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\n  \n 2018\n \n \n (8)\n \n \n
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\n \n\n \n \n \n \n \n Networks of Coadjoint Orbits: from Geometric to Statistical Mechanics.\n \n \n \n\n\n \n Arnaudon, A.; and Takao, S.\n\n\n \n\n\n\n arXiv preprint arXiv:1804.11139. 2018.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n\n\n\n
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@article{arnaudon2018networks,\n  title={Networks of Coadjoint Orbits: from Geometric to Statistical Mechanics},\n  author={Arnaudon, Alexis and Takao, So},\n  journal={arXiv preprint arXiv:1804.11139},\n  year={2018},\n  keywords={networks,stochastic mechanics}\n}\n\n\n
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\n \n\n \n \n \n \n \n String Methods for Stochastic Image and Shape Matching.\n \n \n \n\n\n \n Arnaudon, A.; Holm, D.; and Sommer, S.\n\n\n \n\n\n\n Journal of Mathematical Imaging and Vision,1–15. 2018.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n\n\n\n
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@article{arnaudon2018string,\n  title={String Methods for Stochastic Image and Shape Matching},\n  author={Arnaudon, Alexis and Holm, Darryl and Sommer, Stefan},\n  journal={Journal of Mathematical Imaging and Vision},\n  year={2018},\n  pages={1--15},\n  publisher={Springer},\n  keywords={shape analysis, stochastic mechanics}}\n
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\n \n\n \n \n \n \n \n Engineering solitons and breathers in a deformed ferromagnet: Effect of localised inhomogeneities.\n \n \n \n\n\n \n Saravanan, M.; and Arnaudon, A.\n\n\n \n\n\n\n Physics Letters A. 2018.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n\n\n\n
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@article{saravanan2018,\n  title = {Engineering solitons and breathers in a deformed ferromagnet: Effect of localised inhomogeneities},\n  journal = {Physics Letters A},\n  year = {2018},\n  author = {M. Saravanan and A. Arnaudon},\n  keywords={integrable systems}\n}\n\n\n
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\n \n\n \n \n \n \n \n \n The stochastic Energy-Casimir method.\n \n \n \n \n\n\n \n Arnaudon, A.; Ganaba, N.; and Holm, D. D.\n\n\n \n\n\n\n \"Comptes Rendus Mécanique, 346(4): 279 - 290. 2018.\n \n\n\n\n
\n\n\n\n \n \n \"ThePaper\n  \n \n \n \"The arxiv\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n\n\n\n
\n 
@article{arnaudon2017stochastic,\n\ttitle={The stochastic {E}nergy-{C}asimir method},\n\tauthor={Arnaudon, Alexis and Ganaba, Nader and Holm, Darryl D. },\n\tjournal={"Comptes Rendus M{\\'e}canique},\n\tvolume = {346},\n\tnumber = {4},\n\tpages = {279 - 290},\n\tyear={2018},\n\tdoi = {https://doi.org/10.1016/j.crme.2018.01.003},\n\turl = {http://www.sciencedirect.com/science/article/pii/S1631072118300032},\n\tabstract={   In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for the stability in probability of stochastic dynamical systems with symmetries and multiplicative noise. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top and the compressible Euler equation in two dimensions. The main result of this extension is that stable deterministic equilibria remain stable in probability up to a certain stopping time which depends on the amplitude of the noise for finite dimensional systems and on the amplitude the spatial derivative of the noise for infinite dimensional systems. } ,\n\turl_arXiv={http://arxiv.org/abs/1702.03899},\n\tkeywords={stochastic mechanics}\n}\n
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\n In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for the stability in probability of stochastic dynamical systems with symmetries and multiplicative noise. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top and the compressible Euler equation in two dimensions. The main result of this extension is that stable deterministic equilibria remain stable in probability up to a certain stopping time which depends on the amplitude of the noise for finite dimensional systems and on the amplitude the spatial derivative of the noise for infinite dimensional systems. \n
