate transforms and ray transfer matrices\",\"url_journal\":\"http://josaa.osa.org/abstract.cfm?URI=josaa-29-9-1860\",\"volume\":\"29\",\"year\":\"2012\",\"bdsk-url-1\":\"http://josaa.osa.org/abstract.cfm?URI=josaa-29-9-1860\",\"bdsk-url-2\":\"http://dx.doi.org/10.1364/JOSAA.29.001860\",\"bibtex\":\"@article{Graf2012,\\n\\tabstract = {We investigate the linear propagation of Gaussian-apodized solutions to the paraxial wave equation in free-space and first-order optical systems. In particular, we present complex coordinate transformations that yield a very general and efficient method to apply a Gaussian apodization (possibly with initial phase curvature) to a solution of the paraxial wave equation. Moreover, we show how this method can be extended from free space to describe propagation behavior through nonimaging first-order optical systems by combining our coordinate transform approach with ray transfer matrix methods. Our framework includes several classes of interesting beams that are important in applications as special cases. Among these are, for example, the Bessel\\\\&\\\\#x2013;Gauss and the Airy\\\\&\\\\#x2013;Gauss beams, which are of strong interest to researchers and practitioners in various fields.},\\n\\tauthor = {T. Graf and D. N. Christodoulides and M. S. Mills and J. V. Moloney and S. C. Venkataramani and E. M. 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C.\",\"Wright, E. M.\"],\"key\":\"Graf2012\",\"id\":\"Graf2012\",\"bibbaseid\":\"graf-christodoulides-mills-moloney-venkataramani-wright-propagationofgaussianapodizedparaxialbeamsthroughfirstorderopticalsystemsviacomplexcoordinatetransformsandraytransfermatrices-2012\",\"role\":\"author\",\"urls\":{\" journal\":\"http://josaa.osa.org/abstract.cfm?URI=josaa-29-9-1860\"},\"keyword\":[\"Mathematical methods in physics; Matrix methods in paraxial optics; Lasers and laser optics; Diffraction theory; Dispersion; Nonimaging optical systems; pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"incollection\",\"type\":\"incollection\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Ott\"],\"firstnames\":[\"Edward\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Sommerer\"],\"firstnames\":[\"John\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Antonsen\"],\"firstnames\":[\"Thomas\",\"M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\"],\"suffixes\":[]}],\"booktitle\":\"Lévy Flights and Related Topics in Physics\",\"da\":\"1995/01/01\",\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2021-05-23 18:54:32 -0700\",\"doi\":\"10.1007/3-540-59222-9_34\",\"editor\":[{\"propositions\":[],\"lastnames\":[\"Shlesinger\"],\"firstnames\":[\"MichealF.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Zaslavsky\"],\"firstnames\":[\"GeorgeM.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Frisch\"],\"firstnames\":[\"Uriel\"],\"suffixes\":[]}],\"isbn\":\"978-3-540-59222-8\",\"keywords\":\"pubs\",\"la\":\"English\",\"pages\":\"182-195\",\"publisher\":\"Springer Berlin Heidelberg\",\"se\":\"12\",\"title\":\"Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states\",\"title1\":\"Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states\",\"ty\":\"CHAP\",\"url\":\"http://dx.doi.org/10.1007/3-540-59222-9_34\",\"volume\":\"450\",\"year\":\"1995\",\"bdsk-url-1\":\"http://dx.doi.org/10.1007/3-540-59222-9_34\",\"bdsk-url-2\":\"http://dx.doi.org/10.1007/3-540-59222-9%7B%5C_%7D34\",\"bibtex\":\"@incollection{Shlesinger:1995gd,\\n\\tauthor = {Ott, Edward and Sommerer, John C. and Antonsen, Thomas M. and Venkataramani, Shankar},\\n\\tbooktitle = {L{\\\\'e}vy Flights and Related Topics in Physics},\\n\\tda = {1995/01/01},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2021-05-23 18:54:32 -0700},\\n\\tdoi = {10.1007/3-540-59222-9{\\\\_}34},\\n\\teditor = {Shlesinger, MichealF. and Zaslavsky, GeorgeM. and Frisch, Uriel},\\n\\tisbn = {978-3-540-59222-8},\\n\\tkeywords = {pubs},\\n\\tla = {English},\\n\\tpages = {182-195},\\n\\tpublisher = {Springer Berlin Heidelberg},\\n\\tse = {12},\\n\\ttitle = {Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states},\\n\\ttitle1 = {Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states},\\n\\tty = {CHAP},\\n\\turl = {http://dx.doi.org/10.1007/3-540-59222-9_34},\\n\\tvolume = {450},\\n\\tyear = {1995},\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.1007/3-540-59222-9_34},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1007/3-540-59222-9%7B%5C_%7D34}}\\n\\n\",\"author_short\":[\"Ott, E.\",\"Sommerer, J. 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Rev. Lett.\",\"keywords\":\"pubs\",\"month\":\"Jul\",\"numpages\":\"0\",\"pages\":\"55–58\",\"publisher\":\"American Physical Society\",\"title\":\"Riddling Bifurcation in Chaotic Dynamical Systems\",\"url\":\"http://link.aps.org/doi/10.1103/PhysRevLett.77.55\",\"volume\":\"77\",\"year\":\"1996\",\"bdsk-url-1\":\"http://link.aps.org/doi/10.1103/PhysRevLett.77.55\",\"bdsk-url-2\":\"http://dx.doi.org/10.1103/PhysRevLett.77.55\",\"bibtex\":\"@article{PhysRevLett.77.55,\\n\\tauthor = {Lai, Ying-Cheng and Grebogi, Celso and Yorke, James A. and Venkataramani, S. C.},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.1103/PhysRevLett.77.55},\\n\\tissue = {1},\\n\\tjournal = {Phys. Rev. Lett.},\\n\\tkeywords = {pubs},\\n\\tmonth = {Jul},\\n\\tnumpages = {0},\\n\\tpages = {55--58},\\n\\tpublisher = {American Physical Society},\\n\\ttitle = {Riddling Bifurcation in Chaotic Dynamical Systems},\\n\\turl = {http://link.aps.org/doi/10.1103/PhysRevLett.77.55},\\n\\tvolume = {77},\\n\\tyear = {1996},\\n\\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.77.55},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.77.55}}\\n\\n\",\"author_short\":[\"Lai, Y.\",\"Grebogi, C.\",\"Yorke, J. A.\",\"Venkataramani, S. C.\"],\"key\":\"PhysRevLett.77.55\",\"id\":\"PhysRevLett.77.55\",\"bibbaseid\":\"lai-grebogi-yorke-venkataramani-riddlingbifurcationinchaoticdynamicalsystems-1996\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://link.aps.org/doi/10.1103/PhysRevLett.77.55\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Coppersmith\"],\"firstnames\":[\"S.\",\"N.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Jones\"],\"firstnames\":[\"T.\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Kadanoff\"],\"firstnames\":[\"L.\",\"P.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Levine\"],\"firstnames\":[\"A.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"McCarten\"],\"firstnames\":[\"J.\",\"P.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Nagel\"],\"firstnames\":[\"S.\",\"R.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"S.\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wu\"],\"firstnames\":[\"Xinlei\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.1103/PhysRevLett.78.3983\",\"issue\":\"21\",\"journal\":\"Phys. Rev. Lett.\",\"keywords\":\"pubs\",\"month\":\"May\",\"numpages\":\"0\",\"pages\":\"3983–3986\",\"publisher\":\"American Physical Society\",\"title\":\"Self-Organized Short-Term Memories\",\"url\":\"http://link.aps.org/doi/10.1103/PhysRevLett.78.3983\",\"volume\":\"78\",\"year\":\"1997\",\"bdsk-url-1\":\"http://link.aps.org/doi/10.1103/PhysRevLett.78.3983\",\"bdsk-url-2\":\"http://dx.doi.org/10.1103/PhysRevLett.78.3983\",\"bibtex\":\"@article{PhysRevLett.78.3983,\\n\\tauthor = {Coppersmith, S. N. and Jones, T. C. and Kadanoff, L. P. and Levine, A. and McCarten, J. P. and Nagel, S. R. and Venkataramani, S. C. and Wu, Xinlei},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.1103/PhysRevLett.78.3983},\\n\\tissue = {21},\\n\\tjournal = {Phys. Rev. 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C.\",\"Ott, E.\"],\"key\":\"PhysRevLett.80.3495\",\"id\":\"PhysRevLett.80.3495\",\"bibbaseid\":\"venkataramani-ott-spatiotemporalbifurcationphenomenawithtemporalperioddoublingpatternsinvibratedsand-1998\",\"role\":\"author\",\"urls\":{\" journal\":\"http://link.aps.org/doi/10.1103/PhysRevLett.80.3495\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ott\"],\"firstnames\":[\"Edward\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.1103/PhysRevE.63.046202\",\"issue\":\"4\",\"journal\":\"Phys. Rev. E\",\"keywords\":\"pubs\",\"month\":\"Mar\",\"numpages\":\"27\",\"pages\":\"046202\",\"publisher\":\"American Physical Society\",\"title\":\"Pattern selection in extended periodically forced systems: A continuum coupled map approach\",\"url_journal\":\"http://link.aps.org/doi/10.1103/PhysRevE.63.046202\",\"volume\":\"63\",\"year\":\"2001\",\"bdsk-url-1\":\"http://link.aps.org/doi/10.1103/PhysRevE.63.046202\",\"bdsk-url-2\":\"http://dx.doi.org/10.1103/PhysRevE.63.046202\",\"bibtex\":\"@article{PhysRevE.63.046202,\\n\\tauthor = {Venkataramani, Shankar C. and Ott, Edward},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.1103/PhysRevE.63.046202},\\n\\tissue = {4},\\n\\tjournal = {Phys. Rev. E},\\n\\tkeywords = {pubs},\\n\\tmonth = {Mar},\\n\\tnumpages = {27},\\n\\tpages = {046202},\\n\\tpublisher = {American Physical Society},\\n\\ttitle = {Pattern selection in extended periodically forced systems: A continuum coupled map approach},\\n\\turl_journal = {http://link.aps.org/doi/10.1103/PhysRevE.63.046202},\\n\\tvolume = {63},\\n\\tyear = {2001},\\n\\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.63.046202},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.63.046202}}\\n\\n\",\"author_short\":[\"Venkataramani, S. C.\",\"Ott, E.\"],\"key\":\"PhysRevE.63.046202\",\"id\":\"PhysRevE.63.046202\",\"bibbaseid\":\"venkataramani-ott-patternselectioninextendedperiodicallyforcedsystemsacontinuumcoupledmapapproach-2001\",\"role\":\"author\",\"urls\":{\" journal\":\"http://link.aps.org/doi/10.1103/PhysRevE.63.046202\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We present the first quantitative measurements of shape and energy variation in non-Euclidean plates. Using environmentally responsive gel, we construct non-Euclidean disks of constant imposed Gaussian curvature, $K_{tar}$. We vary the disks' thickness $t_0$ and measure the dependence of configurations, surface curvature, and energy content on $t_0$. For $K_{tar} < 0$, configurations are of a single wavy mode and undergo a set of bifurcations that leads to their refinement with decreasing thickness. This leads to sharp increase in the amount of surface bending as $t_0 \\\\to 0$, and to a slow decay of both bending and stretching energies. Both vary like $t_0^2$, compared with $t_0^3$ of the bending energy in disks with $K_{tar} > 0$.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Klein\"],\"firstnames\":[\"Yael\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Sharon\"],\"firstnames\":[\"Eran\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.1103/PhysRevLett.106.118303\",\"issue\":\"11\",\"journal\":\"Phys. Rev. Lett.\",\"keywords\":\"pubs\",\"month\":\"Mar\",\"numpages\":\"4\",\"pages\":\"118303\",\"publisher\":\"American Physical Society\",\"title\":\"Experimental Study of Shape Transitions and Energy Scaling in Thin Non-Euclidean Plates\",\"url_journal\":\"http://link.aps.org/doi/10.1103/PhysRevLett.106.118303\",\"volume\":\"106\",\"year\":\"2011\",\"bdsk-url-1\":\"http://link.aps.org/doi/10.1103/PhysRevLett.106.118303\",\"bdsk-url-2\":\"http://dx.doi.org/10.1103/PhysRevLett.106.118303\",\"bibtex\":\"@article{KVS2011,\\n\\tabstract = {\\nWe present the first quantitative measurements of shape and energy variation in non-Euclidean plates. Using environmentally responsive gel, we construct non-Euclidean disks of constant imposed Gaussian curvature, $K_{tar}$. We vary the disks' thickness $t_0$ and measure the dependence of configurations, surface curvature, and energy content on $t_0$. For $K_{tar} < 0$, configurations are of a single wavy mode and undergo a set of bifurcations that leads to their refinement with decreasing thickness. This leads to sharp increase in the amount of surface bending as $t_0 \\\\to 0$, and to a slow decay of both bending and stretching energies. Both vary like $t_0^2$, compared with $t_0^3$ of the bending energy in disks with $K_{tar} > 0$.},\\n\\tauthor = {Klein, Yael and Venkataramani, Shankar and Sharon, Eran},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.1103/PhysRevLett.106.118303},\\n\\tissue = {11},\\n\\tjournal = {Phys. Rev. Lett.},\\n\\tkeywords = {pubs},\\n\\tmonth = {Mar},\\n\\tnumpages = {4},\\n\\tpages = {118303},\\n\\tpublisher = {American Physical Society},\\n\\ttitle = {Experimental Study of Shape Transitions and Energy Scaling in Thin Non-Euclidean Plates},\\n\\turl_journal = {http://link.aps.org/doi/10.1103/PhysRevLett.106.118303},\\n\\tvolume = {106},\\n\\tyear = {2011},\\n\\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.106.118303},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.106.118303}}\\n\\n\",\"author_short\":[\"Klein, Y.\",\"Venkataramani, S.\",\"Sharon, E.\"],\"key\":\"KVS2011\",\"id\":\"KVS2011\",\"bibbaseid\":\"klein-venkataramani-sharon-experimentalstudyofshapetransitionsandenergyscalinginthinnoneuclideanplates-2011\",\"role\":\"author\",\"urls\":{\" journal\":\"http://link.aps.org/doi/10.1103/PhysRevLett.106.118303\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"A non-Euclidean plate is a thin elastic object whose intrinsic geometry is not flat and hence has residual stresses arising from being embedded in three dimensional space. Recently, there has been interest in using localized swelling to induce residual stresses that shape flat objects into desired three dimensional structures. A fundamental question is whether we can use the mathematical theory of non-Euclidean plates to deduce the three dimensional configuration of the swelling sheet given the exact knowledge of the imposed geometry. We present and summarize the results of recent mathematical studies on non-Euclidean plates with imposed constant negative Gaussian curvature in both annular and disc geometries. We show in the Föppl–von Kármán approximation to the elastic energy there are only two types of global minimizers – flat and saddle shaped deformations – with localized regions of stretching near the boundary of the domain. We also show that there exist n-wave local minimizers that closely resemble experimental observations and have additional regions of stretching near lines of inflection. Furthermore, in the Kirchhoff approximation to the elastic energy, we show that there exists exact isometric immersions with periodic profiles. The number of waves in these configurations is set by the condition that the bending energy remains finite and grows approximately exponentially with the radius of the annulus. For large radii, these shape are energetically favorable over saddle shapes and could explain why wavy shapes are selected in crochet models of the hyperbolic plane. The predicted morphologies however differ from what is observed in experiments on hydrogel disks highlighting the need for further theoretical studies.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Gemmer\"],\"firstnames\":[\"John\",\"A.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"journal\":\"Soft Matter\",\"keywords\":\"pubs\",\"number\":\"34\",\"pages\":\"8151–8161\",\"publisher\":\"Royal Society of Chemistry\",\"title\":\"Shape transitions in hyperbolic non-Euclidean plates\",\"url_arxiv\":\"http://arxiv.org/abs/1209.0031\",\"url_journal\":\"http://pubs.rsc.org/en/Content/ArticleLanding/2013/SM/c3sm50479d#!divAbstract\",\"volume\":\"9\",\"year\":\"2013\",\"bdsk-url-1\":\"http://dx.doi.org/10.1039/C3SM50479D\",\"bibtex\":\"@article{GV2013,\\n\\tabstract = {A non-Euclidean plate is a thin elastic object whose intrinsic geometry is not flat and hence has residual stresses arising from being embedded in three dimensional space. Recently, there has been interest in using localized swelling to induce residual stresses that shape flat objects into desired three dimensional structures. A fundamental question is whether we can use the mathematical theory of non-Euclidean plates to deduce the three dimensional configuration of the swelling sheet given the exact knowledge of the imposed geometry. We present and summarize the results of recent mathematical studies on non-Euclidean plates with imposed constant negative Gaussian curvature in both annular and disc geometries. We show in the F{\\\\\\\"o}ppl--von K{\\\\'a}rm{\\\\'a}n approximation to the elastic energy there are only two types of global minimizers -- flat and saddle shaped deformations -- with localized regions of stretching near the boundary of the domain. We also show that there exist n-wave local minimizers that closely resemble experimental observations and have additional regions of stretching near lines of inflection. Furthermore, in the Kirchhoff approximation to the elastic energy, we show that there exists exact isometric immersions with periodic profiles. The number of waves in these configurations is set by the condition that the bending energy remains finite and grows approximately exponentially with the radius of the annulus. For large radii, these shape are energetically favorable over saddle shapes and could explain why wavy shapes are selected in crochet models of the hyperbolic plane. The predicted morphologies however differ from what is observed in experiments on hydrogel disks highlighting the need for further theoretical studies.},\\n\\tauthor = {Gemmer, John A. and Venkataramani, Shankar C.},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tjournal = {Soft Matter},\\n\\tkeywords = {pubs},\\n\\tnumber = {34},\\n\\tpages = {8151--8161},\\n\\tpublisher = {Royal Society of Chemistry},\\n\\ttitle = {Shape transitions in hyperbolic non-Euclidean plates},\\n\\turl_arxiv = {http://arxiv.org/abs/1209.0031},\\n\\turl_journal = {http://pubs.rsc.org/en/Content/ArticleLanding/2013/SM/c3sm50479d#!divAbstract},\\n\\tvolume = {9},\\n\\tyear = {2013},\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.1039/C3SM50479D}}\\n\\n\",\"author_short\":[\"Gemmer, J. A.\",\"Venkataramani, S. C.\"],\"key\":\"GV2013\",\"id\":\"GV2013\",\"bibbaseid\":\"gemmer-venkataramani-shapetransitionsinhyperbolicnoneuclideanplates-2013\",\"role\":\"author\",\"urls\":{\" arxiv\":\"http://arxiv.org/abs/1209.0031\",\" journal\":\"http://pubs.rsc.org/en/Content/ArticleLanding/2013/SM/c3sm50479d#!divAbstract\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":2,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"firstnames\":[\"Shankar\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"suffixes\":[]},{\"firstnames\":[\"Thomas\",\"M.\"],\"propositions\":[],\"lastnames\":[\"Antonsen\"],\"suffixes\":[]},{\"firstnames\":[\"Edward\"],\"propositions\":[],\"lastnames\":[\"Ott\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"http://dx.doi.org/10.1016/S0167-2789(97)00184-X\",\"issn\":\"0167-2789\",\"journal\":\"Physica D: Nonlinear Phenomena\",\"keywords\":\"Hamiltonian systems; pubs\",\"number\":\"3–4\",\"pages\":\"412 - 440\",\"title\":\"Anomalous diffusion in bounded temporally irregular flows\",\"url_journal\":\"http://www.sciencedirect.com/science/article/pii/S016727899700184X\",\"volume\":\"112\",\"year\":\"1998\",\"bdsk-url-1\":\"http://www.sciencedirect.com/science/article/pii/S016727899700184X\",\"bdsk-url-2\":\"http://dx.doi.org/10.1016/S0167-2789(97)00184-X\",\"bibtex\":\"@article{Venkataramani1998412,\\n\\tauthor = {Shankar C. Venkataramani and Thomas M. Antonsen and Edward Ott},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {http://dx.doi.org/10.1016/S0167-2789(97)00184-X},\\n\\tissn = {0167-2789},\\n\\tjournal = {Physica D: Nonlinear Phenomena},\\n\\tkeywords = {Hamiltonian systems; pubs},\\n\\tnumber = {3--4},\\n\\tpages = {412 - 440},\\n\\ttitle = {Anomalous diffusion in bounded temporally irregular flows},\\n\\turl_journal = {http://www.sciencedirect.com/science/article/pii/S016727899700184X},\\n\\tvolume = {112},\\n\\tyear = {1998},\\n\\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S016727899700184X},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1016/S0167-2789(97)00184-X}}\\n\\n\",\"author_short\":[\"Venkataramani, S. C.\",\"Antonsen, T. M.\",\"Ott, E.\"],\"key\":\"Venkataramani1998412\",\"id\":\"Venkataramani1998412\",\"bibbaseid\":\"venkataramani-antonsen-ott-anomalousdiffusioninboundedtemporallyirregularflows-1998\",\"role\":\"author\",\"urls\":{\" journal\":\"http://www.sciencedirect.com/science/article/pii/S016727899700184X\"},\"keyword\":[\"Hamiltonian systems; pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"In this paper we investigate the propagation of conical waves in nonlinear media. In particular, we are interested in the effects resulting from applying a Gaussian apodization to an ideal nondiffracting wave. First, we present a multiple scales approach to derive amplitude equations for weakly nonlinear conical waves from a governing equation of cubic nonlinear Schrödinger type. From these equations we obtain asymptotic solutions for the linear and the weakly nonlinear problem for which we state several uniform estimates that describe the deviation from the ideal nondiffracting solution. Moreover, we show numerical simulations based on an implementation of our amplitude equations to support and illustrate our analytical results.\",\"author\":[{\"firstnames\":[\"Tobias\"],\"propositions\":[],\"lastnames\":[\"Graf\"],\"suffixes\":[]},{\"firstnames\":[\"Jerome\"],\"propositions\":[],\"lastnames\":[\"Moloney\"],\"suffixes\":[]},{\"firstnames\":[\"Shankar\"],\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"http://dx.doi.org/10.1016/j.physd.2012.09.004\",\"issn\":\"0167-2789\",\"journal\":\"Physica D: Nonlinear Phenomena\",\"keywords\":\"Uniform estimates; pubs\",\"number\":\"1\",\"pages\":\"32 - 44\",\"title\":\"Asymptotic analysis of weakly nonlinear Bessel-Gauß   beams\",\"url_journal\":\"http://www.sciencedirect.com/science/article/pii/S0167278912002308\",\"volume\":\"243\",\"year\":\"2013\",\"bdsk-url-1\":\"http://www.sciencedirect.com/science/article/pii/S0167278912002308\",\"bdsk-url-2\":\"http://dx.doi.org/10.1016/j.physd.2012.09.004\",\"bibtex\":\"@article{GMV2013,\\n\\tabstract = {In this paper we investigate the propagation of conical waves in nonlinear media. In particular, we are interested in the effects resulting from applying a Gaussian apodization to an ideal nondiffracting wave. First, we present a multiple scales approach to derive amplitude equations for weakly nonlinear conical waves from a governing equation of cubic nonlinear Schr{\\\\\\\"o}dinger type. From these equations we obtain asymptotic solutions for the linear and the weakly nonlinear problem for which we state several uniform estimates that describe the deviation from the ideal nondiffracting solution. Moreover, we show numerical simulations based on an implementation of our amplitude equations to support and illustrate our analytical results.},\\n\\tauthor = {Tobias Graf and Jerome Moloney and Shankar Venkataramani},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {http://dx.doi.org/10.1016/j.physd.2012.09.004},\\n\\tissn = {0167-2789},\\n\\tjournal = {Physica D: Nonlinear Phenomena},\\n\\tkeywords = {Uniform estimates; pubs},\\n\\tnumber = {1},\\n\\tpages = {32 - 44},\\n\\ttitle = {Asymptotic analysis of weakly nonlinear {Bessel}-{Gau}\\\\ss { } beams},\\n\\turl_journal = {http://www.sciencedirect.com/science/article/pii/S0167278912002308},\\n\\tvolume = {243},\\n\\tyear = {2013},\\n\\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0167278912002308},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1016/j.physd.2012.09.004}}\\n\\n\",\"author_short\":[\"Graf, T.\",\"Moloney, J.\",\"Venkataramani, S.\"],\"key\":\"GMV2013\",\"id\":\"GMV2013\",\"bibbaseid\":\"graf-moloney-venkataramani-asymptoticanalysisofweaklynonlinearbesselgaubeams-2013\",\"role\":\"author\",\"urls\":{\" journal\":\"http://www.sciencedirect.com/science/article/pii/S0167278912002308\"},\"keyword\":[\"Uniform estimates; pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"firstnames\":[\"Shankar\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"suffixes\":[]},{\"firstnames\":[\"Thomas\",\"M.\"],\"propositions\":[],\"lastnames\":[\"Antonsen\"],\"suffixes\":[]},{\"firstnames\":[\"Edward\"],\"propositions\":[],\"lastnames\":[\"Ott\"],\"suffixes\":[]},{\"firstnames\":[\"John\",\"C\"],\"propositions\":[],\"lastnames\":[\"Sommerer\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"http://dx.doi.org/10.1016/0375-9601(95)00710-K\",\"issn\":\"0375-9601\",\"journal\":\"Physics Letters A\",\"keywords\":\"Invariant manifold; pubs\",\"number\":\"3–4\",\"pages\":\"173 - 179\",\"title\":\"Characterization of on-off intermittent time series\",\"url_journal\":\"http://www.sciencedirect.com/science/article/pii/037596019500710K\",\"volume\":\"207\",\"year\":\"1995\",\"bdsk-url-1\":\"http://www.sciencedirect.com/science/article/pii/037596019500710K\",\"bdsk-url-2\":\"http://dx.doi.org/10.1016/0375-9601(95)00710-K\",\"bibtex\":\"@article{on-off1995,\\n\\tauthor = {Shankar C. Venkataramani and Thomas M. Antonsen and Edward Ott and John C Sommerer},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {http://dx.doi.org/10.1016/0375-9601(95)00710-K},\\n\\tissn = {0375-9601},\\n\\tjournal = {Physics Letters A},\\n\\tkeywords = {Invariant manifold; pubs},\\n\\tnumber = {3--4},\\n\\tpages = {173 - 179},\\n\\ttitle = {Characterization of on-off intermittent time series},\\n\\turl_journal = {http://www.sciencedirect.com/science/article/pii/037596019500710K},\\n\\tvolume = {207},\\n\\tyear = {1995},\\n\\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/037596019500710K},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1016/0375-9601(95)00710-K}}\\n\\n\",\"author_short\":[\"Venkataramani, S. C.\",\"Antonsen, T. M.\",\"Ott, E.\",\"Sommerer, J. C\"],\"key\":\"on-off1995\",\"id\":\"on-off1995\",\"bibbaseid\":\"venkataramani-antonsen-ott-sommerer-characterizationofonoffintermittenttimeseries-1995\",\"role\":\"author\",\"urls\":{\" journal\":\"http://www.sciencedirect.com/science/article/pii/037596019500710K\"},\"keyword\":[\"Invariant manifold; pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"Wind- and current-driven flotsam, oil spills, pollutants, and nutrients, approaching the nearshore will frequently appear to park just beyond the break zone, where waves break. Moreover, the portion of these tracers that beach will do so only after a long time. Explaining why these tracers park and at what rate they reach the shore has important implications on a variety of different nearshore environmental issues, including the determination of what subscale processes are essential in computer models for the simulation of pollutant transport in the nearshore. Using a simple model we provide an explanation for the underlying mechanism responsible for the parking of tracers, the role played by the bottom topography, and the non-uniform dispersion which leads, in some circumstances, to the eventual landing of all or a portion of the tracers. We refer to the parking phenomenon in this environment as nearshore sticky waters. \",\"author\":[{\"firstnames\":[\"Juan\",\"M.\"],\"propositions\":[],\"lastnames\":[\"Restrepo\"],\"suffixes\":[]},{\"firstnames\":[\"Shankar\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"suffixes\":[]},{\"firstnames\":[\"Clint\"],\"propositions\":[],\"lastnames\":[\"Dawson\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"http://dx.doi.org/10.1016/j.ocemod.2014.06.003\",\"issn\":\"1463-5003\",\"journal\":\"Ocean Modelling\",\"keywords\":\"Waves and currents; pubs\",\"number\":\"0\",\"pages\":\"49 - 58\",\"title\":\"Nearshore sticky waters\",\"url_arxiv\":\"http://arxiv.org/abs/1307.0588\",\"url_journal\":\"http://www.sciencedirect.com/science/article/pii/S1463500314000778\",\"volume\":\"80\",\"year\":\"2014\",\"bdsk-url-1\":\"http://www.sciencedirect.com/science/article/pii/S1463500314000778\",\"bdsk-url-2\":\"http://dx.doi.org/10.1016/j.ocemod.2014.06.003\",\"bibtex\":\"@article{sticky_waters,\\n\\tabstract = {Wind- and current-driven flotsam, oil spills, pollutants, and nutrients, approaching the nearshore will frequently appear to park just beyond the break zone, where waves break. Moreover, the portion of these tracers that beach will do so only after a long time. Explaining why these tracers park and at what rate they reach the shore has important implications on a variety of different nearshore environmental issues, including the determination of what subscale processes are essential in computer models for the simulation of pollutant transport in the nearshore. Using a simple model we provide an explanation for the underlying mechanism responsible for the parking of tracers, the role played by the bottom topography, and the non-uniform dispersion which leads, in some circumstances, to the eventual landing of all or a portion of the tracers. We refer to the parking phenomenon in this environment as nearshore sticky waters. },\\n\\tauthor = {Juan M. Restrepo and Shankar C. Venkataramani and Clint Dawson},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {http://dx.doi.org/10.1016/j.ocemod.2014.06.003},\\n\\tissn = {1463-5003},\\n\\tjournal = {Ocean Modelling},\\n\\tkeywords = {Waves and currents; pubs},\\n\\tnumber = {0},\\n\\tpages = {49 - 58},\\n\\ttitle = {Nearshore sticky waters},\\n\\turl_arxiv = {http://arxiv.org/abs/1307.0588},\\n\\turl_journal = {http://www.sciencedirect.com/science/article/pii/S1463500314000778},\\n\\tvolume = {80},\\n\\tyear = {2014},\\n\\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S1463500314000778},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1016/j.ocemod.2014.06.003}}\\n\\n\",\"author_short\":[\"Restrepo, J. M.\",\"Venkataramani, S. C.\",\"Dawson, C.\"],\"key\":\"sticky_waters\",\"id\":\"sticky_waters\",\"bibbaseid\":\"restrepo-venkataramani-dawson-nearshorestickywaters-2014\",\"role\":\"author\",\"urls\":{\" arxiv\":\"http://arxiv.org/abs/1307.0588\",\" journal\":\"http://www.sciencedirect.com/science/article/pii/S1463500314000778\"},\"keyword\":[\"Waves and currents; pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"firstnames\":[\"Shankar\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"suffixes\":[]},{\"firstnames\":[\"Thomas\",\"M.\"],\"propositions\":[],\"lastnames\":[\"Antonsen\"],\"suffixes\":[]},{\"firstnames\":[\"Edward\"],\"propositions\":[],\"lastnames\":[\"Ott\"],\"suffixes\":[]},{\"firstnames\":[\"John\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Sommerer\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"http://dx.doi.org/10.1016/0167-2789(96)00014-0\",\"issn\":\"0167-2789\",\"journal\":\"Physica D: Nonlinear Phenomena\",\"keywords\":\"Invariant manifold; pubs\",\"note\":\"Measures of Spatio-Temporal Dynamics\",\"number\":\"1–4\",\"pages\":\"66 - 99\",\"title\":\"On-off intermittency: Power spectrum and fractal properties of time series\",\"url_journal\":\"http://www.sciencedirect.com/science/article/pii/0167278996000140\",\"volume\":\"96\",\"year\":\"1996\",\"bdsk-url-1\":\"http://www.sciencedirect.com/science/article/pii/0167278996000140\",\"bdsk-url-2\":\"http://dx.doi.org/10.1016/0167-2789(96)00014-0\",\"bibtex\":\"@article{Venkataramani199666,\\n\\tauthor = {Shankar C. Venkataramani and Thomas M. Antonsen and Edward Ott and John C. Sommerer},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {http://dx.doi.org/10.1016/0167-2789(96)00014-0},\\n\\tissn = {0167-2789},\\n\\tjournal = {Physica D: Nonlinear Phenomena},\\n\\tkeywords = {Invariant manifold; pubs},\\n\\tnote = {Measures of Spatio-Temporal Dynamics},\\n\\tnumber = {1--4},\\n\\tpages = {66 - 99},\\n\\ttitle = {On-off intermittency: Power spectrum and fractal properties of time series},\\n\\turl_journal = {http://www.sciencedirect.com/science/article/pii/0167278996000140},\\n\\tvolume = {96},\\n\\tyear = {1996},\\n\\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0167278996000140},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1016/0167-2789(96)00014-0}}\\n\\n\",\"author_short\":[\"Venkataramani, S. C.\",\"Antonsen, T. M.\",\"Ott, E.\",\"Sommerer, J. C.\"],\"key\":\"Venkataramani199666\",\"id\":\"Venkataramani199666\",\"bibbaseid\":\"venkataramani-antonsen-ott-sommerer-onoffintermittencypowerspectrumandfractalpropertiesoftimeseries-1996\",\"role\":\"author\",\"urls\":{\" journal\":\"http://www.sciencedirect.com/science/article/pii/0167278996000140\"},\"keyword\":[\"Invariant manifold; pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis. Within the Fresnel approximation, we show that this problem can be expressed in a variational form equivalent to the one arising in phase retrieval. Using the uncertainty principle we prove various rigorous lower bounds on the functional; these lower bounds estimate the $L^2$ error for the beam shaping problem in terms of the design parameters. We also use the method of stationary phase to construct a natural ansatz for a minimizer in the short wavelength limit. We illustrate the implications of our results by applying the method of stationary phase coupled with the Gerchberg–Saxton algorithm to beam shaping problems arising in the remote delivery of beams and pulses.\",\"author\":[{\"firstnames\":[\"John\",\"A.\"],\"propositions\":[],\"lastnames\":[\"Gemmer\"],\"suffixes\":[]},{\"firstnames\":[\"Shankar\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"suffixes\":[]},{\"firstnames\":[\"Charles\",\"G.\"],\"propositions\":[],\"lastnames\":[\"Durfee\"],\"suffixes\":[]},{\"firstnames\":[\"Jerome\",\"V.\"],\"propositions\":[],\"lastnames\":[\"Moloney\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"http://dx.doi.org/10.1016/j.physd.2014.06.003\",\"issn\":\"0167-2789\",\"journal\":\"Physica D: Nonlinear Phenomena\",\"keywords\":\"Fresnel approximation; pubs\",\"number\":\"0\",\"pages\":\"15 - 28\",\"title\":\"Optical beam shaping and diffraction free waves: A variational approach\",\"url_arxiv\":\"http://arxiv.org/abs/1307.6289\",\"url_journal\":\"http://www.sciencedirect.com/science/article/pii/S0167278914001195\",\"volume\":\"283\",\"year\":\"2014\",\"bdsk-url-1\":\"http://www.sciencedirect.com/science/article/pii/S0167278914001195\",\"bdsk-url-2\":\"http://dx.doi.org/10.1016/j.physd.2014.06.003\",\"bibtex\":\"@article{GVDM2014,\\n\\tabstract = {We investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis. Within the Fresnel approximation, we show that this problem can be expressed in a variational form equivalent to the one arising in phase retrieval. Using the uncertainty principle we prove various rigorous lower bounds on the functional; these lower bounds estimate the $L^2$ error for the beam shaping problem in terms of the design parameters. We also use the method of stationary phase to construct a natural ansatz for a minimizer in the short wavelength limit. We illustrate the implications of our results by applying the method of stationary phase coupled with the Gerchberg--Saxton algorithm to beam shaping problems arising in the remote delivery of beams and pulses.},\\n\\tauthor = {John A. Gemmer and Shankar C. Venkataramani and Charles G. Durfee and Jerome V. Moloney},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {http://dx.doi.org/10.1016/j.physd.2014.06.003},\\n\\tissn = {0167-2789},\\n\\tjournal = {Physica D: Nonlinear Phenomena},\\n\\tkeywords = {Fresnel approximation; pubs},\\n\\tnumber = {0},\\n\\tpages = {15 - 28},\\n\\ttitle = {Optical beam shaping and diffraction free waves: A variational approach},\\n\\turl_arxiv = {http://arxiv.org/abs/1307.6289},\\n\\turl_journal = {http://www.sciencedirect.com/science/article/pii/S0167278914001195},\\n\\tvolume = {283},\\n\\tyear = {2014},\\n\\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0167278914001195},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1016/j.physd.2014.06.003}}\\n\\n\",\"author_short\":[\"Gemmer, J. A.\",\"Venkataramani, S. C.\",\"Durfee, C. G.\",\"Moloney, J. V.\"],\"key\":\"GVDM2014\",\"id\":\"GVDM2014\",\"bibbaseid\":\"gemmer-venkataramani-durfee-moloney-opticalbeamshapinganddiffractionfreewavesavariationalapproach-2014\",\"role\":\"author\",\"urls\":{\" arxiv\":\"http://arxiv.org/abs/1307.6289\",\" journal\":\"http://www.sciencedirect.com/science/article/pii/S0167278914001195\"},\"keyword\":[\"Fresnel approximation; pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We investigate isometric immersions of disks with constant negative curvature into $R^3$, and the minimizers for the bending energy, i.e. the $L^2$ norm of the principal curvatures over the class of $W^{2,2}$ isometric immersions. We show the existence of smooth immersions of arbitrarily large geodesic balls in $H^2$ into $R^3$. In elucidating the connection between these immersions and the non-existence/singularity results of Hilbert and Amsler, we obtain a lower bound for the $L^∞$ norm of the principal curvatures for such smooth isometric immersions. We also construct piecewise smooth isometric immersions that have a periodic profile, are globally $W^{2,2}$ and numerically have lower bending energy than their smooth counterparts. The number of periods in these configurations is set by the condition that the principal curvatures of the surface remain finite and grow approximately exponentially with the radius of the disk. We discuss the implications of our results on recent experiments on the mechanics of non-Euclidean plates. \",\"author\":[{\"propositions\":[],\"lastnames\":[\"Gemmer\"],\"firstnames\":[\"John\",\"A.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"http://dx.doi.org/10.1016/j.physd.2011.07.002\",\"issn\":\"0167-2789\",\"journal\":\"Physica D: Nonlinear Phenomena\",\"keywords\":\"Morphogenesis in soft tissue; pubs\",\"number\":\"19\",\"pages\":\"1536 - 1552\",\"title\":\"Shape selection in non-Euclidean plates\",\"url_arxiv\":\"http://arxiv.org/abs/1005.4442\",\"url_journal\":\"http://www.sciencedirect.com/science/article/pii/S0167278911001825\",\"volume\":\"240\",\"year\":\"2011\",\"bdsk-url-1\":\"http://www.sciencedirect.com/science/article/pii/S0167278911001825\",\"bdsk-url-2\":\"http://dx.doi.org/10.1016/j.physd.2011.07.002\",\"bibtex\":\"@article{GV2011,\\n\\tabstract = {We investigate isometric immersions of disks with constant negative curvature into $R^3$, and the minimizers for the bending energy, i.e.   the $L^2$ norm of the principal curvatures over the class of $W^{2,2}$ isometric immersions. We show the existence of smooth immersions of arbitrarily large geodesic balls in $H^2$ into $R^3$. In elucidating the connection between these immersions and the non-existence/singularity results of Hilbert and Amsler, we obtain a lower bound for the $L^\\\\infty$ norm of the principal curvatures for such smooth isometric immersions. We also construct piecewise smooth isometric immersions that have a periodic profile, are globally $W^{2,2}$ and numerically have lower bending energy than their smooth counterparts. The number of periods in these configurations is set by the condition that the principal curvatures of the surface remain finite and grow approximately exponentially with the radius of the disk. We discuss the implications of our results on recent experiments on the mechanics of non-Euclidean plates.\\n},\\n\\tauthor = {Gemmer, John A. and Venkataramani, Shankar C.},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {http://dx.doi.org/10.1016/j.physd.2011.07.002},\\n\\tissn = {0167-2789},\\n\\tjournal = {Physica D: Nonlinear Phenomena},\\n\\tkeywords = {Morphogenesis in soft tissue; pubs},\\n\\tnumber = {19},\\n\\tpages = {1536 - 1552},\\n\\ttitle = {Shape selection in non-Euclidean plates},\\n\\turl_arxiv = {http://arxiv.org/abs/1005.4442},\\n\\turl_journal = {http://www.sciencedirect.com/science/article/pii/S0167278911001825},\\n\\tvolume = {240},\\n\\tyear = {2011},\\n\\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0167278911001825},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1016/j.physd.2011.07.002}}\\n\\n\",\"author_short\":[\"Gemmer, J. A.\",\"Venkataramani, S. C.\"],\"key\":\"GV2011\",\"id\":\"GV2011\",\"bibbaseid\":\"gemmer-venkataramani-shapeselectioninnoneuclideanplates-2011\",\"role\":\"author\",\"urls\":{\" arxiv\":\"http://arxiv.org/abs/1005.4442\",\" journal\":\"http://www.sciencedirect.com/science/article/pii/S0167278911001825\"},\"keyword\":[\"Morphogenesis in soft tissue; pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"ABSTRACT CARTHE (http://carthe.org/) is a Gulf of Mexico Research Initiative (GoMRI) consortium established through a competitive peer-reviewed selection process. CARTHE comprises 26 principal investigators from 14 universities and research institutions distributed across four Gulf of Mexico states and other four states. It fuses into one group investigators with unique scientific and technical knowledge and extensive publications related to oil fate/transport processes, oceanic and atmospheric turbulence, air-sea interactions, tropical cyclones and winter storms, and coastal and nearshore modeling and observations. Our primary goal is to accurately predict the fate of hydrocarbons released into the environment. Achieving this goal is particularly challenging since petroleum releases into the environment interact with natural processes across six orders of magnitude of time and space scales. We are developing a multi-scale modeling tool by incorporating state-of-the-art hydrophysical models, each applicable for a restricted range of scales, into a single, interconnected modeling system to predict the physical dispersal of hydrocarbons across scales ranging from the microscale at the wellhead to oceanic and atmospheric mesoscales. CARTHE is also conducting novel in-situ observations and laboratory experiments specifically designed for quantifying submesoscale dispersion as well as for both model validation and parameterization. Finally, we are providing a robust set of uncertainty metrics and analysis tools to assess model performance and quantify predictive uncertainty.\",\"annote\":\"doi: 10.7901/2169-3358-2014.1.544\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Özgökmen\"],\"firstnames\":[\"Tamay\",\"M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Beron-Vera\"],\"firstnames\":[\"Francisco\",\"J.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Bogucki\"],\"firstnames\":[\"Darek\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Chen\"],\"firstnames\":[\"Shuyi\",\"S.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Dawson\"],\"firstnames\":[\"Clint\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Dewar\"],\"firstnames\":[\"William\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Griffa\"],\"firstnames\":[\"Annalisa\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Haus\"],\"firstnames\":[\"Brian\",\"K.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Haza\"],\"firstnames\":[\"Angelique\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Huntley\"],\"firstnames\":[\"Helga\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Iskandarani\"],\"firstnames\":[\"Mohamed\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Jacobs\"],\"firstnames\":[\"Gregg\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Jagers\"],\"firstnames\":[\"Bert\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Kirwan\"],\"firstnames\":[\"A.\",\"D.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Laxague\"],\"firstnames\":[\"Nathan\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Lipphardt\"],\"firstnames\":[\"Bruce\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"MacMahan\"],\"firstnames\":[\"Jamie\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Mariano\"],\"firstnames\":[\"Arthur\",\"J.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Olascoaga\"],\"firstnames\":[\"Josefina\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Novelli\"],\"firstnames\":[\"Guillaume\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Poje\"],\"firstnames\":[\"Andrew\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Reniers\"],\"firstnames\":[\"A.\",\"J.\",\"H.\",\"M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Restrepo\"],\"firstnames\":[\"Juan\",\"M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Rosenheim\"],\"firstnames\":[\"Brad\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ryan\"],\"firstnames\":[\"Edward\",\"H.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Smith\"],\"firstnames\":[\"Conor\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Soloviev\"],\"firstnames\":[\"Alexander\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Zha\"],\"firstnames\":[\"Ge-Cheng\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Zhu\"],\"firstnames\":[\"Ping\"],\"suffixes\":[]}],\"booktitle\":\"International Oil Spill Conference Proceedings\",\"da\":\"2014/05/01\",\"date\":\"2014/05/01\",\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.7901/2169-3358-2014.1.544\",\"isbn\":\"2169-3366\",\"journal\":\"International Oil Spill Conference Proceedings\",\"journal1\":\"International Oil Spill Conference Proceedings\",\"keywords\":\"pubs\",\"m3\":\"doi: 10.7901/2169-3358-2014.1.544\",\"month\":\"2014/11/08\",\"n2\":\"ABSTRACT CARTHE (http://carthe.org/) is a Gulf of Mexico Research Initiative (GoMRI) consortium established through a competitive peer-reviewed selection process. CARTHE comprises 26 principal investigators from 14 universities and research institutions distributed across four Gulf of Mexico states and other four states. It fuses into one group investigators with unique scientific and technical knowledge and extensive publications related to oil fate/transport processes, oceanic and atmospheric turbulence, air-sea interactions, tropical cyclones and winter storms, and coastal and nearshore modeling and observations. Our primary goal is to accurately predict the fate of hydrocarbons released into the environment. Achieving this goal is particularly challenging since petroleum releases into the environment interact with natural processes across six orders of magnitude of time and space scales. We are developing a multi-scale modeling tool by incorporating state-of-the-art hydrophysical models, each applicable for a restricted range of scales, into a single, interconnected modeling system to predict the physical dispersal of hydrocarbons across scales ranging from the microscale at the wellhead to oceanic and atmospheric mesoscales. CARTHE is also conducting novel in-situ observations and laboratory experiments specifically designed for quantifying submesoscale dispersion as well as for both model validation and parameterization. Finally, we are providing a robust set of uncertainty metrics and analysis tools to assess model performance and quantify predictive uncertainty.\",\"number\":\"1\",\"pages\":\"544–560\",\"publisher\":\"American Petroleum Institute\",\"title\":\"Research Overview of the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE)\",\"ty\":\"JOUR\",\"url_journal\":\"http://dx.doi.org/10.7901/2169-3358-2014.1.544\",\"volume\":\"2014\",\"year\":\"2014\",\"year1\":\"2014\",\"bdsk-url-1\":\"http://dx.doi.org/10.7901/2169-3358-2014.1.544\",\"bibtex\":\"@article{CARTHE2014,\\n\\tabstract = {ABSTRACT CARTHE (http://carthe.org/) is a Gulf of Mexico Research Initiative (GoMRI) consortium established through a competitive peer-reviewed selection process. CARTHE comprises 26 principal investigators from 14 universities and research institutions distributed across four Gulf of Mexico states and other four states. It fuses into one group investigators with unique scientific and technical knowledge and extensive publications related to oil fate/transport processes, oceanic and atmospheric turbulence, air-sea interactions, tropical cyclones and winter storms, and coastal and nearshore modeling and observations. Our primary goal is to accurately predict the fate of hydrocarbons released into the environment. Achieving this goal is particularly challenging since petroleum releases into the environment interact with natural processes across six orders of magnitude of time and space scales. We are developing a multi-scale modeling tool by incorporating state-of-the-art hydrophysical models, each applicable for a restricted range of scales, into a single, interconnected modeling system to predict the physical dispersal of hydrocarbons across scales ranging from the microscale at the wellhead to oceanic and atmospheric mesoscales. CARTHE is also conducting novel in-situ observations and laboratory experiments specifically designed for quantifying submesoscale dispersion as well as for both model validation and parameterization. Finally, we are providing a robust set of uncertainty metrics and analysis tools to assess model performance and quantify predictive uncertainty.},\\n\\tannote = {doi: 10.7901/2169-3358-2014.1.544},\\n\\tauthor = {{\\\\\\\"O}zg{\\\\\\\"o}kmen, Tamay M. and Beron-Vera, Francisco J. and Bogucki, Darek and Chen, Shuyi S. and Dawson, Clint and Dewar, William and Griffa, Annalisa and Haus, Brian K. and Haza, Angelique C. and Huntley, Helga and Iskandarani, Mohamed and Jacobs, Gregg and Jagers, Bert and Kirwan, A. D. and Laxague, Nathan and Lipphardt, Bruce and MacMahan, Jamie and Mariano, Arthur J. and Olascoaga, Josefina and Novelli, Guillaume and Poje, Andrew C. and Reniers, A. J. H. M. and Restrepo, Juan M. and Rosenheim, Brad and Ryan, Edward H. and Smith, Conor and Soloviev, Alexander and Venkataramani, Shankar and Zha, Ge-Cheng and Zhu, Ping},\\n\\tbooktitle = {International Oil Spill Conference Proceedings},\\n\\tda = {2014/05/01},\\n\\tdate = {2014/05/01},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.7901/2169-3358-2014.1.544},\\n\\tisbn = {2169-3366},\\n\\tjournal = {International Oil Spill Conference Proceedings},\\n\\tjournal1 = {International Oil Spill Conference Proceedings},\\n\\tkeywords = {pubs},\\n\\tm3 = {doi: 10.7901/2169-3358-2014.1.544},\\n\\tmonth = {2014/11/08},\\n\\tn2 = {ABSTRACT CARTHE (http://carthe.org/) is a Gulf of Mexico Research Initiative (GoMRI) consortium established through a competitive peer-reviewed selection process. CARTHE comprises 26 principal investigators from 14 universities and research institutions distributed across four Gulf of Mexico states and other four states. It fuses into one group investigators with unique scientific and technical knowledge and extensive publications related to oil fate/transport processes, oceanic and atmospheric turbulence, air-sea interactions, tropical cyclones and winter storms, and coastal and nearshore modeling and observations. Our primary goal is to accurately predict the fate of hydrocarbons released into the environment. Achieving this goal is particularly challenging since petroleum releases into the environment interact with natural processes across six orders of magnitude of time and space scales. We are developing a multi-scale modeling tool by incorporating state-of-the-art hydrophysical models, each applicable for a restricted range of scales, into a single, interconnected modeling system to predict the physical dispersal of hydrocarbons across scales ranging from the microscale at the wellhead to oceanic and atmospheric mesoscales. CARTHE is also conducting novel in-situ observations and laboratory experiments specifically designed for quantifying submesoscale dispersion as well as for both model validation and parameterization. Finally, we are providing a robust set of uncertainty metrics and analysis tools to assess model performance and quantify predictive uncertainty.},\\n\\tnumber = {1},\\n\\tpages = {544--560},\\n\\tpublisher = {American Petroleum Institute},\\n\\ttitle = {Research Overview of the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE)},\\n\\tty = {JOUR},\\n\\turl_journal = {http://dx.doi.org/10.7901/2169-3358-2014.1.544},\\n\\tvolume = {2014},\\n\\tyear = {2014},\\n\\tyear1 = {2014},\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.7901/2169-3358-2014.1.544}}\\n\\n\",\"author_short\":[\"Özgökmen, T. M.\",\"Beron-Vera, F. J.\",\"Bogucki, D.\",\"Chen, S. S.\",\"Dawson, C.\",\"Dewar, W.\",\"Griffa, A.\",\"Haus, B. K.\",\"Haza, A. C.\",\"Huntley, H.\",\"Iskandarani, M.\",\"Jacobs, G.\",\"Jagers, B.\",\"Kirwan, A. D.\",\"Laxague, N.\",\"Lipphardt, B.\",\"MacMahan, J.\",\"Mariano, A. J.\",\"Olascoaga, J.\",\"Novelli, G.\",\"Poje, A. C.\",\"Reniers, A. J. H. M.\",\"Restrepo, J. M.\",\"Rosenheim, B.\",\"Ryan, E. H.\",\"Smith, C.\",\"Soloviev, A.\",\"Venkataramani, S.\",\"Zha, G.\",\"Zhu, P.\"],\"key\":\"CARTHE2014\",\"id\":\"CARTHE2014\",\"bibbaseid\":\"zgkmen-beronvera-bogucki-chen-dawson-dewar-griffa-haus-etal-researchoverviewoftheconsortiumforadvancedresearchontransportofhydrocarbonintheenvironmentcarthe-2014\",\"role\":\"author\",\"urls\":{\" journal\":\"http://dx.doi.org/10.7901/2169-3358-2014.1.544\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity, and surface tension. The free boundary in our system develops sharp corners or singularities in certain parameter regimes, and this is an impediment to using existing ``single-scale'' numerical conformal mapping methods. The difficulty is due to the phenomenon of crowding, i.e., the tendency of nodes in the preimage plane to concentrate near the sharp regions of the boundary, leaving the smooth regions of the boundary poorly resolved. A natural idea is to exploit the scale separation between the sharp regions and smooth regions to solve for each region separately and then stitch the solutions together. However, this is not straightforward as conformal maps are rigid ``global'' objects, and it is not obvious how one would patch two conformal maps together to obtain a new conformal map. We develop a ``multiscale'' (i.e., adaptive) conformal mapping method that allows us to carry out this program of stitching conformal maps on different scales together. We successfully apply our method to the electromechanical model problem.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Kent\"],\"firstnames\":[\"Stuart\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.1103/PhysRevE.90.012407\",\"issue\":\"1\",\"journal\":\"Phys. Rev. E\",\"keywords\":\"pubs\",\"month\":\"Jul\",\"numpages\":\"15\",\"pages\":\"012407\",\"publisher\":\"American Physical Society\",\"title\":\"Sharp interfaces in two-dimensional free boundary problems: Interface calculation via matched conformal maps\",\"url_arxiv\":\"http://arxiv.org/abs/1405.6965\",\"url_journal\":\"http://link.aps.org/doi/10.1103/PhysRevE.90.012407\",\"volume\":\"90\",\"year\":\"2014\",\"bdsk-url-1\":\"http://link.aps.org/doi/10.1103/PhysRevE.90.012407\",\"bdsk-url-2\":\"http://dx.doi.org/10.1103/PhysRevE.90.012407\",\"bibtex\":\"@article{PRE_interface,\\n\\tabstract = {We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity, and surface tension. The free boundary in our system develops sharp corners or singularities in certain parameter regimes, and this is an impediment to using existing ``single-scale'' numerical conformal mapping methods. The difficulty is due to the phenomenon of crowding, i.e., the tendency of nodes in the preimage plane to concentrate near the sharp regions of the boundary, leaving the smooth regions of the boundary poorly resolved. A natural idea is to exploit the scale separation between the sharp regions and smooth regions to solve for each region separately and then stitch the solutions together. However, this is not straightforward as conformal maps are rigid ``global'' objects, and it is not obvious how one would patch two conformal maps together to obtain a new conformal map. We develop a ``multiscale'' (i.e., adaptive) conformal mapping method that allows us to carry out this program of stitching conformal maps on different scales together. We successfully apply our method to the electromechanical model problem.},\\n\\tauthor = {Kent, Stuart and Venkataramani, Shankar C.},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.1103/PhysRevE.90.012407},\\n\\tissue = {1},\\n\\tjournal = {Phys. Rev. E},\\n\\tkeywords = {pubs},\\n\\tmonth = {Jul},\\n\\tnumpages = {15},\\n\\tpages = {012407},\\n\\tpublisher = {American Physical Society},\\n\\ttitle = {Sharp interfaces in two-dimensional free boundary problems: Interface calculation via matched conformal maps},\\n\\turl_arxiv = {http://arxiv.org/abs/1405.6965},\\n\\turl_journal = {http://link.aps.org/doi/10.1103/PhysRevE.90.012407},\\n\\tvolume = {90},\\n\\tyear = {2014},\\n\\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.90.012407},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.90.012407}}\\n\\n\",\"author_short\":[\"Kent, S.\",\"Venkataramani, S. C.\"],\"key\":\"PRE_interface\",\"id\":\"PRE_interface\",\"bibbaseid\":\"kent-venkataramani-sharpinterfacesintwodimensionalfreeboundaryproblemsinterfacecalculationviamatchedconformalmaps-2014\",\"role\":\"author\",\"urls\":{\" arxiv\":\"http://arxiv.org/abs/1405.6965\",\" journal\":\"http://link.aps.org/doi/10.1103/PhysRevE.90.012407\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We propose criteria that define a trend for time series with inherent multi-scale features. We call this trend the tendency of a time series. The tendency is defined empirically by a set of criteria and captures the large-scale temporal variability of the original signal as well as the most frequent events in its histogram. Among other properties, the tendency has a variance no larger than that of the original signal; the histogram of the difference between the original signal and the tendency is as symmetric as possible; and with reduced complexity, the tendency captures essential features of the signal. To find the tendency we first use the intrinsic time-scale decomposition (ITD) of the signal, introduced in 2007 by Frei and Osorio, to produce a set of candidate tendencies. We then apply the criteria to each of the candidates to single out the one that best agrees with them. While the criteria for the tendency are independent of the signal decomposition scheme, it is found that the ITD is a simple and stable methodology, well suited for multi-scale signals. The ITD is a relatively new decomposition and little is known about its outcomes. In this study we take the first steps towards a probabilistic model of the ITD analysis of random time series. This analysis yields details concerning the universality and scaling properties of the components of the decomposition.\",\"author\":[{\"firstnames\":[\"Juan\",\"M\"],\"propositions\":[],\"lastnames\":[\"Restrepo\"],\"suffixes\":[]},{\"firstnames\":[\"Shankar\"],\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"suffixes\":[]},{\"firstnames\":[\"Darin\"],\"propositions\":[],\"lastnames\":[\"Comeau\"],\"suffixes\":[]},{\"firstnames\":[\"Hermann\"],\"propositions\":[],\"lastnames\":[\"Flaschka\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"journal\":\"New Journal of Physics\",\"keywords\":\"pubs\",\"number\":\"8\",\"pages\":\"085004\",\"title\":\"Defining a trend for time series using the intrinsic time-scale decomposition\",\"url_arxiv\":\"http://arxiv.org/abs/1404.3827\",\"url_journal\":\"http://stacks.iop.org/1367-2630/16/i=8/a=085004\",\"volume\":\"16\",\"year\":\"2014\",\"bdsk-url-1\":\"http://stacks.iop.org/1367-2630/16/i=8/a=085004\",\"bibtex\":\"@article{itd_paper,\\n\\tabstract = {We propose criteria that define a trend for time series with inherent multi-scale features. We call this trend the tendency of a time series. The tendency is defined empirically by a set of criteria and captures the large-scale temporal variability of the original signal as well as the most frequent events in its histogram. Among other properties, the tendency has a variance no larger than that of the original signal; the histogram of the difference between the original signal and the tendency is as symmetric as possible; and with reduced complexity, the tendency captures essential features of the signal. To find the tendency we first use the intrinsic time-scale decomposition (ITD) of the signal, introduced in 2007 by Frei and Osorio, to produce a set of candidate tendencies. We then apply the criteria to each of the candidates to single out the one that best agrees with them. While the criteria for the tendency are independent of the signal decomposition scheme, it is found that the ITD is a simple and stable methodology, well suited for multi-scale signals. The ITD is a relatively new decomposition and little is known about its outcomes. In this study we take the first steps towards a probabilistic model of the ITD analysis of random time series. This analysis yields details concerning the universality and scaling properties of the components of the decomposition.},\\n\\tauthor = {Juan M Restrepo and Shankar Venkataramani and Darin Comeau and Hermann Flaschka},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tjournal = {New Journal of Physics},\\n\\tkeywords = {pubs},\\n\\tnumber = {8},\\n\\tpages = {085004},\\n\\ttitle = {Defining a trend for time series using the intrinsic time-scale decomposition},\\n\\turl_arxiv = {http://arxiv.org/abs/1404.3827},\\n\\turl_journal = {http://stacks.iop.org/1367-2630/16/i=8/a=085004},\\n\\tvolume = {16},\\n\\tyear = {2014},\\n\\tBdsk-Url-1 = {http://stacks.iop.org/1367-2630/16/i=8/a=085004}}\\n\\n\",\"author_short\":[\"Restrepo, J. M\",\"Venkataramani, S.\",\"Comeau, D.\",\"Flaschka, H.\"],\"key\":\"itd_paper\",\"id\":\"itd_paper\",\"bibbaseid\":\"restrepo-venkataramani-comeau-flaschka-definingatrendfortimeseriesusingtheintrinsictimescaledecomposition-2014\",\"role\":\"author\",\"urls\":{\" arxiv\":\"http://arxiv.org/abs/1404.3827\",\" journal\":\"http://stacks.iop.org/1367-2630/16/i=8/a=085004\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We investigate the behaviour of non-Euclidean plates with constant negative Gaussian curvature using the Föppl–von Kármán reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. In particular we show that are only two types of global minimizers—deformations that remain flat and saddle shaped deformations with isolated regions of stretching near the edge of the annulus. We also show that there exist local minimizers with a periodic profile that have additional boundary layers near their lines of inflection. These additional boundary layers are a new phenomenon in thin elastic sheets and are necessary to regularize jump discontinuities in the azimuthal curvature across lines of inflection. We rigorously derive scaling laws for the width of these boundary layers as a function of the thickness of the sheet.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Gemmer\"],\"firstnames\":[\"John\",\"A.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]}],\"coden\":\"NONLE5\",\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.1088/0951-7715/25/12/3553\",\"fjournal\":\"Nonlinearity\",\"issn\":\"0951-7715\",\"journal\":\"Nonlinearity\",\"keywords\":\"pubs\",\"mrclass\":\"74K20 (35Q74)\",\"mrnumber\":\"2997707\",\"number\":\"12\",\"pages\":\"3553–3581\",\"title\":\"Defects and boundary layers in non-Euclidean plates\",\"url_arxiv\":\"http://arxiv.org/abs/1203.4329\",\"url_journal\":\"http://dx.doi.org/10.1088/0951-7715/25/12/3553\",\"volume\":\"25\",\"year\":\"2012\",\"bdsk-url-1\":\"http://dx.doi.org/10.1088/0951-7715/25/12/3553\",\"bdsk-url-2\":\"http://stacks.iop.org/0951-7715/25/i=12/a=3553\",\"bibtex\":\"@article{GV2012,\\n\\tabstract = {We investigate the behaviour of non-Euclidean plates with constant negative Gaussian curvature using the F{\\\\\\\"o}ppl--von K{\\\\'a}rm{\\\\'a}n reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. In particular we show that are only two types of global minimizers---deformations that remain flat and saddle shaped deformations with isolated regions of stretching near the edge of the annulus. We also show that there exist local minimizers with a periodic profile that have additional boundary layers near their lines of inflection. These additional boundary layers are a new phenomenon in thin elastic sheets and are necessary to regularize jump discontinuities in the azimuthal curvature across lines of inflection. We rigorously derive scaling laws for the width of these boundary layers as a function of the thickness of the sheet.},\\n\\tauthor = {Gemmer, John A. and Venkataramani, Shankar C.},\\n\\tcoden = {NONLE5},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.1088/0951-7715/25/12/3553},\\n\\tfjournal = {Nonlinearity},\\n\\tissn = {0951-7715},\\n\\tjournal = {Nonlinearity},\\n\\tkeywords = {pubs},\\n\\tmrclass = {74K20 (35Q74)},\\n\\tmrnumber = {2997707},\\n\\tnumber = {12},\\n\\tpages = {3553--3581},\\n\\ttitle = {Defects and boundary layers in non-{E}uclidean plates},\\n\\turl_arxiv = {http://arxiv.org/abs/1203.4329},\\n\\turl_journal = {http://dx.doi.org/10.1088/0951-7715/25/12/3553},\\n\\tvolume = {25},\\n\\tyear = {2012},\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.1088/0951-7715/25/12/3553},\\n\\tBdsk-Url-2 = {http://stacks.iop.org/0951-7715/25/i=12/a=3553}}\\n\\n\",\"author_short\":[\"Gemmer, J. A.\",\"Venkataramani, S. C.\"],\"key\":\"GV2012\",\"id\":\"GV2012\",\"bibbaseid\":\"gemmer-venkataramani-defectsandboundarylayersinnoneuclideanplates-2012\",\"role\":\"author\",\"urls\":{\" arxiv\":\"http://arxiv.org/abs/1203.4329\",\" journal\":\"http://dx.doi.org/10.1088/0951-7715/25/12/3553\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross–Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen in experimental studies of the corresponding physical systems and in numerical simulations of the microscopic equations that describe these systems.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Ercolani\"],\"firstnames\":[\"N.\",\"M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"S.\",\"C.\"],\"suffixes\":[]}],\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.1007/s00332-008-9035-9\",\"fjournal\":\"Journal of Nonlinear Science\",\"issn\":\"0938-8974\",\"journal\":\"J. Nonlinear Sci.\",\"keywords\":\"pubs\",\"mrclass\":\"35K25 (35A15 35K58 74R05)\",\"mrnumber\":\"2511257 (2010d:35149)\",\"mrreviewer\":\"Daniela Giachetti\",\"number\":\"3\",\"pages\":\"267–300\",\"title\":\"A variational theory for point defects in patterns\",\"url_arxiv\":\"http://arxiv.org/abs/0706.2917\",\"url_journal\":\"http://dx.doi.org/10.1007/s00332-008-9035-9\",\"volume\":\"19\",\"year\":\"2009\",\"bdsk-url-1\":\"http://dx.doi.org/10.1007/s00332-008-9035-9\",\"bibtex\":\"@article{patt_defects,\\n\\tabstract = {\\nWe derive a rigorous scaling law for minimizers in a natural version of the regularized Cross--Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen in experimental studies of the corresponding physical systems and in numerical simulations of the microscopic equations that describe these systems.},\\n\\tauthor = {Ercolani, N. M. and Venkataramani, S. C.},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.1007/s00332-008-9035-9},\\n\\tfjournal = {Journal of Nonlinear Science},\\n\\tissn = {0938-8974},\\n\\tjournal = {J. Nonlinear Sci.},\\n\\tkeywords = {pubs},\\n\\tmrclass = {35K25 (35A15 35K58 74R05)},\\n\\tmrnumber = {2511257 (2010d:35149)},\\n\\tmrreviewer = {Daniela Giachetti},\\n\\tnumber = {3},\\n\\tpages = {267--300},\\n\\ttitle = {A variational theory for point defects in patterns},\\n\\turl_arxiv = {http://arxiv.org/abs/0706.2917},\\n\\turl_journal = {http://dx.doi.org/10.1007/s00332-008-9035-9},\\n\\tvolume = {19},\\n\\tyear = {2009},\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.1007/s00332-008-9035-9}}\\n\\n\",\"author_short\":[\"Ercolani, N. M.\",\"Venkataramani, S. C.\"],\"key\":\"patt_defects\",\"id\":\"patt_defects\",\"bibbaseid\":\"ercolani-venkataramani-avariationaltheoryforpointdefectsinpatterns-2009\",\"role\":\"author\",\"urls\":{\" arxiv\":\"http://arxiv.org/abs/0706.2917\",\" journal\":\"http://dx.doi.org/10.1007/s00332-008-9035-9\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We investigate the electrostatic equilibria of N discrete charges of size 1/N on a two dimensional conductor (domain). We study the distribution of the charges on symmetric domains including the ellipse, the hypotrochoid and various regular polygons, with an emphasis on understanding the distributions of the charges, as the shape of the underlying conductor becomes singular. We find that there are two regimes of behavior, a symmetric regime for smooth conductors, and a symmetry broken regime for ``singular'' domains. For smooth conductors, the locations of the charges can be determined, to within O(logN/N2‾‾‾‾‾‾‾‾‾∠̌s) by an integral equation due to Pommerenke [ Math. Ann., 179: 212–218, (1969)]. We present a derivation of a related (but different) integral equation, which has the same solutions. We also solve the equation to obtain (asymptotic) solutions which show universal behavior in the distribution of the charges in conductors with somewhat smooth cusps. Conductors with sharp cusps and singularities show qualitatively different behavior, where the symmetry of the problem is broken, and the distribution of the discrete charges does not respect the symmetry of the underlying domain. We investigate the symmetry breaking both theoretically, and numerically, and find good agreement between our theory and the numerics. We also find that the universality in the distribution of the charges near the cusps persists in the symmetry broken regime, although this distribution is very different from the one given by the integral equation.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Berkenbusch\"],\"firstnames\":[\"Marko\",\"K.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Claus\"],\"firstnames\":[\"Isabelle\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Dunn\"],\"firstnames\":[\"Catherine\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Kadanoff\"],\"firstnames\":[\"Leo\",\"P.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Nicewicz\"],\"firstnames\":[\"Maciej\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]}],\"coden\":\"JSTPSB\",\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.1023/B:JOSS.0000041741.27244.ac\",\"fjournal\":\"Journal of Statistical Physics\",\"issn\":\"0022-4715\",\"journal\":\"J. Statist. Phys.\",\"keywords\":\"pubs\",\"mrclass\":\"78A30 (37J40 37N20 78A35)\",\"mrnumber\":\"2096037 (2006d:78009)\",\"mrreviewer\":\"T. Erber\",\"number\":\"5-6\",\"pages\":\"1301–1358\",\"title\":\"Discrete charges on a two dimensional conductor\",\"url_arxiv\":\"http://arxiv.org/abs/cond-mat/0310257\",\"url_journal\":\"http://dx.doi.org/10.1023/B:JOSS.0000041741.27244.ac\",\"volume\":\"116\",\"year\":\"2004\",\"bdsk-url-1\":\"http://dx.doi.org/10.1023/B:JOSS.0000041741.27244.ac\",\"bibtex\":\"@article{MR2096037,\\n\\tabstract = {We investigate the electrostatic equilibria of N discrete charges of size 1/N on a two dimensional conductor (domain). We study the distribution of the charges on symmetric domains including the ellipse, the hypotrochoid and various regular polygons, with an emphasis on understanding the distributions of the charges, as the shape of the underlying conductor becomes singular. We find that there are two regimes of behavior, a symmetric regime for smooth conductors, and a symmetry broken regime for ``singular'' domains. For smooth conductors, the locations of the charges can be determined, to within O(logN/N2{\\\\^a}€¾{\\\\^a}€¾{\\\\^a}€¾{\\\\^a}€¾{\\\\^a}€¾{\\\\^a}€¾{\\\\^a}€¾{\\\\^a}€¾{\\\\^a}€¾{\\\\^a}ˆ{\\\\v s}) by an integral equation due to Pommerenke [ Math. Ann., 179: 212--218, (1969)]. We present a derivation of a related (but different) integral equation, which has the same solutions. We also solve the equation to obtain (asymptotic) solutions which show universal behavior in the distribution of the charges in conductors with somewhat smooth cusps. Conductors with sharp cusps and singularities show qualitatively different behavior, where the symmetry of the problem is broken, and the distribution of the discrete charges does not respect the symmetry of the underlying domain. We investigate the symmetry breaking both theoretically, and numerically, and find good agreement between our theory and the numerics. We also find that the universality in the distribution of the charges near the cusps persists in the symmetry broken regime, although this distribution is very different from the one given by the integral equation.},\\n\\tauthor = {Berkenbusch, Marko K. and Claus, Isabelle and Dunn, Catherine and Kadanoff, Leo P. and Nicewicz, Maciej and Venkataramani, Shankar C.},\\n\\tcoden = {JSTPSB},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.1023/B:JOSS.0000041741.27244.ac},\\n\\tfjournal = {Journal of Statistical Physics},\\n\\tissn = {0022-4715},\\n\\tjournal = {J. Statist. Phys.},\\n\\tkeywords = {pubs},\\n\\tmrclass = {78A30 (37J40 37N20 78A35)},\\n\\tmrnumber = {2096037 (2006d:78009)},\\n\\tmrreviewer = {T. Erber},\\n\\tnumber = {5-6},\\n\\tpages = {1301--1358},\\n\\ttitle = {Discrete charges on a two dimensional conductor},\\n\\turl_arxiv = {http://arxiv.org/abs/cond-mat/0310257},\\n\\turl_journal = {http://dx.doi.org/10.1023/B:JOSS.0000041741.27244.ac},\\n\\tvolume = {116},\\n\\tyear = {2004},\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.1023/B:JOSS.0000041741.27244.ac}}\\n\\n\",\"author_short\":[\"Berkenbusch, M. K.\",\"Claus, I.\",\"Dunn, C.\",\"Kadanoff, L. P.\",\"Nicewicz, M.\",\"Venkataramani, S. C.\"],\"key\":\"MR2096037\",\"id\":\"MR2096037\",\"bibbaseid\":\"berkenbusch-claus-dunn-kadanoff-nicewicz-venkataramani-discretechargesonatwodimensionalconductor-2004\",\"role\":\"author\",\"urls\":{\" arxiv\":\"http://arxiv.org/abs/cond-mat/0310257\",\" journal\":\"http://dx.doi.org/10.1023/B:JOSS.0000041741.27244.ac\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"We study the linearized Föppl–von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle 2 Î$±$. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness, σ, and the bending angle. We show that the minimum energy scales as σ5/3 Î$±$7/3. This scaling is in sharp contrast with previously obtained results for the linearized theory of thin sheets with isotropic compression boundary conditions, where the energy scales as σ.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]}],\"coden\":\"NONLE5\",\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.1088/0951-7715/17/1/017\",\"fjournal\":\"Nonlinearity\",\"issn\":\"0951-7715\",\"journal\":\"Nonlinearity\",\"keywords\":\"pubs\",\"mrclass\":\"74K15 (46N10 47J20 49J40 74G65)\",\"mrnumber\":\"2023444 (2005b:74077)\",\"mrreviewer\":\"Yi-Chung Shu\",\"number\":\"1\",\"pages\":\"301–312\",\"title\":\"Lower bounds for the energy in a crumpled elastic sheet—a minimal ridge\",\"url_arxiv\":\"http://arxiv.org/abs/math/0210012\",\"url_journal\":\"http://dx.doi.org/10.1088/0951-7715/17/1/017\",\"volume\":\"17\",\"year\":\"2004\",\"bdsk-url-1\":\"http://dx.doi.org/10.1088/0951-7715/17/1/017\",\"bibtex\":\"@article{MR2023444,\\n\\tabstract = {We study the linearized F{\\\\\\\"o}ppl--von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle 2 {\\\\^I}$\\\\pm$. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness, {\\\\\\\"I}ƒ, and the bending angle. We show that the minimum energy scales as {\\\\\\\"I}ƒ5/3 {\\\\^I}$\\\\pm$7/3. This scaling is in sharp contrast with previously obtained results for the linearized theory of thin sheets with isotropic compression boundary conditions, where the energy scales as {\\\\\\\"I}ƒ.},\\n\\tauthor = {Venkataramani, Shankar C.},\\n\\tcoden = {NONLE5},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.1088/0951-7715/17/1/017},\\n\\tfjournal = {Nonlinearity},\\n\\tissn = {0951-7715},\\n\\tjournal = {Nonlinearity},\\n\\tkeywords = {pubs},\\n\\tmrclass = {74K15 (46N10 47J20 49J40 74G65)},\\n\\tmrnumber = {2023444 (2005b:74077)},\\n\\tmrreviewer = {Yi-Chung Shu},\\n\\tnumber = {1},\\n\\tpages = {301--312},\\n\\ttitle = {Lower bounds for the energy in a crumpled elastic sheet---a minimal ridge},\\n\\turl_arxiv = {http://arxiv.org/abs/math/0210012},\\n\\turl_journal = {http://dx.doi.org/10.1088/0951-7715/17/1/017},\\n\\tvolume = {17},\\n\\tyear = {2004},\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.1088/0951-7715/17/1/017}}\\n\\n\",\"author_short\":[\"Venkataramani, S. C.\"],\"key\":\"MR2023444\",\"id\":\"MR2023444\",\"bibbaseid\":\"venkataramani-lowerboundsfortheenergyinacrumpledelasticsheetaminimalridge-2004\",\"role\":\"author\",\"urls\":{\" arxiv\":\"http://arxiv.org/abs/math/0210012\",\" journal\":\"http://dx.doi.org/10.1088/0951-7715/17/1/017\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"S.\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Witten\"],\"firstnames\":[\"T.\",\"A.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Kramer\"],\"firstnames\":[\"E.\",\"M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Geroch\"],\"firstnames\":[\"R.\",\"P.\"],\"suffixes\":[]}],\"coden\":\"JMAPAQ\",\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.1063/1.533394\",\"fjournal\":\"Journal of Mathematical Physics\",\"issn\":\"0022-2488\",\"journal\":\"J. Math. Phys.\",\"keywords\":\"pubs\",\"mrclass\":\"53A07 (53C42)\",\"mrnumber\":\"1765831 (2001j:53008)\",\"mrreviewer\":\"Anders Linnér\",\"number\":\"7\",\"pages\":\"5107–5128\",\"title\":\"Limitations on the smooth confinement of an unstretchable manifold\",\"url_journal\":\"http://dx.doi.org/10.1063/1.533394\",\"volume\":\"41\",\"year\":\"2000\",\"bdsk-url-1\":\"http://dx.doi.org/10.1063/1.533394\",\"bibtex\":\"@article{MR1765831,\\n\\tauthor = {Venkataramani, S. C. and Witten, T. A. and Kramer, E. M. and Geroch, R. P.},\\n\\tcoden = {JMAPAQ},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.1063/1.533394},\\n\\tfjournal = {Journal of Mathematical Physics},\\n\\tissn = {0022-2488},\\n\\tjournal = {J. Math. Phys.},\\n\\tkeywords = {pubs},\\n\\tmrclass = {53A07 (53C42)},\\n\\tmrnumber = {1765831 (2001j:53008)},\\n\\tmrreviewer = {Anders Linn{\\\\'e}r},\\n\\tnumber = {7},\\n\\tpages = {5107--5128},\\n\\ttitle = {Limitations on the smooth confinement of an unstretchable manifold},\\n\\turl_journal = {http://dx.doi.org/10.1063/1.533394},\\n\\tvolume = {41},\\n\\tyear = {2000},\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.1063/1.533394}}\\n\\n\",\"author_short\":[\"Venkataramani, S. C.\",\"Witten, T. A.\",\"Kramer, E. M.\",\"Geroch, R. P.\"],\"key\":\"MR1765831\",\"id\":\"MR1765831\",\"bibbaseid\":\"venkataramani-witten-kramer-geroch-limitationsonthesmoothconfinementofanunstretchablemanifold-2000\",\"role\":\"author\",\"urls\":{\" journal\":\"http://dx.doi.org/10.1063/1.533394\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Brenner\"],\"firstnames\":[\"Michael\",\"P.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Constantin\"],\"firstnames\":[\"Peter\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Kadanoff\"],\"firstnames\":[\"Leo\",\"P.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Schenkel\"],\"firstnames\":[\"Alain\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\",\"C.\"],\"suffixes\":[]}],\"coden\":\"NONLE5\",\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"doi\":\"10.1088/0951-7715/12/4/320\",\"fjournal\":\"Nonlinearity\",\"issn\":\"0951-7715\",\"journal\":\"Nonlinearity\",\"keywords\":\"pubs\",\"mrclass\":\"76N99 (35K55 92C17)\",\"mrnumber\":\"1709861 (2001d:76107)\",\"number\":\"4\",\"pages\":\"1071–1098\",\"title\":\"Diffusion, attraction and collapse\",\"url_journal\":\"http://dx.doi.org/10.1088/0951-7715/12/4/320\",\"volume\":\"12\",\"year\":\"1999\",\"bdsk-url-1\":\"http://dx.doi.org/10.1088/0951-7715/12/4/320\",\"bibtex\":\"@article{MR1709861,\\n\\tauthor = {Brenner, Michael P. and Constantin, Peter and Kadanoff, Leo P. and Schenkel, Alain and Venkataramani, Shankar C.},\\n\\tcoden = {NONLE5},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tdoi = {10.1088/0951-7715/12/4/320},\\n\\tfjournal = {Nonlinearity},\\n\\tissn = {0951-7715},\\n\\tjournal = {Nonlinearity},\\n\\tkeywords = {pubs},\\n\\tmrclass = {76N99 (35K55 92C17)},\\n\\tmrnumber = {1709861 (2001d:76107)},\\n\\tnumber = {4},\\n\\tpages = {1071--1098},\\n\\ttitle = {Diffusion, attraction and collapse},\\n\\turl_journal = {http://dx.doi.org/10.1088/0951-7715/12/4/320},\\n\\tvolume = {12},\\n\\tyear = {1999},\\n\\tBdsk-Url-1 = {http://dx.doi.org/10.1088/0951-7715/12/4/320}}\\n\\n\",\"author_short\":[\"Brenner, M. P.\",\"Constantin, P.\",\"Kadanoff, L. P.\",\"Schenkel, A.\",\"Venkataramani, S. C.\"],\"key\":\"MR1709861\",\"id\":\"MR1709861\",\"bibbaseid\":\"brenner-constantin-kadanoff-schenkel-venkataramani-diffusionattractionandcollapse-1999\",\"role\":\"author\",\"urls\":{\" journal\":\"http://dx.doi.org/10.1088/0951-7715/12/4/320\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Jacobson\"],\"firstnames\":[\"Ted\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Venkataramani\"],\"firstnames\":[\"Shankar\"],\"suffixes\":[]}],\"coden\":\"CQGRDG\",\"date-added\":\"2017-01-29 16:04:45 +0000\",\"date-modified\":\"2017-01-29 20:11:00 +0000\",\"fjournal\":\"Classical and Quantum Gravity\",\"issn\":\"0264-9381\",\"journal\":\"Classical Quantum Gravity\",\"keywords\":\"pubs\",\"mrclass\":\"83C75 (57N10)\",\"mrnumber\":\"1330301 (96e:83055)\",\"mrreviewer\":\"Robert J. Low\",\"number\":\"4\",\"pages\":\"1055–1061\",\"title\":\"Topology of event horizons and topological censorship\",\"url_journal\":\"http://stacks.iop.org/0264-9381/12/1055\",\"volume\":\"12\",\"year\":\"1995\",\"bdsk-url-1\":\"http://stacks.iop.org/0264-9381/12/1055\",\"bibtex\":\"@article{MR1330301,\\n\\tauthor = {Jacobson, Ted and Venkataramani, Shankar},\\n\\tcoden = {CQGRDG},\\n\\tdate-added = {2017-01-29 16:04:45 +0000},\\n\\tdate-modified = {2017-01-29 20:11:00 +0000},\\n\\tfjournal = {Classical and Quantum Gravity},\\n\\tissn = {0264-9381},\\n\\tjournal = {Classical Quantum Gravity},\\n\\tkeywords = {pubs},\\n\\tmrclass = {83C75 (57N10)},\\n\\tmrnumber = {1330301 (96e:83055)},\\n\\tmrreviewer = {Robert J. Low},\\n\\tnumber = {4},\\n\\tpages = {1055--1061},\\n\\ttitle = {Topology of event horizons and topological censorship},\\n\\turl_journal = {http://stacks.iop.org/0264-9381/12/1055},\\n\\tvolume = {12},\\n\\tyear = {1995},\\n\\tBdsk-Url-1 = {http://stacks.iop.org/0264-9381/12/1055}}\\n\",\"author_short\":[\"Jacobson, T.\",\"Venkataramani, S.\"],\"key\":\"MR1330301\",\"id\":\"MR1330301\",\"bibbaseid\":\"jacobson-venkataramani-topologyofeventhorizonsandtopologicalcensorship-1995\",\"role\":\"author\",\"urls\":{\" journal\":\"http://stacks.iop.org/0264-9381/12/1055\"},\"keyword\":[\"pubs\"],\"metadata\":{\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\"html\":\"\"}],\n      metadata: {\"owner\":\"venkataramani, s\",\"authorlinks\":{\"venkataramani, s\":\"https://www.math.arizona.edu/~shankar/pub/pub.html\"}},\n      ownerID: \"74pLu7kQM3n6W6AqZ\"\n    };\n  </script>\n\n  <script type=\"text/javascript\">\n  var site$;\n  if (typeof $ != 'undefined') {\n    console.log('existing jquery: storing and then restoring');\n    site$ = $;\n    $ = null;\n  }\n  </script>\n\n  <script src=\"https://ajax.googleapis.com/ajax/libs/jquery/2.2.4/jquery.min.js\">\n  </script>\n  <script type=\"text/javascript\">\n  if (site$) {\n    console.log('existing jquery: avoiding conflict and restoring');\n    bb$ = $.noConflict(true);\n    $ = site$;\n  } else {\n    bb$ = $;\n  }\n  </script>\n\n  <script src=\"//bibbase.org/js/bibbase.min.js\"\n          type=\"text/javascript\">\n  </script>\n\n  <script type=\"text/javascript\"\n          src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML\">\n  </script>\n  <script type=\"text/x-mathjax-config\">\n    MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\\\(','\\\\)']]},\n                        skipTags: [\"body\"],\n                        processClass: \"bibbase_paper\"});\n  </script>\n\n  <style>\n  @media print {\n    .dontprint {\n        display: none !important;\n    }\n\n  .bibbase_group {\n    background-color: #E0E0E0;\n    font-style: italic;\n    font-size: larger;\n    text-shadow: 0px 0px 3px #FFFFFF;\n    border-radius: 4px 4px 4px 4px;\n    -moz-border-radius: 4px 4px 4px 4px;\n    -webkit-border-radius: 4px;\n    padding: 5px 40px 5px;\n    margin-top: 10px;\n    margin-bottom: 5px;\n    cursor: pointer;\n  }\n\n  .bibbase_paper {\n    margin-bottom: 5px;\n  }\n\n  }\n  </style>\n\n  \n  <div style=\"float: right; margin-right: 10px; margin-top: 10px; text-align: right; font-size: 12px\">\n    generated by\n    <a href=\"//bibbase.org\"\n       onclick=\"trackOutboundLink('bibbase', 'logo clicked', window.location.href, '//bibbase.org'); return false;\">\n      <img src=\"//bibbase.org/img/logo.svg\"\n           style=\"vertical-align: middle; margin-left: 3px; height: 16px;\"/\n           alt=\"bibbase.org\"\n           title=\"BibBase – The easiest way to maintain your publications page.\"\n        ></a>\n    \n  </div>\n  \n\n  <div id=\"bibbase_header\" class=\"dontprint\" style=\"\">\n\n    <ul class=\"nav nav-pills\" style=\"margin: 0px;\">\n\n      <li class=\"dropdown\" id=\"groupby_dropdown\">\n      <a class=\"dropdown-toggle\"\n         data-toggle=\"dropdown\"\n         href=\"#\">\n          Group by\n          <b class=\"caret\"></b>\n      </a>\n      <ul class=\"dropdown-menu\">\n        <li class=\"groupby year\"><a onclick=\"groupby('year')\">\n            Year</a>\n        </li>\n        <li class=\"groupby author\"><a onclick=\"groupby('author_short')\">\n            Author</a>\n        </li>\n        <li class=\"groupby type\"><a onclick=\"groupby('type')\">\n            Type</a>\n        </li>\n        <li class=\"groupby keyword\"><a onclick=\"groupby('keyword')\">\n            Keyword</a>\n        </li>\n        <li class=\"groupby downloads\"><a onclick=\"groupby('downloads')\">\n            Downloads</a>\n        </li>\n      </ul>\n      </li>\n\n\n      <li class=\"dropdown\" id=\"menu_dropdown\">\n      <a class=\"dropdown-toggle\"\n         data-toggle=\"dropdown\"\n         href=\"#\" alt=\"controls\">\n          <i class=\"fa fa-reorder\" alt=\"controls\"></i>\n          <b class=\"caret\"></b>\n      </a>\n      <ul class=\"dropdown-menu\">\n        <li>\n          <a onclick=\"toggleAll()\">\n            <i class=\"fa fa-chevron-down fa-fw\"></i> Expand/Collapse All\n          </a>\n        </li>\n        <li>\n          <a download=\"pub_list.bib\" href=\"data:text/bibtex;base64,@article{Yamamoto:2021wk,
	abstract = {A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This is seen in leaves, flowers, fungi, corals, and marine invertebrates. We investigate this morphology from the perspective of non-Euclidean plate theory. We identify a novel type of defect, a branch-point of the normal map, that allows for the generation of such complex wrinkling patterns in thin elastic hyperbolic surfaces, even in the absence of stretching. We argue that branch points are the natural defects in hyperbolic sheets, they carry a topological charge which gives them a degree of robustness, and they can influence the overall morphology of a hyperbolic surface without concentrating elastic energy. We develop a theory for branch points and investigate their role in determining the mechanical response of hyperbolic sheets to weak external forces.},
	author = {Yamamoto, Kenneth K. and Shearman, Toby L. and Struckmeyer, Erik J. and Gemmer, John A. and Venkataramani, Shankar C.},
	da = {2021/07/13},
	date-added = {2021-07-18 21:03:52 -0700},
	date-modified = {2021-07-18 21:04:38 -0700},
	doi = {10.1140/epje/s10189-021-00099-6},
	id = {Yamamoto2021},
	isbn = {1292-895X},
	journal = {The European Physical Journal E},
	keywords = {pubs},
	number = {7},
	pages = {95},
	title = {Nature's forms are frilly, flexible, and functional},
	ty = {JOUR},
	url = {https://doi.org/10.1140/epje/s10189-021-00099-6},
	url_arxiv = {https://arxiv.org/abs/2103.10509},
	volume = {44},
	year = {2021},
	Bdsk-Url-1 = {https://doi.org/10.1140/epje/s10189-021-00099-6}}