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\n \n\n \n \n \n \n \n Noise and dissipation on coadjoint orbits.\n \n \n \n\n\n \n \n\n\n \n\n\n\n Journal of Nonlinear Science, 28(1): 91–145. 2018.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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\n  \n\n  \n  \n  \n  \n  \n  Structure preserving noise and dissipation in the Toda lattice.\n  \n  \n  \n\n\n  \n  Arnaudon, A.\n\n\n  \n\n\n\n  Journal of Physics A: Mathematical and Theoretical.  2018.\n  \n\n\n\n
\n\n\n\n  \n\n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n\n\n\n
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@article{arnaudon2018structure,\n\ttitle={Structure preserving noise and dissipation in the Toda lattice},\n\tauthor={Arnaudon, Alexis},\n\tjournal={Journal of Physics A: Mathematical and Theoretical},\n\tyear={2018},\n\tpublisher={IOP Publishing}, \n\tkeywords={stochastic mechanics}\n}\n\n
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\n  \n\n  \n  \n  \n  \n  \n  Contractions of group representations via geometric quantisation.\n  \n  \n  \n\n\n  \n  Akylzhanov, R.;  and Arnaudon, A.\n\n\n  \n\n\n\n  arXiv preprint arXiv:1802.03348.  2018.\n  \n\n\n\n
\n\n\n\n  \n\n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n\n\n\n
\n  
@article{akylzhanov2018contractions,\n\ttitle={Contractions of group representations via geometric quantisation},\n\tauthor={Akylzhanov, Rauan and Arnaudon, Alexis},\n\tjournal={arXiv preprint arXiv:1802.03348},\n\tyear={2018},\n\tkeywords={others}\n}\n\n
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\n  \n\n  \n  \n  \n  \n  \n  \n    Un-reduction in field theory.\n  \n  \n  \n  \n\n\n  \n  Arnaudon, A.; López, M. C.;  and Holm, D. D.\n\n\n  \n\n\n\n  Letters in Mathematical Physics, 108(1): 225–247. Jan 2018.\n  \n\n\n\n
\n\n\n\n  \n  \n    \"Un-reductionPaper\n   \n  \n  \n    \"Un-reduction arxiv\n   \n  \n\n  \n  \n    doi\n   \n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n\n\n\n
\n  
@article{Arnaudon2018,\n\tauthor="Arnaudon, Alexis\n\t\tand L{\\'o}pez, Marco Castrill{\\'o}n\n\t\tand Holm, Darryl D.",\n\ttitle="Un-reduction in field theory",\n\tjournal="Letters in Mathematical Physics",\n\tyear="2018",\n\tmonth="Jan",\n\tday="01",\n\tvolume="108",\n\tnumber="1",\n\tpages="225--247",\n\tissn="1573-0530",\n\tdoi="10.1007/s11005-017-1000-9",\n\turl="https://doi.org/10.1007/s11005-017-1000-9",\n\turl_arXiv="https://arxiv.org/pdf/1509.06919",\n\tkeywords="shape analysis"\n}\n\n
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\n       \n      2017\n      \n        \n        (8)\n        \n      \n    
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\n  \n\n  \n  \n  \n  \n  \n  \n    Differential geometry and stochastic dynamics with deep learning numerics.\n  \n  \n  \n  \n\n\n  \n  Kühnel, L.; Arnaudon, A.;  and Sommer, S.\n\n\n  \n\n\n\n  arXiv preprint arXiv:1712.08364.  2017.\n  \n\n\n\n
\n\n\n\n  \n  \n    \"Differential arxiv\n   \n  \n\n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n  \n  \n\n\n\n
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@article{kuhnel2017differential,\n\ttitle={Differential geometry and stochastic dynamics with deep learning numerics},\n\tauthor={K{\\"u}hnel, Line and Arnaudon, Alexis and Sommer, Stefan},\n\tjournal={arXiv preprint arXiv:1712.08364},\n\turl_ArXiv= {http://arxiv.org/abs/1712.08364},\n\tyear={2017},\n\tkeywords={shape analysis,stochastic mechanics}\n}\n\n
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\n  \n\n  \n  \n  \n  \n  \n  \n    Stochastic metamorphosis with template uncertainties.\n  \n  \n  \n  \n\n\n  \n  Arnaudon, A.; Holm, D. D.;  and Sommer, S.\n\n\n  \n\n\n\n  to appear in a World Scientific Press book.  2017.\n  \n\n\n\n
\n\n\n\n  \n  \n    \"Stochastic arxiv\n   \n  \n\n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n  \n  \n\n\n\n
\n  
@article{arnaudon2017stochastic,\n\ttitle={Stochastic metamorphosis with template uncertainties},\n\tauthor={Arnaudon, Alexis and Holm, Darryl D. and Sommer, Stefan},\n\tjournal={to appear in a World Scientific Press book},\n\turl_ArXiv= {http://arxiv.org/abs/1711.07231},\n\tyear={2017},\n\tkeywords={shape analysis,stochastic mechanics}\n}\n\n
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\n  \n\n  \n  \n  \n  \n  \n  \n    A Geometric Framework for Stochastic Shape Analysis.\n  \n  \n  \n  \n\n\n  \n  Arnaudon, A.; Holm, D. D.;  and Sommer, S.\n\n\n  \n\n\n\n  to appear in Foundation in Computational Mathematics.  2017.\n  \n\n\n\n
\n\n\n\n  \n  \n    \"A arxiv\n   \n  \n\n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n  \n  \n\n\n\n
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@article{arnaudon2017geometric,\n\ttitle={A Geometric Framework for Stochastic Shape Analysis},\n\tauthor={Arnaudon, Alexis and Holm, Darryl D. and Sommer, Stefan},\n\tjournal={to appear in Foundation in Computational Mathematics},\n\turl_ArXiv= {http://arxiv.org/abs/1703.09971},\n\tyear={2017},\n\tkeywords={shape analysis,stochastic mechanics}\n}\n\n
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\n  \n\n  \n  \n  \n  \n  \n  \n    Bridge Simulation and Metric Estimation on Landmark Manifolds.\n  \n  \n  \n  \n\n\n  \n  Sommer, S.; Arnaudon, A.; Kühnel, L.;  and Joshi, S.\n\n\n  \n\n\n\n  In  2017. \n  \n\n\n\n
\n\n\n\n  \n  \n    \"Bridge arxiv\n   \n  \n\n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n  \n  \n\n\n\n
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@inproceedings{sommer2017bridge,\n\ttitle={Bridge Simulation and Metric Estimation on Landmark Manifolds},\n\tauthor={Sommer, Stefan and Arnaudon, Alexis and K{\\"u}hnel, Line and Joshi, Sarang},\n\tjournal={MFCA2017, arXiv preprint arXiv:1705.10943},\n\turl_ArXiv= {http://arxiv.org/abs/1705.10943},\n\tyear={2017},\n\tkeywords={shape analysis, stochastic mechanics}\n}\n\n
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\n  \n\n  \n  \n  \n  \n  \n  \n    A stochastic large deformation model for computational anatomy.\n  \n  \n  \n  \n\n\n  \n  Arnaudon, A.; Holm, D. D.; Pai, A.;  and Sommer, S.\n\n\n  \n\n\n\n  In International Conference on Information Processing in Medical Imaging, pages 571–582,  2017. Springer\n  \n\n\n\n
\n\n\n\n  \n  \n    \"A arxiv\n   \n  \n  \n    \"APaper\n   \n  \n\n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n  \n  \n\n\n\n
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@inproceedings{arnaudon2016stochastic,\n\ttitle={A stochastic large deformation model for computational anatomy},\n\tauthor={Arnaudon, Alexis and Holm, Darryl D. and Pai, Akshay and Sommer, Stefan},\n\tbooktitle={International Conference on Information Processing in Medical Imaging},\n\tpages={571--582},\n\tyear={2017},\n\torganization={Springer},\n\turl_ArXiv= {http://arxiv.org/abs/1612.05323},\n\turl={https://link.springer.com/chapter/10.1007/978-3-319-59050-9_45},\n\tkeywords={shape analysis, stochastic mechanics}\n}\n\n
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\n  \n\n  \n  \n  \n  \n  \n  Integrability of the hyperbolic reduced Maxwell-Bloch equations for strongly correlated Bose-Einstein condensates.\n  \n  \n  \n\n\n  \n  Arnaudon, A.;  and Gibbon, J. D\n\n\n  \n\n\n\n  Physical Review A, 96(1): 013610.  2017.\n  \n\n\n\n
\n\n\n\n  \n\n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n\n\n\n
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@article{arnaudon2017integrability,\n\ttitle={Integrability of the hyperbolic reduced Maxwell-Bloch equations for strongly correlated Bose-Einstein condensates},\n\tauthor={Arnaudon, Alexis and Gibbon, John D},\n\tjournal={Physical Review A},\n\tvolume={96},\n\tnumber={1},\n\tpages={013610},\n\tyear={2017},\n\tpublisher={APS},\n\tkeywords="integrable systems"\n}\n\n\n
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\n  \n\n  \n  \n  \n  \n  \n  \n    .\n  \n  \n  \n  \n\n\n  \n  Arnaudon, A.; De Castro, A. L.;  and Holm, D. D.\n\n\n  \n\n\n\n  Noise and Dissipation in Rigid Body Motion, pages 1–12. Albeverio, S.; Cruzeiro, A. B.;  and Holm, D. D., editor(s). Springer International Publishing, Cham,  2017.\n  \n\n\n\n