@article{Venkataramani:2021tn,
	abstract = {We argue that a natural explanation for a variety of robust galaxy scaling relations comes from the perspective of pattern formation and self-organization as a result of symmetry breaking. We propose a simple Lagrangian model that combines a conventional model for normal matter in a galaxy with a conventional model for stripe pattern formation in systems that break continuous translation invariance. We show that the energy stored in the pattern field acts as an effective dark matter. Our theory reproduces the gross features of elliptic galaxies as well as disk galaxies (HSB and LSB) including their detailed rotation curves, the radial acceleration relation, and the Freeman law. We investigate the stability of disk galaxies in the context of our model and obtain scaling relations for the central dispersion for elliptical galaxies. A natural interpretation of our results is that (1) `dark matter'is potentially a collective, emergent phenomenon and not necessarily an as yet undiscovered particle, and (2) MOND is an effective theory for the description of a self-organized complex system rather than a fundamental description of nature that modifies Newton's second law.},
	author = {Venkataramani, Shankar C. and Newell, Alan C.},
	da = {2021/06/18},
	date-added = {2021-07-18 20:58:08 -0700},
	date-modified = {2021-07-18 20:59:43 -0700},
	doi = {10.1140/epjs/s11734-021-00196-9},
	id = {Venkataramani2021},
	isbn = {1951-6401},
	journal = {The European Physical Journal Special Topics},
	keywords = {pubs},
	title = {Pattern dark matter and galaxy scaling relations},
	ty = {JOUR},
	url = {https://doi.org/10.1140/epjs/s11734-021-00196-9},
	url_arxiv = {https://arxiv.org/abs/2101.08372},
	year = {2021},
	Bdsk-Url-1 = {https://doi.org/10.1140/epjs/s11734-021-00196-9}}