\n\n\n\n  \n  \n    \"NoisePaper\n   \n  \n\n  \n  \n    doi\n   \n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n\n\n\n
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@inbook{arnaudon2016noise2,\n\tauthor="Arnaudon, Alexis\n\t\tand De Castro, Alex L.\n\t\tand Holm, Darryl D.",\n\teditor="Albeverio, Sergio\n\t\tand Cruzeiro, Ana Bela\n\t\tand Holm, Darryl D.",\n\ttitle="Noise and Dissipation in Rigid Body Motion",\n\tbookTitle="Stochastic Geometric Mechanics : CIB, Lausanne, Switzerland, January-June 2015",\n\tyear="2017",\n\tpublisher="Springer International Publishing",\n\taddress="Cham",\n\tpages="1--12",\n\tisbn="978-3-319-63453-1",\n\tdoi="10.1007/978-3-319-63453-1_1",\n\turl="https://doi.org/10.1007/978-3-319-63453-1_1",\n\tkeywords="stochastic mechanics"\n}\n\n\n
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\n  \n\n  \n  \n  \n  \n  \n  \n    $G$-Strands on symmetric spaces.\n  \n  \n  \n  \n\n\n  \n  Arnaudon, A.; Holm, D. D.;  and Ivanov, R. I.\n\n\n  \n\n\n\n  Proc. Roy. Soc. A, 473.  2017.\n  \n\n\n\n
\n\n\n\n  \n  \n    \"$G$-StrandsPaper\n   \n  \n  \n    \"$G$-Strands arxiv\n   \n  \n\n  \n  \n    doi\n   \n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n   \n  \n    abstract \n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n\n\n\n
\n  
@article{arnaudon2017strand,\n\ttitle={$G$-Strands on symmetric spaces},\n\tauthor={Arnaudon, Alexis and Holm, Darryl D. and Ivanov, Rossen I.},\n\tjournal={Proc. Roy. Soc. A},\n\tyear={2017},\n\tdoi= {10.1098/rspa.2016.0795},\n\turl= {http://rspa.royalsocietypublishing.org/content/473/2199/20160795},\n\tvolume={473},\n\tabstract={    \ntudy the G-strand equations that are extensions of the classical chiral model of particle physics in the particular setting of broken symmetries described by symmetric spaces. These equations are simple field theory models whose configuration space is a Lie group, or in this case a symmetric space. In this class of systems, we derive several models that are completely integrable on finite dimensional Lie group G and we treat in more details examples with symmetric space SU(2)/S1 and SO(4)/SO(3). The later model simplifies to an apparently new integrable 9 dimensional system. We also study the G-strands on the infinite dimensional group of diffeomorphisms, which gives, together with the Sobolev norm, systems of 1+2 Camassa-Holm equations. The solutions of these equations on the complementary space related to the Witt algebra decomposition are the odd function solutions.},\n\turl_arXiv={http://arxiv.org/abs/1702.02911},\n       \tkeywords={integrable systems}\n}\n\n
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\n  tudy the G-strand equations that are extensions of the classical chiral model of particle physics in the particular setting of broken symmetries described by symmetric spaces. These equations are simple field theory models whose configuration space is a Lie group, or in this case a symmetric space. In this class of systems, we derive several models that are completely integrable on finite dimensional Lie group G and we treat in more details examples with symmetric space SU(2)/S1 and SO(4)/SO(3). The later model simplifies to an apparently new integrable 9 dimensional system. We also study the G-strands on the infinite dimensional group of diffeomorphisms, which gives, together with the Sobolev norm, systems of 1+2 Camassa-Holm equations. The solutions of these equations on the complementary space related to the Witt algebra decomposition are the odd function solutions.\n
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\n  \n\n  \n  \n  \n  \n  \n  \n    On a Lagrangian Reduction and a Deformation of Completely Integrable Systems.\n  \n  \n  \n  \n\n\n  \n  Arnaudon, A.\n\n\n  \n\n\n\n  Journal of Nonlinear Science, 26(5): 1133–1160.  2016.\n  \n\n\n\n
\n\n\n\n  \n  \n    \"OnPaper\n   \n  \n  \n    \"On arxiv\n   \n  \n\n  \n  \n    doi\n   \n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n   \n  \n    abstract \n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n\n\n\n
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@Article{Arnaudon2016,\n\tauthor="Arnaudon, Alexis",\n\ttitle="On a Lagrangian Reduction and a Deformation of Completely Integrable Systems",\n\tjournal="Journal of Nonlinear Science",\n\tyear="2016",\n\tvolume="26",\n\tnumber="5",\n\tpages="1133--1160",\n\tabstract="We develop a theory of Lagrangian reduction on loop groups for completely integrable systems after having exchanged the role of the space and time variables in the multi-time interpretation of integrable hierarchies. We then insert the Sobolev norm $H^1$ in the Lagrangian and derive a deformation of the corresponding hierarchies. The integrability of the deformed equations is altered, and a notion of weak integrability is introduced. We implement this scheme in the AKNS and SO(3) hierarchies and obtain known and new equations. Among them, we found two important equations, the Camassa--Holm equation, viewed as a deformation of the KdV equation, and a deformation of the NLS equation.",\n\tissn="1432-1467",\n\tdoi="10.1007/s00332-016-9300-2",\n\turl="http://dx.doi.org/10.1007/s00332-016-9300-2",\n\turl_ArXiv= "http://arxiv.org/abs/1501.02745",\n\tkeywords="integrable systems"\n}\n
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\n  We develop a theory of Lagrangian reduction on loop groups for completely integrable systems after having exchanged the role of the space and time variables in the multi-time interpretation of integrable hierarchies. We then insert the Sobolev norm $H^1$ in the Lagrangian and derive a deformation of the corresponding hierarchies. The integrability of the deformed equations is altered, and a notion of weak integrability is introduced. We implement this scheme in the AKNS and SO(3) hierarchies and obtain known and new equations. Among them, we found two important equations, the Camassa–Holm equation, viewed as a deformation of the KdV equation, and a deformation of the NLS equation.\n
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\n  \n\n  \n  \n  \n  \n  \n  \n    On a deformation of the nonlinear Schrödinger equation.\n  \n  \n  \n  \n\n\n  \n  Arnaudon, A.\n\n\n  \n\n\n\n  Journal of Physics A: Mathematical and Theoretical, 49(12): 125202.  2016.\n  \n\n\n\n
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@article{1751-8121-49-12-125202,\n\tauthor={Arnaudon, Alexis},\n\ttitle={On a deformation of the nonlinear Schrödinger equation},\n\tjournal={Journal of Physics A: Mathematical and Theoretical},\n\tvolume={49},\n\tnumber={12},\n\tpages={125202},\n\turl={http://stacks.iop.org/1751-8121/49/i=12/a=125202},\n\tyear={2016},\n\tabstract={We study a deformation of the nonlinear Schrödinger (NLS) equation recently derived in the context of deformation of hierarchies of integrable systems. Although this new equation has not been shown to be completely integrable, its solitary wave solutions exhibit typical soliton behaviour, including near elastic collisions. We will first focus on standing wave solutions which can be smooth or peaked, then with the help of numerical simulations we will study solitary waves, their interactions and finally rogue waves in the modulational instability regime. Interestingly, the structure of the solution during the collision of solitary waves or during the rogue wave events is sharper and has larger amplitudes than in the classical NLS equation.},\n\turl_arXiv={http://arxiv.org/abs/1507.02591},\n\tkeywords={integrable systems}\n}\n\n
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\n  We study a deformation of the nonlinear Schrödinger (NLS) equation recently derived in the context of deformation of hierarchies of integrable systems. Although this new equation has not been shown to be completely integrable, its solitary wave solutions exhibit typical soliton behaviour, including near elastic collisions. We will first focus on standing wave solutions which can be smooth or peaked, then with the help of numerical simulations we will study solitary waves, their interactions and finally rogue waves in the modulational instability regime. Interestingly, the structure of the solution during the collision of solitary waves or during the rogue wave events is sharper and has larger amplitudes than in the classical NLS equation.\n