@article{Zhang20211Computing,
	abstract = {Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they appear as `unphysical' singularities, with non-integrable energy densities in coarse-grained macroscopic models. We develop a principled approach for enriching coarse-grained theories with enough of the `micro-physics' to obtain thermodynamically consistent, well-set models that allow for the investigations of dynamics and interactions of defects in extended systems. We also develop associated numerical methods that are applicable to computing energy driven behaviors of defects across the amorphous-soft-crystalline materials spectrum. Our methods can handle order parameters that have a head-tail symmetry, i.e. director fields, in systems with a continuous translation symmetry, as in nematic liquid crystals, and in systems where the translation symmetry is broken, as in smectics and convection patterns. We illustrate our methods with explicit computations.},
	author = {Chiqun Zhang and Amit Acharya and Alan C. Newell and Shankar C. Venkataramani},
	date-added = {2021-05-29 14:50:02 -0700},
	date-modified = {2021-05-29 14:50:42 -0700},
	doi = {https://doi.org/10.1016/j.physd.2020.132828},
	issn = {0167-2789},
	journal = {Physica D: Nonlinear Phenomena},
	keywords = {pubs,Defects in materials, Non-orientability, Effective theories, Liquid crystals, Pattern formation, Computation of defects},
	pages = {132828},
	title = {Computing with non-orientable defects: Nematics, smectics and natural patterns},
	url = {https://www.sciencedirect.com/science/article/pii/S0167278920308290},
	volume = {417},
	year = {2021},
	Bdsk-Url-1 = {https://www.sciencedirect.com/science/article/pii/S0167278920308290},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.physd.2020.132828}}



@article{jaramillo2019microstructure,
	author = {Jaramillo, Gabriela and Venkataramani, Shankar C.},
	date-added = {2021-05-29 14:38:32 -0700},
	date-modified = {2021-05-29 14:39:29 -0700},
	doi = {10.1137/19M1306907},
	eprint = {https://doi.org/10.1137/19M1306907},
	journal = {Multiscale Modeling \& Simulation},
	keywords = {pubs},
	number = {2},
	pages = {886-920},
	title = {A Modified Split Bregman Algorithm for Computing Microstructures Through Young Measures},
	url = {https://doi.org/10.1137/19M1306907},
	url_arxiv = {https://arxiv.org/abs/1912.03360},
	volume = {19},
	year = {2021},
	Bdsk-Url-1 = {https://doi.org/10.1137/19M1306907}}



@article{shearman2021distributed,
	author = {Shearman, Toby L and Venkataramani, Shankar C},
	date-added = {2021-05-23 19:13:38 -0700},
	date-modified = {2021-05-23 19:14:52 -0700},
	journal = {Journal of Nonlinear Science},
	keywords = {pubs},
	number = {1},
	pages = {1--60},
	publisher = {Springer},
	title = {Distributed Branch Points and the Shape of Elastic Surfaces with Constant Negative Curvature},
	url_arxiv = {https://arxiv.org/abs/2006.14461},
	volume = {31},
	year = {2021}}



@article{PatternDM,
	abstract = {Galaxies are built by complex physical processes with significant inherent stochasticity. It is therefore surprising that the inferred dark matter distributions in galaxies are correlated with the observed baryon distributions leading to various `Baryon-Halo conspiracies'. The fact that no dark matter candidate has been definitively identified invites a search for alternative explanations for such correlations and we present an approach motivated by the behaviors of self organized patterns. We propose a nonlocal relativistic Lagrangian theory for a `pattern field' which acts as an `effective dark matter', built on the idea that defects in this pattern field couple to the baryonic matter distribution. The model applies to rotation supported systems and, for them, we compute galactic rotation curves, obtain a radial acceleration relation with two branches, and deduce the Freeman limit for central surface brightness.},
	author = {Shankar C. Venkataramani and Alan C. Newell},
	date-added = {2021-05-23 19:11:31 -0700},
	date-modified = {2021-05-23 19:17:57 -0700},
	doi = {https://doi.org/10.1016/j.physletb.2020.136060},
	issn = {0370-2693},
	journal = {Physics Letters B},
	keywords = {pubs,Self-organized patterns, Symmetry breaking, Defects, Dark matter, Galaxy scaling relations},
	pages = {136060},
	title = {Disk galaxies and their dark halos as self-organized patterns},
	url = {https://www.sciencedirect.com/science/article/pii/S0370269320308637},
	url_arxiv = {https://arxiv.org/abs/1910.14649},
	volume = {813},
	year = {2021},
	Bdsk-Url-1 = {https://www.sciencedirect.com/science/article/pii/S0370269320308637},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.physletb.2020.136060}}



@article{Acharya2020mechanics,
	abstract = {Growth and other dynamical processes in soft materials can create novel types of mesoscopic defects including discontinuities for the second and higher derivatives of the deformation, and terminating defects for these discontinuities. These higher-order defects move ``easily", and can thus confer a great degree of flexibility to the material. We develop a general continuum mechanical framework from which we can derive the dynamics of higher order defects in a thermodynamically consistent manner. We illustrate our framework by obtaining the explicit dynamical equations for the next higher order defects in an elastic body beyond dislocations, phase boundaries, and disclinations, namely, surfaces of inflection and branch lines.},
	author = {Acharya, Amit and Venkataramani, Shankar C.},
	da = {2020/04/16},
	date-added = {2020-05-25 22:56:27 -0700},
	date-modified = {2020-05-25 23:08:19 -0700},
	doi = {10.1186/s41313-020-00018-w},
	id = {Acharya2020},
	isbn = {2509-8012},
	journal = {Materials Theory},
	keywords = {pubs},
	number = {1},
	pages = {2},
	title = {Mechanics of moving defects in growing sheets: 3-d, small deformation theory},
	ty = {JOUR},
	url = {https://doi.org/10.1186/s41313-020-00018-w},
	url_arxiv = {https://arxiv.org/abs/1906.08122},
	volume = {4},
	year = {2020},
	Bdsk-Url-1 = {https://doi.org/10.1186/s41313-020-00018-w}}



@inproceedings{Sethuraman2019growth,
	abstract = {We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known that the graph evolution condenses, that is a.s. in the limit graph there will be a single random node with infinite degree, while all others have finite degree. In this note, we establish a.s. law of large numbers type limits and fluctuation results, as {\$}{\$}n{$\backslash$}uparrow {$\backslash$}infty {\$}{\$}, for the counts of the number of nodes with degree {\$}{\$}k{$\backslash$}ge 1{\$}{\$}at time {\$}{\$}n{$\backslash$}ge 1{\$}{\$}. These limits rigorously verify and extend a physical picture of Krapivisky et al. (Phys Rev Lett 85:4629--4632, 2000 {$[$}16{$]$}) on how the condensation arises with respect to the degree distribution.},
	address = {Cham},
	author = {Sethuraman, Sunder and Venkataramani, Shankar C.},
	booktitle = {Probability and Analysis in Interacting Physical Systems},
	da = {2019//},
	date-added = {2019-11-04 23:11:43 -0700},
	date-modified = {2019-11-04 23:14:02 -0700},
	editor = {Friz, Peter and K{\"o}nig, Wolfgang and Mukherjee, Chiranjib and Olla, Stefano},
	id = {10.1007/978-3-030-15338-0{\_}9},
	isbn = {978-3-030-15338-0},
	keywords = {pubs},
	pages = {243--265},
	publisher = {Springer International Publishing},
	title = {On the Growth of a Superlinear Preferential Attachment Scheme},
	ty = {CONF},
	url = {https://link.springer.com/chapter/10.1007/978-3-030-15338-0_9},
	url_arxiv = {https://arxiv.org/abs/1704.05568},
	year = {2019},
	Bdsk-Url-1 = {https://link.springer.com/chapter/10.1007/978-3-030-15338-0_9}}



@article{NV19,
	abstract = {In this essay we explore analogies between macroscopic patterns, which result from a sequence of phase transitions/instabilities starting from a homogeneous state, and similar phenomena in cosmology, where a sequence of phase transitions in the early universe is believed to have separated the fundamental forces from each other, and also shaped the structure and distribution of matter in the universe. We discuss three distinct aspects of this analogy: (i) Defects and topological charges in macroscopic patterns are analogous to spins and charges of quarks and leptons; (ii) Defects in generic 3+1 stripe patterns carry an energy density that accounts for phenomena that are currently attributed to dark matter; (iii) Space-time patterns of interacting nonlinear waves display behaviors reminiscent of quantum phenomena including inflation, entanglement and dark energy.
R{\'e}sum{\'e}
Dans cet article, nous explorons plusieurs analogies entre la formation de structures p{\'e}riodiques macroscopiques, qui r{\'e}sultent de la succession de transitions de phase ou d'instabilit{\'e}s, et certains ph{\'e}nom{\`e}nes similaires en cosmologie, o{\`u} une suite de transitions de phase dans l'univers primordial aurait donn{\'e} lieu {\`a} la s{\'e}paration des forces fondamentales et {\`a} la formation des structures. Nous consid{\'e}rons trois analogies diff{\'e}rentes : (i) les d{\'e}fauts et charges topologiques dans les structures macroscopiques sont analogues aux spins et charges des quarks et des leptons ; (ii) les d{\'e}fauts dans les structures p{\'e}riodiques g{\'e}n{\'e}riques (en dimensions 3+1) ont une densit{\'e} d'{\'e}nergie qui donne lieu {\`a} certains ph{\'e}nom{\`e}nes attribu{\'e}s {\`a} la pr{\'e}sence de mati{\`e}re noire ; (iii) les structures spatio-temporelles r{\'e}sultant de l'interaction d'ondes non lin{\'e}aires ont des comportements qui rappellent certains ph{\'e}nom{\`e}nes quantiques, tels que l'inflation cosmique, l'enchev{\^e}trement quantique et l'{\'e}nergie noire.},
	author = {Alan C. Newell and Shankar C. Venkataramani},
	date-added = {2019-11-04 23:01:37 -0700},
	date-modified = {2019-11-04 23:03:49 -0700},
	doi = {https://doi.org/10.1016/j.crme.2019.03.004},
	issn = {1631-0721},
	journal = {Comptes Rendus M{\'e}canique},
	keywords = {pubs,Pattern formation, Cosmology, Phase transitions, Formation de motifs, Cosmologie, Transition de phase},
	note = {Patterns and dynamics: homage to Pierre Coullet / Formes et dynamique: hommage {\`a} Pierre Coullet},
	number = {4},
	pages = {318 - 331},
	title = {Pattern universes},
	url_arxiv = {https://arxiv.org/abs/1811.10546},
	url_journal = {http://www.sciencedirect.com/science/article/pii/S1631072119300464},
	volume = {347},
	year = {2019},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S1631072119300464},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.crme.2019.03.004}}



@article{2018b,
	abstract = {We propose a time dependent Eulerian model for sea surface entrainment, buoyancy transport and droplet dynamics of ocean oil. The model captures the microscale vertical oil mass exchanges in the neighborhood of the sea surface. This model is in turn part of an oil fate model designed to capture oil dynamics at large spatio-temporal scales typical of environmental studies. The adiabatic dynamics of the droplets are upscaled by a combination of filtering and stochastic parametrization. The upscaling addresses the computational burden of resolving the microscale. The upscaled droplet dynamics are tested against data and the mass exchange mechanism is incorporated into a nearshore oil transport model in order to highlight the importance of incorporating vertical mass exchanges and droplet distribution dynamics in predicting the distributing of shoaling oil.},
	author = {Jorge Ram\'{i}rez and Saeed Moghimi and Juan M. Restrepo and Shankar Venkataramani},
	date-added = {2019-03-20 20:59:16 -0700},
	date-modified = {2019-03-20 21:42:06 -0700},
	doi = {https://doi.org/10.1016/j.ocemod.2018.06.004},
	issn = {1463-5003},
	journal = {Ocean Modelling},
	keywords = {Oil spill; Oil fate model; Oil entrainment; Ocean oil transport; Ocean pollution; pubs},
	month = {September},
	pages = {1 - 12},
	title = {Modelling the mass exchange dynamics of oceanic surface and subsurface oil},
	url = {http://www.sciencedirect.com/science/article/pii/S1463500318302087},
	url_arxiv = {https://arxiv.org/abs/1703.05361},
	volume = {129},
	year = {2018},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S1463500318302087},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.ocemod.2018.06.004}}



@article{2019a,
	author = {Venkataramani, Shankar C.},
	date-added = {2019-03-20 20:33:42 -0700},
	date-modified = {2019-03-20 20:35:03 -0700},
	doi = {10.1073/pnas.1820937116},
	eprint = {https://www.pnas.org/content/116/5/1477.full.pdf},
	issn = {0027-8424},
	journal = {Proceedings of the National Academy of Sciences},
	keywords = {pubs},
	month = {January},
	number = {5},
	pages = {1477--1479},
	publisher = {National Academy of Sciences},
	title = {Buckling sheets open a door to understanding self-organization in soft matter},
	url = {https://www.pnas.org/content/116/5/1477},
	url_arxiv = {https://arxiv.org/abs/1901.03032},
	volume = {116},
	year = {2019},
	Bdsk-Url-1 = {https://www.pnas.org/content/116/5/1477},
	Bdsk-Url-2 = {https://doi.org/10.1073/pnas.1820937116}}



@article{jaramillo2018target,
	abstract = {We analyze the effect of adding a weak, localized, inhomogeneity to a two dimensional array of oscillators with nonlocal coupling. We propose and also justify a model for the phase dynamics in this system. Our model is a generalization of a viscous eikonal equation that is known to describe the phase modulation of traveling waves in reaction--diffusion systems. We show the existence of a branch of target pattern solutions that bifurcates from the spatially homogeneous state when , the strength of the inhomogeneity, is nonzero and we also show that these target patterns have an asymptotic wavenumber that is small beyond all orders in . The strategy of our proof is to pose a good ansatz for an approximate form of the solution and use the implicit function theorem to prove the existence of a solution in its vicinity. The analysis presents two challenges. First, the linearization about the homogeneous state is a convolution operator of diffusive type and hence not invertible on the usual Sobolev spaces. Second, a regular perturbation expansion in  does not provide a good ansatz for applying the implicit function theorem since the nonlinearities play a major role in determining the relevant approximation, which also needs to be `correct' to all orders in . We overcome these two points by proving Fredholm properties for the linearization in appropriate Kondratiev spaces and using a refined ansatz for the approximate solution which was obtained using matched asymptotics.},
	author = {Jaramillo, Gabriela and Venkataramani, Shankar C},
	da = {2018/07/27},
	date-added = {2019-03-20 14:49:42 -0700},
	date-modified = {2019-03-20 15:07:42 -0700},
	doi = {10.1088/1361-6544/aac9a6},
	isbn = {0951-7715; 1361-6544},
	journal = {Nonlinearity},
	keywords = {pubs},
	number = {9},
	pages = {4162-4201},
	publisher = {IOP Publishing},
	title = {Target patterns in a 2D array of oscillators with nonlocal coupling},
	ty = {JOUR},
	url_arxiv = {https://arxiv.org/abs/1706.00524},
	url_journal = {https://iopscience.iop.org/article/10.1088/1361-6544/aac9a6/pdf},
	volume = {31},
	year = {2018},
	Bdsk-Url-1 = {http://dx.doi.org/10.1088/1361-6544/aac9a6}}



@article{pattern-universe,
	abstract = {We connect the theories of the deformation of elastic surfaces and phase surfaces arising in the description of almost periodic patterns. In particular, we show striking parallels between expansions for the energy of elastic surfaces in powers of the thickness h and the free energy averaged over a period of an almost periodic pattern expanded in powers of ϵ, the inverse aspect ratio of the pattern field. In both cases, the resulting energy can be expressed in terms of the first and second fundamental forms of the surfaces involved, the elastic surface in the former case and the phase surface in the latter. We discuss various results that are obtained by exploiting this analogy and also address some of the outstanding questions. One common result of particular interest concerns the condensation of the Gaussian curvature onto isolated point defects in two dimensions and onto loop filaments in three dimensions. 

We also lay out an ambitious and somewhat speculative program to build a multi-scale model of the universe inspired by patterns, in which the short (spatial and temporal) scale structure on the Planck scales is given by a nearly periodic microstructure, and macroscopic/slowly varying/averaged behaviors on scales much larger than the Planck scale leads to a hierarchy of structures and features including analogues of quarks, leptons, dark matter, dark energy and inflationary cosmology.
},
	author = {Alan C. Newell and Shankar C. Venkataramani},
	date-added = {2017-10-15 18:02:26 +0000},
	date-modified = {2017-10-15 18:15:10 +0000},
	doi = {http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full},
	journal = {Studies in Applied Mathematics},
	keywords = {pubs},
	number = {2},
	pages = {322--368},
	title = {Elastic sheets, phase surfaces and pattern universes},
	url_arxiv = {arxiv.org/abs/1612.01007},
	url_journal = {http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full},
	volume = {139},
	year = {2017},
	Bdsk-Url-1 = {http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full}}



@article{Venkataramani:2017aa,
	abstract = {We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal'model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.},
	author = {Venkataramani, Shankar C. and Venkataramani, Raman C. and Restrepo, Juan M.},
	da = {2017//},
	date-added = {2017-05-01 21:34:13 +0000},
	date-modified = {2017-05-02 18:16:58 +0000},
	doi = {10.1007/s10955-017-1761-7},
	id = {Venkataramani2017},
	isbn = {1572-9613},
	journal = {Journal of Statistical Physics},
	keywords = {pubs},
	number = {3},
	pages = {892--933},
	title = {Dimension Reduction for Systems with Slow Relaxation},
	ty = {JOUR},
	url_arxiv = {http://arxiv.org/abs/1609.09222},
	url_journal = {http://dx.doi.org/10.1007/s10955-017-1761-7},
	volume = {167},
	year = {2017},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10955-017-1761-7}}



@article{Rosenthal_Displacement_2017,
	abstract = {Abstract We show that modifying a Bayesian data assimilation scheme by incorporating kinematically-consistent displacement corrections produces a scheme that is demonstrably better at estimating partially observed state vectors in a setting where feature information is important. While the displacement transformation is generic, here we implement it within an ensemble Kalman Filter framework and demonstrate its effectiveness in tracking stochastically perturbed vortices. },
	author = {W. Steven Rosenthal and Shankar Venkataramani and Arthur J. Mariano and Juan M. Restrepo},
	date-added = {2017-01-29 16:07:29 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {http://dx.doi.org/10.1016/j.jcp.2016.10.025},
	issn = {0021-9991},
	journal = {Journal of Computational Physics},
	keywords = {Displacement assimilation; Data assimilation; Uncertainty quantification; Ensemble Kalman Filter; Vortex dynamics; pubs},
	pages = {594 - 614},
	title = {Displacement data assimilation},
	url_arxiv = {https://arxiv.org/abs/1602.02209},
	url_journal = {http://www.sciencedirect.com/science/article/pii/S002199911630523X},
	volume = {330},
	year = {2017},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.jcp.2016.10.025},
	Bdsk-Url-2 = {http://www.sciencedirect.com/science/article/pii/S002199911630523X}}



@incollection{OTT:2001aa,
	annote = {doi:10.1142/9789812811516{\_}0014},
	author = {Ott, Edward and Venkataramani, Shankar C.},
	booktitle = {Proceedings of the 5th Experimental Chaos Conference},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2021-05-23 18:55:49 -0700},
	doi = {doi:10.1142/9789812811516{\_}0014},
	isbn = {978-981-02-4561-0},
	keywords = {pubs},
	m1 = {0},
	m3 = {doi:10.1142/9789812811516{\_}0014},
	month = {2016/11/23},
	pages = {143-153},
	publisher = {World Scientific},
	title = {Continuum Coupled Maps: A model for patterns in vibrated sand},
	ty = {CHAP},
	url = {http://dx.doi.org/10.1142/9789812811516_0014},
	year = {2001},
	year1 = {2001/04/01},
	Bdsk-Url-1 = {http://dx.doi.org/10.1142/9789812811516_0014},
	Bdsk-Url-2 = {http://dx.doi.org/10.1142/9789812811516%7B%5C_%7D0014}}



@article{AdWR_2016,
	abstract = {Abstract We develop a stochastic parametrization, based on a `simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the ``missing physics'' to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation.  We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.},
	author = {Restrepo, Juan M. and Venkataramani, Shankar},
	date = {2016/12//},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {http://dx.doi.org/10.1016/j.advwatres.2016.11.002},
	isbn = {0309-1708},
	journal = {Advances in Water Resources},
	keywords = {Longshore currents; Stochastic parametrization; Parameter sensitivity; Consistently of model sensitivity; Data assimilation;; pubs},
	month = {12},
	pages = {186--197},
	title = {Stochastic longshore current dynamics},
	ty = {JOUR},
	url_arxiv = {https://arxiv.org/abs/1612.01046},
	url_journal = {http://www.sciencedirect.com/science/article/pii/S0309170816306157},
	volume = {98},
	year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0309170816306157},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.advwatres.2016.11.002}}



@article{GSSV2016,
	abstract = {The edges of torn plastic sheets and growing leaves often display hierarchical buckling
 patterns. We show that this complex morphology i) emerges even in zero strain configurations, and ii) is driven by a competition between the two principal curvatures, rather than between bending  and stretching.   We identify the key role of branch point (or ``monkey saddle'') singularities in generating complex wrinkling patterns in isometric immersions, and show how they arise naturally from minimizing the elastic energy.},
	author = {{Gemmer, John} and {Sharon, Eran} and {Shearman, Toby} and {Venkataramani, Shankar C.}},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1209/0295-5075/114/24003},
	journal = {Europhys. Lett.},
	keywords = {pubs},
	number = 2,
	pages = {24003},
	title = {Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets},
	url_arxiv = {https://arxiv.org/abs/1601.06863},
	url_journal = {http://dx.doi.org/10.1209/0295-5075/114/24003},
	volume = 114,
	year = 2016,
	Bdsk-Url-1 = {http://dx.doi.org/10.1209/0295-5075/114/24003}}



@article{jmse3041504,
	abstract = {We introduce a model for the dynamics of oil in suspension, appropriate for shallow waters, including the nearshore environment. This model is capable of oil mass conservation and does so by evolving the oil on the sea surface as well as the oil in the subsurface. The shallower portion of the continental shelf poses compounding unique modeling challenges. Many of these relate to the complex nature of advection and dispersion of oil in an environment in which wind, waves, as well as currents all play a role, as does the complex bathymetry and the nearshore geography. In this study we present an overview of the model as well as derive the most fundamental of processes, namely, the shallow water advectiion and dispersion processes. With regard to this basic transport, we superate several fundamental challenges associated with creating a transport model for oil and other buoyant pollutants, capable of capturing the dynamics at the large spatio-temporal scales demanded by environmental and hazard mitigation studies. Some of the strategies are related to dimension reduction and upscaling, and leave discussion of these to companion papers. Here we focus on wave-filtering, ensemble and depth-averaging. Integral to the model is the proposal of an ocean dynamics model that is consistent with the transport. This ocean dynamics model is detailed here. The ocean/oil transport model is applied to a couple of physically-inspired oil-spill problems in demonstrate its specialized capabilities.},
	author = {Restrepo, Juan M. and Ram\'{i}rez, Jorge M. and Venkataramani, Shankar},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.3390/jmse3041504},
	issn = {2077-1312},
	journal = {Journal of Marine Science and Engineering},
	keywords = {pubs},
	number = {4},
	pages = {1504},
	title = {An Oil Fate Model for Shallow-Waters},
	url_journal = {http://www.mdpi.com/2077-1312/3/4/1504},
	volume = {3},
	year = {2015},
	Bdsk-Url-1 = {http://www.mdpi.com/2077-1312/3/4/1504},
	Bdsk-Url-2 = {http://dx.doi.org/10.3390/jmse3041504}}



@article{pref-attach,
	abstract = {We consider a general class of preferential attachment schemes evolving by a reinforcement rule with respect to certain sublinear weights. In these schemes, which grow a random network, the sequence of degree distributions is an object of interest which sheds light on the evolving structures. In this article, we use a fluid limit approach to prove a functional law of large numbers for the degree structure in this class, starting from a variety of initial conditions. The method appears robust and applies in particular to `non-tree' evolutions where cycles may develop in the network. A main part of the argument is to analyze an infinite system of coupled ODEs, corresponding to a rate formulation of the law of large numbers limit, in terms of $C_0$-semigroup/dynamical systems methods. These results also resolve a question in Chung, Handjani and Jungreis (2003). },
	author = {Choi, Jihyeok and Sethuraman, Sunder and Venkataramani, Shankar C.},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1002/rsa.20615},
	issn = {1098-2418},
	journal = {Random Structures and Algorithms},
	keywords = {pubs},
	number = {4},
	pages = {703-731},
	title = {A scaling limit for the degree distribution in sublinear preferential attachment schemes},
	url_arxiv = {http://arxiv.org/abs/1402.4088},
	url_journal = {http://onlinelibrary.wiley.com/doi/10.1002/rsa.20615/full},
	volume = {48},
	year = {2016},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/rsa.20615}}



@article{Graf2012,
	abstract = {We investigate the linear propagation of Gaussian-apodized solutions to the paraxial wave equation in free-space and first-order optical systems. In particular, we present complex coordinate transformations that yield a very general and efficient method to apply a Gaussian apodization (possibly with initial phase curvature) to a solution of the paraxial wave equation. Moreover, we show how this method can be extended from free space to describe propagation behavior through nonimaging first-order optical systems by combining our coordinate transform approach with ray transfer matrix methods. Our framework includes several classes of interesting beams that are important in applications as special cases. Among these are, for example, the Bessel\&\#x2013;Gauss and the Airy\&\#x2013;Gauss beams, which are of strong interest to researchers and practitioners in various fields.},
	author = {T. Graf and D. N. Christodoulides and M. S. Mills and J. V. Moloney and S. C. Venkataramani and E. M. Wright},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1364/JOSAA.29.001860},
	journal = {J. Opt. Soc. Am. A},
	keywords = {Mathematical methods in physics; Matrix methods in paraxial optics; Lasers and laser optics; Diffraction theory; Dispersion; Nonimaging optical systems; pubs},
	month = {Sep},
	number = {9},
	pages = {1860--1869},
	publisher = {OSA},
	title = {Propagation of Gaussian-apodized paraxial beams through first-order optical systems via complex coordinate transforms and ray transfer matrices},
	url_journal = {http://josaa.osa.org/abstract.cfm?URI=josaa-29-9-1860},
	volume = {29},
	year = {2012},
	Bdsk-Url-1 = {http://josaa.osa.org/abstract.cfm?URI=josaa-29-9-1860},
	Bdsk-Url-2 = {http://dx.doi.org/10.1364/JOSAA.29.001860}}



@incollection{Shlesinger:1995gd,
	author = {Ott, Edward and Sommerer, John C. and Antonsen, Thomas M. and Venkataramani, Shankar},
	booktitle = {L{\'e}vy Flights and Related Topics in Physics},
	da = {1995/01/01},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2021-05-23 18:54:32 -0700},
	doi = {10.1007/3-540-59222-9{\_}34},
	editor = {Shlesinger, MichealF. and Zaslavsky, GeorgeM. and Frisch, Uriel},
	isbn = {978-3-540-59222-8},
	keywords = {pubs},
	la = {English},
	pages = {182-195},
	publisher = {Springer Berlin Heidelberg},
	se = {12},
	title = {Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states},
	title1 = {Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states},
	ty = {CHAP},
	url = {http://dx.doi.org/10.1007/3-540-59222-9_34},
	volume = {450},
	year = {1995},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/3-540-59222-9_34},
	Bdsk-Url-2 = {http://dx.doi.org/10.1007/3-540-59222-9%7B%5C_%7D34}}



@periodical{venkataramani1998cones,
	author = {Venkataramani, Shankar},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	journal = {Physics world},
	keywords = {pubs},
	number = {7},
	title = {Cones, creases and crumpled sheets},
	volume = {11},
	year = {1998}}



@article{PhysRevLett.77.55,
	author = {Lai, Ying-Cheng and Grebogi, Celso and Yorke, James A. and Venkataramani, S. C.},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1103/PhysRevLett.77.55},
	issue = {1},
	journal = {Phys. Rev. Lett.},
	keywords = {pubs},
	month = {Jul},
	numpages = {0},
	pages = {55--58},
	publisher = {American Physical Society},
	title = {Riddling Bifurcation in Chaotic Dynamical Systems},
	url = {http://link.aps.org/doi/10.1103/PhysRevLett.77.55},
	volume = {77},
	year = {1996},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.77.55},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.77.55}}



@article{PhysRevLett.78.3983,
	author = {Coppersmith, S. N. and Jones, T. C. and Kadanoff, L. P. and Levine, A. and McCarten, J. P. and Nagel, S. R. and Venkataramani, S. C. and Wu, Xinlei},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1103/PhysRevLett.78.3983},
	issue = {21},
	journal = {Phys. Rev. Lett.},
	keywords = {pubs},
	month = {May},
	numpages = {0},
	pages = {3983--3986},
	publisher = {American Physical Society},
	title = {Self-Organized Short-Term Memories},
	url = {http://link.aps.org/doi/10.1103/PhysRevLett.78.3983},
	volume = {78},
	year = {1997},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.78.3983},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.78.3983}}



@article{PhysRevE.59.4970,
	author = {Povinelli, M. L. and Coppersmith, S. N. and Kadanoff, L. P. and Nagel, S. R. and Venkataramani, S. C.},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1103/PhysRevE.59.4970},
	issue = {5},
	journal = {Phys. Rev. E},
	keywords = {pubs},
	month = {May},
	numpages = {0},
	pages = {4970--4982},
	publisher = {American Physical Society},
	title = {Noise stabilization of self-organized memories},
	url_journal = {http://link.aps.org/doi/10.1103/PhysRevE.59.4970},
	volume = {59},
	year = {1999},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.59.4970},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.59.4970}}



@article{PhysRevE.64.016215,
	author = {Kim, J. W. and Vaishnav, J. Y. and Ott, E. and Venkataramani, S. C. and Losert, W.},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1103/PhysRevE.64.016215},
	issue = {1},
	journal = {Phys. Rev. E},
	keywords = {pubs},
	month = {Jun},
	numpages = {5},
	pages = {016215},
	publisher = {American Physical Society},
	title = {Front propagation of spatiotemporal chaos},
	url_journal = {http://link.aps.org/doi/10.1103/PhysRevE.64.016215},
	volume = {64},
	year = {2001},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.64.016215},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.64.016215}}