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\n  \n\n  \n  \n  \n  \n  \n  \n    Computational issues in chemo-dynamical modelling of the formation and evolution of galaxies.\n  \n  \n  \n  \n\n\n  \n  Revaz, Y.; Arnaudon, A.; Nichols, M.; Bonvin, V.;  and Jablonka, P.\n\n\n  \n\n\n\n  A&A, 588: A21.  2016.\n  \n\n\n\n
\n\n\n\n  \n  \n    \"ComputationalPaper\n   \n  \n  \n    \"Computational arxiv\n   \n  \n\n  \n  \n    doi\n   \n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n   \n  \n    abstract \n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n\n\n\n
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@article{ refId0,\n\tauthor = {Revaz, Yves and Arnaudon, Alexis and Nichols, Matthew and Bonvin, Vivien and Jablonka, Pascale},\n\ttitle = {Computational issues in chemo-dynamical modelling of the formation and evolution of galaxies},\n\tdoi= "10.1051/0004-6361/201526438",\n\turl= "http://dx.doi.org/10.1051/0004-6361/201526438",\n\tjournal = {A&A},\n\tyear = 2016,\n\tvolume = 588,\n\tpages = "A21",\n\turl_arXiv={http://arxiv.org/abs/1601.02017},\n\tabstract={Chemo-dynamical N-body simulations are an essential tool for understanding the formation and evolution of galaxies. As the number of observationally determined stellar abundances continues to climb, these simulations are able to provide new constraints on the early star formaton history and chemical evolution inside both the Milky Way and Local Group dwarf galaxies. Here, we aim to reproduce the low α-element scatter observed in metal-poor stars. We first demonstrate that as stellar particles inside simulations drop below a mass threshold, increases in the resolution produce an unacceptably large scatter as one particle is no longer a good approximation of an entire stellar population. This threshold occurs at around 103M⊙, a mass limit easily reached in current (and future) simulations. By simulating the Sextans and Fornax dwarf spheroidal galaxies we show that this increase in scatter at high resolutions arises from stochastic supernovae explosions. In order to reduce this scatter down to the observed value, we show the necessity of introducing a metal mixing scheme into particle-based simulations. The impact of the method used to inject the metals into the surrounding gas is also discussed. We finally summarise the best approach for accurately reproducing the scatter in simulations of both Local Group dwarf galaxies and in the Milky Way. },\n\tkeywords={computational astrophysics}\n}\n
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\n  Chemo-dynamical N-body simulations are an essential tool for understanding the formation and evolution of galaxies. As the number of observationally determined stellar abundances continues to climb, these simulations are able to provide new constraints on the early star formaton history and chemical evolution inside both the Milky Way and Local Group dwarf galaxies. Here, we aim to reproduce the low α-element scatter observed in metal-poor stars. We first demonstrate that as stellar particles inside simulations drop below a mass threshold, increases in the resolution produce an unacceptably large scatter as one particle is no longer a good approximation of an entire stellar population. This threshold occurs at around 103M⊙, a mass limit easily reached in current (and future) simulations. By simulating the Sextans and Fornax dwarf spheroidal galaxies we show that this increase in scatter at high resolutions arises from stochastic supernovae explosions. In order to reduce this scatter down to the observed value, we show the necessity of introducing a metal mixing scheme into particle-based simulations. The impact of the method used to inject the metals into the surrounding gas is also discussed. We finally summarise the best approach for accurately reproducing the scatter in simulations of both Local Group dwarf galaxies and in the Milky Way. \n
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\n  \n\n  \n  \n  \n  \n  \n  \n    The stochastic integrable AKNS hierarchy.\n  \n  \n  \n  \n\n\n  \n  Arnaudon, A.\n\n\n  \n\n\n\n  arXiv preprint arXiv:1511.07080.  2015.\n  \n\n\n\n