@article{PhysRevE.65.016603,
	author = {DiDonna, B. A. and Witten, T. A. and Venkataramani, S. C. and Kramer, E. M.},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1103/PhysRevE.65.016603},
	issue = {1},
	journal = {Phys. Rev. E},
	keywords = {pubs},
	month = {Dec},
	numpages = {25},
	pages = {016603},
	publisher = {American Physical Society},
	title = {Singularities, structures, and scaling in deformed m-dimensional elastic manifolds},
	url_journal = {http://link.aps.org/doi/10.1103/PhysRevE.65.016603},
	volume = {65},
	year = {2001},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.65.016603},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.65.016603}}



@article{PhysRevE.65.036613,
	author = {Gopinathan, Ajay and Witten, T. A. and Venkataramani, S. C.},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1103/PhysRevE.65.036613},
	issue = {3},
	journal = {Phys. Rev. E},
	keywords = {pubs},
	month = {Feb},
	numpages = {11},
	pages = {036613},
	publisher = {American Physical Society},
	title = {Trapping of vibrational energy in crumpled sheets},
	url_journal = {http://link.aps.org/doi/10.1103/PhysRevE.65.036613},
	volume = {65},
	year = {2002},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.65.036613},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.65.036613}}



@article{PhysRevLett.77.5361,
	author = {Venkataramani, Shankar C. and Hunt, Brian R. and Ott, Edward and Gauthier, Daniel J. and Bienfang, Joshua C.},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1103/PhysRevLett.77.5361},
	issue = {27},
	journal = {Phys. Rev. Lett.},
	keywords = {pubs},
	month = {Dec},
	numpages = {0},
	pages = {5361--5364},
	publisher = {American Physical Society},
	title = {Transitions to Bubbling of Chaotic Systems},
	url_journal = {http://link.aps.org/doi/10.1103/PhysRevLett.77.5361},
	volume = {77},
	year = {1996},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.77.5361},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.77.5361}}



@article{PhysRevLett.78.3864,
	author = {Venkataramani, Shankar C. and Antonsen, Thomas M. and Ott, Edward},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1103/PhysRevLett.78.3864},
	issue = {20},
	journal = {Phys. Rev. Lett.},
	keywords = {pubs},
	month = {May},
	numpages = {0},
	pages = {3864--3867},
	publisher = {American Physical Society},
	title = {L\'evy Flights in Fluid Flows with no Kolmogorov-Arnold-Moser Surfaces},
	url_journal = {http://link.aps.org/doi/10.1103/PhysRevLett.78.3864},
	volume = {78},
	year = {1997},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.78.3864},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.78.3864}}



@article{PhysRevE.54.1346,
	author = {Venkataramani, Shankar C. and Hunt, Brian R. and Ott, Edward},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1103/PhysRevE.54.1346},
	issue = {2},
	journal = {Phys. Rev. E},
	keywords = {pubs},
	month = {Aug},
	numpages = {0},
	pages = {1346--1360},
	publisher = {American Physical Society},
	title = {Bubbling transition},
	url_journal = {http://link.aps.org/doi/10.1103/PhysRevE.54.1346},
	volume = {54},
	year = {1996},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.54.1346},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.54.1346}}



@article{PhysRevLett.80.3495,
	author = {Venkataramani, Shankar C. and Ott, Edward},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1103/PhysRevLett.80.3495},
	issue = {16},
	journal = {Phys. Rev. Lett.},
	keywords = {pubs},
	month = {Apr},
	numpages = {0},
	pages = {3495--3498},
	publisher = {American Physical Society},
	title = {Spatiotemporal Bifurcation Phenomena with Temporal Period Doubling: Patterns in Vibrated Sand},
	url_journal = {http://link.aps.org/doi/10.1103/PhysRevLett.80.3495},
	volume = {80},
	year = {1998},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.80.3495},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.80.3495}}



@article{PhysRevE.63.046202,
	author = {Venkataramani, Shankar C. and Ott, Edward},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1103/PhysRevE.63.046202},
	issue = {4},
	journal = {Phys. Rev. E},
	keywords = {pubs},
	month = {Mar},
	numpages = {27},
	pages = {046202},
	publisher = {American Physical Society},
	title = {Pattern selection in extended periodically forced systems: A continuum coupled map approach},
	url_journal = {http://link.aps.org/doi/10.1103/PhysRevE.63.046202},
	volume = {63},
	year = {2001},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.63.046202},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.63.046202}}



@article{KVS2011,
	abstract = {
We present the first quantitative measurements of shape and energy variation in non-Euclidean plates. Using environmentally responsive gel, we construct non-Euclidean disks of constant imposed Gaussian curvature, $K_{tar}$. We vary the disks' thickness $t_0$ and measure the dependence of configurations, surface curvature, and energy content on $t_0$. For $K_{tar} < 0$, configurations are of a single wavy mode and undergo a set of bifurcations that leads to their refinement with decreasing thickness. This leads to sharp increase in the amount of surface bending as $t_0 \to 0$, and to a slow decay of both bending and stretching energies. Both vary like $t_0^2$, compared with $t_0^3$ of the bending energy in disks with $K_{tar} > 0$.},
	author = {Klein, Yael and Venkataramani, Shankar and Sharon, Eran},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1103/PhysRevLett.106.118303},
	issue = {11},
	journal = {Phys. Rev. Lett.},
	keywords = {pubs},
	month = {Mar},
	numpages = {4},
	pages = {118303},
	publisher = {American Physical Society},
	title = {Experimental Study of Shape Transitions and Energy Scaling in Thin Non-Euclidean Plates},
	url_journal = {http://link.aps.org/doi/10.1103/PhysRevLett.106.118303},
	volume = {106},
	year = {2011},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.106.118303},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.106.118303}}



@article{GV2013,
	abstract = {A non-Euclidean plate is a thin elastic object whose intrinsic geometry is not flat and hence has residual stresses arising from being embedded in three dimensional space. Recently, there has been interest in using localized swelling to induce residual stresses that shape flat objects into desired three dimensional structures. A fundamental question is whether we can use the mathematical theory of non-Euclidean plates to deduce the three dimensional configuration of the swelling sheet given the exact knowledge of the imposed geometry. We present and summarize the results of recent mathematical studies on non-Euclidean plates with imposed constant negative Gaussian curvature in both annular and disc geometries. We show in the F{\"o}ppl--von K{\'a}rm{\'a}n approximation to the elastic energy there are only two types of global minimizers -- flat and saddle shaped deformations -- with localized regions of stretching near the boundary of the domain. We also show that there exist n-wave local minimizers that closely resemble experimental observations and have additional regions of stretching near lines of inflection. Furthermore, in the Kirchhoff approximation to the elastic energy, we show that there exists exact isometric immersions with periodic profiles. The number of waves in these configurations is set by the condition that the bending energy remains finite and grows approximately exponentially with the radius of the annulus. For large radii, these shape are energetically favorable over saddle shapes and could explain why wavy shapes are selected in crochet models of the hyperbolic plane. The predicted morphologies however differ from what is observed in experiments on hydrogel disks highlighting the need for further theoretical studies.},
	author = {Gemmer, John A. and Venkataramani, Shankar C.},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	journal = {Soft Matter},
	keywords = {pubs},
	number = {34},
	pages = {8151--8161},
	publisher = {Royal Society of Chemistry},
	title = {Shape transitions in hyperbolic non-Euclidean plates},
	url_arxiv = {http://arxiv.org/abs/1209.0031},
	url_journal = {http://pubs.rsc.org/en/Content/ArticleLanding/2013/SM/c3sm50479d#!divAbstract},
	volume = {9},
	year = {2013},
	Bdsk-Url-1 = {http://dx.doi.org/10.1039/C3SM50479D}}



@article{Venkataramani1998412,
	author = {Shankar C. Venkataramani and Thomas M. Antonsen and Edward Ott},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {http://dx.doi.org/10.1016/S0167-2789(97)00184-X},
	issn = {0167-2789},
	journal = {Physica D: Nonlinear Phenomena},
	keywords = {Hamiltonian systems; pubs},
	number = {3--4},
	pages = {412 - 440},
	title = {Anomalous diffusion in bounded temporally irregular flows},
	url_journal = {http://www.sciencedirect.com/science/article/pii/S016727899700184X},
	volume = {112},
	year = {1998},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S016727899700184X},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/S0167-2789(97)00184-X}}



@article{GMV2013,
	abstract = {In this paper we investigate the propagation of conical waves in nonlinear media. In particular, we are interested in the effects resulting from applying a Gaussian apodization to an ideal nondiffracting wave. First, we present a multiple scales approach to derive amplitude equations for weakly nonlinear conical waves from a governing equation of cubic nonlinear Schr{\"o}dinger type. From these equations we obtain asymptotic solutions for the linear and the weakly nonlinear problem for which we state several uniform estimates that describe the deviation from the ideal nondiffracting solution. Moreover, we show numerical simulations based on an implementation of our amplitude equations to support and illustrate our analytical results.},
	author = {Tobias Graf and Jerome Moloney and Shankar Venkataramani},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {http://dx.doi.org/10.1016/j.physd.2012.09.004},
	issn = {0167-2789},
	journal = {Physica D: Nonlinear Phenomena},
	keywords = {Uniform estimates; pubs},
	number = {1},
	pages = {32 - 44},
	title = {Asymptotic analysis of weakly nonlinear {Bessel}-{Gau}\ss { } beams},
	url_journal = {http://www.sciencedirect.com/science/article/pii/S0167278912002308},
	volume = {243},
	year = {2013},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0167278912002308},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.physd.2012.09.004}}



@article{on-off1995,
	author = {Shankar C. Venkataramani and Thomas M. Antonsen and Edward Ott and John C Sommerer},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {http://dx.doi.org/10.1016/0375-9601(95)00710-K},
	issn = {0375-9601},
	journal = {Physics Letters A},
	keywords = {Invariant manifold; pubs},
	number = {3--4},
	pages = {173 - 179},
	title = {Characterization of on-off intermittent time series},
	url_journal = {http://www.sciencedirect.com/science/article/pii/037596019500710K},
	volume = {207},
	year = {1995},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/037596019500710K},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/0375-9601(95)00710-K}}



@article{sticky_waters,
	abstract = {Wind- and current-driven flotsam, oil spills, pollutants, and nutrients, approaching the nearshore will frequently appear to park just beyond the break zone, where waves break. Moreover, the portion of these tracers that beach will do so only after a long time. Explaining why these tracers park and at what rate they reach the shore has important implications on a variety of different nearshore environmental issues, including the determination of what subscale processes are essential in computer models for the simulation of pollutant transport in the nearshore. Using a simple model we provide an explanation for the underlying mechanism responsible for the parking of tracers, the role played by the bottom topography, and the non-uniform dispersion which leads, in some circumstances, to the eventual landing of all or a portion of the tracers. We refer to the parking phenomenon in this environment as nearshore sticky waters. },
	author = {Juan M. Restrepo and Shankar C. Venkataramani and Clint Dawson},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {http://dx.doi.org/10.1016/j.ocemod.2014.06.003},
	issn = {1463-5003},
	journal = {Ocean Modelling},
	keywords = {Waves and currents; pubs},
	number = {0},
	pages = {49 - 58},
	title = {Nearshore sticky waters},
	url_arxiv = {http://arxiv.org/abs/1307.0588},
	url_journal = {http://www.sciencedirect.com/science/article/pii/S1463500314000778},
	volume = {80},
	year = {2014},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S1463500314000778},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.ocemod.2014.06.003}}



@article{Venkataramani199666,
	author = {Shankar C. Venkataramani and Thomas M. Antonsen and Edward Ott and John C. Sommerer},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {http://dx.doi.org/10.1016/0167-2789(96)00014-0},
	issn = {0167-2789},
	journal = {Physica D: Nonlinear Phenomena},
	keywords = {Invariant manifold; pubs},
	note = {Measures of Spatio-Temporal Dynamics},
	number = {1--4},
	pages = {66 - 99},
	title = {On-off intermittency: Power spectrum and fractal properties of time series},
	url_journal = {http://www.sciencedirect.com/science/article/pii/0167278996000140},
	volume = {96},
	year = {1996},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0167278996000140},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/0167-2789(96)00014-0}}



@article{GVDM2014,
	abstract = {We investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis. Within the Fresnel approximation, we show that this problem can be expressed in a variational form equivalent to the one arising in phase retrieval. Using the uncertainty principle we prove various rigorous lower bounds on the functional; these lower bounds estimate the $L^2$ error for the beam shaping problem in terms of the design parameters. We also use the method of stationary phase to construct a natural ansatz for a minimizer in the short wavelength limit. We illustrate the implications of our results by applying the method of stationary phase coupled with the Gerchberg--Saxton algorithm to beam shaping problems arising in the remote delivery of beams and pulses.},
	author = {John A. Gemmer and Shankar C. Venkataramani and Charles G. Durfee and Jerome V. Moloney},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {http://dx.doi.org/10.1016/j.physd.2014.06.003},
	issn = {0167-2789},
	journal = {Physica D: Nonlinear Phenomena},
	keywords = {Fresnel approximation; pubs},
	number = {0},
	pages = {15 - 28},
	title = {Optical beam shaping and diffraction free waves: A variational approach},
	url_arxiv = {http://arxiv.org/abs/1307.6289},
	url_journal = {http://www.sciencedirect.com/science/article/pii/S0167278914001195},
	volume = {283},
	year = {2014},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0167278914001195},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.physd.2014.06.003}}



@article{GV2011,
	abstract = {We investigate isometric immersions of disks with constant negative curvature into $R^3$, and the minimizers for the bending energy, i.e.   the $L^2$ norm of the principal curvatures over the class of $W^{2,2}$ isometric immersions. We show the existence of smooth immersions of arbitrarily large geodesic balls in $H^2$ into $R^3$. In elucidating the connection between these immersions and the non-existence/singularity results of Hilbert and Amsler, we obtain a lower bound for the $L^\infty$ norm of the principal curvatures for such smooth isometric immersions. We also construct piecewise smooth isometric immersions that have a periodic profile, are globally $W^{2,2}$ and numerically have lower bending energy than their smooth counterparts. The number of periods in these configurations is set by the condition that the principal curvatures of the surface remain finite and grow approximately exponentially with the radius of the disk. We discuss the implications of our results on recent experiments on the mechanics of non-Euclidean plates.
},
	author = {Gemmer, John A. and Venkataramani, Shankar C.},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {http://dx.doi.org/10.1016/j.physd.2011.07.002},
	issn = {0167-2789},
	journal = {Physica D: Nonlinear Phenomena},
	keywords = {Morphogenesis in soft tissue; pubs},
	number = {19},
	pages = {1536 - 1552},
	title = {Shape selection in non-Euclidean plates},
	url_arxiv = {http://arxiv.org/abs/1005.4442},
	url_journal = {http://www.sciencedirect.com/science/article/pii/S0167278911001825},
	volume = {240},
	year = {2011},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0167278911001825},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.physd.2011.07.002}}



@article{CARTHE2014,
	abstract = {ABSTRACT CARTHE (http://carthe.org/) is a Gulf of Mexico Research Initiative (GoMRI) consortium established through a competitive peer-reviewed selection process. CARTHE comprises 26 principal investigators from 14 universities and research institutions distributed across four Gulf of Mexico states and other four states. It fuses into one group investigators with unique scientific and technical knowledge and extensive publications related to oil fate/transport processes, oceanic and atmospheric turbulence, air-sea interactions, tropical cyclones and winter storms, and coastal and nearshore modeling and observations. Our primary goal is to accurately predict the fate of hydrocarbons released into the environment. Achieving this goal is particularly challenging since petroleum releases into the environment interact with natural processes across six orders of magnitude of time and space scales. We are developing a multi-scale modeling tool by incorporating state-of-the-art hydrophysical models, each applicable for a restricted range of scales, into a single, interconnected modeling system to predict the physical dispersal of hydrocarbons across scales ranging from the microscale at the wellhead to oceanic and atmospheric mesoscales. CARTHE is also conducting novel in-situ observations and laboratory experiments specifically designed for quantifying submesoscale dispersion as well as for both model validation and parameterization. Finally, we are providing a robust set of uncertainty metrics and analysis tools to assess model performance and quantify predictive uncertainty.},
	annote = {doi: 10.7901/2169-3358-2014.1.544},
	author = {{\"O}zg{\"o}kmen, Tamay M. and Beron-Vera, Francisco J. and Bogucki, Darek and Chen, Shuyi S. and Dawson, Clint and Dewar, William and Griffa, Annalisa and Haus, Brian K. and Haza, Angelique C. and Huntley, Helga and Iskandarani, Mohamed and Jacobs, Gregg and Jagers, Bert and Kirwan, A. D. and Laxague, Nathan and Lipphardt, Bruce and MacMahan, Jamie and Mariano, Arthur J. and Olascoaga, Josefina and Novelli, Guillaume and Poje, Andrew C. and Reniers, A. J. H. M. and Restrepo, Juan M. and Rosenheim, Brad and Ryan, Edward H. and Smith, Conor and Soloviev, Alexander and Venkataramani, Shankar and Zha, Ge-Cheng and Zhu, Ping},
	booktitle = {International Oil Spill Conference Proceedings},
	da = {2014/05/01},
	date = {2014/05/01},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.7901/2169-3358-2014.1.544},
	isbn = {2169-3366},
	journal = {International Oil Spill Conference Proceedings},
	journal1 = {International Oil Spill Conference Proceedings},
	keywords = {pubs},
	m3 = {doi: 10.7901/2169-3358-2014.1.544},
	month = {2014/11/08},
	n2 = {ABSTRACT CARTHE (http://carthe.org/) is a Gulf of Mexico Research Initiative (GoMRI) consortium established through a competitive peer-reviewed selection process. CARTHE comprises 26 principal investigators from 14 universities and research institutions distributed across four Gulf of Mexico states and other four states. It fuses into one group investigators with unique scientific and technical knowledge and extensive publications related to oil fate/transport processes, oceanic and atmospheric turbulence, air-sea interactions, tropical cyclones and winter storms, and coastal and nearshore modeling and observations. Our primary goal is to accurately predict the fate of hydrocarbons released into the environment. Achieving this goal is particularly challenging since petroleum releases into the environment interact with natural processes across six orders of magnitude of time and space scales. We are developing a multi-scale modeling tool by incorporating state-of-the-art hydrophysical models, each applicable for a restricted range of scales, into a single, interconnected modeling system to predict the physical dispersal of hydrocarbons across scales ranging from the microscale at the wellhead to oceanic and atmospheric mesoscales. CARTHE is also conducting novel in-situ observations and laboratory experiments specifically designed for quantifying submesoscale dispersion as well as for both model validation and parameterization. Finally, we are providing a robust set of uncertainty metrics and analysis tools to assess model performance and quantify predictive uncertainty.},
	number = {1},
	pages = {544--560},
	publisher = {American Petroleum Institute},
	title = {Research Overview of the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE)},
	ty = {JOUR},
	url_journal = {http://dx.doi.org/10.7901/2169-3358-2014.1.544},
	volume = {2014},
	year = {2014},
	year1 = {2014},
	Bdsk-Url-1 = {http://dx.doi.org/10.7901/2169-3358-2014.1.544}}



@article{PRE_interface,
	abstract = {We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity, and surface tension. The free boundary in our system develops sharp corners or singularities in certain parameter regimes, and this is an impediment to using existing ``single-scale'' numerical conformal mapping methods. The difficulty is due to the phenomenon of crowding, i.e., the tendency of nodes in the preimage plane to concentrate near the sharp regions of the boundary, leaving the smooth regions of the boundary poorly resolved. A natural idea is to exploit the scale separation between the sharp regions and smooth regions to solve for each region separately and then stitch the solutions together. However, this is not straightforward as conformal maps are rigid ``global'' objects, and it is not obvious how one would patch two conformal maps together to obtain a new conformal map. We develop a ``multiscale'' (i.e., adaptive) conformal mapping method that allows us to carry out this program of stitching conformal maps on different scales together. We successfully apply our method to the electromechanical model problem.},
	author = {Kent, Stuart and Venkataramani, Shankar C.},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1103/PhysRevE.90.012407},
	issue = {1},
	journal = {Phys. Rev. E},
	keywords = {pubs},
	month = {Jul},
	numpages = {15},
	pages = {012407},
	publisher = {American Physical Society},
	title = {Sharp interfaces in two-dimensional free boundary problems: Interface calculation via matched conformal maps},
	url_arxiv = {http://arxiv.org/abs/1405.6965},
	url_journal = {http://link.aps.org/doi/10.1103/PhysRevE.90.012407},
	volume = {90},
	year = {2014},
	Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.90.012407},
	Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.90.012407}}



@article{itd_paper,
	abstract = {We propose criteria that define a trend for time series with inherent multi-scale features. We call this trend the tendency of a time series. The tendency is defined empirically by a set of criteria and captures the large-scale temporal variability of the original signal as well as the most frequent events in its histogram. Among other properties, the tendency has a variance no larger than that of the original signal; the histogram of the difference between the original signal and the tendency is as symmetric as possible; and with reduced complexity, the tendency captures essential features of the signal. To find the tendency we first use the intrinsic time-scale decomposition (ITD) of the signal, introduced in 2007 by Frei and Osorio, to produce a set of candidate tendencies. We then apply the criteria to each of the candidates to single out the one that best agrees with them. While the criteria for the tendency are independent of the signal decomposition scheme, it is found that the ITD is a simple and stable methodology, well suited for multi-scale signals. The ITD is a relatively new decomposition and little is known about its outcomes. In this study we take the first steps towards a probabilistic model of the ITD analysis of random time series. This analysis yields details concerning the universality and scaling properties of the components of the decomposition.},
	author = {Juan M Restrepo and Shankar Venkataramani and Darin Comeau and Hermann Flaschka},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	journal = {New Journal of Physics},
	keywords = {pubs},
	number = {8},
	pages = {085004},
	title = {Defining a trend for time series using the intrinsic time-scale decomposition},
	url_arxiv = {http://arxiv.org/abs/1404.3827},
	url_journal = {http://stacks.iop.org/1367-2630/16/i=8/a=085004},
	volume = {16},
	year = {2014},
	Bdsk-Url-1 = {http://stacks.iop.org/1367-2630/16/i=8/a=085004}}



@article{GV2012,
	abstract = {We investigate the behaviour of non-Euclidean plates with constant negative Gaussian curvature using the F{\"o}ppl--von K{\'a}rm{\'a}n reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. In particular we show that are only two types of global minimizers---deformations that remain flat and saddle shaped deformations with isolated regions of stretching near the edge of the annulus. We also show that there exist local minimizers with a periodic profile that have additional boundary layers near their lines of inflection. These additional boundary layers are a new phenomenon in thin elastic sheets and are necessary to regularize jump discontinuities in the azimuthal curvature across lines of inflection. We rigorously derive scaling laws for the width of these boundary layers as a function of the thickness of the sheet.},
	author = {Gemmer, John A. and Venkataramani, Shankar C.},
	coden = {NONLE5},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1088/0951-7715/25/12/3553},
	fjournal = {Nonlinearity},
	issn = {0951-7715},
	journal = {Nonlinearity},
	keywords = {pubs},
	mrclass = {74K20 (35Q74)},
	mrnumber = {2997707},
	number = {12},
	pages = {3553--3581},
	title = {Defects and boundary layers in non-{E}uclidean plates},
	url_arxiv = {http://arxiv.org/abs/1203.4329},
	url_journal = {http://dx.doi.org/10.1088/0951-7715/25/12/3553},
	volume = {25},
	year = {2012},
	Bdsk-Url-1 = {http://dx.doi.org/10.1088/0951-7715/25/12/3553},
	Bdsk-Url-2 = {http://stacks.iop.org/0951-7715/25/i=12/a=3553}}



@article{patt_defects,
	abstract = {
We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross--Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen in experimental studies of the corresponding physical systems and in numerical simulations of the microscopic equations that describe these systems.},
	author = {Ercolani, N. M. and Venkataramani, S. C.},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1007/s00332-008-9035-9},
	fjournal = {Journal of Nonlinear Science},
	issn = {0938-8974},
	journal = {J. Nonlinear Sci.},
	keywords = {pubs},
	mrclass = {35K25 (35A15 35K58 74R05)},
	mrnumber = {2511257 (2010d:35149)},
	mrreviewer = {Daniela Giachetti},
	number = {3},
	pages = {267--300},
	title = {A variational theory for point defects in patterns},
	url_arxiv = {http://arxiv.org/abs/0706.2917},
	url_journal = {http://dx.doi.org/10.1007/s00332-008-9035-9},
	volume = {19},
	year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00332-008-9035-9}}



@article{MR2096037,
	abstract = {We investigate the electrostatic equilibria of N discrete charges of size 1/N on a two dimensional conductor (domain). We study the distribution of the charges on symmetric domains including the ellipse, the hypotrochoid and various regular polygons, with an emphasis on understanding the distributions of the charges, as the shape of the underlying conductor becomes singular. We find that there are two regimes of behavior, a symmetric regime for smooth conductors, and a symmetry broken regime for ``singular'' domains. For smooth conductors, the locations of the charges can be determined, to within O(logN/N2{\^a}€¾{\^a}€¾{\^a}€¾{\^a}€¾{\^a}€¾{\^a}€¾{\^a}€¾{\^a}€¾{\^a}€¾{\^a}ˆ{\v s}) by an integral equation due to Pommerenke [ Math. Ann., 179: 212--218, (1969)]. We present a derivation of a related (but different) integral equation, which has the same solutions. We also solve the equation to obtain (asymptotic) solutions which show universal behavior in the distribution of the charges in conductors with somewhat smooth cusps. Conductors with sharp cusps and singularities show qualitatively different behavior, where the symmetry of the problem is broken, and the distribution of the discrete charges does not respect the symmetry of the underlying domain. We investigate the symmetry breaking both theoretically, and numerically, and find good agreement between our theory and the numerics. We also find that the universality in the distribution of the charges near the cusps persists in the symmetry broken regime, although this distribution is very different from the one given by the integral equation.},
	author = {Berkenbusch, Marko K. and Claus, Isabelle and Dunn, Catherine and Kadanoff, Leo P. and Nicewicz, Maciej and Venkataramani, Shankar C.},
	coden = {JSTPSB},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1023/B:JOSS.0000041741.27244.ac},
	fjournal = {Journal of Statistical Physics},
	issn = {0022-4715},
	journal = {J. Statist. Phys.},
	keywords = {pubs},
	mrclass = {78A30 (37J40 37N20 78A35)},
	mrnumber = {2096037 (2006d:78009)},
	mrreviewer = {T. Erber},
	number = {5-6},
	pages = {1301--1358},
	title = {Discrete charges on a two dimensional conductor},
	url_arxiv = {http://arxiv.org/abs/cond-mat/0310257},
	url_journal = {http://dx.doi.org/10.1023/B:JOSS.0000041741.27244.ac},
	volume = {116},
	year = {2004},
	Bdsk-Url-1 = {http://dx.doi.org/10.1023/B:JOSS.0000041741.27244.ac}}



@article{MR2023444,
	abstract = {We study the linearized F{\"o}ppl--von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle 2 {\^I}$\pm$. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness, {\"I}ƒ, and the bending angle. We show that the minimum energy scales as {\"I}ƒ5/3 {\^I}$\pm$7/3. This scaling is in sharp contrast with previously obtained results for the linearized theory of thin sheets with isotropic compression boundary conditions, where the energy scales as {\"I}ƒ.},
	author = {Venkataramani, Shankar C.},
	coden = {NONLE5},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1088/0951-7715/17/1/017},
	fjournal = {Nonlinearity},
	issn = {0951-7715},
	journal = {Nonlinearity},
	keywords = {pubs},
	mrclass = {74K15 (46N10 47J20 49J40 74G65)},
	mrnumber = {2023444 (2005b:74077)},
	mrreviewer = {Yi-Chung Shu},
	number = {1},
	pages = {301--312},
	title = {Lower bounds for the energy in a crumpled elastic sheet---a minimal ridge},
	url_arxiv = {http://arxiv.org/abs/math/0210012},
	url_journal = {http://dx.doi.org/10.1088/0951-7715/17/1/017},
	volume = {17},
	year = {2004},
	Bdsk-Url-1 = {http://dx.doi.org/10.1088/0951-7715/17/1/017}}



@article{MR1765831,
	author = {Venkataramani, S. C. and Witten, T. A. and Kramer, E. M. and Geroch, R. P.},
	coden = {JMAPAQ},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1063/1.533394},
	fjournal = {Journal of Mathematical Physics},
	issn = {0022-2488},
	journal = {J. Math. Phys.},
	keywords = {pubs},
	mrclass = {53A07 (53C42)},
	mrnumber = {1765831 (2001j:53008)},
	mrreviewer = {Anders Linn{\'e}r},
	number = {7},
	pages = {5107--5128},
	title = {Limitations on the smooth confinement of an unstretchable manifold},
	url_journal = {http://dx.doi.org/10.1063/1.533394},
	volume = {41},
	year = {2000},
	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.533394}}



@article{MR1709861,
	author = {Brenner, Michael P. and Constantin, Peter and Kadanoff, Leo P. and Schenkel, Alain and Venkataramani, Shankar C.},
	coden = {NONLE5},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	doi = {10.1088/0951-7715/12/4/320},
	fjournal = {Nonlinearity},
	issn = {0951-7715},
	journal = {Nonlinearity},
	keywords = {pubs},
	mrclass = {76N99 (35K55 92C17)},
	mrnumber = {1709861 (2001d:76107)},
	number = {4},
	pages = {1071--1098},
	title = {Diffusion, attraction and collapse},
	url_journal = {http://dx.doi.org/10.1088/0951-7715/12/4/320},
	volume = {12},
	year = {1999},
	Bdsk-Url-1 = {http://dx.doi.org/10.1088/0951-7715/12/4/320}}



@article{MR1330301,
	author = {Jacobson, Ted and Venkataramani, Shankar},
	coden = {CQGRDG},
	date-added = {2017-01-29 16:04:45 +0000},
	date-modified = {2017-01-29 20:11:00 +0000},
	fjournal = {Classical and Quantum Gravity},
	issn = {0264-9381},
	journal = {Classical Quantum Gravity},
	keywords = {pubs},
	mrclass = {83C75 (57N10)},
	mrnumber = {1330301 (96e:83055)},
	mrreviewer = {Robert J. Low},
	number = {4},
	pages = {1055--1061},
	title = {Topology of event horizons and topological censorship},
	url_journal = {http://stacks.iop.org/0264-9381/12/1055},
	volume = {12},
	year = {1995},
	Bdsk-Url-1 = {http://stacks.iop.org/0264-9381/12/1055}}
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K.; Shearman, T. L.; Struckmeyer, E. J.; Gemmer, J. A.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>The European Physical Journal E</i>, 44(7): 95.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://doi.org/10.1140/epje/s10189-021-00099-6\"\n     onclick=\"log_download('yamamoto-shearman-struckmeyer-gemmer-venkataramani-naturesformsarefrillyflexibleandfunctional-2021', 'https://doi.org/10.1140/epje/s10189-021-00099-6', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Nature&#x27;s forms are frilly, flexible, and functional [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n  <a href=\"https://arxiv.org/abs/2103.10509\"\n     onclick=\"log_download('yamamoto-shearman-struckmeyer-gemmer-venkataramani-naturesformsarefrillyflexibleandfunctional-2021', 'https://arxiv.org/abs/2103.10509', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Nature&#x27;s forms are frilly, flexible, and functional [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1140/epje/s10189-021-00099-6\"\n     onclick=\"log_download('yamamoto-shearman-struckmeyer-gemmer-venkataramani-naturesformsarefrillyflexibleandfunctional-2021', 'http://doi.org/10.1140/epje/s10189-021-00099-6', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/yamamoto-shearman-struckmeyer-gemmer-venkataramani-naturesformsarefrillyflexibleandfunctional-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>14 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('yamamoto-shearman-struckmeyer-gemmer-venkataramani-naturesformsarefrillyflexibleandfunctional-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{Yamamoto:2021wk,\n\tabstract = {A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This is seen in leaves, flowers, fungi, corals, and marine invertebrates. We investigate this morphology from the perspective of non-Euclidean plate theory. We identify a novel type of defect, a branch-point of the normal map, that allows for the generation of such complex wrinkling patterns in thin elastic hyperbolic surfaces, even in the absence of stretching. We argue that branch points are the natural defects in hyperbolic sheets, they carry a topological charge which gives them a degree of robustness, and they can influence the overall morphology of a hyperbolic surface without concentrating elastic energy. We develop a theory for branch points and investigate their role in determining the mechanical response of hyperbolic sheets to weak external forces.},\n\tauthor = {Yamamoto, Kenneth K. and Shearman, Toby L. and Struckmeyer, Erik J. and Gemmer, John A. and Venkataramani, Shankar C.},\n\tda = {2021/07/13},\n\tdate-added = {2021-07-18 21:03:52 -0700},\n\tdate-modified = {2021-07-18 21:04:38 -0700},\n\tdoi = {10.1140/epje/s10189-021-00099-6},\n\tid = {Yamamoto2021},\n\tisbn = {1292-895X},\n\tjournal = {The European Physical Journal E},\n\tkeywords = {pubs},\n\tnumber = {7},\n\tpages = {95},\n\ttitle = {Nature&#x27;s forms are frilly, flexible, and functional},\n\tty = {JOUR},\n\turl = {https://doi.org/10.1140/epje/s10189-021-00099-6},\n\turl_arxiv = {https://arxiv.org/abs/2103.10509},\n\tvolume = {44},\n\tyear = {2021},\n\tBdsk-Url-1 = {https://doi.org/10.1140/epje/s10189-021-00099-6}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This is seen in leaves, flowers, fungi, corals, and marine invertebrates. We investigate this morphology from the perspective of non-Euclidean plate theory. We identify a novel type of defect, a branch-point of the normal map, that allows for the generation of such complex wrinkling patterns in thin elastic hyperbolic surfaces, even in the absence of stretching. We argue that branch points are the natural defects in hyperbolic sheets, they carry a topological charge which gives them a degree of robustness, and they can influence the overall morphology of a hyperbolic surface without concentrating elastic energy. We develop a theory for branch points and investigate their role in determining the mechanical response of hyperbolic sheets to weak external forces.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"venkataramani-newell-patterndarkmatterandgalaxyscalingrelations-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1140/epjs/s11734-021-00196-9\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'venkataramani-newell-patterndarkmatterandgalaxyscalingrelations-2021', 'https://doi.org/10.1140/epjs/s11734-021-00196-9', event);\">\n    Pattern dark matter and galaxy scaling relations.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>;  and Newell, A. C.\n</span>\n\n  \n\n</span>\n\n  <i>The European Physical Journal Special Topics</i>.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://doi.org/10.1140/epjs/s11734-021-00196-9\"\n     onclick=\"log_download('venkataramani-newell-patterndarkmatterandgalaxyscalingrelations-2021', 'https://doi.org/10.1140/epjs/s11734-021-00196-9', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Pattern dark matter and galaxy scaling relations [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n  <a href=\"https://arxiv.org/abs/2101.08372\"\n     onclick=\"log_download('venkataramani-newell-patterndarkmatterandgalaxyscalingrelations-2021', 'https://arxiv.org/abs/2101.08372', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Pattern dark matter and galaxy scaling relations [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1140/epjs/s11734-021-00196-9\"\n     onclick=\"log_download('venkataramani-newell-patterndarkmatterandgalaxyscalingrelations-2021', 'http://doi.org/10.1140/epjs/s11734-021-00196-9', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-newell-patterndarkmatterandgalaxyscalingrelations-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>12 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-newell-patterndarkmatterandgalaxyscalingrelations-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{Venkataramani:2021tn,\n\tabstract = {We argue that a natural explanation for a variety of robust galaxy scaling relations comes from the perspective of pattern formation and self-organization as a result of symmetry breaking. We propose a simple Lagrangian model that combines a conventional model for normal matter in a galaxy with a conventional model for stripe pattern formation in systems that break continuous translation invariance. We show that the energy stored in the pattern field acts as an effective dark matter. Our theory reproduces the gross features of elliptic galaxies as well as disk galaxies (HSB and LSB) including their detailed rotation curves, the radial acceleration relation, and the Freeman law. We investigate the stability of disk galaxies in the context of our model and obtain scaling relations for the central dispersion for elliptical galaxies. A natural interpretation of our results is that (1) &#x60;dark matter&#x27;is potentially a collective, emergent phenomenon and not necessarily an as yet undiscovered particle, and (2) MOND is an effective theory for the description of a self-organized complex system rather than a fundamental description of nature that modifies Newton&#x27;s second law.},\n\tauthor = {Venkataramani, Shankar C. and Newell, Alan C.},\n\tda = {2021/06/18},\n\tdate-added = {2021-07-18 20:58:08 -0700},\n\tdate-modified = {2021-07-18 20:59:43 -0700},\n\tdoi = {10.1140/epjs/s11734-021-00196-9},\n\tid = {Venkataramani2021},\n\tisbn = {1951-6401},\n\tjournal = {The European Physical Journal Special Topics},\n\tkeywords = {pubs},\n\ttitle = {Pattern dark matter and galaxy scaling relations},\n\tty = {JOUR},\n\turl = {https://doi.org/10.1140/epjs/s11734-021-00196-9},\n\turl_arxiv = {https://arxiv.org/abs/2101.08372},\n\tyear = {2021},\n\tBdsk-Url-1 = {https://doi.org/10.1140/epjs/s11734-021-00196-9}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We argue that a natural explanation for a variety of robust galaxy scaling relations comes from the perspective of pattern formation and self-organization as a result of symmetry breaking. We propose a simple Lagrangian model that combines a conventional model for normal matter in a galaxy with a conventional model for stripe pattern formation in systems that break continuous translation invariance. We show that the energy stored in the pattern field acts as an effective dark matter. Our theory reproduces the gross features of elliptic galaxies as well as disk galaxies (HSB and LSB) including their detailed rotation curves, the radial acceleration relation, and the Freeman law. We investigate the stability of disk galaxies in the context of our model and obtain scaling relations for the central dispersion for elliptical galaxies. A natural interpretation of our results is that (1) `dark matter'is potentially a collective, emergent phenomenon and not necessarily an as yet undiscovered particle, and (2) MOND is an effective theory for the description of a self-organized complex system rather than a fundamental description of nature that modifies Newton's second law.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhang-acharya-newell-venkataramani-computingwithnonorientabledefectsnematicssmecticsandnaturalpatterns-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.sciencedirect.com/science/article/pii/S0167278920308290\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'zhang-acharya-newell-venkataramani-computingwithnonorientabledefectsnematicssmecticsandnaturalpatterns-2021', 'https://www.sciencedirect.com/science/article/pii/S0167278920308290', event);\">\n    Computing with non-orientable defects: Nematics, smectics and natural patterns.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Zhang, C.; Acharya, A.; Newell, A. C.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Physica D: Nonlinear Phenomena</i>, 417: 132828.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.sciencedirect.com/science/article/pii/S0167278920308290\"\n     onclick=\"log_download('zhang-acharya-newell-venkataramani-computingwithnonorientabledefectsnematicssmecticsandnaturalpatterns-2021', 'https://www.sciencedirect.com/science/article/pii/S0167278920308290', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Computing with non-orientable defects: Nematics, smectics and natural patterns [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/https://doi.org/10.1016/j.physd.2020.132828\"\n     onclick=\"log_download('zhang-acharya-newell-venkataramani-computingwithnonorientabledefectsnematicssmecticsandnaturalpatterns-2021', 'http://doi.org/https://doi.org/10.1016/j.physd.2020.132828', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhang-acharya-newell-venkataramani-computingwithnonorientabledefectsnematicssmecticsandnaturalpatterns-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>7 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhang-acharya-newell-venkataramani-computingwithnonorientabledefectsnematicssmecticsandnaturalpatterns-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{Zhang20211Computing,\n\tabstract = {Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they appear as &#x60;unphysical&#x27; singularities, with non-integrable energy densities in coarse-grained macroscopic models. We develop a principled approach for enriching coarse-grained theories with enough of the &#x60;micro-physics&#x27; to obtain thermodynamically consistent, well-set models that allow for the investigations of dynamics and interactions of defects in extended systems. We also develop associated numerical methods that are applicable to computing energy driven behaviors of defects across the amorphous-soft-crystalline materials spectrum. Our methods can handle order parameters that have a head-tail symmetry, i.e. director fields, in systems with a continuous translation symmetry, as in nematic liquid crystals, and in systems where the translation symmetry is broken, as in smectics and convection patterns. We illustrate our methods with explicit computations.},\n\tauthor = {Chiqun Zhang and Amit Acharya and Alan C. Newell and Shankar C. Venkataramani},\n\tdate-added = {2021-05-29 14:50:02 -0700},\n\tdate-modified = {2021-05-29 14:50:42 -0700},\n\tdoi = {https://doi.org/10.1016/j.physd.2020.132828},\n\tissn = {0167-2789},\n\tjournal = {Physica D: Nonlinear Phenomena},\n\tkeywords = {pubs,Defects in materials, Non-orientability, Effective theories, Liquid crystals, Pattern formation, Computation of defects},\n\tpages = {132828},\n\ttitle = {Computing with non-orientable defects: Nematics, smectics and natural patterns},\n\turl = {https://www.sciencedirect.com/science/article/pii/S0167278920308290},\n\tvolume = {417},\n\tyear = {2021},\n\tBdsk-Url-1 = {https://www.sciencedirect.com/science/article/pii/S0167278920308290},\n\tBdsk-Url-2 = {https://doi.org/10.1016/j.physd.2020.132828}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they appear as `unphysical' singularities, with non-integrable energy densities in coarse-grained macroscopic models. We develop a principled approach for enriching coarse-grained theories with enough of the `micro-physics' to obtain thermodynamically consistent, well-set models that allow for the investigations of dynamics and interactions of defects in extended systems. We also develop associated numerical methods that are applicable to computing energy driven behaviors of defects across the amorphous-soft-crystalline materials spectrum. Our methods can handle order parameters that have a head-tail symmetry, i.e. director fields, in systems with a continuous translation symmetry, as in nematic liquid crystals, and in systems where the translation symmetry is broken, as in smectics and convection patterns. We illustrate our methods with explicit computations.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"jaramillo-venkataramani-amodifiedsplitbregmanalgorithmforcomputingmicrostructuresthroughyoungmeasures-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1137/19M1306907\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'jaramillo-venkataramani-amodifiedsplitbregmanalgorithmforcomputingmicrostructuresthroughyoungmeasures-2021', 'https://doi.org/10.1137/19M1306907', event);\">\n    A Modified Split Bregman Algorithm for Computing Microstructures Through Young Measures.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Jaramillo, G.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Multiscale Modeling & Simulation</i>, 19(2): 886-920.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://doi.org/10.1137/19M1306907\"\n     onclick=\"log_download('jaramillo-venkataramani-amodifiedsplitbregmanalgorithmforcomputingmicrostructuresthroughyoungmeasures-2021', 'https://doi.org/10.1137/19M1306907', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A Modified Split Bregman Algorithm for Computing Microstructures Through Young Measures [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n  <a href=\"https://arxiv.org/abs/1912.03360\"\n     onclick=\"log_download('jaramillo-venkataramani-amodifiedsplitbregmanalgorithmforcomputingmicrostructuresthroughyoungmeasures-2021', 'https://arxiv.org/abs/1912.03360', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A Modified Split Bregman Algorithm for Computing Microstructures Through Young Measures [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1137/19M1306907\"\n     onclick=\"log_download('jaramillo-venkataramani-amodifiedsplitbregmanalgorithmforcomputingmicrostructuresthroughyoungmeasures-2021', 'http://doi.org/10.1137/19M1306907', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/jaramillo-venkataramani-amodifiedsplitbregmanalgorithmforcomputingmicrostructuresthroughyoungmeasures-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>5 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('jaramillo-venkataramani-amodifiedsplitbregmanalgorithmforcomputingmicrostructuresthroughyoungmeasures-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{jaramillo2019microstructure,\n\tauthor = {Jaramillo, Gabriela and Venkataramani, Shankar C.},\n\tdate-added = {2021-05-29 14:38:32 -0700},\n\tdate-modified = {2021-05-29 14:39:29 -0700},\n\tdoi = {10.1137/19M1306907},\n\teprint = {https://doi.org/10.1137/19M1306907},\n\tjournal = {Multiscale Modeling \\&amp; Simulation},\n\tkeywords = {pubs},\n\tnumber = {2},\n\tpages = {886-920},\n\ttitle = {A Modified Split Bregman Algorithm for Computing Microstructures Through Young Measures},\n\turl = {https://doi.org/10.1137/19M1306907},\n\turl_arxiv = {https://arxiv.org/abs/1912.03360},\n\tvolume = {19},\n\tyear = {2021},\n\tBdsk-Url-1 = {https://doi.org/10.1137/19M1306907}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"shearman-venkataramani-distributedbranchpointsandtheshapeofelasticsurfaceswithconstantnegativecurvature-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/2006.14461\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'shearman-venkataramani-distributedbranchpointsandtheshapeofelasticsurfaceswithconstantnegativecurvature-2021', 'https://arxiv.org/abs/2006.14461', event);\">\n    Distributed Branch Points and the Shape of Elastic Surfaces with Constant Negative Curvature.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Shearman, T. L;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C</a>\n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear Science</i>, 31(1): 1–60.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://arxiv.org/abs/2006.14461\"\n     onclick=\"log_download('shearman-venkataramani-distributedbranchpointsandtheshapeofelasticsurfaceswithconstantnegativecurvature-2021', 'https://arxiv.org/abs/2006.14461', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Distributed Branch Points and the Shape of Elastic Surfaces with Constant Negative Curvature [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/shearman-venkataramani-distributedbranchpointsandtheshapeofelasticsurfaceswithconstantnegativecurvature-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>4 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('shearman-venkataramani-distributedbranchpointsandtheshapeofelasticsurfaceswithconstantnegativecurvature-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{shearman2021distributed,\n\tauthor = {Shearman, Toby L and Venkataramani, Shankar C},\n\tdate-added = {2021-05-23 19:13:38 -0700},\n\tdate-modified = {2021-05-23 19:14:52 -0700},\n\tjournal = {Journal of Nonlinear Science},\n\tkeywords = {pubs},\n\tnumber = {1},\n\tpages = {1--60},\n\tpublisher = {Springer},\n\ttitle = {Distributed Branch Points and the Shape of Elastic Surfaces with Constant Negative Curvature},\n\turl_arxiv = {https://arxiv.org/abs/2006.14461},\n\tvolume = {31},\n\tyear = {2021}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"venkataramani-newell-diskgalaxiesandtheirdarkhalosasselforganizedpatterns-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.sciencedirect.com/science/article/pii/S0370269320308637\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'venkataramani-newell-diskgalaxiesandtheirdarkhalosasselforganizedpatterns-2021', 'https://www.sciencedirect.com/science/article/pii/S0370269320308637', event);\">\n    Disk galaxies and their dark halos as self-organized patterns.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>;  and Newell, A. C.\n</span>\n\n  \n\n</span>\n\n  <i>Physics Letters B</i>, 813: 136060.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.sciencedirect.com/science/article/pii/S0370269320308637\"\n     onclick=\"log_download('venkataramani-newell-diskgalaxiesandtheirdarkhalosasselforganizedpatterns-2021', 'https://www.sciencedirect.com/science/article/pii/S0370269320308637', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Disk galaxies and their dark halos as self-organized patterns [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n  <a href=\"https://arxiv.org/abs/1910.14649\"\n     onclick=\"log_download('venkataramani-newell-diskgalaxiesandtheirdarkhalosasselforganizedpatterns-2021', 'https://arxiv.org/abs/1910.14649', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Disk galaxies and their dark halos as self-organized patterns [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/https://doi.org/10.1016/j.physletb.2020.136060\"\n     onclick=\"log_download('venkataramani-newell-diskgalaxiesandtheirdarkhalosasselforganizedpatterns-2021', 'http://doi.org/https://doi.org/10.1016/j.physletb.2020.136060', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-newell-diskgalaxiesandtheirdarkhalosasselforganizedpatterns-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>6 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-newell-diskgalaxiesandtheirdarkhalosasselforganizedpatterns-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{PatternDM,\n\tabstract = {Galaxies are built by complex physical processes with significant inherent stochasticity. It is therefore surprising that the inferred dark matter distributions in galaxies are correlated with the observed baryon distributions leading to various &#x60;Baryon-Halo conspiracies&#x27;. The fact that no dark matter candidate has been definitively identified invites a search for alternative explanations for such correlations and we present an approach motivated by the behaviors of self organized patterns. We propose a nonlocal relativistic Lagrangian theory for a &#x60;pattern field&#x27; which acts as an &#x60;effective dark matter&#x27;, built on the idea that defects in this pattern field couple to the baryonic matter distribution. The model applies to rotation supported systems and, for them, we compute galactic rotation curves, obtain a radial acceleration relation with two branches, and deduce the Freeman limit for central surface brightness.},\n\tauthor = {Shankar C. Venkataramani and Alan C. Newell},\n\tdate-added = {2021-05-23 19:11:31 -0700},\n\tdate-modified = {2021-05-23 19:17:57 -0700},\n\tdoi = {https://doi.org/10.1016/j.physletb.2020.136060},\n\tissn = {0370-2693},\n\tjournal = {Physics Letters B},\n\tkeywords = {pubs,Self-organized patterns, Symmetry breaking, Defects, Dark matter, Galaxy scaling relations},\n\tpages = {136060},\n\ttitle = {Disk galaxies and their dark halos as self-organized patterns},\n\turl = {https://www.sciencedirect.com/science/article/pii/S0370269320308637},\n\turl_arxiv = {https://arxiv.org/abs/1910.14649},\n\tvolume = {813},\n\tyear = {2021},\n\tBdsk-Url-1 = {https://www.sciencedirect.com/science/article/pii/S0370269320308637},\n\tBdsk-Url-2 = {https://doi.org/10.1016/j.physletb.2020.136060}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Galaxies are built by complex physical processes with significant inherent stochasticity. It is therefore surprising that the inferred dark matter distributions in galaxies are correlated with the observed baryon distributions leading to various `Baryon-Halo conspiracies'. The fact that no dark matter candidate has been definitively identified invites a search for alternative explanations for such correlations and we present an approach motivated by the behaviors of self organized patterns. We propose a nonlocal relativistic Lagrangian theory for a `pattern field' which acts as an `effective dark matter', built on the idea that defects in this pattern field couple to the baryonic matter distribution. The model applies to rotation supported systems and, for them, we compute galactic rotation curves, obtain a radial acceleration relation with two branches, and deduce the Freeman limit for central surface brightness.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2020\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2020')\"\n      onkeypress=\"toggleGroup('group_2020')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2020</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"acharya-venkataramani-mechanicsofmovingdefectsingrowingsheets3dsmalldeformationtheory-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1186/s41313-020-00018-w\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'acharya-venkataramani-mechanicsofmovingdefectsingrowingsheets3dsmalldeformationtheory-2020', 'https://doi.org/10.1186/s41313-020-00018-w', event);\">\n    Mechanics of moving defects in growing sheets: 3-d, small deformation theory.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Acharya, A.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Materials Theory</i>, 4(1): 2.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://doi.org/10.1186/s41313-020-00018-w\"\n     onclick=\"log_download('acharya-venkataramani-mechanicsofmovingdefectsingrowingsheets3dsmalldeformationtheory-2020', 'https://doi.org/10.1186/s41313-020-00018-w', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Mechanics of moving defects in growing sheets: 3-d, small deformation theory [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n  <a href=\"https://arxiv.org/abs/1906.08122\"\n     onclick=\"log_download('acharya-venkataramani-mechanicsofmovingdefectsingrowingsheets3dsmalldeformationtheory-2020', 'https://arxiv.org/abs/1906.08122', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Mechanics of moving defects in growing sheets: 3-d, small deformation theory [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1186/s41313-020-00018-w\"\n     onclick=\"log_download('acharya-venkataramani-mechanicsofmovingdefectsingrowingsheets3dsmalldeformationtheory-2020', 'http://doi.org/10.1186/s41313-020-00018-w', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/acharya-venkataramani-mechanicsofmovingdefectsingrowingsheets3dsmalldeformationtheory-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>4 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('acharya-venkataramani-mechanicsofmovingdefectsingrowingsheets3dsmalldeformationtheory-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{Acharya2020mechanics,\n\tabstract = {Growth and other dynamical processes in soft materials can create novel types of mesoscopic defects including discontinuities for the second and higher derivatives of the deformation, and terminating defects for these discontinuities. These higher-order defects move &#x60;&#x60;easily&quot;, and can thus confer a great degree of flexibility to the material. We develop a general continuum mechanical framework from which we can derive the dynamics of higher order defects in a thermodynamically consistent manner. We illustrate our framework by obtaining the explicit dynamical equations for the next higher order defects in an elastic body beyond dislocations, phase boundaries, and disclinations, namely, surfaces of inflection and branch lines.},\n\tauthor = {Acharya, Amit and Venkataramani, Shankar C.},\n\tda = {2020/04/16},\n\tdate-added = {2020-05-25 22:56:27 -0700},\n\tdate-modified = {2020-05-25 23:08:19 -0700},\n\tdoi = {10.1186/s41313-020-00018-w},\n\tid = {Acharya2020},\n\tisbn = {2509-8012},\n\tjournal = {Materials Theory},\n\tkeywords = {pubs},\n\tnumber = {1},\n\tpages = {2},\n\ttitle = {Mechanics of moving defects in growing sheets: 3-d, small deformation theory},\n\tty = {JOUR},\n\turl = {https://doi.org/10.1186/s41313-020-00018-w},\n\turl_arxiv = {https://arxiv.org/abs/1906.08122},\n\tvolume = {4},\n\tyear = {2020},\n\tBdsk-Url-1 = {https://doi.org/10.1186/s41313-020-00018-w}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Growth and other dynamical processes in soft materials can create novel types of mesoscopic defects including discontinuities for the second and higher derivatives of the deformation, and terminating defects for these discontinuities. These higher-order defects move ``easily\", and can thus confer a great degree of flexibility to the material. We develop a general continuum mechanical framework from which we can derive the dynamics of higher order defects in a thermodynamically consistent manner. We illustrate our framework by obtaining the explicit dynamical equations for the next higher order defects in an elastic body beyond dislocations, phase boundaries, and disclinations, namely, surfaces of inflection and branch lines.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2019\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2019')\"\n      onkeypress=\"toggleGroup('group_2019')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2019</span>\n      <span class=\"bibbase_group_count\">\n        \n        (3)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"sethuraman-venkataramani-onthegrowthofasuperlinearpreferentialattachmentscheme-2019\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://link.springer.com/chapter/10.1007/978-3-030-15338-0_9\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'sethuraman-venkataramani-onthegrowthofasuperlinearpreferentialattachmentscheme-2019', 'https://link.springer.com/chapter/10.1007/978-3-030-15338-0_9', event);\">\n    On the Growth of a Superlinear Preferential Attachment Scheme.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Sethuraman, S.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  In Friz, P.; König, W.; Mukherjee, C.;  and Olla, S., editor(s), <i>Probability and Analysis in Interacting Physical Systems</i>, pages 243–265, Cham,  2019. Springer International Publishing\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://link.springer.com/chapter/10.1007/978-3-030-15338-0_9\"\n     onclick=\"log_download('sethuraman-venkataramani-onthegrowthofasuperlinearpreferentialattachmentscheme-2019', 'https://link.springer.com/chapter/10.1007/978-3-030-15338-0_9', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"On the Growth of a Superlinear Preferential Attachment Scheme [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n  <a href=\"https://arxiv.org/abs/1704.05568\"\n     onclick=\"log_download('sethuraman-venkataramani-onthegrowthofasuperlinearpreferentialattachmentscheme-2019', 'https://arxiv.org/abs/1704.05568', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"On the Growth of a Superlinear Preferential Attachment Scheme [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/sethuraman-venkataramani-onthegrowthofasuperlinearpreferentialattachmentscheme-2019\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('sethuraman-venkataramani-onthegrowthofasuperlinearpreferentialattachmentscheme-2019')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{Sethuraman2019growth,\n\tabstract = {We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known that the graph evolution condenses, that is a.s. in the limit graph there will be a single random node with infinite degree, while all others have finite degree. In this note, we establish a.s. law of large numbers type limits and fluctuation results, as {\\$}{\\$}n{$\\backslash$}uparrow {$\\backslash$}infty {\\$}{\\$}, for the counts of the number of nodes with degree {\\$}{\\$}k{$\\backslash$}ge 1{\\$}{\\$}at time {\\$}{\\$}n{$\\backslash$}ge 1{\\$}{\\$}. These limits rigorously verify and extend a physical picture of Krapivisky et al. (Phys Rev Lett 85:4629--4632, 2000 {$[$}16{$]$}) on how the condensation arises with respect to the degree distribution.},\n\taddress = {Cham},\n\tauthor = {Sethuraman, Sunder and Venkataramani, Shankar C.},\n\tbooktitle = {Probability and Analysis in Interacting Physical Systems},\n\tda = {2019//},\n\tdate-added = {2019-11-04 23:11:43 -0700},\n\tdate-modified = {2019-11-04 23:14:02 -0700},\n\teditor = {Friz, Peter and K{\\&quot;o}nig, Wolfgang and Mukherjee, Chiranjib and Olla, Stefano},\n\tid = {10.1007/978-3-030-15338-0{\\_}9},\n\tisbn = {978-3-030-15338-0},\n\tkeywords = {pubs},\n\tpages = {243--265},\n\tpublisher = {Springer International Publishing},\n\ttitle = {On the Growth of a Superlinear Preferential Attachment Scheme},\n\tty = {CONF},\n\turl = {https://link.springer.com/chapter/10.1007/978-3-030-15338-0_9},\n\turl_arxiv = {https://arxiv.org/abs/1704.05568},\n\tyear = {2019},\n\tBdsk-Url-1 = {https://link.springer.com/chapter/10.1007/978-3-030-15338-0_9}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known that the graph evolution condenses, that is a.s. in the limit graph there will be a single random node with infinite degree, while all others have finite degree. In this note, we establish a.s. law of large numbers type limits and fluctuation results, as $}{$n$\\$uparrow $\\$infty $}{$, for the counts of the number of nodes with degree $}{$k$\\$ge 1$}{$at time $}{$n$\\$ge 1$}{$. These limits rigorously verify and extend a physical picture of Krapivisky et al. (Phys Rev Lett 85:4629–4632, 2000 $[$16$]$) on how the condensation arises with respect to the degree distribution.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"newell-venkataramani-patternuniverses-2019\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/1811.10546\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'newell-venkataramani-patternuniverses-2019', 'https://arxiv.org/abs/1811.10546', event);\">\n    Pattern universes.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Newell, A. C.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Comptes Rendus Mécanique</i>, 347(4): 318 - 331.  2019.\n  <span class=\"note\">Patterns and dynamics: homage to Pierre Coullet / Formes et dynamique: hommage à Pierre Coullet</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://arxiv.org/abs/1811.10546\"\n     onclick=\"log_download('newell-venkataramani-patternuniverses-2019', 'https://arxiv.org/abs/1811.10546', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Pattern universes [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S1631072119300464\"\n     onclick=\"log_download('newell-venkataramani-patternuniverses-2019', 'http://www.sciencedirect.com/science/article/pii/S1631072119300464', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Pattern universes [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/https://doi.org/10.1016/j.crme.2019.03.004\"\n     onclick=\"log_download('newell-venkataramani-patternuniverses-2019', 'http://doi.org/https://doi.org/10.1016/j.crme.2019.03.004', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/newell-venkataramani-patternuniverses-2019\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>3 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('newell-venkataramani-patternuniverses-2019')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{NV19,\n\tabstract = {In this essay we explore analogies between macroscopic patterns, which result from a sequence of phase transitions/instabilities starting from a homogeneous state, and similar phenomena in cosmology, where a sequence of phase transitions in the early universe is believed to have separated the fundamental forces from each other, and also shaped the structure and distribution of matter in the universe. We discuss three distinct aspects of this analogy: (i) Defects and topological charges in macroscopic patterns are analogous to spins and charges of quarks and leptons; (ii) Defects in generic 3+1 stripe patterns carry an energy density that accounts for phenomena that are currently attributed to dark matter; (iii) Space-time patterns of interacting nonlinear waves display behaviors reminiscent of quantum phenomena including inflation, entanglement and dark energy.\nR{\\&#x27;e}sum{\\&#x27;e}\nDans cet article, nous explorons plusieurs analogies entre la formation de structures p{\\&#x27;e}riodiques macroscopiques, qui r{\\&#x27;e}sultent de la succession de transitions de phase ou d&#x27;instabilit{\\&#x27;e}s, et certains ph{\\&#x27;e}nom{\\&#x60;e}nes similaires en cosmologie, o{\\&#x60;u} une suite de transitions de phase dans l&#x27;univers primordial aurait donn{\\&#x27;e} lieu {\\&#x60;a} la s{\\&#x27;e}paration des forces fondamentales et {\\&#x60;a} la formation des structures. Nous consid{\\&#x27;e}rons trois analogies diff{\\&#x27;e}rentes : (i) les d{\\&#x27;e}fauts et charges topologiques dans les structures macroscopiques sont analogues aux spins et charges des quarks et des leptons ; (ii) les d{\\&#x27;e}fauts dans les structures p{\\&#x27;e}riodiques g{\\&#x27;e}n{\\&#x27;e}riques (en dimensions 3+1) ont une densit{\\&#x27;e} d&#x27;{\\&#x27;e}nergie qui donne lieu {\\&#x60;a} certains ph{\\&#x27;e}nom{\\&#x60;e}nes attribu{\\&#x27;e}s {\\&#x60;a} la pr{\\&#x27;e}sence de mati{\\&#x60;e}re noire ; (iii) les structures spatio-temporelles r{\\&#x27;e}sultant de l&#x27;interaction d&#x27;ondes non lin{\\&#x27;e}aires ont des comportements qui rappellent certains ph{\\&#x27;e}nom{\\&#x60;e}nes quantiques, tels que l&#x27;inflation cosmique, l&#x27;enchev{\\^e}trement quantique et l&#x27;{\\&#x27;e}nergie noire.},\n\tauthor = {Alan C. Newell and Shankar C. Venkataramani},\n\tdate-added = {2019-11-04 23:01:37 -0700},\n\tdate-modified = {2019-11-04 23:03:49 -0700},\n\tdoi = {https://doi.org/10.1016/j.crme.2019.03.004},\n\tissn = {1631-0721},\n\tjournal = {Comptes Rendus M{\\&#x27;e}canique},\n\tkeywords = {pubs,Pattern formation, Cosmology, Phase transitions, Formation de motifs, Cosmologie, Transition de phase},\n\tnote = {Patterns and dynamics: homage to Pierre Coullet / Formes et dynamique: hommage {\\&#x60;a} Pierre Coullet},\n\tnumber = {4},\n\tpages = {318 - 331},\n\ttitle = {Pattern universes},\n\turl_arxiv = {https://arxiv.org/abs/1811.10546},\n\turl_journal = {http://www.sciencedirect.com/science/article/pii/S1631072119300464},\n\tvolume = {347},\n\tyear = {2019},\n\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S1631072119300464},\n\tBdsk-Url-2 = {https://doi.org/10.1016/j.crme.2019.03.004}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this essay we explore analogies between macroscopic patterns, which result from a sequence of phase transitions/instabilities starting from a homogeneous state, and similar phenomena in cosmology, where a sequence of phase transitions in the early universe is believed to have separated the fundamental forces from each other, and also shaped the structure and distribution of matter in the universe. We discuss three distinct aspects of this analogy: (i) Defects and topological charges in macroscopic patterns are analogous to spins and charges of quarks and leptons; (ii) Defects in generic 3+1 stripe patterns carry an energy density that accounts for phenomena that are currently attributed to dark matter; (iii) Space-time patterns of interacting nonlinear waves display behaviors reminiscent of quantum phenomena including inflation, entanglement and dark energy. Résumé Dans cet article, nous explorons plusieurs analogies entre la formation de structures périodiques macroscopiques, qui résultent de la succession de transitions de phase ou d'instabilités, et certains phénomènes similaires en cosmologie, où une suite de transitions de phase dans l'univers primordial aurait donné lieu à la séparation des forces fondamentales et à la formation des structures. Nous considérons trois analogies différentes : (i) les défauts et charges topologiques dans les structures macroscopiques sont analogues aux spins et charges des quarks et des leptons ; (ii) les défauts dans les structures périodiques génériques (en dimensions 3+1) ont une densité d'énergie qui donne lieu à certains phénomènes attribués à la présence de matière noire ; (iii) les structures spatio-temporelles résultant de l'interaction d'ondes non linéaires ont des comportements qui rappellent certains phénomènes quantiques, tels que l'inflation cosmique, l'enchevêtrement quantique et l'énergie noire.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"venkataramani-bucklingsheetsopenadoortounderstandingselforganizationinsoftmatter-2019\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.pnas.org/content/116/5/1477\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'venkataramani-bucklingsheetsopenadoortounderstandingselforganizationinsoftmatter-2019', 'https://www.pnas.org/content/116/5/1477', event);\">\n    Buckling sheets open a door to understanding self-organization in soft matter.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Proceedings of the National Academy of Sciences</i>, 116(5): 1477–1479. January 2019.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.pnas.org/content/116/5/1477\"\n     onclick=\"log_download('venkataramani-bucklingsheetsopenadoortounderstandingselforganizationinsoftmatter-2019', 'https://www.pnas.org/content/116/5/1477', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Buckling sheets open a door to understanding self-organization in soft matter [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n  <a href=\"https://arxiv.org/abs/1901.03032\"\n     onclick=\"log_download('venkataramani-bucklingsheetsopenadoortounderstandingselforganizationinsoftmatter-2019', 'https://arxiv.org/abs/1901.03032', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Buckling sheets open a door to understanding self-organization in soft matter [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1073/pnas.1820937116\"\n     onclick=\"log_download('venkataramani-bucklingsheetsopenadoortounderstandingselforganizationinsoftmatter-2019', 'http://doi.org/10.1073/pnas.1820937116', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-bucklingsheetsopenadoortounderstandingselforganizationinsoftmatter-2019\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-bucklingsheetsopenadoortounderstandingselforganizationinsoftmatter-2019')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{2019a,\n\tauthor = {Venkataramani, Shankar C.},\n\tdate-added = {2019-03-20 20:33:42 -0700},\n\tdate-modified = {2019-03-20 20:35:03 -0700},\n\tdoi = {10.1073/pnas.1820937116},\n\teprint = {https://www.pnas.org/content/116/5/1477.full.pdf},\n\tissn = {0027-8424},\n\tjournal = {Proceedings of the National Academy of Sciences},\n\tkeywords = {pubs},\n\tmonth = {January},\n\tnumber = {5},\n\tpages = {1477--1479},\n\tpublisher = {National Academy of Sciences},\n\ttitle = {Buckling sheets open a door to understanding self-organization in soft matter},\n\turl = {https://www.pnas.org/content/116/5/1477},\n\turl_arxiv = {https://arxiv.org/abs/1901.03032},\n\tvolume = {116},\n\tyear = {2019},\n\tBdsk-Url-1 = {https://www.pnas.org/content/116/5/1477},\n\tBdsk-Url-2 = {https://doi.org/10.1073/pnas.1820937116}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2018\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2018')\"\n      onkeypress=\"toggleGroup('group_2018')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2018</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"ramirez-moghimi-restrepo-venkataramani-modellingthemassexchangedynamicsofoceanicsurfaceandsubsurfaceoil-2018\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S1463500318302087\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'ramirez-moghimi-restrepo-venkataramani-modellingthemassexchangedynamicsofoceanicsurfaceandsubsurfaceoil-2018', 'http://www.sciencedirect.com/science/article/pii/S1463500318302087', event);\">\n    Modelling the mass exchange dynamics of oceanic surface and subsurface oil.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Ramírez, J.; Moghimi, S.; Restrepo, J. M.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Ocean Modelling</i>, 129: 1 - 12. September 2018.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S1463500318302087\"\n     onclick=\"log_download('ramirez-moghimi-restrepo-venkataramani-modellingthemassexchangedynamicsofoceanicsurfaceandsubsurfaceoil-2018', 'http://www.sciencedirect.com/science/article/pii/S1463500318302087', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Modelling the mass exchange dynamics of oceanic surface and subsurface oil [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n  <a href=\"https://arxiv.org/abs/1703.05361\"\n     onclick=\"log_download('ramirez-moghimi-restrepo-venkataramani-modellingthemassexchangedynamicsofoceanicsurfaceandsubsurfaceoil-2018', 'https://arxiv.org/abs/1703.05361', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Modelling the mass exchange dynamics of oceanic surface and subsurface oil [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/https://doi.org/10.1016/j.ocemod.2018.06.004\"\n     onclick=\"log_download('ramirez-moghimi-restrepo-venkataramani-modellingthemassexchangedynamicsofoceanicsurfaceandsubsurfaceoil-2018', 'http://doi.org/https://doi.org/10.1016/j.ocemod.2018.06.004', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/ramirez-moghimi-restrepo-venkataramani-modellingthemassexchangedynamicsofoceanicsurfaceandsubsurfaceoil-2018\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('ramirez-moghimi-restrepo-venkataramani-modellingthemassexchangedynamicsofoceanicsurfaceandsubsurfaceoil-2018')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{2018b,\n\tabstract = {We propose a time dependent Eulerian model for sea surface entrainment, buoyancy transport and droplet dynamics of ocean oil. The model captures the microscale vertical oil mass exchanges in the neighborhood of the sea surface. This model is in turn part of an oil fate model designed to capture oil dynamics at large spatio-temporal scales typical of environmental studies. The adiabatic dynamics of the droplets are upscaled by a combination of filtering and stochastic parametrization. The upscaling addresses the computational burden of resolving the microscale. The upscaled droplet dynamics are tested against data and the mass exchange mechanism is incorporated into a nearshore oil transport model in order to highlight the importance of incorporating vertical mass exchanges and droplet distribution dynamics in predicting the distributing of shoaling oil.},\n\tauthor = {Jorge Ram\\&#x27;{i}rez and Saeed Moghimi and Juan M. Restrepo and Shankar Venkataramani},\n\tdate-added = {2019-03-20 20:59:16 -0700},\n\tdate-modified = {2019-03-20 21:42:06 -0700},\n\tdoi = {https://doi.org/10.1016/j.ocemod.2018.06.004},\n\tissn = {1463-5003},\n\tjournal = {Ocean Modelling},\n\tkeywords = {Oil spill; Oil fate model; Oil entrainment; Ocean oil transport; Ocean pollution; pubs},\n\tmonth = {September},\n\tpages = {1 - 12},\n\ttitle = {Modelling the mass exchange dynamics of oceanic surface and subsurface oil},\n\turl = {http://www.sciencedirect.com/science/article/pii/S1463500318302087},\n\turl_arxiv = {https://arxiv.org/abs/1703.05361},\n\tvolume = {129},\n\tyear = {2018},\n\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S1463500318302087},\n\tBdsk-Url-2 = {https://doi.org/10.1016/j.ocemod.2018.06.004}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We propose a time dependent Eulerian model for sea surface entrainment, buoyancy transport and droplet dynamics of ocean oil. The model captures the microscale vertical oil mass exchanges in the neighborhood of the sea surface. This model is in turn part of an oil fate model designed to capture oil dynamics at large spatio-temporal scales typical of environmental studies. The adiabatic dynamics of the droplets are upscaled by a combination of filtering and stochastic parametrization. The upscaling addresses the computational burden of resolving the microscale. The upscaled droplet dynamics are tested against data and the mass exchange mechanism is incorporated into a nearshore oil transport model in order to highlight the importance of incorporating vertical mass exchanges and droplet distribution dynamics in predicting the distributing of shoaling oil.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"jaramillo-venkataramani-targetpatternsina2darrayofoscillatorswithnonlocalcoupling-2018\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://iopscience.iop.org/article/10.1088/1361-6544/aac9a6/pdf\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'jaramillo-venkataramani-targetpatternsina2darrayofoscillatorswithnonlocalcoupling-2018', 'https://iopscience.iop.org/article/10.1088/1361-6544/aac9a6/pdf', event);\">\n    Target patterns in a 2D array of oscillators with nonlocal coupling.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Jaramillo, G.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C</a>\n</span>\n\n  \n\n</span>\n\n  <i>Nonlinearity</i>, 31(9): 4162-4201.  2018.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://arxiv.org/abs/1706.00524\"\n     onclick=\"log_download('jaramillo-venkataramani-targetpatternsina2darrayofoscillatorswithnonlocalcoupling-2018', 'https://arxiv.org/abs/1706.00524', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Target patterns in a 2D array of oscillators with nonlocal coupling [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"https://iopscience.iop.org/article/10.1088/1361-6544/aac9a6/pdf\"\n     onclick=\"log_download('jaramillo-venkataramani-targetpatternsina2darrayofoscillatorswithnonlocalcoupling-2018', 'https://iopscience.iop.org/article/10.1088/1361-6544/aac9a6/pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Target patterns in a 2D array of oscillators with nonlocal coupling [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1088/1361-6544/aac9a6\"\n     onclick=\"log_download('jaramillo-venkataramani-targetpatternsina2darrayofoscillatorswithnonlocalcoupling-2018', 'http://doi.org/10.1088/1361-6544/aac9a6', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/jaramillo-venkataramani-targetpatternsina2darrayofoscillatorswithnonlocalcoupling-2018\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('jaramillo-venkataramani-targetpatternsina2darrayofoscillatorswithnonlocalcoupling-2018')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{jaramillo2018target,\n\tabstract = {We analyze the effect of adding a weak, localized, inhomogeneity to a two dimensional array of oscillators with nonlocal coupling. We propose and also justify a model for the phase dynamics in this system. Our model is a generalization of a viscous eikonal equation that is known to describe the phase modulation of traveling waves in reaction--diffusion systems. We show the existence of a branch of target pattern solutions that bifurcates from the spatially homogeneous state when , the strength of the inhomogeneity, is nonzero and we also show that these target patterns have an asymptotic wavenumber that is small beyond all orders in . The strategy of our proof is to pose a good ansatz for an approximate form of the solution and use the implicit function theorem to prove the existence of a solution in its vicinity. The analysis presents two challenges. First, the linearization about the homogeneous state is a convolution operator of diffusive type and hence not invertible on the usual Sobolev spaces. Second, a regular perturbation expansion in  does not provide a good ansatz for applying the implicit function theorem since the nonlinearities play a major role in determining the relevant approximation, which also needs to be &#x60;correct&#x27; to all orders in . We overcome these two points by proving Fredholm properties for the linearization in appropriate Kondratiev spaces and using a refined ansatz for the approximate solution which was obtained using matched asymptotics.