\n\n\n\n  \n  \n    \"The arxiv\n   \n  \n\n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n   \n  \n    abstract \n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n  \n  \n\n\n\n
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@article{arnaudon2015integrable,\n\tAuthor = {Arnaudon, Alexis},\n\tjournal={arXiv preprint arXiv:1511.07080},\n\tTitle = {The stochastic integrable {AKNS} hierarchy},\n\tYear = {2015},\n\turl_arXiv={http://arxiv.org/abs/1511.07080},\n\tabstract={     We derive a stochastic AKNS hierarchy using geometrical methods. The integrability is shown via a stochastic zero curvature relation associated with a stochastic isospectral problem. We expose some of the stochastic integrable partial differential equations which extend the stochastic KdV equation discovered by M. Wadati in 1983 for all the AKNS flows. We also show how to find stochastic solitons from the stochastic evolution of the scattering data of the stochastic IST. We finally expose some properties of these equations and also briefly study a stochastic Camassa-Holm equation which reduces to a stochastic Hamiltonian system of peakons. },\n\tkeywords={integrable systems,stochastic mechanics}\n\t}\n\n  \t\n
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\n  We derive a stochastic AKNS hierarchy using geometrical methods. The integrability is shown via a stochastic zero curvature relation associated with a stochastic isospectral problem. We expose some of the stochastic integrable partial differential equations which extend the stochastic KdV equation discovered by M. Wadati in 1983 for all the AKNS flows. We also show how to find stochastic solitons from the stochastic evolution of the scattering data of the stochastic IST. We finally expose some properties of these equations and also briefly study a stochastic Camassa-Holm equation which reduces to a stochastic Hamiltonian system of peakons. \n
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\n  \n\n  \n  \n  \n  \n  \n  \n    Covariant un-reduction for curve matching.\n  \n  \n  \n  \n\n\n  \n  Arnaudon, A.; López, M. C.;  and Holm, D. D.\n\n\n  \n\n\n\n  In MFCA2015, arXiv:1508.05325,  2015. \n  \n\n\n\n
\n\n\n\n  \n  \n    \"Covariant arxiv\n   \n  \n\n  \n\n  \n  link\n   \n  \n\n  bibtex\n    \n\n  \n   \n  \n    abstract \n  \n\n  \n\n  \n  \n  \n  \n  \n  \n  \n\n   \n  \n  \n  \n  \n\n\n\n
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@inproceedings{arnaudon2015covariant,\n\ttitle={Covariant un-reduction for curve matching},\n\tauthor={Arnaudon, Alexis\n\t\tand L{\\'o}pez, Marco Castrill{\\'o}n\n\t        and Holm, Darryl D.},\n\tbooktitle={MFCA2015, arXiv:1508.05325},\n\tyear={2015},\n\turl_arXiv={http://arxiv.org/abs/1508.05325},\n\tabstract={     The process of un-reduction, a sort of reversal of reduction by the Lie group symmetries of a variational problem, is explored in the setting of field theories. This process is applied to the problem of curve matching in the plane, when the curves depend on more than one independent variable. This situation occurs in a variety of instances such as matching of surfaces or comparison of evolution between species. A discussion of the appropriate Lagrangian involved in the variational principle is given, as well as some initial numerical investigations. },\n\tkeywords={shape analysis}\n}\n\n
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\n  The process of un-reduction, a sort of reversal of reduction by the Lie group symmetries of a variational problem, is explored in the setting of field theories. This process is applied to the problem of curve matching in the plane, when the curves depend on more than one independent variable. This situation occurs in a variety of instances such as matching of surfaces or comparison of evolution between species. A discussion of the appropriate Lagrangian involved in the variational principle is given, as well as some initial numerical investigations. \n
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