},\n\tauthor = {Jaramillo, Gabriela and Venkataramani, Shankar C},\n\tda = {2018/07/27},\n\tdate-added = {2019-03-20 14:49:42 -0700},\n\tdate-modified = {2019-03-20 15:07:42 -0700},\n\tdoi = {10.1088/1361-6544/aac9a6},\n\tisbn = {0951-7715; 1361-6544},\n\tjournal = {Nonlinearity},\n\tkeywords = {pubs},\n\tnumber = {9},\n\tpages = {4162-4201},\n\tpublisher = {IOP Publishing},\n\ttitle = {Target patterns in a 2D array of oscillators with nonlocal coupling},\n\tty = {JOUR},\n\turl_arxiv = {https://arxiv.org/abs/1706.00524},\n\turl_journal = {https://iopscience.iop.org/article/10.1088/1361-6544/aac9a6/pdf},\n\tvolume = {31},\n\tyear = {2018},\n\tBdsk-Url-1 = {http://dx.doi.org/10.1088/1361-6544/aac9a6}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We analyze the effect of adding a weak, localized, inhomogeneity to a two dimensional array of oscillators with nonlocal coupling. We propose and also justify a model for the phase dynamics in this system. Our model is a generalization of a viscous eikonal equation that is known to describe the phase modulation of traveling waves in reaction–diffusion systems. We show the existence of a branch of target pattern solutions that bifurcates from the spatially homogeneous state when , the strength of the inhomogeneity, is nonzero and we also show that these target patterns have an asymptotic wavenumber that is small beyond all orders in . The strategy of our proof is to pose a good ansatz for an approximate form of the solution and use the implicit function theorem to prove the existence of a solution in its vicinity. The analysis presents two challenges. First, the linearization about the homogeneous state is a convolution operator of diffusive type and hence not invertible on the usual Sobolev spaces. Second, a regular perturbation expansion in does not provide a good ansatz for applying the implicit function theorem since the nonlinearities play a major role in determining the relevant approximation, which also needs to be `correct' to all orders in . We overcome these two points by proving Fredholm properties for the linearization in appropriate Kondratiev spaces and using a refined ansatz for the approximate solution which was obtained using matched asymptotics.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2017\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2017')\"\n      onkeypress=\"toggleGroup('group_2017')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2017</span>\n      <span class=\"bibbase_group_count\">\n        \n        (3)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"newell-venkataramani-elasticsheetsphasesurfacesandpatternuniverses-2017\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://bibbase.org/f/J9gZq33SPmmZsfyhm/arxiv.org/abs/1612.01007\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'newell-venkataramani-elasticsheetsphasesurfacesandpatternuniverses-2017', 'https://bibbase.org/f/J9gZq33SPmmZsfyhm/arxiv.org/abs/1612.01007', event);\">\n    Elastic sheets, phase surfaces and pattern universes.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Newell, A. C.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Studies in Applied Mathematics</i>, 139(2): 322–368.  2017.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bibbase.org/f/J9gZq33SPmmZsfyhm/arxiv.org/abs/1612.01007\"\n     onclick=\"log_download('newell-venkataramani-elasticsheetsphasesurfacesandpatternuniverses-2017', 'https://bibbase.org/f/J9gZq33SPmmZsfyhm/arxiv.org/abs/1612.01007', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Elastic sheets, phase surfaces and pattern universes [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full\"\n     onclick=\"log_download('newell-venkataramani-elasticsheetsphasesurfacesandpatternuniverses-2017', 'http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Elastic sheets, phase surfaces and pattern universes [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full\"\n     onclick=\"log_download('newell-venkataramani-elasticsheetsphasesurfacesandpatternuniverses-2017', 'http://doi.org/http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/newell-venkataramani-elasticsheetsphasesurfacesandpatternuniverses-2017\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('newell-venkataramani-elasticsheetsphasesurfacesandpatternuniverses-2017')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{pattern-universe,\n\tabstract = {We connect the theories of the deformation of elastic surfaces and phase surfaces arising in the description of almost periodic patterns. In particular, we show striking parallels between expansions for the energy of elastic surfaces in powers of the thickness h and the free energy averaged over a period of an almost periodic pattern expanded in powers of ϵ, the inverse aspect ratio of the pattern field. In both cases, the resulting energy can be expressed in terms of the first and second fundamental forms of the surfaces involved, the elastic surface in the former case and the phase surface in the latter. We discuss various results that are obtained by exploiting this analogy and also address some of the outstanding questions. One common result of particular interest concerns the condensation of the Gaussian curvature onto isolated point defects in two dimensions and onto loop filaments in three dimensions. \n\nWe also lay out an ambitious and somewhat speculative program to build a multi-scale model of the universe inspired by patterns, in which the short (spatial and temporal) scale structure on the Planck scales is given by a nearly periodic microstructure, and macroscopic/slowly varying/averaged behaviors on scales much larger than the Planck scale leads to a hierarchy of structures and features including analogues of quarks, leptons, dark matter, dark energy and inflationary cosmology.\n},\n\tauthor = {Alan C. Newell and Shankar C. Venkataramani},\n\tdate-added = {2017-10-15 18:02:26 +0000},\n\tdate-modified = {2017-10-15 18:15:10 +0000},\n\tdoi = {http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full},\n\tjournal = {Studies in Applied Mathematics},\n\tkeywords = {pubs},\n\tnumber = {2},\n\tpages = {322--368},\n\ttitle = {Elastic sheets, phase surfaces and pattern universes},\n\turl_arxiv = {arxiv.org/abs/1612.01007},\n\turl_journal = {http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full},\n\tvolume = {139},\n\tyear = {2017},\n\tBdsk-Url-1 = {http://onlinelibrary.wiley.com/doi/10.1111/sapm.12184/full}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We connect the theories of the deformation of elastic surfaces and phase surfaces arising in the description of almost periodic patterns. In particular, we show striking parallels between expansions for the energy of elastic surfaces in powers of the thickness h and the free energy averaged over a period of an almost periodic pattern expanded in powers of ϵ, the inverse aspect ratio of the pattern field. In both cases, the resulting energy can be expressed in terms of the first and second fundamental forms of the surfaces involved, the elastic surface in the former case and the phase surface in the latter. We discuss various results that are obtained by exploiting this analogy and also address some of the outstanding questions. One common result of particular interest concerns the condensation of the Gaussian curvature onto isolated point defects in two dimensions and onto loop filaments in three dimensions. We also lay out an ambitious and somewhat speculative program to build a multi-scale model of the universe inspired by patterns, in which the short (spatial and temporal) scale structure on the Planck scales is given by a nearly periodic microstructure, and macroscopic/slowly varying/averaged behaviors on scales much larger than the Planck scale leads to a hierarchy of structures and features including analogues of quarks, leptons, dark matter, dark energy and inflationary cosmology. \n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"venkataramani-venkataramani-restrepo-dimensionreductionforsystemswithslowrelaxation-2017\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/1609.09222\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'venkataramani-venkataramani-restrepo-dimensionreductionforsystemswithslowrelaxation-2017', 'http://arxiv.org/abs/1609.09222', event);\">\n    Dimension Reduction for Systems with Slow Relaxation.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>; Venkataramani, R. C.;  and Restrepo, J. M.\n</span>\n\n  \n\n</span>\n\n  <i>Journal of Statistical Physics</i>, 167(3): 892–933.  2017.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/1609.09222\"\n     onclick=\"log_download('venkataramani-venkataramani-restrepo-dimensionreductionforsystemswithslowrelaxation-2017', 'http://arxiv.org/abs/1609.09222', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Dimension Reduction for Systems with Slow Relaxation [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://dx.doi.org/10.1007/s10955-017-1761-7\"\n     onclick=\"log_download('venkataramani-venkataramani-restrepo-dimensionreductionforsystemswithslowrelaxation-2017', 'http://dx.doi.org/10.1007/s10955-017-1761-7', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Dimension Reduction for Systems with Slow Relaxation [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s10955-017-1761-7\"\n     onclick=\"log_download('venkataramani-venkataramani-restrepo-dimensionreductionforsystemswithslowrelaxation-2017', 'http://doi.org/10.1007/s10955-017-1761-7', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-venkataramani-restrepo-dimensionreductionforsystemswithslowrelaxation-2017\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-venkataramani-restrepo-dimensionreductionforsystemswithslowrelaxation-2017')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{Venkataramani:2017aa,\n\tabstract = {We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize &#x60;optimal&#x27;model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.},\n\tauthor = {Venkataramani, Shankar C. and Venkataramani, Raman C. and Restrepo, Juan M.},\n\tda = {2017//},\n\tdate-added = {2017-05-01 21:34:13 +0000},\n\tdate-modified = {2017-05-02 18:16:58 +0000},\n\tdoi = {10.1007/s10955-017-1761-7},\n\tid = {Venkataramani2017},\n\tisbn = {1572-9613},\n\tjournal = {Journal of Statistical Physics},\n\tkeywords = {pubs},\n\tnumber = {3},\n\tpages = {892--933},\n\ttitle = {Dimension Reduction for Systems with Slow Relaxation},\n\tty = {JOUR},\n\turl_arxiv = {http://arxiv.org/abs/1609.09222},\n\turl_journal = {http://dx.doi.org/10.1007/s10955-017-1761-7},\n\tvolume = {167},\n\tyear = {2017},\n\tBdsk-Url-1 = {http://dx.doi.org/10.1007/s10955-017-1761-7}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal'model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"rosenthal-venkataramani-mariano-restrepo-displacementdataassimilation-2017\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/1602.02209\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'rosenthal-venkataramani-mariano-restrepo-displacementdataassimilation-2017', 'https://arxiv.org/abs/1602.02209', event);\">\n    Displacement data assimilation.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Rosenthal, W. S.; <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S.</a>; Mariano, A. J.;  and Restrepo, J. M.\n</span>\n\n  \n\n</span>\n\n  <i>Journal of Computational Physics</i>, 330: 594 - 614.  2017.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://arxiv.org/abs/1602.02209\"\n     onclick=\"log_download('rosenthal-venkataramani-mariano-restrepo-displacementdataassimilation-2017', 'https://arxiv.org/abs/1602.02209', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Displacement data assimilation [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S002199911630523X\"\n     onclick=\"log_download('rosenthal-venkataramani-mariano-restrepo-displacementdataassimilation-2017', 'http://www.sciencedirect.com/science/article/pii/S002199911630523X', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Displacement data assimilation [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/http://dx.doi.org/10.1016/j.jcp.2016.10.025\"\n     onclick=\"log_download('rosenthal-venkataramani-mariano-restrepo-displacementdataassimilation-2017', 'http://doi.org/http://dx.doi.org/10.1016/j.jcp.2016.10.025', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/rosenthal-venkataramani-mariano-restrepo-displacementdataassimilation-2017\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('rosenthal-venkataramani-mariano-restrepo-displacementdataassimilation-2017')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{Rosenthal_Displacement_2017,\n\tabstract = {Abstract We show that modifying a Bayesian data assimilation scheme by incorporating kinematically-consistent displacement corrections produces a scheme that is demonstrably better at estimating partially observed state vectors in a setting where feature information is important. While the displacement transformation is generic, here we implement it within an ensemble Kalman Filter framework and demonstrate its effectiveness in tracking stochastically perturbed vortices. },\n\tauthor = {W. Steven Rosenthal and Shankar Venkataramani and Arthur J. Mariano and Juan M. Restrepo},\n\tdate-added = {2017-01-29 16:07:29 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {http://dx.doi.org/10.1016/j.jcp.2016.10.025},\n\tissn = {0021-9991},\n\tjournal = {Journal of Computational Physics},\n\tkeywords = {Displacement assimilation; Data assimilation; Uncertainty quantification; Ensemble Kalman Filter; Vortex dynamics; pubs},\n\tpages = {594 - 614},\n\ttitle = {Displacement data assimilation},\n\turl_arxiv = {https://arxiv.org/abs/1602.02209},\n\turl_journal = {http://www.sciencedirect.com/science/article/pii/S002199911630523X},\n\tvolume = {330},\n\tyear = {2017},\n\tBdsk-Url-1 = {http://dx.doi.org/10.1016/j.jcp.2016.10.025},\n\tBdsk-Url-2 = {http://www.sciencedirect.com/science/article/pii/S002199911630523X}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Abstract We show that modifying a Bayesian data assimilation scheme by incorporating kinematically-consistent displacement corrections produces a scheme that is demonstrably better at estimating partially observed state vectors in a setting where feature information is important. While the displacement transformation is generic, here we implement it within an ensemble Kalman Filter framework and demonstrate its effectiveness in tracking stochastically perturbed vortices. \n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2016\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2016')\"\n      onkeypress=\"toggleGroup('group_2016')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2016</span>\n      <span class=\"bibbase_group_count\">\n        \n        (3)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"restrepo-venkataramani-stochasticlongshorecurrentdynamics-2016\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/1612.01046\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'restrepo-venkataramani-stochasticlongshorecurrentdynamics-2016', 'https://arxiv.org/abs/1612.01046', event);\">\n    Stochastic longshore current dynamics.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Restrepo, J. M.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Advances in Water Resources</i>, 98: 186–197. 12 2016.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://arxiv.org/abs/1612.01046\"\n     onclick=\"log_download('restrepo-venkataramani-stochasticlongshorecurrentdynamics-2016', 'https://arxiv.org/abs/1612.01046', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Stochastic longshore current dynamics [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S0309170816306157\"\n     onclick=\"log_download('restrepo-venkataramani-stochasticlongshorecurrentdynamics-2016', 'http://www.sciencedirect.com/science/article/pii/S0309170816306157', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Stochastic longshore current dynamics [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/http://dx.doi.org/10.1016/j.advwatres.2016.11.002\"\n     onclick=\"log_download('restrepo-venkataramani-stochasticlongshorecurrentdynamics-2016', 'http://doi.org/http://dx.doi.org/10.1016/j.advwatres.2016.11.002', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/restrepo-venkataramani-stochasticlongshorecurrentdynamics-2016\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('restrepo-venkataramani-stochasticlongshorecurrentdynamics-2016')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{AdWR_2016,\n\tabstract = {Abstract We develop a stochastic parametrization, based on a &#x60;simple&#x27; deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the &#x60;&#x60;missing physics&#x27;&#x27; to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation.  We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model&#x27;s resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.},\n\tauthor = {Restrepo, Juan M. and Venkataramani, Shankar},\n\tdate = {2016/12//},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {http://dx.doi.org/10.1016/j.advwatres.2016.11.002},\n\tisbn = {0309-1708},\n\tjournal = {Advances in Water Resources},\n\tkeywords = {Longshore currents; Stochastic parametrization; Parameter sensitivity; Consistently of model sensitivity; Data assimilation;; pubs},\n\tmonth = {12},\n\tpages = {186--197},\n\ttitle = {Stochastic longshore current dynamics},\n\tty = {JOUR},\n\turl_arxiv = {https://arxiv.org/abs/1612.01046},\n\turl_journal = {http://www.sciencedirect.com/science/article/pii/S0309170816306157},\n\tvolume = {98},\n\tyear = {2016},\n\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0309170816306157},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1016/j.advwatres.2016.11.002}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Abstract We develop a stochastic parametrization, based on a `simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the ``missing physics'' to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"gemmer-sharon-shearman-venkataramani-isometricimmersionsenergyminimizationandselfsimilarbucklinginnoneuclideanelasticsheets-2016\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/1601.06863\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'gemmer-sharon-shearman-venkataramani-isometricimmersionsenergyminimizationandselfsimilarbucklinginnoneuclideanelasticsheets-2016', 'https://arxiv.org/abs/1601.06863', event);\">\n    Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Gemmer, John; Sharon, Eran; Shearman, Toby;  and Venkataramani, Shankar C.\n</span>\n\n  \n\n</span>\n\n  <i>Europhys. Lett.</i>, 114(2): 24003.  2016.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://arxiv.org/abs/1601.06863\"\n     onclick=\"log_download('gemmer-sharon-shearman-venkataramani-isometricimmersionsenergyminimizationandselfsimilarbucklinginnoneuclideanelasticsheets-2016', 'https://arxiv.org/abs/1601.06863', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://dx.doi.org/10.1209/0295-5075/114/24003\"\n     onclick=\"log_download('gemmer-sharon-shearman-venkataramani-isometricimmersionsenergyminimizationandselfsimilarbucklinginnoneuclideanelasticsheets-2016', 'http://dx.doi.org/10.1209/0295-5075/114/24003', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1209/0295-5075/114/24003\"\n     onclick=\"log_download('gemmer-sharon-shearman-venkataramani-isometricimmersionsenergyminimizationandselfsimilarbucklinginnoneuclideanelasticsheets-2016', 'http://doi.org/10.1209/0295-5075/114/24003', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/gemmer-sharon-shearman-venkataramani-isometricimmersionsenergyminimizationandselfsimilarbucklinginnoneuclideanelasticsheets-2016\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('gemmer-sharon-shearman-venkataramani-isometricimmersionsenergyminimizationandselfsimilarbucklinginnoneuclideanelasticsheets-2016')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{GSSV2016,\n\tabstract = {The edges of torn plastic sheets and growing leaves often display hierarchical buckling\n patterns. We show that this complex morphology i) emerges even in zero strain configurations, and ii) is driven by a competition between the two principal curvatures, rather than between bending  and stretching.   We identify the key role of branch point (or &#x60;&#x60;monkey saddle&#x27;&#x27;) singularities in generating complex wrinkling patterns in isometric immersions, and show how they arise naturally from minimizing the elastic energy.},\n\tauthor = {{Gemmer, John} and {Sharon, Eran} and {Shearman, Toby} and {Venkataramani, Shankar C.}},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1209/0295-5075/114/24003},\n\tjournal = {Europhys. Lett.},\n\tkeywords = {pubs},\n\tnumber = 2,\n\tpages = {24003},\n\ttitle = {Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets},\n\turl_arxiv = {https://arxiv.org/abs/1601.06863},\n\turl_journal = {http://dx.doi.org/10.1209/0295-5075/114/24003},\n\tvolume = 114,\n\tyear = 2016,\n\tBdsk-Url-1 = {http://dx.doi.org/10.1209/0295-5075/114/24003}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The edges of torn plastic sheets and growing leaves often display hierarchical buckling patterns. We show that this complex morphology i) emerges even in zero strain configurations, and ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. We identify the key role of branch point (or ``monkey saddle'') singularities in generating complex wrinkling patterns in isometric immersions, and show how they arise naturally from minimizing the elastic energy.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"choi-sethuraman-venkataramani-ascalinglimitforthedegreedistributioninsublinearpreferentialattachmentschemes-2016\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/1402.4088\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'choi-sethuraman-venkataramani-ascalinglimitforthedegreedistributioninsublinearpreferentialattachmentschemes-2016', 'http://arxiv.org/abs/1402.4088', event);\">\n    A scaling limit for the degree distribution in sublinear preferential attachment schemes.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Choi, J.; Sethuraman, S.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Random Structures and Algorithms</i>, 48(4): 703-731.  2016.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/1402.4088\"\n     onclick=\"log_download('choi-sethuraman-venkataramani-ascalinglimitforthedegreedistributioninsublinearpreferentialattachmentschemes-2016', 'http://arxiv.org/abs/1402.4088', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A scaling limit for the degree distribution in sublinear preferential attachment schemes [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://onlinelibrary.wiley.com/doi/10.1002/rsa.20615/full\"\n     onclick=\"log_download('choi-sethuraman-venkataramani-ascalinglimitforthedegreedistributioninsublinearpreferentialattachmentschemes-2016', 'http://onlinelibrary.wiley.com/doi/10.1002/rsa.20615/full', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A scaling limit for the degree distribution in sublinear preferential attachment schemes [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1002/rsa.20615\"\n     onclick=\"log_download('choi-sethuraman-venkataramani-ascalinglimitforthedegreedistributioninsublinearpreferentialattachmentschemes-2016', 'http://doi.org/10.1002/rsa.20615', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/choi-sethuraman-venkataramani-ascalinglimitforthedegreedistributioninsublinearpreferentialattachmentschemes-2016\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('choi-sethuraman-venkataramani-ascalinglimitforthedegreedistributioninsublinearpreferentialattachmentschemes-2016')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{pref-attach,\n\tabstract = {We consider a general class of preferential attachment schemes evolving by a reinforcement rule with respect to certain sublinear weights. In these schemes, which grow a random network, the sequence of degree distributions is an object of interest which sheds light on the evolving structures. In this article, we use a fluid limit approach to prove a functional law of large numbers for the degree structure in this class, starting from a variety of initial conditions. The method appears robust and applies in particular to &#x60;non-tree&#x27; evolutions where cycles may develop in the network. A main part of the argument is to analyze an infinite system of coupled ODEs, corresponding to a rate formulation of the law of large numbers limit, in terms of $C_0$-semigroup/dynamical systems methods. These results also resolve a question in Chung, Handjani and Jungreis (2003). },\n\tauthor = {Choi, Jihyeok and Sethuraman, Sunder and Venkataramani, Shankar C.},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1002/rsa.20615},\n\tissn = {1098-2418},\n\tjournal = {Random Structures and Algorithms},\n\tkeywords = {pubs},\n\tnumber = {4},\n\tpages = {703-731},\n\ttitle = {A scaling limit for the degree distribution in sublinear preferential attachment schemes},\n\turl_arxiv = {http://arxiv.org/abs/1402.4088},\n\turl_journal = {http://onlinelibrary.wiley.com/doi/10.1002/rsa.20615/full},\n\tvolume = {48},\n\tyear = {2016},\n\tBdsk-Url-1 = {http://dx.doi.org/10.1002/rsa.20615}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We consider a general class of preferential attachment schemes evolving by a reinforcement rule with respect to certain sublinear weights. In these schemes, which grow a random network, the sequence of degree distributions is an object of interest which sheds light on the evolving structures. In this article, we use a fluid limit approach to prove a functional law of large numbers for the degree structure in this class, starting from a variety of initial conditions. The method appears robust and applies in particular to `non-tree' evolutions where cycles may develop in the network. A main part of the argument is to analyze an infinite system of coupled ODEs, corresponding to a rate formulation of the law of large numbers limit, in terms of $C_0$-semigroup/dynamical systems methods. These results also resolve a question in Chung, Handjani and Jungreis (2003). \n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2015\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2015')\"\n      onkeypress=\"toggleGroup('group_2015')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2015</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"restrepo-ramirez-venkataramani-anoilfatemodelforshallowwaters-2015\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://www.mdpi.com/2077-1312/3/4/1504\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'restrepo-ramirez-venkataramani-anoilfatemodelforshallowwaters-2015', 'http://www.mdpi.com/2077-1312/3/4/1504', event);\">\n    An Oil Fate Model for Shallow-Waters.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Restrepo, J. M.; Ramírez, J. M.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Journal of Marine Science and Engineering</i>, 3(4): 1504.  2015.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://www.mdpi.com/2077-1312/3/4/1504\"\n     onclick=\"log_download('restrepo-ramirez-venkataramani-anoilfatemodelforshallowwaters-2015', 'http://www.mdpi.com/2077-1312/3/4/1504', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"An Oil Fate Model for Shallow-Waters [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3390/jmse3041504\"\n     onclick=\"log_download('restrepo-ramirez-venkataramani-anoilfatemodelforshallowwaters-2015', 'http://doi.org/10.3390/jmse3041504', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/restrepo-ramirez-venkataramani-anoilfatemodelforshallowwaters-2015\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('restrepo-ramirez-venkataramani-anoilfatemodelforshallowwaters-2015')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{jmse3041504,\n\tabstract = {We introduce a model for the dynamics of oil in suspension, appropriate for shallow waters, including the nearshore environment. This model is capable of oil mass conservation and does so by evolving the oil on the sea surface as well as the oil in the subsurface. The shallower portion of the continental shelf poses compounding unique modeling challenges. Many of these relate to the complex nature of advection and dispersion of oil in an environment in which wind, waves, as well as currents all play a role, as does the complex bathymetry and the nearshore geography. In this study we present an overview of the model as well as derive the most fundamental of processes, namely, the shallow water advectiion and dispersion processes. With regard to this basic transport, we superate several fundamental challenges associated with creating a transport model for oil and other buoyant pollutants, capable of capturing the dynamics at the large spatio-temporal scales demanded by environmental and hazard mitigation studies. Some of the strategies are related to dimension reduction and upscaling, and leave discussion of these to companion papers. Here we focus on wave-filtering, ensemble and depth-averaging. Integral to the model is the proposal of an ocean dynamics model that is consistent with the transport. This ocean dynamics model is detailed here. The ocean/oil transport model is applied to a couple of physically-inspired oil-spill problems in demonstrate its specialized capabilities.},\n\tauthor = {Restrepo, Juan M. and Ram\\&#x27;{i}rez, Jorge M. and Venkataramani, Shankar},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.3390/jmse3041504},\n\tissn = {2077-1312},\n\tjournal = {Journal of Marine Science and Engineering},\n\tkeywords = {pubs},\n\tnumber = {4},\n\tpages = {1504},\n\ttitle = {An Oil Fate Model for Shallow-Waters},\n\turl_journal = {http://www.mdpi.com/2077-1312/3/4/1504},\n\tvolume = {3},\n\tyear = {2015},\n\tBdsk-Url-1 = {http://www.mdpi.com/2077-1312/3/4/1504},\n\tBdsk-Url-2 = {http://dx.doi.org/10.3390/jmse3041504}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We introduce a model for the dynamics of oil in suspension, appropriate for shallow waters, including the nearshore environment. This model is capable of oil mass conservation and does so by evolving the oil on the sea surface as well as the oil in the subsurface. The shallower portion of the continental shelf poses compounding unique modeling challenges. Many of these relate to the complex nature of advection and dispersion of oil in an environment in which wind, waves, as well as currents all play a role, as does the complex bathymetry and the nearshore geography. In this study we present an overview of the model as well as derive the most fundamental of processes, namely, the shallow water advectiion and dispersion processes. With regard to this basic transport, we superate several fundamental challenges associated with creating a transport model for oil and other buoyant pollutants, capable of capturing the dynamics at the large spatio-temporal scales demanded by environmental and hazard mitigation studies. Some of the strategies are related to dimension reduction and upscaling, and leave discussion of these to companion papers. Here we focus on wave-filtering, ensemble and depth-averaging. Integral to the model is the proposal of an ocean dynamics model that is consistent with the transport. This ocean dynamics model is detailed here. The ocean/oil transport model is applied to a couple of physically-inspired oil-spill problems in demonstrate its specialized capabilities.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2014\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2014')\"\n      onkeypress=\"toggleGroup('group_2014')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2014</span>\n      <span class=\"bibbase_group_count\">\n        \n        (5)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"restrepo-venkataramani-dawson-nearshorestickywaters-2014\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/1307.0588\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'restrepo-venkataramani-dawson-nearshorestickywaters-2014', 'http://arxiv.org/abs/1307.0588', event);\">\n    Nearshore sticky waters.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Restrepo, J. M.; <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>;  and Dawson, C.\n</span>\n\n  \n\n</span>\n\n  <i>Ocean Modelling</i>, 80(0): 49 - 58.  2014.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/1307.0588\"\n     onclick=\"log_download('restrepo-venkataramani-dawson-nearshorestickywaters-2014', 'http://arxiv.org/abs/1307.0588', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Nearshore sticky waters [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S1463500314000778\"\n     onclick=\"log_download('restrepo-venkataramani-dawson-nearshorestickywaters-2014', 'http://www.sciencedirect.com/science/article/pii/S1463500314000778', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Nearshore sticky waters [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/http://dx.doi.org/10.1016/j.ocemod.2014.06.003\"\n     onclick=\"log_download('restrepo-venkataramani-dawson-nearshorestickywaters-2014', 'http://doi.org/http://dx.doi.org/10.1016/j.ocemod.2014.06.003', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/restrepo-venkataramani-dawson-nearshorestickywaters-2014\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('restrepo-venkataramani-dawson-nearshorestickywaters-2014')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{sticky_waters,\n\tabstract = {Wind- and current-driven flotsam, oil spills, pollutants, and nutrients, approaching the nearshore will frequently appear to park just beyond the break zone, where waves break. Moreover, the portion of these tracers that beach will do so only after a long time. Explaining why these tracers park and at what rate they reach the shore has important implications on a variety of different nearshore environmental issues, including the determination of what subscale processes are essential in computer models for the simulation of pollutant transport in the nearshore. Using a simple model we provide an explanation for the underlying mechanism responsible for the parking of tracers, the role played by the bottom topography, and the non-uniform dispersion which leads, in some circumstances, to the eventual landing of all or a portion of the tracers. We refer to the parking phenomenon in this environment as nearshore sticky waters. },\n\tauthor = {Juan M. Restrepo and Shankar C. Venkataramani and Clint Dawson},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {http://dx.doi.org/10.1016/j.ocemod.2014.06.003},\n\tissn = {1463-5003},\n\tjournal = {Ocean Modelling},\n\tkeywords = {Waves and currents; pubs},\n\tnumber = {0},\n\tpages = {49 - 58},\n\ttitle = {Nearshore sticky waters},\n\turl_arxiv = {http://arxiv.org/abs/1307.0588},\n\turl_journal = {http://www.sciencedirect.com/science/article/pii/S1463500314000778},\n\tvolume = {80},\n\tyear = {2014},\n\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S1463500314000778},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1016/j.ocemod.2014.06.003}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Wind- and current-driven flotsam, oil spills, pollutants, and nutrients, approaching the nearshore will frequently appear to park just beyond the break zone, where waves break. Moreover, the portion of these tracers that beach will do so only after a long time. Explaining why these tracers park and at what rate they reach the shore has important implications on a variety of different nearshore environmental issues, including the determination of what subscale processes are essential in computer models for the simulation of pollutant transport in the nearshore. Using a simple model we provide an explanation for the underlying mechanism responsible for the parking of tracers, the role played by the bottom topography, and the non-uniform dispersion which leads, in some circumstances, to the eventual landing of all or a portion of the tracers. We refer to the parking phenomenon in this environment as nearshore sticky waters. \n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"gemmer-venkataramani-durfee-moloney-opticalbeamshapinganddiffractionfreewavesavariationalapproach-2014\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/1307.6289\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'gemmer-venkataramani-durfee-moloney-opticalbeamshapinganddiffractionfreewavesavariationalapproach-2014', 'http://arxiv.org/abs/1307.6289', event);\">\n    Optical beam shaping and diffraction free waves: A variational approach.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Gemmer, J. A.; <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>; Durfee, C. G.;  and Moloney, J. V.\n</span>\n\n  \n\n</span>\n\n  <i>Physica D: Nonlinear Phenomena</i>, 283(0): 15 - 28.  2014.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/1307.6289\"\n     onclick=\"log_download('gemmer-venkataramani-durfee-moloney-opticalbeamshapinganddiffractionfreewavesavariationalapproach-2014', 'http://arxiv.org/abs/1307.6289', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Optical beam shaping and diffraction free waves: A variational approach [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S0167278914001195\"\n     onclick=\"log_download('gemmer-venkataramani-durfee-moloney-opticalbeamshapinganddiffractionfreewavesavariationalapproach-2014', 'http://www.sciencedirect.com/science/article/pii/S0167278914001195', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Optical beam shaping and diffraction free waves: A variational approach [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/http://dx.doi.org/10.1016/j.physd.2014.06.003\"\n     onclick=\"log_download('gemmer-venkataramani-durfee-moloney-opticalbeamshapinganddiffractionfreewavesavariationalapproach-2014', 'http://doi.org/http://dx.doi.org/10.1016/j.physd.2014.06.003', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/gemmer-venkataramani-durfee-moloney-opticalbeamshapinganddiffractionfreewavesavariationalapproach-2014\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('gemmer-venkataramani-durfee-moloney-opticalbeamshapinganddiffractionfreewavesavariationalapproach-2014')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{GVDM2014,\n\tabstract = {We investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis. Within the Fresnel approximation, we show that this problem can be expressed in a variational form equivalent to the one arising in phase retrieval. Using the uncertainty principle we prove various rigorous lower bounds on the functional; these lower bounds estimate the $L^2$ error for the beam shaping problem in terms of the design parameters. We also use the method of stationary phase to construct a natural ansatz for a minimizer in the short wavelength limit. We illustrate the implications of our results by applying the method of stationary phase coupled with the Gerchberg--Saxton algorithm to beam shaping problems arising in the remote delivery of beams and pulses.},\n\tauthor = {John A. Gemmer and Shankar C. Venkataramani and Charles G. Durfee and Jerome V. Moloney},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {http://dx.doi.org/10.1016/j.physd.2014.06.003},\n\tissn = {0167-2789},\n\tjournal = {Physica D: Nonlinear Phenomena},\n\tkeywords = {Fresnel approximation; pubs},\n\tnumber = {0},\n\tpages = {15 - 28},\n\ttitle = {Optical beam shaping and diffraction free waves: A variational approach},\n\turl_arxiv = {http://arxiv.org/abs/1307.6289},\n\turl_journal = {http://www.sciencedirect.com/science/article/pii/S0167278914001195},\n\tvolume = {283},\n\tyear = {2014},\n\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0167278914001195},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1016/j.physd.2014.06.003}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis. Within the Fresnel approximation, we show that this problem can be expressed in a variational form equivalent to the one arising in phase retrieval. Using the uncertainty principle we prove various rigorous lower bounds on the functional; these lower bounds estimate the $L^2$ error for the beam shaping problem in terms of the design parameters. We also use the method of stationary phase to construct a natural ansatz for a minimizer in the short wavelength limit. We illustrate the implications of our results by applying the method of stationary phase coupled with the Gerchberg–Saxton algorithm to beam shaping problems arising in the remote delivery of beams and pulses.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zgkmen-beronvera-bogucki-chen-dawson-dewar-griffa-haus-etal-researchoverviewoftheconsortiumforadvancedresearchontransportofhydrocarbonintheenvironmentcarthe-2014\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://dx.doi.org/10.7901/2169-3358-2014.1.544\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'zgkmen-beronvera-bogucki-chen-dawson-dewar-griffa-haus-etal-researchoverviewoftheconsortiumforadvancedresearchontransportofhydrocarbonintheenvironmentcarthe-2014', 'http://dx.doi.org/10.7901/2169-3358-2014.1.544', event);\">\n    Research Overview of the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE).\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Özgökmen, T. M.; Beron-Vera, F. J.; Bogucki, D.; Chen, S. S.; Dawson, C.; Dewar, W.; Griffa, A.; Haus, B. K.; Haza, A. C.; Huntley, H.; Iskandarani, M.; Jacobs, G.; Jagers, B.; Kirwan, A. D.; Laxague, N.; Lipphardt, B.; MacMahan, J.; Mariano, A. J.; Olascoaga, J.; Novelli, G.; Poje, A. C.; Reniers, A. J. H. M.; Restrepo, J. M.; Rosenheim, B.; Ryan, E. H.; Smith, C.; Soloviev, A.; <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S.</a>; Zha, G.;  and Zhu, P.\n</span>\n\n  \n\n</span>\n\n  <i>International Oil Spill Conference Proceedings</i>, 2014(1): 544–560. 2014/11/08 2014.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://dx.doi.org/10.7901/2169-3358-2014.1.544\"\n     onclick=\"log_download('zgkmen-beronvera-bogucki-chen-dawson-dewar-griffa-haus-etal-researchoverviewoftheconsortiumforadvancedresearchontransportofhydrocarbonintheenvironmentcarthe-2014', 'http://dx.doi.org/10.7901/2169-3358-2014.1.544', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Research Overview of the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE) [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.7901/2169-3358-2014.1.544\"\n     onclick=\"log_download('zgkmen-beronvera-bogucki-chen-dawson-dewar-griffa-haus-etal-researchoverviewoftheconsortiumforadvancedresearchontransportofhydrocarbonintheenvironmentcarthe-2014', 'http://doi.org/10.7901/2169-3358-2014.1.544', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zgkmen-beronvera-bogucki-chen-dawson-dewar-griffa-haus-etal-researchoverviewoftheconsortiumforadvancedresearchontransportofhydrocarbonintheenvironmentcarthe-2014\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zgkmen-beronvera-bogucki-chen-dawson-dewar-griffa-haus-etal-researchoverviewoftheconsortiumforadvancedresearchontransportofhydrocarbonintheenvironmentcarthe-2014')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{CARTHE2014,\n\tabstract = {ABSTRACT CARTHE (http://carthe.org/) is a Gulf of Mexico Research Initiative (GoMRI) consortium established through a competitive peer-reviewed selection process. CARTHE comprises 26 principal investigators from 14 universities and research institutions distributed across four Gulf of Mexico states and other four states. It fuses into one group investigators with unique scientific and technical knowledge and extensive publications related to oil fate/transport processes, oceanic and atmospheric turbulence, air-sea interactions, tropical cyclones and winter storms, and coastal and nearshore modeling and observations. Our primary goal is to accurately predict the fate of hydrocarbons released into the environment. Achieving this goal is particularly challenging since petroleum releases into the environment interact with natural processes across six orders of magnitude of time and space scales. We are developing a multi-scale modeling tool by incorporating state-of-the-art hydrophysical models, each applicable for a restricted range of scales, into a single, interconnected modeling system to predict the physical dispersal of hydrocarbons across scales ranging from the microscale at the wellhead to oceanic and atmospheric mesoscales. CARTHE is also conducting novel in-situ observations and laboratory experiments specifically designed for quantifying submesoscale dispersion as well as for both model validation and parameterization. Finally, we are providing a robust set of uncertainty metrics and analysis tools to assess model performance and quantify predictive uncertainty.},\n\tannote = {doi: 10.7901/2169-3358-2014.1.544},\n\tauthor = {{\\&quot;O}zg{\\&quot;o}kmen, Tamay M. and Beron-Vera, Francisco J. and Bogucki, Darek and Chen, Shuyi S. and Dawson, Clint and Dewar, William and Griffa, Annalisa and Haus, Brian K. and Haza, Angelique C. and Huntley, Helga and Iskandarani, Mohamed and Jacobs, Gregg and Jagers, Bert and Kirwan, A. D. and Laxague, Nathan and Lipphardt, Bruce and MacMahan, Jamie and Mariano, Arthur J. and Olascoaga, Josefina and Novelli, Guillaume and Poje, Andrew C. and Reniers, A. J. H. M. and Restrepo, Juan M. and Rosenheim, Brad and Ryan, Edward H. and Smith, Conor and Soloviev, Alexander and Venkataramani, Shankar and Zha, Ge-Cheng and Zhu, Ping},\n\tbooktitle = {International Oil Spill Conference Proceedings},\n\tda = {2014/05/01},\n\tdate = {2014/05/01},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.7901/2169-3358-2014.1.544},\n\tisbn = {2169-3366},\n\tjournal = {International Oil Spill Conference Proceedings},\n\tjournal1 = {International Oil Spill Conference Proceedings},\n\tkeywords = {pubs},\n\tm3 = {doi: 10.7901/2169-3358-2014.1.544},\n\tmonth = {2014/11/08},\n\tn2 = {ABSTRACT CARTHE (http://carthe.org/) is a Gulf of Mexico Research Initiative (GoMRI) consortium established through a competitive peer-reviewed selection process. CARTHE comprises 26 principal investigators from 14 universities and research institutions distributed across four Gulf of Mexico states and other four states. It fuses into one group investigators with unique scientific and technical knowledge and extensive publications related to oil fate/transport processes, oceanic and atmospheric turbulence, air-sea interactions, tropical cyclones and winter storms, and coastal and nearshore modeling and observations. Our primary goal is to accurately predict the fate of hydrocarbons released into the environment. Achieving this goal is particularly challenging since petroleum releases into the environment interact with natural processes across six orders of magnitude of time and space scales. We are developing a multi-scale modeling tool by incorporating state-of-the-art hydrophysical models, each applicable for a restricted range of scales, into a single, interconnected modeling system to predict the physical dispersal of hydrocarbons across scales ranging from the microscale at the wellhead to oceanic and atmospheric mesoscales. CARTHE is also conducting novel in-situ observations and laboratory experiments specifically designed for quantifying submesoscale dispersion as well as for both model validation and parameterization. Finally, we are providing a robust set of uncertainty metrics and analysis tools to assess model performance and quantify predictive uncertainty.},\n\tnumber = {1},\n\tpages = {544--560},\n\tpublisher = {American Petroleum Institute},\n\ttitle = {Research Overview of the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE)},\n\tty = {JOUR},\n\turl_journal = {http://dx.doi.org/10.7901/2169-3358-2014.1.544},\n\tvolume = {2014},\n\tyear = {2014},\n\tyear1 = {2014},\n\tBdsk-Url-1 = {http://dx.doi.org/10.7901/2169-3358-2014.1.544}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  ABSTRACT CARTHE (http://carthe.org/) is a Gulf of Mexico Research Initiative (GoMRI) consortium established through a competitive peer-reviewed selection process. CARTHE comprises 26 principal investigators from 14 universities and research institutions distributed across four Gulf of Mexico states and other four states. It fuses into one group investigators with unique scientific and technical knowledge and extensive publications related to oil fate/transport processes, oceanic and atmospheric turbulence, air-sea interactions, tropical cyclones and winter storms, and coastal and nearshore modeling and observations. Our primary goal is to accurately predict the fate of hydrocarbons released into the environment. Achieving this goal is particularly challenging since petroleum releases into the environment interact with natural processes across six orders of magnitude of time and space scales. We are developing a multi-scale modeling tool by incorporating state-of-the-art hydrophysical models, each applicable for a restricted range of scales, into a single, interconnected modeling system to predict the physical dispersal of hydrocarbons across scales ranging from the microscale at the wellhead to oceanic and atmospheric mesoscales. CARTHE is also conducting novel in-situ observations and laboratory experiments specifically designed for quantifying submesoscale dispersion as well as for both model validation and parameterization. Finally, we are providing a robust set of uncertainty metrics and analysis tools to assess model performance and quantify predictive uncertainty.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"kent-venkataramani-sharpinterfacesintwodimensionalfreeboundaryproblemsinterfacecalculationviamatchedconformalmaps-2014\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/1405.6965\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'kent-venkataramani-sharpinterfacesintwodimensionalfreeboundaryproblemsinterfacecalculationviamatchedconformalmaps-2014', 'http://arxiv.org/abs/1405.6965', event);\">\n    Sharp interfaces in two-dimensional free boundary problems: Interface calculation via matched conformal maps.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Kent, S.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Phys. Rev. E</i>, 90: 012407. Jul 2014.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/1405.6965\"\n     onclick=\"log_download('kent-venkataramani-sharpinterfacesintwodimensionalfreeboundaryproblemsinterfacecalculationviamatchedconformalmaps-2014', 'http://arxiv.org/abs/1405.6965', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Sharp interfaces in two-dimensional free boundary problems: Interface calculation via matched conformal maps [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevE.90.012407\"\n     onclick=\"log_download('kent-venkataramani-sharpinterfacesintwodimensionalfreeboundaryproblemsinterfacecalculationviamatchedconformalmaps-2014', 'http://link.aps.org/doi/10.1103/PhysRevE.90.012407', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Sharp interfaces in two-dimensional free boundary problems: Interface calculation via matched conformal maps [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1103/PhysRevE.90.012407\"\n     onclick=\"log_download('kent-venkataramani-sharpinterfacesintwodimensionalfreeboundaryproblemsinterfacecalculationviamatchedconformalmaps-2014', 'http://doi.org/10.1103/PhysRevE.90.012407', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/kent-venkataramani-sharpinterfacesintwodimensionalfreeboundaryproblemsinterfacecalculationviamatchedconformalmaps-2014\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('kent-venkataramani-sharpinterfacesintwodimensionalfreeboundaryproblemsinterfacecalculationviamatchedconformalmaps-2014')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{PRE_interface,\n\tabstract = {We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity, and surface tension. The free boundary in our system develops sharp corners or singularities in certain parameter regimes, and this is an impediment to using existing &#x60;&#x60;single-scale&#x27;&#x27; numerical conformal mapping methods. The difficulty is due to the phenomenon of crowding, i.e., the tendency of nodes in the preimage plane to concentrate near the sharp regions of the boundary, leaving the smooth regions of the boundary poorly resolved. A natural idea is to exploit the scale separation between the sharp regions and smooth regions to solve for each region separately and then stitch the solutions together. However, this is not straightforward as conformal maps are rigid &#x60;&#x60;global&#x27;&#x27; objects, and it is not obvious how one would patch two conformal maps together to obtain a new conformal map. We develop a &#x60;&#x60;multiscale&#x27;&#x27; (i.e., adaptive) conformal mapping method that allows us to carry out this program of stitching conformal maps on different scales together. We successfully apply our method to the electromechanical model problem.},\n\tauthor = {Kent, Stuart and Venkataramani, Shankar C.},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1103/PhysRevE.90.012407},\n\tissue = {1},\n\tjournal = {Phys. Rev. E},\n\tkeywords = {pubs},\n\tmonth = {Jul},\n\tnumpages = {15},\n\tpages = {012407},\n\tpublisher = {American Physical Society},\n\ttitle = {Sharp interfaces in two-dimensional free boundary problems: Interface calculation via matched conformal maps},\n\turl_arxiv = {http://arxiv.org/abs/1405.6965},\n\turl_journal = {http://link.aps.org/doi/10.1103/PhysRevE.90.012407},\n\tvolume = {90},\n\tyear = {2014},\n\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.90.012407},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.90.012407}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity, and surface tension. The free boundary in our system develops sharp corners or singularities in certain parameter regimes, and this is an impediment to using existing ``single-scale'' numerical conformal mapping methods. The difficulty is due to the phenomenon of crowding, i.e., the tendency of nodes in the preimage plane to concentrate near the sharp regions of the boundary, leaving the smooth regions of the boundary poorly resolved. A natural idea is to exploit the scale separation between the sharp regions and smooth regions to solve for each region separately and then stitch the solutions together. However, this is not straightforward as conformal maps are rigid ``global'' objects, and it is not obvious how one would patch two conformal maps together to obtain a new conformal map. We develop a ``multiscale'' (i.e., adaptive) conformal mapping method that allows us to carry out this program of stitching conformal maps on different scales together. We successfully apply our method to the electromechanical model problem.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"restrepo-venkataramani-comeau-flaschka-definingatrendfortimeseriesusingtheintrinsictimescaledecomposition-2014\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/1404.3827\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'restrepo-venkataramani-comeau-flaschka-definingatrendfortimeseriesusingtheintrinsictimescaledecomposition-2014', 'http://arxiv.org/abs/1404.3827', event);\">\n    Defining a trend for time series using the intrinsic time-scale decomposition.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Restrepo, J. M; <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S.</a>; Comeau, D.;  and Flaschka, H.\n</span>\n\n  \n\n</span>\n\n  <i>New Journal of Physics</i>, 16(8): 085004.  2014.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/1404.3827\"\n     onclick=\"log_download('restrepo-venkataramani-comeau-flaschka-definingatrendfortimeseriesusingtheintrinsictimescaledecomposition-2014', 'http://arxiv.org/abs/1404.3827', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Defining a trend for time series using the intrinsic time-scale decomposition [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://stacks.iop.org/1367-2630/16/i=8/a=085004\"\n     onclick=\"log_download('restrepo-venkataramani-comeau-flaschka-definingatrendfortimeseriesusingtheintrinsictimescaledecomposition-2014', 'http://stacks.iop.org/1367-2630/16/i=8/a=085004', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Defining a trend for time series using the intrinsic time-scale decomposition [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/restrepo-venkataramani-comeau-flaschka-definingatrendfortimeseriesusingtheintrinsictimescaledecomposition-2014\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('restrepo-venkataramani-comeau-flaschka-definingatrendfortimeseriesusingtheintrinsictimescaledecomposition-2014')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{itd_paper,\n\tabstract = {We propose criteria that define a trend for time series with inherent multi-scale features. We call this trend the tendency of a time series. The tendency is defined empirically by a set of criteria and captures the large-scale temporal variability of the original signal as well as the most frequent events in its histogram. Among other properties, the tendency has a variance no larger than that of the original signal; the histogram of the difference between the original signal and the tendency is as symmetric as possible; and with reduced complexity, the tendency captures essential features of the signal. To find the tendency we first use the intrinsic time-scale decomposition (ITD) of the signal, introduced in 2007 by Frei and Osorio, to produce a set of candidate tendencies. We then apply the criteria to each of the candidates to single out the one that best agrees with them. While the criteria for the tendency are independent of the signal decomposition scheme, it is found that the ITD is a simple and stable methodology, well suited for multi-scale signals. The ITD is a relatively new decomposition and little is known about its outcomes. In this study we take the first steps towards a probabilistic model of the ITD analysis of random time series. This analysis yields details concerning the universality and scaling properties of the components of the decomposition.},\n\tauthor = {Juan M Restrepo and Shankar Venkataramani and Darin Comeau and Hermann Flaschka},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tjournal = {New Journal of Physics},\n\tkeywords = {pubs},\n\tnumber = {8},\n\tpages = {085004},\n\ttitle = {Defining a trend for time series using the intrinsic time-scale decomposition},\n\turl_arxiv = {http://arxiv.org/abs/1404.3827},\n\turl_journal = {http://stacks.iop.org/1367-2630/16/i=8/a=085004},\n\tvolume = {16},\n\tyear = {2014},\n\tBdsk-Url-1 = {http://stacks.iop.org/1367-2630/16/i=8/a=085004}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We propose criteria that define a trend for time series with inherent multi-scale features. We call this trend the tendency of a time series. The tendency is defined empirically by a set of criteria and captures the large-scale temporal variability of the original signal as well as the most frequent events in its histogram. Among other properties, the tendency has a variance no larger than that of the original signal; the histogram of the difference between the original signal and the tendency is as symmetric as possible; and with reduced complexity, the tendency captures essential features of the signal. To find the tendency we first use the intrinsic time-scale decomposition (ITD) of the signal, introduced in 2007 by Frei and Osorio, to produce a set of candidate tendencies. We then apply the criteria to each of the candidates to single out the one that best agrees with them. While the criteria for the tendency are independent of the signal decomposition scheme, it is found that the ITD is a simple and stable methodology, well suited for multi-scale signals. The ITD is a relatively new decomposition and little is known about its outcomes. In this study we take the first steps towards a probabilistic model of the ITD analysis of random time series. This analysis yields details concerning the universality and scaling properties of the components of the decomposition.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2013\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2013')\"\n      onkeypress=\"toggleGroup('group_2013')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2013</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"gemmer-venkataramani-shapetransitionsinhyperbolicnoneuclideanplates-2013\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/1209.0031\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'gemmer-venkataramani-shapetransitionsinhyperbolicnoneuclideanplates-2013', 'http://arxiv.org/abs/1209.0031', event);\">\n    Shape transitions in hyperbolic non-Euclidean plates.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Gemmer, J. A.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Soft Matter</i>, 9(34): 8151–8161.  2013.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/1209.0031\"\n     onclick=\"log_download('gemmer-venkataramani-shapetransitionsinhyperbolicnoneuclideanplates-2013', 'http://arxiv.org/abs/1209.0031', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Shape transitions in hyperbolic non-Euclidean plates [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://pubs.rsc.org/en/Content/ArticleLanding/2013/SM/c3sm50479d#!divAbstract\"\n     onclick=\"log_download('gemmer-venkataramani-shapetransitionsinhyperbolicnoneuclideanplates-2013', 'http://pubs.rsc.org/en/Content/ArticleLanding/2013/SM/c3sm50479d#!divAbstract', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Shape transitions in hyperbolic non-Euclidean plates [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/gemmer-venkataramani-shapetransitionsinhyperbolicnoneuclideanplates-2013\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>2 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('gemmer-venkataramani-shapetransitionsinhyperbolicnoneuclideanplates-2013')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{GV2013,\n\tabstract = {A non-Euclidean plate is a thin elastic object whose intrinsic geometry is not flat and hence has residual stresses arising from being embedded in three dimensional space. Recently, there has been interest in using localized swelling to induce residual stresses that shape flat objects into desired three dimensional structures. A fundamental question is whether we can use the mathematical theory of non-Euclidean plates to deduce the three dimensional configuration of the swelling sheet given the exact knowledge of the imposed geometry. We present and summarize the results of recent mathematical studies on non-Euclidean plates with imposed constant negative Gaussian curvature in both annular and disc geometries. We show in the F{\\&quot;o}ppl--von K{\\&#x27;a}rm{\\&#x27;a}n approximation to the elastic energy there are only two types of global minimizers -- flat and saddle shaped deformations -- with localized regions of stretching near the boundary of the domain. We also show that there exist n-wave local minimizers that closely resemble experimental observations and have additional regions of stretching near lines of inflection. Furthermore, in the Kirchhoff approximation to the elastic energy, we show that there exists exact isometric immersions with periodic profiles. The number of waves in these configurations is set by the condition that the bending energy remains finite and grows approximately exponentially with the radius of the annulus. For large radii, these shape are energetically favorable over saddle shapes and could explain why wavy shapes are selected in crochet models of the hyperbolic plane. The predicted morphologies however differ from what is observed in experiments on hydrogel disks highlighting the need for further theoretical studies.},\n\tauthor = {Gemmer, John A. and Venkataramani, Shankar C.},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tjournal = {Soft Matter},\n\tkeywords = {pubs},\n\tnumber = {34},\n\tpages = {8151--8161},\n\tpublisher = {Royal Society of Chemistry},\n\ttitle = {Shape transitions in hyperbolic non-Euclidean plates},\n\turl_arxiv = {http://arxiv.org/abs/1209.0031},\n\turl_journal = {http://pubs.rsc.org/en/Content/ArticleLanding/2013/SM/c3sm50479d#!divAbstract},\n\tvolume = {9},\n\tyear = {2013},\n\tBdsk-Url-1 = {http://dx.doi.org/10.1039/C3SM50479D}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  A non-Euclidean plate is a thin elastic object whose intrinsic geometry is not flat and hence has residual stresses arising from being embedded in three dimensional space. Recently, there has been interest in using localized swelling to induce residual stresses that shape flat objects into desired three dimensional structures. A fundamental question is whether we can use the mathematical theory of non-Euclidean plates to deduce the three dimensional configuration of the swelling sheet given the exact knowledge of the imposed geometry. We present and summarize the results of recent mathematical studies on non-Euclidean plates with imposed constant negative Gaussian curvature in both annular and disc geometries. We show in the Föppl–von Kármán approximation to the elastic energy there are only two types of global minimizers – flat and saddle shaped deformations – with localized regions of stretching near the boundary of the domain. We also show that there exist n-wave local minimizers that closely resemble experimental observations and have additional regions of stretching near lines of inflection. Furthermore, in the Kirchhoff approximation to the elastic energy, we show that there exists exact isometric immersions with periodic profiles. The number of waves in these configurations is set by the condition that the bending energy remains finite and grows approximately exponentially with the radius of the annulus. For large radii, these shape are energetically favorable over saddle shapes and could explain why wavy shapes are selected in crochet models of the hyperbolic plane. The predicted morphologies however differ from what is observed in experiments on hydrogel disks highlighting the need for further theoretical studies.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"graf-moloney-venkataramani-asymptoticanalysisofweaklynonlinearbesselgaubeams-2013\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S0167278912002308\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'graf-moloney-venkataramani-asymptoticanalysisofweaklynonlinearbesselgaubeams-2013', 'http://www.sciencedirect.com/science/article/pii/S0167278912002308', event);\">\n    Asymptotic analysis of weakly nonlinear Bessel-Gauß   beams.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Graf, T.; Moloney, J.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Physica D: Nonlinear Phenomena</i>, 243(1): 32 - 44.  2013.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S0167278912002308\"\n     onclick=\"log_download('graf-moloney-venkataramani-asymptoticanalysisofweaklynonlinearbesselgaubeams-2013', 'http://www.sciencedirect.com/science/article/pii/S0167278912002308', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Asymptotic analysis of weakly nonlinear Bessel-Gauß   beams [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/http://dx.doi.org/10.1016/j.physd.2012.09.004\"\n     onclick=\"log_download('graf-moloney-venkataramani-asymptoticanalysisofweaklynonlinearbesselgaubeams-2013', 'http://doi.org/http://dx.doi.org/10.1016/j.physd.2012.09.004', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/graf-moloney-venkataramani-asymptoticanalysisofweaklynonlinearbesselgaubeams-2013\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('graf-moloney-venkataramani-asymptoticanalysisofweaklynonlinearbesselgaubeams-2013')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{GMV2013,\n\tabstract = {In this paper we investigate the propagation of conical waves in nonlinear media. In particular, we are interested in the effects resulting from applying a Gaussian apodization to an ideal nondiffracting wave. First, we present a multiple scales approach to derive amplitude equations for weakly nonlinear conical waves from a governing equation of cubic nonlinear Schr{\\&quot;o}dinger type. From these equations we obtain asymptotic solutions for the linear and the weakly nonlinear problem for which we state several uniform estimates that describe the deviation from the ideal nondiffracting solution. Moreover, we show numerical simulations based on an implementation of our amplitude equations to support and illustrate our analytical results.},\n\tauthor = {Tobias Graf and Jerome Moloney and Shankar Venkataramani},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {http://dx.doi.org/10.1016/j.physd.2012.09.004},\n\tissn = {0167-2789},\n\tjournal = {Physica D: Nonlinear Phenomena},\n\tkeywords = {Uniform estimates; pubs},\n\tnumber = {1},\n\tpages = {32 - 44},\n\ttitle = {Asymptotic analysis of weakly nonlinear {Bessel}-{Gau}\\ss { } beams},\n\turl_journal = {http://www.sciencedirect.com/science/article/pii/S0167278912002308},\n\tvolume = {243},\n\tyear = {2013},\n\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0167278912002308},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1016/j.physd.2012.09.004}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper we investigate the propagation of conical waves in nonlinear media. In particular, we are interested in the effects resulting from applying a Gaussian apodization to an ideal nondiffracting wave. First, we present a multiple scales approach to derive amplitude equations for weakly nonlinear conical waves from a governing equation of cubic nonlinear Schrödinger type. From these equations we obtain asymptotic solutions for the linear and the weakly nonlinear problem for which we state several uniform estimates that describe the deviation from the ideal nondiffracting solution. Moreover, we show numerical simulations based on an implementation of our amplitude equations to support and illustrate our analytical results.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2012\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2012')\"\n      onkeypress=\"toggleGroup('group_2012')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2012</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"graf-christodoulides-mills-moloney-venkataramani-wright-propagationofgaussianapodizedparaxialbeamsthroughfirstorderopticalsystemsviacomplexcoordinatetransformsandraytransfermatrices-2012\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://josaa.osa.org/abstract.cfm?URI=josaa-29-9-1860\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'graf-christodoulides-mills-moloney-venkataramani-wright-propagationofgaussianapodizedparaxialbeamsthroughfirstorderopticalsystemsviacomplexcoordinatetransformsandraytransfermatrices-2012', 'http://josaa.osa.org/abstract.cfm?URI=josaa-29-9-1860', event);\">\n    Propagation of Gaussian-apodized paraxial beams through first-order optical systems via complex coordinate transforms and ray transfer matrices.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Graf, T.; Christodoulides, D. N.; Mills, M. S.; Moloney, J. V.; <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>;  and Wright, E. M.\n</span>\n\n  \n\n</span>\n\n  <i>J. Opt. Soc. Am. A</i>, 29(9): 1860–1869. Sep 2012.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://josaa.osa.org/abstract.cfm?URI=josaa-29-9-1860\"\n     onclick=\"log_download('graf-christodoulides-mills-moloney-venkataramani-wright-propagationofgaussianapodizedparaxialbeamsthroughfirstorderopticalsystemsviacomplexcoordinatetransformsandraytransfermatrices-2012', 'http://josaa.osa.org/abstract.cfm?URI=josaa-29-9-1860', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Propagation of Gaussian-apodized paraxial beams through first-order optical systems via complex coordinate transforms and ray transfer matrices [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1364/JOSAA.29.001860\"\n     onclick=\"log_download('graf-christodoulides-mills-moloney-venkataramani-wright-propagationofgaussianapodizedparaxialbeamsthroughfirstorderopticalsystemsviacomplexcoordinatetransformsandraytransfermatrices-2012', 'http://doi.org/10.1364/JOSAA.29.001860', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/graf-christodoulides-mills-moloney-venkataramani-wright-propagationofgaussianapodizedparaxialbeamsthroughfirstorderopticalsystemsviacomplexcoordinatetransformsandraytransfermatrices-2012\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('graf-christodoulides-mills-moloney-venkataramani-wright-propagationofgaussianapodizedparaxialbeamsthroughfirstorderopticalsystemsviacomplexcoordinatetransformsandraytransfermatrices-2012')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{Graf2012,\n\tabstract = {We investigate the linear propagation of Gaussian-apodized solutions to the paraxial wave equation in free-space and first-order optical systems. In particular, we present complex coordinate transformations that yield a very general and efficient method to apply a Gaussian apodization (possibly with initial phase curvature) to a solution of the paraxial wave equation. Moreover, we show how this method can be extended from free space to describe propagation behavior through nonimaging first-order optical systems by combining our coordinate transform approach with ray transfer matrix methods. Our framework includes several classes of interesting beams that are important in applications as special cases. Among these are, for example, the Bessel\\&amp;\\#x2013;Gauss and the Airy\\&amp;\\#x2013;Gauss beams, which are of strong interest to researchers and practitioners in various fields.},\n\tauthor = {T. Graf and D. N. Christodoulides and M. S. Mills and J. V. Moloney and S. C. Venkataramani and E. M. Wright},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1364/JOSAA.29.001860},\n\tjournal = {J. Opt. Soc. Am. A},\n\tkeywords = {Mathematical methods in physics; Matrix methods in paraxial optics; Lasers and laser optics; Diffraction theory; Dispersion; Nonimaging optical systems; pubs},\n\tmonth = {Sep},\n\tnumber = {9},\n\tpages = {1860--1869},\n\tpublisher = {OSA},\n\ttitle = {Propagation of Gaussian-apodized paraxial beams through first-order optical systems via complex coordinate transforms and ray transfer matrices},\n\turl_journal = {http://josaa.osa.org/abstract.cfm?URI=josaa-29-9-1860},\n\tvolume = {29},\n\tyear = {2012},\n\tBdsk-Url-1 = {http://josaa.osa.org/abstract.cfm?URI=josaa-29-9-1860},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1364/JOSAA.29.001860}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We investigate the linear propagation of Gaussian-apodized solutions to the paraxial wave equation in free-space and first-order optical systems. In particular, we present complex coordinate transformations that yield a very general and efficient method to apply a Gaussian apodization (possibly with initial phase curvature) to a solution of the paraxial wave equation. Moreover, we show how this method can be extended from free space to describe propagation behavior through nonimaging first-order optical systems by combining our coordinate transform approach with ray transfer matrix methods. Our framework includes several classes of interesting beams that are important in applications as special cases. Among these are, for example, the Bessel&#x2013;Gauss and the Airy&#x2013;Gauss beams, which are of strong interest to researchers and practitioners in various fields.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"gemmer-venkataramani-defectsandboundarylayersinnoneuclideanplates-2012\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/1203.4329\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'gemmer-venkataramani-defectsandboundarylayersinnoneuclideanplates-2012', 'http://arxiv.org/abs/1203.4329', event);\">\n    Defects and boundary layers in non-Euclidean plates.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Gemmer, J. A.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Nonlinearity</i>, 25(12): 3553–3581.  2012.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/1203.4329\"\n     onclick=\"log_download('gemmer-venkataramani-defectsandboundarylayersinnoneuclideanplates-2012', 'http://arxiv.org/abs/1203.4329', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Defects and boundary layers in non-Euclidean plates [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://dx.doi.org/10.1088/0951-7715/25/12/3553\"\n     onclick=\"log_download('gemmer-venkataramani-defectsandboundarylayersinnoneuclideanplates-2012', 'http://dx.doi.org/10.1088/0951-7715/25/12/3553', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Defects and boundary layers in non-Euclidean plates [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1088/0951-7715/25/12/3553\"\n     onclick=\"log_download('gemmer-venkataramani-defectsandboundarylayersinnoneuclideanplates-2012', 'http://doi.org/10.1088/0951-7715/25/12/3553', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/gemmer-venkataramani-defectsandboundarylayersinnoneuclideanplates-2012\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('gemmer-venkataramani-defectsandboundarylayersinnoneuclideanplates-2012')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{GV2012,\n\tabstract = {We investigate the behaviour of non-Euclidean plates with constant negative Gaussian curvature using the F{\\&quot;o}ppl--von K{\\&#x27;a}rm{\\&#x27;a}n reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. In particular we show that are only two types of global minimizers---deformations that remain flat and saddle shaped deformations with isolated regions of stretching near the edge of the annulus. We also show that there exist local minimizers with a periodic profile that have additional boundary layers near their lines of inflection. These additional boundary layers are a new phenomenon in thin elastic sheets and are necessary to regularize jump discontinuities in the azimuthal curvature across lines of inflection. We rigorously derive scaling laws for the width of these boundary layers as a function of the thickness of the sheet.},\n\tauthor = {Gemmer, John A. and Venkataramani, Shankar C.},\n\tcoden = {NONLE5},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1088/0951-7715/25/12/3553},\n\tfjournal = {Nonlinearity},\n\tissn = {0951-7715},\n\tjournal = {Nonlinearity},\n\tkeywords = {pubs},\n\tmrclass = {74K20 (35Q74)},\n\tmrnumber = {2997707},\n\tnumber = {12},\n\tpages = {3553--3581},\n\ttitle = {Defects and boundary layers in non-{E}uclidean plates},\n\turl_arxiv = {http://arxiv.org/abs/1203.4329},\n\turl_journal = {http://dx.doi.org/10.1088/0951-7715/25/12/3553},\n\tvolume = {25},\n\tyear = {2012},\n\tBdsk-Url-1 = {http://dx.doi.org/10.1088/0951-7715/25/12/3553},\n\tBdsk-Url-2 = {http://stacks.iop.org/0951-7715/25/i=12/a=3553}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We investigate the behaviour of non-Euclidean plates with constant negative Gaussian curvature using the Föppl–von Kármán reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. In particular we show that are only two types of global minimizers—deformations that remain flat and saddle shaped deformations with isolated regions of stretching near the edge of the annulus. We also show that there exist local minimizers with a periodic profile that have additional boundary layers near their lines of inflection. These additional boundary layers are a new phenomenon in thin elastic sheets and are necessary to regularize jump discontinuities in the azimuthal curvature across lines of inflection. We rigorously derive scaling laws for the width of these boundary layers as a function of the thickness of the sheet.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2011\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2011')\"\n      onkeypress=\"toggleGroup('group_2011')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2011</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"klein-venkataramani-sharon-experimentalstudyofshapetransitionsandenergyscalinginthinnoneuclideanplates-2011\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevLett.106.118303\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'klein-venkataramani-sharon-experimentalstudyofshapetransitionsandenergyscalinginthinnoneuclideanplates-2011', 'http://link.aps.org/doi/10.1103/PhysRevLett.106.118303', event);\">\n    Experimental Study of Shape Transitions and Energy Scaling in Thin Non-Euclidean Plates.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Klein, Y.; <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S.</a>;  and Sharon, E.\n</span>\n\n  \n\n</span>\n\n  <i>Phys. Rev. Lett.</i>, 106: 118303. Mar 2011.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevLett.106.118303\"\n     onclick=\"log_download('klein-venkataramani-sharon-experimentalstudyofshapetransitionsandenergyscalinginthinnoneuclideanplates-2011', 'http://link.aps.org/doi/10.1103/PhysRevLett.106.118303', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Experimental Study of Shape Transitions and Energy Scaling in Thin Non-Euclidean Plates [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1103/PhysRevLett.106.118303\"\n     onclick=\"log_download('klein-venkataramani-sharon-experimentalstudyofshapetransitionsandenergyscalinginthinnoneuclideanplates-2011', 'http://doi.org/10.1103/PhysRevLett.106.118303', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/klein-venkataramani-sharon-experimentalstudyofshapetransitionsandenergyscalinginthinnoneuclideanplates-2011\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('klein-venkataramani-sharon-experimentalstudyofshapetransitionsandenergyscalinginthinnoneuclideanplates-2011')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{KVS2011,\n\tabstract = {\nWe present the first quantitative measurements of shape and energy variation in non-Euclidean plates. Using environmentally responsive gel, we construct non-Euclidean disks of constant imposed Gaussian curvature, $K_{tar}$. We vary the disks&#x27; thickness $t_0$ and measure the dependence of configurations, surface curvature, and energy content on $t_0$. For $K_{tar} &lt; 0$, configurations are of a single wavy mode and undergo a set of bifurcations that leads to their refinement with decreasing thickness. This leads to sharp increase in the amount of surface bending as $t_0 \\to 0$, and to a slow decay of both bending and stretching energies. Both vary like $t_0^2$, compared with $t_0^3$ of the bending energy in disks with $K_{tar} &gt; 0$.},\n\tauthor = {Klein, Yael and Venkataramani, Shankar and Sharon, Eran},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1103/PhysRevLett.106.118303},\n\tissue = {11},\n\tjournal = {Phys. Rev. Lett.},\n\tkeywords = {pubs},\n\tmonth = {Mar},\n\tnumpages = {4},\n\tpages = {118303},\n\tpublisher = {American Physical Society},\n\ttitle = {Experimental Study of Shape Transitions and Energy Scaling in Thin Non-Euclidean Plates},\n\turl_journal = {http://link.aps.org/doi/10.1103/PhysRevLett.106.118303},\n\tvolume = {106},\n\tyear = {2011},\n\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.106.118303},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.106.118303}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We present the first quantitative measurements of shape and energy variation in non-Euclidean plates. Using environmentally responsive gel, we construct non-Euclidean disks of constant imposed Gaussian curvature, $K_{tar}$. We vary the disks' thickness $t_0$ and measure the dependence of configurations, surface curvature, and energy content on $t_0$. For $K_{tar} < 0$, configurations are of a single wavy mode and undergo a set of bifurcations that leads to their refinement with decreasing thickness. This leads to sharp increase in the amount of surface bending as $t_0 \\to 0$, and to a slow decay of both bending and stretching energies. Both vary like $t_0^2$, compared with $t_0^3$ of the bending energy in disks with $K_{tar} > 0$.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"gemmer-venkataramani-shapeselectioninnoneuclideanplates-2011\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/1005.4442\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'gemmer-venkataramani-shapeselectioninnoneuclideanplates-2011', 'http://arxiv.org/abs/1005.4442', event);\">\n    Shape selection in non-Euclidean plates.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Gemmer, J. A.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Physica D: Nonlinear Phenomena</i>, 240(19): 1536 - 1552.  2011.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/1005.4442\"\n     onclick=\"log_download('gemmer-venkataramani-shapeselectioninnoneuclideanplates-2011', 'http://arxiv.org/abs/1005.4442', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Shape selection in non-Euclidean plates [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S0167278911001825\"\n     onclick=\"log_download('gemmer-venkataramani-shapeselectioninnoneuclideanplates-2011', 'http://www.sciencedirect.com/science/article/pii/S0167278911001825', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Shape selection in non-Euclidean plates [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/http://dx.doi.org/10.1016/j.physd.2011.07.002\"\n     onclick=\"log_download('gemmer-venkataramani-shapeselectioninnoneuclideanplates-2011', 'http://doi.org/http://dx.doi.org/10.1016/j.physd.2011.07.002', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/gemmer-venkataramani-shapeselectioninnoneuclideanplates-2011\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('gemmer-venkataramani-shapeselectioninnoneuclideanplates-2011')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{GV2011,\n\tabstract = {We investigate isometric immersions of disks with constant negative curvature into $R^3$, and the minimizers for the bending energy, i.e.   the $L^2$ norm of the principal curvatures over the class of $W^{2,2}$ isometric immersions. We show the existence of smooth immersions of arbitrarily large geodesic balls in $H^2$ into $R^3$. In elucidating the connection between these immersions and the non-existence/singularity results of Hilbert and Amsler, we obtain a lower bound for the $L^\\infty$ norm of the principal curvatures for such smooth isometric immersions. We also construct piecewise smooth isometric immersions that have a periodic profile, are globally $W^{2,2}$ and numerically have lower bending energy than their smooth counterparts. The number of periods in these configurations is set by the condition that the principal curvatures of the surface remain finite and grow approximately exponentially with the radius of the disk. We discuss the implications of our results on recent experiments on the mechanics of non-Euclidean plates.\n},\n\tauthor = {Gemmer, John A. and Venkataramani, Shankar C.},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {http://dx.doi.org/10.1016/j.physd.2011.07.002},\n\tissn = {0167-2789},\n\tjournal = {Physica D: Nonlinear Phenomena},\n\tkeywords = {Morphogenesis in soft tissue; pubs},\n\tnumber = {19},\n\tpages = {1536 - 1552},\n\ttitle = {Shape selection in non-Euclidean plates},\n\turl_arxiv = {http://arxiv.org/abs/1005.4442},\n\turl_journal = {http://www.sciencedirect.com/science/article/pii/S0167278911001825},\n\tvolume = {240},\n\tyear = {2011},\n\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0167278911001825},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1016/j.physd.2011.07.002}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We investigate isometric immersions of disks with constant negative curvature into $R^3$, and the minimizers for the bending energy, i.e. the $L^2$ norm of the principal curvatures over the class of $W^{2,2}$ isometric immersions. We show the existence of smooth immersions of arbitrarily large geodesic balls in $H^2$ into $R^3$. In elucidating the connection between these immersions and the non-existence/singularity results of Hilbert and Amsler, we obtain a lower bound for the $L^∞$ norm of the principal curvatures for such smooth isometric immersions. We also construct piecewise smooth isometric immersions that have a periodic profile, are globally $W^{2,2}$ and numerically have lower bending energy than their smooth counterparts. The number of periods in these configurations is set by the condition that the principal curvatures of the surface remain finite and grow approximately exponentially with the radius of the disk. We discuss the implications of our results on recent experiments on the mechanics of non-Euclidean plates. \n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2009\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2009')\"\n      onkeypress=\"toggleGroup('group_2009')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2009</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"ercolani-venkataramani-avariationaltheoryforpointdefectsinpatterns-2009\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/0706.2917\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'ercolani-venkataramani-avariationaltheoryforpointdefectsinpatterns-2009', 'http://arxiv.org/abs/0706.2917', event);\">\n    A variational theory for point defects in patterns.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Ercolani, N. M.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>J. Nonlinear Sci.</i>, 19(3): 267–300.  2009.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/0706.2917\"\n     onclick=\"log_download('ercolani-venkataramani-avariationaltheoryforpointdefectsinpatterns-2009', 'http://arxiv.org/abs/0706.2917', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A variational theory for point defects in patterns [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://dx.doi.org/10.1007/s00332-008-9035-9\"\n     onclick=\"log_download('ercolani-venkataramani-avariationaltheoryforpointdefectsinpatterns-2009', 'http://dx.doi.org/10.1007/s00332-008-9035-9', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A variational theory for point defects in patterns [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s00332-008-9035-9\"\n     onclick=\"log_download('ercolani-venkataramani-avariationaltheoryforpointdefectsinpatterns-2009', 'http://doi.org/10.1007/s00332-008-9035-9', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/ercolani-venkataramani-avariationaltheoryforpointdefectsinpatterns-2009\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('ercolani-venkataramani-avariationaltheoryforpointdefectsinpatterns-2009')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{patt_defects,\n\tabstract = {\nWe derive a rigorous scaling law for minimizers in a natural version of the regularized Cross--Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen in experimental studies of the corresponding physical systems and in numerical simulations of the microscopic equations that describe these systems.},\n\tauthor = {Ercolani, N. M. and Venkataramani, S. C.},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1007/s00332-008-9035-9},\n\tfjournal = {Journal of Nonlinear Science},\n\tissn = {0938-8974},\n\tjournal = {J. Nonlinear Sci.},\n\tkeywords = {pubs},\n\tmrclass = {35K25 (35A15 35K58 74R05)},\n\tmrnumber = {2511257 (2010d:35149)},\n\tmrreviewer = {Daniela Giachetti},\n\tnumber = {3},\n\tpages = {267--300},\n\ttitle = {A variational theory for point defects in patterns},\n\turl_arxiv = {http://arxiv.org/abs/0706.2917},\n\turl_journal = {http://dx.doi.org/10.1007/s00332-008-9035-9},\n\tvolume = {19},\n\tyear = {2009},\n\tBdsk-Url-1 = {http://dx.doi.org/10.1007/s00332-008-9035-9}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross–Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen in experimental studies of the corresponding physical systems and in numerical simulations of the microscopic equations that describe these systems.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2004\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2004')\"\n      onkeypress=\"toggleGroup('group_2004')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2004</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"berkenbusch-claus-dunn-kadanoff-nicewicz-venkataramani-discretechargesonatwodimensionalconductor-2004\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/cond-mat/0310257\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'berkenbusch-claus-dunn-kadanoff-nicewicz-venkataramani-discretechargesonatwodimensionalconductor-2004', 'http://arxiv.org/abs/cond-mat/0310257', event);\">\n    Discrete charges on a two dimensional conductor.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Berkenbusch, M. K.; Claus, I.; Dunn, C.; Kadanoff, L. P.; Nicewicz, M.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>J. Statist. Phys.</i>, 116(5-6): 1301–1358.  2004.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/cond-mat/0310257\"\n     onclick=\"log_download('berkenbusch-claus-dunn-kadanoff-nicewicz-venkataramani-discretechargesonatwodimensionalconductor-2004', 'http://arxiv.org/abs/cond-mat/0310257', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Discrete charges on a two dimensional conductor [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://dx.doi.org/10.1023/B:JOSS.0000041741.27244.ac\"\n     onclick=\"log_download('berkenbusch-claus-dunn-kadanoff-nicewicz-venkataramani-discretechargesonatwodimensionalconductor-2004', 'http://dx.doi.org/10.1023/B:JOSS.0000041741.27244.ac', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Discrete charges on a two dimensional conductor [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1023/B:JOSS.0000041741.27244.ac\"\n     onclick=\"log_download('berkenbusch-claus-dunn-kadanoff-nicewicz-venkataramani-discretechargesonatwodimensionalconductor-2004', 'http://doi.org/10.1023/B:JOSS.0000041741.27244.ac', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/berkenbusch-claus-dunn-kadanoff-nicewicz-venkataramani-discretechargesonatwodimensionalconductor-2004\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('berkenbusch-claus-dunn-kadanoff-nicewicz-venkataramani-discretechargesonatwodimensionalconductor-2004')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{MR2096037,\n\tabstract = {We investigate the electrostatic equilibria of N discrete charges of size 1/N on a two dimensional conductor (domain). We study the distribution of the charges on symmetric domains including the ellipse, the hypotrochoid and various regular polygons, with an emphasis on understanding the distributions of the charges, as the shape of the underlying conductor becomes singular. We find that there are two regimes of behavior, a symmetric regime for smooth conductors, and a symmetry broken regime for &#x60;&#x60;singular&#x27;&#x27; domains. For smooth conductors, the locations of the charges can be determined, to within O(logN/N2{\\^a}€¾{\\^a}€¾{\\^a}€¾{\\^a}€¾{\\^a}€¾{\\^a}€¾{\\^a}€¾{\\^a}€¾{\\^a}€¾{\\^a}ˆ{\\v s}) by an integral equation due to Pommerenke [ Math. Ann., 179: 212--218, (1969)]. We present a derivation of a related (but different) integral equation, which has the same solutions. We also solve the equation to obtain (asymptotic) solutions which show universal behavior in the distribution of the charges in conductors with somewhat smooth cusps. Conductors with sharp cusps and singularities show qualitatively different behavior, where the symmetry of the problem is broken, and the distribution of the discrete charges does not respect the symmetry of the underlying domain. We investigate the symmetry breaking both theoretically, and numerically, and find good agreement between our theory and the numerics. We also find that the universality in the distribution of the charges near the cusps persists in the symmetry broken regime, although this distribution is very different from the one given by the integral equation.},\n\tauthor = {Berkenbusch, Marko K. and Claus, Isabelle and Dunn, Catherine and Kadanoff, Leo P. and Nicewicz, Maciej and Venkataramani, Shankar C.},\n\tcoden = {JSTPSB},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1023/B:JOSS.0000041741.27244.ac},\n\tfjournal = {Journal of Statistical Physics},\n\tissn = {0022-4715},\n\tjournal = {J. Statist. Phys.},\n\tkeywords = {pubs},\n\tmrclass = {78A30 (37J40 37N20 78A35)},\n\tmrnumber = {2096037 (2006d:78009)},\n\tmrreviewer = {T. Erber},\n\tnumber = {5-6},\n\tpages = {1301--1358},\n\ttitle = {Discrete charges on a two dimensional conductor},\n\turl_arxiv = {http://arxiv.org/abs/cond-mat/0310257},\n\turl_journal = {http://dx.doi.org/10.1023/B:JOSS.0000041741.27244.ac},\n\tvolume = {116},\n\tyear = {2004},\n\tBdsk-Url-1 = {http://dx.doi.org/10.1023/B:JOSS.0000041741.27244.ac}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We investigate the electrostatic equilibria of N discrete charges of size 1/N on a two dimensional conductor (domain). We study the distribution of the charges on symmetric domains including the ellipse, the hypotrochoid and various regular polygons, with an emphasis on understanding the distributions of the charges, as the shape of the underlying conductor becomes singular. We find that there are two regimes of behavior, a symmetric regime for smooth conductors, and a symmetry broken regime for ``singular'' domains. For smooth conductors, the locations of the charges can be determined, to within O(logN/N2‾‾‾‾‾‾‾‾‾∠̌s) by an integral equation due to Pommerenke [ Math. Ann., 179: 212–218, (1969)]. We present a derivation of a related (but different) integral equation, which has the same solutions. We also solve the equation to obtain (asymptotic) solutions which show universal behavior in the distribution of the charges in conductors with somewhat smooth cusps. Conductors with sharp cusps and singularities show qualitatively different behavior, where the symmetry of the problem is broken, and the distribution of the discrete charges does not respect the symmetry of the underlying domain. We investigate the symmetry breaking both theoretically, and numerically, and find good agreement between our theory and the numerics. We also find that the universality in the distribution of the charges near the cusps persists in the symmetry broken regime, although this distribution is very different from the one given by the integral equation.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"venkataramani-lowerboundsfortheenergyinacrumpledelasticsheetaminimalridge-2004\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/math/0210012\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'venkataramani-lowerboundsfortheenergyinacrumpledelasticsheetaminimalridge-2004', 'http://arxiv.org/abs/math/0210012', event);\">\n    Lower bounds for the energy in a crumpled elastic sheet—a minimal ridge.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Nonlinearity</i>, 17(1): 301–312.  2004.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/math/0210012\"\n     onclick=\"log_download('venkataramani-lowerboundsfortheenergyinacrumpledelasticsheetaminimalridge-2004', 'http://arxiv.org/abs/math/0210012', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Lower bounds for the energy in a crumpled elastic sheet—a minimal ridge [link]\"\n       title=\" arxiv\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> arxiv</span></a>\n  &nbsp;\n  \n  <a href=\"http://dx.doi.org/10.1088/0951-7715/17/1/017\"\n     onclick=\"log_download('venkataramani-lowerboundsfortheenergyinacrumpledelasticsheetaminimalridge-2004', 'http://dx.doi.org/10.1088/0951-7715/17/1/017', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Lower bounds for the energy in a crumpled elastic sheet—a minimal ridge [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1088/0951-7715/17/1/017\"\n     onclick=\"log_download('venkataramani-lowerboundsfortheenergyinacrumpledelasticsheetaminimalridge-2004', 'http://doi.org/10.1088/0951-7715/17/1/017', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-lowerboundsfortheenergyinacrumpledelasticsheetaminimalridge-2004\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-lowerboundsfortheenergyinacrumpledelasticsheetaminimalridge-2004')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{MR2023444,\n\tabstract = {We study the linearized F{\\&quot;o}ppl--von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle 2 {\\^I}$\\pm$. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness, {\\&quot;I}ƒ, and the bending angle. We show that the minimum energy scales as {\\&quot;I}ƒ5/3 {\\^I}$\\pm$7/3. This scaling is in sharp contrast with previously obtained results for the linearized theory of thin sheets with isotropic compression boundary conditions, where the energy scales as {\\&quot;I}ƒ.},\n\tauthor = {Venkataramani, Shankar C.},\n\tcoden = {NONLE5},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1088/0951-7715/17/1/017},\n\tfjournal = {Nonlinearity},\n\tissn = {0951-7715},\n\tjournal = {Nonlinearity},\n\tkeywords = {pubs},\n\tmrclass = {74K15 (46N10 47J20 49J40 74G65)},\n\tmrnumber = {2023444 (2005b:74077)},\n\tmrreviewer = {Yi-Chung Shu},\n\tnumber = {1},\n\tpages = {301--312},\n\ttitle = {Lower bounds for the energy in a crumpled elastic sheet---a minimal ridge},\n\turl_arxiv = {http://arxiv.org/abs/math/0210012},\n\turl_journal = {http://dx.doi.org/10.1088/0951-7715/17/1/017},\n\tvolume = {17},\n\tyear = {2004},\n\tBdsk-Url-1 = {http://dx.doi.org/10.1088/0951-7715/17/1/017}}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We study the linearized Föppl–von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle 2 Î$±$. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness, σ, and the bending angle. We show that the minimum energy scales as σ5/3 Î$±$7/3. This scaling is in sharp contrast with previously obtained results for the linearized theory of thin sheets with isotropic compression boundary conditions, where the energy scales as σ.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2002\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2002')\"\n      onkeypress=\"toggleGroup('group_2002')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2002</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"gopinathan-witten-venkataramani-trappingofvibrationalenergyincrumpledsheets-2002\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevE.65.036613\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'gopinathan-witten-venkataramani-trappingofvibrationalenergyincrumpledsheets-2002', 'http://link.aps.org/doi/10.1103/PhysRevE.65.036613', event);\">\n    Trapping of vibrational energy in crumpled sheets.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Gopinathan, A.; Witten, T. A.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Phys. Rev. E</i>, 65: 036613. Feb 2002.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevE.65.036613\"\n     onclick=\"log_download('gopinathan-witten-venkataramani-trappingofvibrationalenergyincrumpledsheets-2002', 'http://link.aps.org/doi/10.1103/PhysRevE.65.036613', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Trapping of vibrational energy in crumpled sheets [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1103/PhysRevE.65.036613\"\n     onclick=\"log_download('gopinathan-witten-venkataramani-trappingofvibrationalenergyincrumpledsheets-2002', 'http://doi.org/10.1103/PhysRevE.65.036613', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/gopinathan-witten-venkataramani-trappingofvibrationalenergyincrumpledsheets-2002\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('gopinathan-witten-venkataramani-trappingofvibrationalenergyincrumpledsheets-2002')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{PhysRevE.65.036613,\n\tauthor = {Gopinathan, Ajay and Witten, T. A. and Venkataramani, S. C.},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1103/PhysRevE.65.036613},\n\tissue = {3},\n\tjournal = {Phys. Rev. E},\n\tkeywords = {pubs},\n\tmonth = {Feb},\n\tnumpages = {11},\n\tpages = {036613},\n\tpublisher = {American Physical Society},\n\ttitle = {Trapping of vibrational energy in crumpled sheets},\n\turl_journal = {http://link.aps.org/doi/10.1103/PhysRevE.65.036613},\n\tvolume = {65},\n\tyear = {2002},\n\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.65.036613},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.65.036613}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2001\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2001')\"\n      onkeypress=\"toggleGroup('group_2001')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2001</span>\n      <span class=\"bibbase_group_count\">\n        \n        (4)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"ott-venkataramani-continuumcoupledmapsamodelforpatternsinvibratedsand-2001\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://dx.doi.org/10.1142/9789812811516_0014\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'ott-venkataramani-continuumcoupledmapsamodelforpatternsinvibratedsand-2001', 'http://dx.doi.org/10.1142/9789812811516_0014', event);\">\n    Continuum Coupled Maps: A model for patterns in vibrated sand.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Ott, E.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  In <i>Proceedings of the 5th Experimental Chaos Conference</i>, pages 143-153. World Scientific, 2016/11/23 2001.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://dx.doi.org/10.1142/9789812811516_0014\"\n     onclick=\"log_download('ott-venkataramani-continuumcoupledmapsamodelforpatternsinvibratedsand-2001', 'http://dx.doi.org/10.1142/9789812811516_0014', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Continuum Coupled Maps: A model for patterns in vibrated sand [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/doi:10.1142/9789812811516_0014\"\n     onclick=\"log_download('ott-venkataramani-continuumcoupledmapsamodelforpatternsinvibratedsand-2001', 'http://doi.org/doi:10.1142/9789812811516_0014', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/ott-venkataramani-continuumcoupledmapsamodelforpatternsinvibratedsand-2001\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('ott-venkataramani-continuumcoupledmapsamodelforpatternsinvibratedsand-2001')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@incollection{OTT:2001aa,\n\tannote = {doi:10.1142/9789812811516{\\_}0014},\n\tauthor = {Ott, Edward and Venkataramani, Shankar C.},\n\tbooktitle = {Proceedings of the 5th Experimental Chaos Conference},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2021-05-23 18:55:49 -0700},\n\tdoi = {doi:10.1142/9789812811516{\\_}0014},\n\tisbn = {978-981-02-4561-0},\n\tkeywords = {pubs},\n\tm1 = {0},\n\tm3 = {doi:10.1142/9789812811516{\\_}0014},\n\tmonth = {2016/11/23},\n\tpages = {143-153},\n\tpublisher = {World Scientific},\n\ttitle = {Continuum Coupled Maps: A model for patterns in vibrated sand},\n\tty = {CHAP},\n\turl = {http://dx.doi.org/10.1142/9789812811516_0014},\n\tyear = {2001},\n\tyear1 = {2001/04/01},\n\tBdsk-Url-1 = {http://dx.doi.org/10.1142/9789812811516_0014},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1142/9789812811516%7B%5C_%7D0014}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"kim-vaishnav-ott-venkataramani-losert-frontpropagationofspatiotemporalchaos-2001\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevE.64.016215\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'kim-vaishnav-ott-venkataramani-losert-frontpropagationofspatiotemporalchaos-2001', 'http://link.aps.org/doi/10.1103/PhysRevE.64.016215', event);\">\n    Front propagation of spatiotemporal chaos.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Kim, J. W.; Vaishnav, J. Y.; Ott, E.; <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>;  and Losert, W.\n</span>\n\n  \n\n</span>\n\n  <i>Phys. Rev. E</i>, 64: 016215. Jun 2001.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevE.64.016215\"\n     onclick=\"log_download('kim-vaishnav-ott-venkataramani-losert-frontpropagationofspatiotemporalchaos-2001', 'http://link.aps.org/doi/10.1103/PhysRevE.64.016215', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Front propagation of spatiotemporal chaos [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1103/PhysRevE.64.016215\"\n     onclick=\"log_download('kim-vaishnav-ott-venkataramani-losert-frontpropagationofspatiotemporalchaos-2001', 'http://doi.org/10.1103/PhysRevE.64.016215', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/kim-vaishnav-ott-venkataramani-losert-frontpropagationofspatiotemporalchaos-2001\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('kim-vaishnav-ott-venkataramani-losert-frontpropagationofspatiotemporalchaos-2001')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{PhysRevE.64.016215,\n\tauthor = {Kim, J. W. and Vaishnav, J. Y. and Ott, E. and Venkataramani, S. C. and Losert, W.},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1103/PhysRevE.64.016215},\n\tissue = {1},\n\tjournal = {Phys. Rev. E},\n\tkeywords = {pubs},\n\tmonth = {Jun},\n\tnumpages = {5},\n\tpages = {016215},\n\tpublisher = {American Physical Society},\n\ttitle = {Front propagation of spatiotemporal chaos},\n\turl_journal = {http://link.aps.org/doi/10.1103/PhysRevE.64.016215},\n\tvolume = {64},\n\tyear = {2001},\n\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.64.016215},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.64.016215}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"didonna-witten-venkataramani-kramer-singularitiesstructuresandscalingindeformedmdimensionalelasticmanifolds-2001\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevE.65.016603\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'didonna-witten-venkataramani-kramer-singularitiesstructuresandscalingindeformedmdimensionalelasticmanifolds-2001', 'http://link.aps.org/doi/10.1103/PhysRevE.65.016603', event);\">\n    Singularities, structures, and scaling in deformed m-dimensional elastic manifolds.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  DiDonna, B. A.; Witten, T. A.; <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>;  and Kramer, E. M.\n</span>\n\n  \n\n</span>\n\n  <i>Phys. Rev. E</i>, 65: 016603. Dec 2001.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevE.65.016603\"\n     onclick=\"log_download('didonna-witten-venkataramani-kramer-singularitiesstructuresandscalingindeformedmdimensionalelasticmanifolds-2001', 'http://link.aps.org/doi/10.1103/PhysRevE.65.016603', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Singularities, structures, and scaling in deformed m-dimensional elastic manifolds [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1103/PhysRevE.65.016603\"\n     onclick=\"log_download('didonna-witten-venkataramani-kramer-singularitiesstructuresandscalingindeformedmdimensionalelasticmanifolds-2001', 'http://doi.org/10.1103/PhysRevE.65.016603', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/didonna-witten-venkataramani-kramer-singularitiesstructuresandscalingindeformedmdimensionalelasticmanifolds-2001\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('didonna-witten-venkataramani-kramer-singularitiesstructuresandscalingindeformedmdimensionalelasticmanifolds-2001')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{PhysRevE.65.016603,\n\tauthor = {DiDonna, B. A. and Witten, T. A. and Venkataramani, S. C. and Kramer, E. M.},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1103/PhysRevE.65.016603},\n\tissue = {1},\n\tjournal = {Phys. Rev. E},\n\tkeywords = {pubs},\n\tmonth = {Dec},\n\tnumpages = {25},\n\tpages = {016603},\n\tpublisher = {American Physical Society},\n\ttitle = {Singularities, structures, and scaling in deformed m-dimensional elastic manifolds},\n\turl_journal = {http://link.aps.org/doi/10.1103/PhysRevE.65.016603},\n\tvolume = {65},\n\tyear = {2001},\n\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.65.016603},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.65.016603}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"venkataramani-ott-patternselectioninextendedperiodicallyforcedsystemsacontinuumcoupledmapapproach-2001\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevE.63.046202\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'venkataramani-ott-patternselectioninextendedperiodicallyforcedsystemsacontinuumcoupledmapapproach-2001', 'http://link.aps.org/doi/10.1103/PhysRevE.63.046202', event);\">\n    Pattern selection in extended periodically forced systems: A continuum coupled map approach.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>;  and Ott, E.\n</span>\n\n  \n\n</span>\n\n  <i>Phys. Rev. E</i>, 63: 046202. Mar 2001.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevE.63.046202\"\n     onclick=\"log_download('venkataramani-ott-patternselectioninextendedperiodicallyforcedsystemsacontinuumcoupledmapapproach-2001', 'http://link.aps.org/doi/10.1103/PhysRevE.63.046202', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Pattern selection in extended periodically forced systems: A continuum coupled map approach [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1103/PhysRevE.63.046202\"\n     onclick=\"log_download('venkataramani-ott-patternselectioninextendedperiodicallyforcedsystemsacontinuumcoupledmapapproach-2001', 'http://doi.org/10.1103/PhysRevE.63.046202', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-ott-patternselectioninextendedperiodicallyforcedsystemsacontinuumcoupledmapapproach-2001\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-ott-patternselectioninextendedperiodicallyforcedsystemsacontinuumcoupledmapapproach-2001')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{PhysRevE.63.046202,\n\tauthor = {Venkataramani, Shankar C. and Ott, Edward},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1103/PhysRevE.63.046202},\n\tissue = {4},\n\tjournal = {Phys. Rev. E},\n\tkeywords = {pubs},\n\tmonth = {Mar},\n\tnumpages = {27},\n\tpages = {046202},\n\tpublisher = {American Physical Society},\n\ttitle = {Pattern selection in extended periodically forced systems: A continuum coupled map approach},\n\turl_journal = {http://link.aps.org/doi/10.1103/PhysRevE.63.046202},\n\tvolume = {63},\n\tyear = {2001},\n\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.63.046202},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.63.046202}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2000\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2000')\"\n      onkeypress=\"toggleGroup('group_2000')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2000</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"venkataramani-witten-kramer-geroch-limitationsonthesmoothconfinementofanunstretchablemanifold-2000\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://dx.doi.org/10.1063/1.533394\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'venkataramani-witten-kramer-geroch-limitationsonthesmoothconfinementofanunstretchablemanifold-2000', 'http://dx.doi.org/10.1063/1.533394', event);\">\n    Limitations on the smooth confinement of an unstretchable manifold.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>; Witten, T. A.; Kramer, E. M.;  and Geroch, R. P.\n</span>\n\n  \n\n</span>\n\n  <i>J. Math. Phys.</i>, 41(7): 5107–5128.  2000.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://dx.doi.org/10.1063/1.533394\"\n     onclick=\"log_download('venkataramani-witten-kramer-geroch-limitationsonthesmoothconfinementofanunstretchablemanifold-2000', 'http://dx.doi.org/10.1063/1.533394', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Limitations on the smooth confinement of an unstretchable manifold [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1063/1.533394\"\n     onclick=\"log_download('venkataramani-witten-kramer-geroch-limitationsonthesmoothconfinementofanunstretchablemanifold-2000', 'http://doi.org/10.1063/1.533394', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-witten-kramer-geroch-limitationsonthesmoothconfinementofanunstretchablemanifold-2000\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-witten-kramer-geroch-limitationsonthesmoothconfinementofanunstretchablemanifold-2000')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{MR1765831,\n\tauthor = {Venkataramani, S. C. and Witten, T. A. and Kramer, E. M. and Geroch, R. P.},\n\tcoden = {JMAPAQ},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1063/1.533394},\n\tfjournal = {Journal of Mathematical Physics},\n\tissn = {0022-2488},\n\tjournal = {J. Math. Phys.},\n\tkeywords = {pubs},\n\tmrclass = {53A07 (53C42)},\n\tmrnumber = {1765831 (2001j:53008)},\n\tmrreviewer = {Anders Linn{\\&#x27;e}r},\n\tnumber = {7},\n\tpages = {5107--5128},\n\ttitle = {Limitations on the smooth confinement of an unstretchable manifold},\n\turl_journal = {http://dx.doi.org/10.1063/1.533394},\n\tvolume = {41},\n\tyear = {2000},\n\tBdsk-Url-1 = {http://dx.doi.org/10.1063/1.533394}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1999\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1999')\"\n      onkeypress=\"toggleGroup('group_1999')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1999</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"povinelli-coppersmith-kadanoff-nagel-venkataramani-noisestabilizationofselforganizedmemories-1999\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevE.59.4970\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'povinelli-coppersmith-kadanoff-nagel-venkataramani-noisestabilizationofselforganizedmemories-1999', 'http://link.aps.org/doi/10.1103/PhysRevE.59.4970', event);\">\n    Noise stabilization of self-organized memories.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Povinelli, M. L.; Coppersmith, S. N.; Kadanoff, L. P.; Nagel, S. R.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Phys. Rev. E</i>, 59: 4970–4982. May 1999.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevE.59.4970\"\n     onclick=\"log_download('povinelli-coppersmith-kadanoff-nagel-venkataramani-noisestabilizationofselforganizedmemories-1999', 'http://link.aps.org/doi/10.1103/PhysRevE.59.4970', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Noise stabilization of self-organized memories [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1103/PhysRevE.59.4970\"\n     onclick=\"log_download('povinelli-coppersmith-kadanoff-nagel-venkataramani-noisestabilizationofselforganizedmemories-1999', 'http://doi.org/10.1103/PhysRevE.59.4970', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/povinelli-coppersmith-kadanoff-nagel-venkataramani-noisestabilizationofselforganizedmemories-1999\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('povinelli-coppersmith-kadanoff-nagel-venkataramani-noisestabilizationofselforganizedmemories-1999')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{PhysRevE.59.4970,\n\tauthor = {Povinelli, M. L. and Coppersmith, S. N. and Kadanoff, L. P. and Nagel, S. R. and Venkataramani, S. C.},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1103/PhysRevE.59.4970},\n\tissue = {5},\n\tjournal = {Phys. Rev. E},\n\tkeywords = {pubs},\n\tmonth = {May},\n\tnumpages = {0},\n\tpages = {4970--4982},\n\tpublisher = {American Physical Society},\n\ttitle = {Noise stabilization of self-organized memories},\n\turl_journal = {http://link.aps.org/doi/10.1103/PhysRevE.59.4970},\n\tvolume = {59},\n\tyear = {1999},\n\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.59.4970},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.59.4970}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"brenner-constantin-kadanoff-schenkel-venkataramani-diffusionattractionandcollapse-1999\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://dx.doi.org/10.1088/0951-7715/12/4/320\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'brenner-constantin-kadanoff-schenkel-venkataramani-diffusionattractionandcollapse-1999', 'http://dx.doi.org/10.1088/0951-7715/12/4/320', event);\">\n    Diffusion, attraction and collapse.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Brenner, M. P.; Constantin, P.; Kadanoff, L. P.; Schenkel, A.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Nonlinearity</i>, 12(4): 1071–1098.  1999.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://dx.doi.org/10.1088/0951-7715/12/4/320\"\n     onclick=\"log_download('brenner-constantin-kadanoff-schenkel-venkataramani-diffusionattractionandcollapse-1999', 'http://dx.doi.org/10.1088/0951-7715/12/4/320', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Diffusion, attraction and collapse [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1088/0951-7715/12/4/320\"\n     onclick=\"log_download('brenner-constantin-kadanoff-schenkel-venkataramani-diffusionattractionandcollapse-1999', 'http://doi.org/10.1088/0951-7715/12/4/320', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/brenner-constantin-kadanoff-schenkel-venkataramani-diffusionattractionandcollapse-1999\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('brenner-constantin-kadanoff-schenkel-venkataramani-diffusionattractionandcollapse-1999')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{MR1709861,\n\tauthor = {Brenner, Michael P. and Constantin, Peter and Kadanoff, Leo P. and Schenkel, Alain and Venkataramani, Shankar C.},\n\tcoden = {NONLE5},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1088/0951-7715/12/4/320},\n\tfjournal = {Nonlinearity},\n\tissn = {0951-7715},\n\tjournal = {Nonlinearity},\n\tkeywords = {pubs},\n\tmrclass = {76N99 (35K55 92C17)},\n\tmrnumber = {1709861 (2001d:76107)},\n\tnumber = {4},\n\tpages = {1071--1098},\n\ttitle = {Diffusion, attraction and collapse},\n\turl_journal = {http://dx.doi.org/10.1088/0951-7715/12/4/320},\n\tvolume = {12},\n\tyear = {1999},\n\tBdsk-Url-1 = {http://dx.doi.org/10.1088/0951-7715/12/4/320}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1998\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1998')\"\n      onkeypress=\"toggleGroup('group_1998')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1998</span>\n      <span class=\"bibbase_group_count\">\n        \n        (3)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"venkataramani-conescreasesandcrumpledsheets-1998\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Cones, creases and crumpled sheets.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S.</a>\n</span>\n\n  \n\n</span>\n\n   1998.<!-- NOTE FROM BIBBASE: This entry has an invalid bibtex entry type: periodical. Therefore, we don't know how to render it properly. Please consider fixing this. -->\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-conescreasesandcrumpledsheets-1998\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-conescreasesandcrumpledsheets-1998')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@periodical{venkataramani1998cones,\n\tauthor = {Venkataramani, Shankar},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tjournal = {Physics world},\n\tkeywords = {pubs},\n\tnumber = {7},\n\ttitle = {Cones, creases and crumpled sheets},\n\tvolume = {11},\n\tyear = {1998}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"venkataramani-ott-spatiotemporalbifurcationphenomenawithtemporalperioddoublingpatternsinvibratedsand-1998\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevLett.80.3495\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'venkataramani-ott-spatiotemporalbifurcationphenomenawithtemporalperioddoublingpatternsinvibratedsand-1998', 'http://link.aps.org/doi/10.1103/PhysRevLett.80.3495', event);\">\n    Spatiotemporal Bifurcation Phenomena with Temporal Period Doubling: Patterns in Vibrated Sand.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>;  and Ott, E.\n</span>\n\n  \n\n</span>\n\n  <i>Phys. Rev. Lett.</i>, 80: 3495–3498. Apr 1998.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevLett.80.3495\"\n     onclick=\"log_download('venkataramani-ott-spatiotemporalbifurcationphenomenawithtemporalperioddoublingpatternsinvibratedsand-1998', 'http://link.aps.org/doi/10.1103/PhysRevLett.80.3495', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Spatiotemporal Bifurcation Phenomena with Temporal Period Doubling: Patterns in Vibrated Sand [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1103/PhysRevLett.80.3495\"\n     onclick=\"log_download('venkataramani-ott-spatiotemporalbifurcationphenomenawithtemporalperioddoublingpatternsinvibratedsand-1998', 'http://doi.org/10.1103/PhysRevLett.80.3495', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-ott-spatiotemporalbifurcationphenomenawithtemporalperioddoublingpatternsinvibratedsand-1998\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-ott-spatiotemporalbifurcationphenomenawithtemporalperioddoublingpatternsinvibratedsand-1998')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{PhysRevLett.80.3495,\n\tauthor = {Venkataramani, Shankar C. and Ott, Edward},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1103/PhysRevLett.80.3495},\n\tissue = {16},\n\tjournal = {Phys. Rev. Lett.},\n\tkeywords = {pubs},\n\tmonth = {Apr},\n\tnumpages = {0},\n\tpages = {3495--3498},\n\tpublisher = {American Physical Society},\n\ttitle = {Spatiotemporal Bifurcation Phenomena with Temporal Period Doubling: Patterns in Vibrated Sand},\n\turl_journal = {http://link.aps.org/doi/10.1103/PhysRevLett.80.3495},\n\tvolume = {80},\n\tyear = {1998},\n\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.80.3495},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.80.3495}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"venkataramani-antonsen-ott-anomalousdiffusioninboundedtemporallyirregularflows-1998\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S016727899700184X\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'venkataramani-antonsen-ott-anomalousdiffusioninboundedtemporallyirregularflows-1998', 'http://www.sciencedirect.com/science/article/pii/S016727899700184X', event);\">\n    Anomalous diffusion in bounded temporally irregular flows.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>; Antonsen, T. M.;  and Ott, E.\n</span>\n\n  \n\n</span>\n\n  <i>Physica D: Nonlinear Phenomena</i>, 112(3–4): 412 - 440.  1998.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S016727899700184X\"\n     onclick=\"log_download('venkataramani-antonsen-ott-anomalousdiffusioninboundedtemporallyirregularflows-1998', 'http://www.sciencedirect.com/science/article/pii/S016727899700184X', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Anomalous diffusion in bounded temporally irregular flows [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/http://dx.doi.org/10.1016/S0167-2789(97)00184-X\"\n     onclick=\"log_download('venkataramani-antonsen-ott-anomalousdiffusioninboundedtemporallyirregularflows-1998', 'http://doi.org/http://dx.doi.org/10.1016/S0167-2789(97)00184-X', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-antonsen-ott-anomalousdiffusioninboundedtemporallyirregularflows-1998\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-antonsen-ott-anomalousdiffusioninboundedtemporallyirregularflows-1998')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{Venkataramani1998412,\n\tauthor = {Shankar C. Venkataramani and Thomas M. Antonsen and Edward Ott},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {http://dx.doi.org/10.1016/S0167-2789(97)00184-X},\n\tissn = {0167-2789},\n\tjournal = {Physica D: Nonlinear Phenomena},\n\tkeywords = {Hamiltonian systems; pubs},\n\tnumber = {3--4},\n\tpages = {412 - 440},\n\ttitle = {Anomalous diffusion in bounded temporally irregular flows},\n\turl_journal = {http://www.sciencedirect.com/science/article/pii/S016727899700184X},\n\tvolume = {112},\n\tyear = {1998},\n\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S016727899700184X},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1016/S0167-2789(97)00184-X}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1997\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1997')\"\n      onkeypress=\"toggleGroup('group_1997')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1997</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"coppersmith-jones-kadanoff-levine-mccarten-nagel-venkataramani-wu-selforganizedshorttermmemories-1997\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevLett.78.3983\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'coppersmith-jones-kadanoff-levine-mccarten-nagel-venkataramani-wu-selforganizedshorttermmemories-1997', 'http://link.aps.org/doi/10.1103/PhysRevLett.78.3983', event);\">\n    Self-Organized Short-Term Memories.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Coppersmith, S. N.; Jones, T. C.; Kadanoff, L. P.; Levine, A.; McCarten, J. P.; Nagel, S. R.; <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>;  and Wu, X.\n</span>\n\n  \n\n</span>\n\n  <i>Phys. Rev. Lett.</i>, 78: 3983–3986. May 1997.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevLett.78.3983\"\n     onclick=\"log_download('coppersmith-jones-kadanoff-levine-mccarten-nagel-venkataramani-wu-selforganizedshorttermmemories-1997', 'http://link.aps.org/doi/10.1103/PhysRevLett.78.3983', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Self-Organized Short-Term Memories [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1103/PhysRevLett.78.3983\"\n     onclick=\"log_download('coppersmith-jones-kadanoff-levine-mccarten-nagel-venkataramani-wu-selforganizedshorttermmemories-1997', 'http://doi.org/10.1103/PhysRevLett.78.3983', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/coppersmith-jones-kadanoff-levine-mccarten-nagel-venkataramani-wu-selforganizedshorttermmemories-1997\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('coppersmith-jones-kadanoff-levine-mccarten-nagel-venkataramani-wu-selforganizedshorttermmemories-1997')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{PhysRevLett.78.3983,\n\tauthor = {Coppersmith, S. N. and Jones, T. C. and Kadanoff, L. P. and Levine, A. and McCarten, J. P. and Nagel, S. R. and Venkataramani, S. C. and Wu, Xinlei},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1103/PhysRevLett.78.3983},\n\tissue = {21},\n\tjournal = {Phys. Rev. Lett.},\n\tkeywords = {pubs},\n\tmonth = {May},\n\tnumpages = {0},\n\tpages = {3983--3986},\n\tpublisher = {American Physical Society},\n\ttitle = {Self-Organized Short-Term Memories},\n\turl = {http://link.aps.org/doi/10.1103/PhysRevLett.78.3983},\n\tvolume = {78},\n\tyear = {1997},\n\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.78.3983},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.78.3983}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"venkataramani-antonsen-ott-lvyflightsinfluidflowswithnokolmogorovarnoldmosersurfaces-1997\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevLett.78.3864\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'venkataramani-antonsen-ott-lvyflightsinfluidflowswithnokolmogorovarnoldmosersurfaces-1997', 'http://link.aps.org/doi/10.1103/PhysRevLett.78.3864', event);\">\n    Lévy Flights in Fluid Flows with no Kolmogorov-Arnold-Moser Surfaces.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>; Antonsen, T. M.;  and Ott, E.\n</span>\n\n  \n\n</span>\n\n  <i>Phys. Rev. Lett.</i>, 78: 3864–3867. May 1997.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevLett.78.3864\"\n     onclick=\"log_download('venkataramani-antonsen-ott-lvyflightsinfluidflowswithnokolmogorovarnoldmosersurfaces-1997', 'http://link.aps.org/doi/10.1103/PhysRevLett.78.3864', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Lévy Flights in Fluid Flows with no Kolmogorov-Arnold-Moser Surfaces [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1103/PhysRevLett.78.3864\"\n     onclick=\"log_download('venkataramani-antonsen-ott-lvyflightsinfluidflowswithnokolmogorovarnoldmosersurfaces-1997', 'http://doi.org/10.1103/PhysRevLett.78.3864', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-antonsen-ott-lvyflightsinfluidflowswithnokolmogorovarnoldmosersurfaces-1997\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-antonsen-ott-lvyflightsinfluidflowswithnokolmogorovarnoldmosersurfaces-1997')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{PhysRevLett.78.3864,\n\tauthor = {Venkataramani, Shankar C. and Antonsen, Thomas M. and Ott, Edward},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1103/PhysRevLett.78.3864},\n\tissue = {20},\n\tjournal = {Phys. Rev. Lett.},\n\tkeywords = {pubs},\n\tmonth = {May},\n\tnumpages = {0},\n\tpages = {3864--3867},\n\tpublisher = {American Physical Society},\n\ttitle = {L\\&#x27;evy Flights in Fluid Flows with no Kolmogorov-Arnold-Moser Surfaces},\n\turl_journal = {http://link.aps.org/doi/10.1103/PhysRevLett.78.3864},\n\tvolume = {78},\n\tyear = {1997},\n\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.78.3864},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.78.3864}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1996\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1996')\"\n      onkeypress=\"toggleGroup('group_1996')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1996</span>\n      <span class=\"bibbase_group_count\">\n        \n        (4)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"lai-grebogi-yorke-venkataramani-riddlingbifurcationinchaoticdynamicalsystems-1996\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevLett.77.55\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'lai-grebogi-yorke-venkataramani-riddlingbifurcationinchaoticdynamicalsystems-1996', 'http://link.aps.org/doi/10.1103/PhysRevLett.77.55', event);\">\n    Riddling Bifurcation in Chaotic Dynamical Systems.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Lai, Y.; Grebogi, C.; Yorke, J. A.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Phys. Rev. Lett.</i>, 77: 55–58. Jul 1996.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevLett.77.55\"\n     onclick=\"log_download('lai-grebogi-yorke-venkataramani-riddlingbifurcationinchaoticdynamicalsystems-1996', 'http://link.aps.org/doi/10.1103/PhysRevLett.77.55', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Riddling Bifurcation in Chaotic Dynamical Systems [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1103/PhysRevLett.77.55\"\n     onclick=\"log_download('lai-grebogi-yorke-venkataramani-riddlingbifurcationinchaoticdynamicalsystems-1996', 'http://doi.org/10.1103/PhysRevLett.77.55', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/lai-grebogi-yorke-venkataramani-riddlingbifurcationinchaoticdynamicalsystems-1996\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('lai-grebogi-yorke-venkataramani-riddlingbifurcationinchaoticdynamicalsystems-1996')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{PhysRevLett.77.55,\n\tauthor = {Lai, Ying-Cheng and Grebogi, Celso and Yorke, James A. and Venkataramani, S. C.},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1103/PhysRevLett.77.55},\n\tissue = {1},\n\tjournal = {Phys. Rev. Lett.},\n\tkeywords = {pubs},\n\tmonth = {Jul},\n\tnumpages = {0},\n\tpages = {55--58},\n\tpublisher = {American Physical Society},\n\ttitle = {Riddling Bifurcation in Chaotic Dynamical Systems},\n\turl = {http://link.aps.org/doi/10.1103/PhysRevLett.77.55},\n\tvolume = {77},\n\tyear = {1996},\n\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.77.55},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.77.55}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"venkataramani-hunt-ott-gauthier-bienfang-transitionstobubblingofchaoticsystems-1996\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevLett.77.5361\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'venkataramani-hunt-ott-gauthier-bienfang-transitionstobubblingofchaoticsystems-1996', 'http://link.aps.org/doi/10.1103/PhysRevLett.77.5361', event);\">\n    Transitions to Bubbling of Chaotic Systems.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>; Hunt, B. R.; Ott, E.; Gauthier, D. J.;  and Bienfang, J. C.\n</span>\n\n  \n\n</span>\n\n  <i>Phys. Rev. Lett.</i>, 77: 5361–5364. Dec 1996.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevLett.77.5361\"\n     onclick=\"log_download('venkataramani-hunt-ott-gauthier-bienfang-transitionstobubblingofchaoticsystems-1996', 'http://link.aps.org/doi/10.1103/PhysRevLett.77.5361', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Transitions to Bubbling of Chaotic Systems [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1103/PhysRevLett.77.5361\"\n     onclick=\"log_download('venkataramani-hunt-ott-gauthier-bienfang-transitionstobubblingofchaoticsystems-1996', 'http://doi.org/10.1103/PhysRevLett.77.5361', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-hunt-ott-gauthier-bienfang-transitionstobubblingofchaoticsystems-1996\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-hunt-ott-gauthier-bienfang-transitionstobubblingofchaoticsystems-1996')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{PhysRevLett.77.5361,\n\tauthor = {Venkataramani, Shankar C. and Hunt, Brian R. and Ott, Edward and Gauthier, Daniel J. and Bienfang, Joshua C.},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1103/PhysRevLett.77.5361},\n\tissue = {27},\n\tjournal = {Phys. Rev. Lett.},\n\tkeywords = {pubs},\n\tmonth = {Dec},\n\tnumpages = {0},\n\tpages = {5361--5364},\n\tpublisher = {American Physical Society},\n\ttitle = {Transitions to Bubbling of Chaotic Systems},\n\turl_journal = {http://link.aps.org/doi/10.1103/PhysRevLett.77.5361},\n\tvolume = {77},\n\tyear = {1996},\n\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.77.5361},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.77.5361}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"venkataramani-hunt-ott-bubblingtransition-1996\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevE.54.1346\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'venkataramani-hunt-ott-bubblingtransition-1996', 'http://link.aps.org/doi/10.1103/PhysRevE.54.1346', event);\">\n    Bubbling transition.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>; Hunt, B. R.;  and Ott, E.\n</span>\n\n  \n\n</span>\n\n  <i>Phys. Rev. E</i>, 54: 1346–1360. Aug 1996.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://link.aps.org/doi/10.1103/PhysRevE.54.1346\"\n     onclick=\"log_download('venkataramani-hunt-ott-bubblingtransition-1996', 'http://link.aps.org/doi/10.1103/PhysRevE.54.1346', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Bubbling transition [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1103/PhysRevE.54.1346\"\n     onclick=\"log_download('venkataramani-hunt-ott-bubblingtransition-1996', 'http://doi.org/10.1103/PhysRevE.54.1346', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-hunt-ott-bubblingtransition-1996\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-hunt-ott-bubblingtransition-1996')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{PhysRevE.54.1346,\n\tauthor = {Venkataramani, Shankar C. and Hunt, Brian R. and Ott, Edward},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {10.1103/PhysRevE.54.1346},\n\tissue = {2},\n\tjournal = {Phys. Rev. E},\n\tkeywords = {pubs},\n\tmonth = {Aug},\n\tnumpages = {0},\n\tpages = {1346--1360},\n\tpublisher = {American Physical Society},\n\ttitle = {Bubbling transition},\n\turl_journal = {http://link.aps.org/doi/10.1103/PhysRevE.54.1346},\n\tvolume = {54},\n\tyear = {1996},\n\tBdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.54.1346},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevE.54.1346}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"venkataramani-antonsen-ott-sommerer-onoffintermittencypowerspectrumandfractalpropertiesoftimeseries-1996\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/0167278996000140\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'venkataramani-antonsen-ott-sommerer-onoffintermittencypowerspectrumandfractalpropertiesoftimeseries-1996', 'http://www.sciencedirect.com/science/article/pii/0167278996000140', event);\">\n    On-off intermittency: Power spectrum and fractal properties of time series.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>; Antonsen, T. M.; Ott, E.;  and Sommerer, J. C.\n</span>\n\n  \n\n</span>\n\n  <i>Physica D: Nonlinear Phenomena</i>, 96(1–4): 66 - 99.  1996.\n  <span class=\"note\">Measures of Spatio-Temporal Dynamics</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/0167278996000140\"\n     onclick=\"log_download('venkataramani-antonsen-ott-sommerer-onoffintermittencypowerspectrumandfractalpropertiesoftimeseries-1996', 'http://www.sciencedirect.com/science/article/pii/0167278996000140', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"On-off intermittency: Power spectrum and fractal properties of time series [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/http://dx.doi.org/10.1016/0167-2789(96)00014-0\"\n     onclick=\"log_download('venkataramani-antonsen-ott-sommerer-onoffintermittencypowerspectrumandfractalpropertiesoftimeseries-1996', 'http://doi.org/http://dx.doi.org/10.1016/0167-2789(96)00014-0', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-antonsen-ott-sommerer-onoffintermittencypowerspectrumandfractalpropertiesoftimeseries-1996\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-antonsen-ott-sommerer-onoffintermittencypowerspectrumandfractalpropertiesoftimeseries-1996')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{Venkataramani199666,\n\tauthor = {Shankar C. Venkataramani and Thomas M. Antonsen and Edward Ott and John C. Sommerer},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {http://dx.doi.org/10.1016/0167-2789(96)00014-0},\n\tissn = {0167-2789},\n\tjournal = {Physica D: Nonlinear Phenomena},\n\tkeywords = {Invariant manifold; pubs},\n\tnote = {Measures of Spatio-Temporal Dynamics},\n\tnumber = {1--4},\n\tpages = {66 - 99},\n\ttitle = {On-off intermittency: Power spectrum and fractal properties of time series},\n\turl_journal = {http://www.sciencedirect.com/science/article/pii/0167278996000140},\n\tvolume = {96},\n\tyear = {1996},\n\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0167278996000140},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1016/0167-2789(96)00014-0}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1995\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1995')\"\n      onkeypress=\"toggleGroup('group_1995')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1995</span>\n      <span class=\"bibbase_group_count\">\n        \n        (3)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"ott-sommerer-antonsen-venkataramani-blowoutbifurcationssymmetrybreakingofspatiallysymmetricchaoticstates-1995\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://dx.doi.org/10.1007/3-540-59222-9_34\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'ott-sommerer-antonsen-venkataramani-blowoutbifurcationssymmetrybreakingofspatiallysymmetricchaoticstates-1995', 'http://dx.doi.org/10.1007/3-540-59222-9_34', event);\">\n    Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Ott, E.; Sommerer, J. C.; Antonsen, T. M.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S.</a>\n</span>\n\n  \n\n</span>\n\n  In Shlesinger, M.; Zaslavsky, G.;  and Frisch, U., editor(s), <i>Lévy Flights and Related Topics in Physics</i>, volume 450, pages 182-195. Springer Berlin Heidelberg,  1995.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://dx.doi.org/10.1007/3-540-59222-9_34\"\n     onclick=\"log_download('ott-sommerer-antonsen-venkataramani-blowoutbifurcationssymmetrybreakingofspatiallysymmetricchaoticstates-1995', 'http://dx.doi.org/10.1007/3-540-59222-9_34', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/3-540-59222-9_34\"\n     onclick=\"log_download('ott-sommerer-antonsen-venkataramani-blowoutbifurcationssymmetrybreakingofspatiallysymmetricchaoticstates-1995', 'http://doi.org/10.1007/3-540-59222-9_34', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/ott-sommerer-antonsen-venkataramani-blowoutbifurcationssymmetrybreakingofspatiallysymmetricchaoticstates-1995\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('ott-sommerer-antonsen-venkataramani-blowoutbifurcationssymmetrybreakingofspatiallysymmetricchaoticstates-1995')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@incollection{Shlesinger:1995gd,\n\tauthor = {Ott, Edward and Sommerer, John C. and Antonsen, Thomas M. and Venkataramani, Shankar},\n\tbooktitle = {L{\\&#x27;e}vy Flights and Related Topics in Physics},\n\tda = {1995/01/01},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2021-05-23 18:54:32 -0700},\n\tdoi = {10.1007/3-540-59222-9{\\_}34},\n\teditor = {Shlesinger, MichealF. and Zaslavsky, GeorgeM. and Frisch, Uriel},\n\tisbn = {978-3-540-59222-8},\n\tkeywords = {pubs},\n\tla = {English},\n\tpages = {182-195},\n\tpublisher = {Springer Berlin Heidelberg},\n\tse = {12},\n\ttitle = {Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states},\n\ttitle1 = {Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states},\n\tty = {CHAP},\n\turl = {http://dx.doi.org/10.1007/3-540-59222-9_34},\n\tvolume = {450},\n\tyear = {1995},\n\tBdsk-Url-1 = {http://dx.doi.org/10.1007/3-540-59222-9_34},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1007/3-540-59222-9%7B%5C_%7D34}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"venkataramani-antonsen-ott-sommerer-characterizationofonoffintermittenttimeseries-1995\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/037596019500710K\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'venkataramani-antonsen-ott-sommerer-characterizationofonoffintermittenttimeseries-1995', 'http://www.sciencedirect.com/science/article/pii/037596019500710K', event);\">\n    Characterization of on-off intermittent time series.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S. C.</a>; Antonsen, T. M.; Ott, E.;  and Sommerer, J. C\n</span>\n\n  \n\n</span>\n\n  <i>Physics Letters A</i>, 207(3–4): 173 - 179.  1995.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/037596019500710K\"\n     onclick=\"log_download('venkataramani-antonsen-ott-sommerer-characterizationofonoffintermittenttimeseries-1995', 'http://www.sciencedirect.com/science/article/pii/037596019500710K', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Characterization of on-off intermittent time series [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/http://dx.doi.org/10.1016/0375-9601(95)00710-K\"\n     onclick=\"log_download('venkataramani-antonsen-ott-sommerer-characterizationofonoffintermittenttimeseries-1995', 'http://doi.org/http://dx.doi.org/10.1016/0375-9601(95)00710-K', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/venkataramani-antonsen-ott-sommerer-characterizationofonoffintermittenttimeseries-1995\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('venkataramani-antonsen-ott-sommerer-characterizationofonoffintermittenttimeseries-1995')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{on-off1995,\n\tauthor = {Shankar C. Venkataramani and Thomas M. Antonsen and Edward Ott and John C Sommerer},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tdoi = {http://dx.doi.org/10.1016/0375-9601(95)00710-K},\n\tissn = {0375-9601},\n\tjournal = {Physics Letters A},\n\tkeywords = {Invariant manifold; pubs},\n\tnumber = {3--4},\n\tpages = {173 - 179},\n\ttitle = {Characterization of on-off intermittent time series},\n\turl_journal = {http://www.sciencedirect.com/science/article/pii/037596019500710K},\n\tvolume = {207},\n\tyear = {1995},\n\tBdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/037596019500710K},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1016/0375-9601(95)00710-K}}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"jacobson-venkataramani-topologyofeventhorizonsandtopologicalcensorship-1995\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://stacks.iop.org/0264-9381/12/1055\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'jacobson-venkataramani-topologyofeventhorizonsandtopologicalcensorship-1995', 'http://stacks.iop.org/0264-9381/12/1055', event);\">\n    Topology of event horizons and topological censorship.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Jacobson, T.;  and <a class=\"bibbase author link\" href=\"https://www.math.arizona.edu/~shankar/pub/pub.html\">Venkataramani, S.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Classical Quantum Gravity</i>, 12(4): 1055–1061.  1995.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://stacks.iop.org/0264-9381/12/1055\"\n     onclick=\"log_download('jacobson-venkataramani-topologyofeventhorizonsandtopologicalcensorship-1995', 'http://stacks.iop.org/0264-9381/12/1055', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Topology of event horizons and topological censorship [link]\"\n       title=\" journal\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> journal</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/jacobson-venkataramani-topologyofeventhorizonsandtopologicalcensorship-1995\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('jacobson-venkataramani-topologyofeventhorizonsandtopologicalcensorship-1995')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{MR1330301,\n\tauthor = {Jacobson, Ted and Venkataramani, Shankar},\n\tcoden = {CQGRDG},\n\tdate-added = {2017-01-29 16:04:45 +0000},\n\tdate-modified = {2017-01-29 20:11:00 +0000},\n\tfjournal = {Classical and Quantum Gravity},\n\tissn = {0264-9381},\n\tjournal = {Classical Quantum Gravity},\n\tkeywords = {pubs},\n\tmrclass = {83C75 (57N10)},\n\tmrnumber = {1330301 (96e:83055)},\n\tmrreviewer = {Robert J. Low},\n\tnumber = {4},\n\tpages = {1055--1061},\n\ttitle = {Topology of event horizons and topological censorship},\n\turl_journal = {http://stacks.iop.org/0264-9381/12/1055},\n\tvolume = {12},\n\tyear = {1995},\n\tBdsk-Url-1 = {http://stacks.iop.org/0264-9381/12/1055}}\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n\n\n\n  </div>\n\n\n  <!-- Modal -->\n\n  <!-- <iframe id=\"bibbase_network_frame\" -->\n  <!--         src=\"//bibbase.org/network/control\" -->\n  <!--         style=\"display: none;\"> -->\n  <!-- </iframe> -->\n\n</div>\n"}; document.write(bibbase_data.data);