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2020
(4)

Upscaling the interplay between diffusion and polynomial drifts through a composite thin strip with periodic microstructure.
Cirillo, E.; de Bonis, I.; Muntean, A.; and Richardson, O.
*Meccanica*. 2020.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Upscaling the interplay between diffusion and polynomial drifts through a composite thin strip with periodic microstructure}, type = {article}, year = {2020}, keywords = {Concentration localization,Derivation of nonlinear transmission boundary cond,Diffusion,Dimension reduction,Polynomial drifts,Upscaling}, id = {70cf2de3-f461-311a-9b44-f355a3e26830}, created = {2020-10-22T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2020-10-23T14:35:35.655Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2020, The Author(s). We study the upscaling of a system of many interacting particles through a heterogenous thin elongated obstacle as modeled via a two-dimensional diffusion problem with a one-directional nonlinear convective drift.Assuming that the obstacle can be described well by a thin composite strip with periodically placed microstructures, we aim at deriving the upscaled model equations as well as the effective transport coefficients for suitable scalings in terms of both the inherent thickness at the strip and the typical length scales of the microscopic heterogeneities. Aiming at computable scenarios, we consider that the heterogeneity of the strip is made of an array of periodically arranged impenetrable solid rectangles and identify two scaling regimes what concerns the small asymptotics parameter for the upscaling procedure: the characteristic size of the microstructure is either significantly smaller than the thickness of the thin obstacle or it is of the same order of magnitude.We scale up the diffusion–polynomial drift model and list computable formulas for the effective diffusion and drift tensorial coefficients for both scaling regimes. Our upscaling procedure combines ideas of two-scale asymptotics homogenization with dimension reduction arguments. Consequences of these results for the construction of more general transmission boundary conditions are discussed. We illustrate numerically the concentration profile of the chemical species passing through the upscaled strip in the finite thickness regime and point out that trapping of concentration inside the strip is likely to occur in at least two conceptually different transport situations: (i) full diffusion/dispersion matrix and nonlinear horizontal drift, and (ii) diagonal diffusion matrix and oblique nonlinear drift.}, bibtype = {article}, author = {Cirillo, E.N.M. and de Bonis, I. and Muntean, A. and Richardson, O.}, doi = {10.1007/s11012-020-01253-8}, journal = {Meccanica} }

© 2020, The Author(s). We study the upscaling of a system of many interacting particles through a heterogenous thin elongated obstacle as modeled via a two-dimensional diffusion problem with a one-directional nonlinear convective drift.Assuming that the obstacle can be described well by a thin composite strip with periodically placed microstructures, we aim at deriving the upscaled model equations as well as the effective transport coefficients for suitable scalings in terms of both the inherent thickness at the strip and the typical length scales of the microscopic heterogeneities. Aiming at computable scenarios, we consider that the heterogeneity of the strip is made of an array of periodically arranged impenetrable solid rectangles and identify two scaling regimes what concerns the small asymptotics parameter for the upscaling procedure: the characteristic size of the microstructure is either significantly smaller than the thickness of the thin obstacle or it is of the same order of magnitude.We scale up the diffusion–polynomial drift model and list computable formulas for the effective diffusion and drift tensorial coefficients for both scaling regimes. Our upscaling procedure combines ideas of two-scale asymptotics homogenization with dimension reduction arguments. Consequences of these results for the construction of more general transmission boundary conditions are discussed. We illustrate numerically the concentration profile of the chemical species passing through the upscaled strip in the finite thickness regime and point out that trapping of concentration inside the strip is likely to occur in at least two conceptually different transport situations: (i) full diffusion/dispersion matrix and nonlinear horizontal drift, and (ii) diagonal diffusion matrix and oblique nonlinear drift.

Uniqueness and stability with respect to parameters of solutions to a fluid-like driven system for active-passive pedestrian dynamics.
Thieu, T.; Colangeli, M.; and Muntean, A.
*Journal of Mathematical Analysis and Applications*. 2020.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Uniqueness and stability with respect to parameters of solutions to a fluid-like driven system for active-passive pedestrian dynamics}, type = {article}, year = {2020}, keywords = {Double nonlinear parabolic equation,Forchheimer flows,Nonlinear coupling,Pedestrian flows}, id = {2dca5ed6-10e1-3706-83a4-51dbec717524}, created = {2020-10-31T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2020-11-03T07:05:39.240Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2020 Elsevier Inc. We study a system of parabolic equations consisting of a double nonlinear parabolic equation of Forchheimer type coupled with a semilinear parabolic equation. The system describes a fluid-like driven system for active-passive pedestrian dynamics. The structure of the nonlinearity of the coupling allows us to prove the uniqueness of solutions. We provide also the stability estimate of solutions with respect to selected parameters.}, bibtype = {article}, author = {Thieu, T.K.T. and Colangeli, M. and Muntean, A.}, doi = {10.1016/j.jmaa.2020.124702}, journal = {Journal of Mathematical Analysis and Applications} }

© 2020 Elsevier Inc. We study a system of parabolic equations consisting of a double nonlinear parabolic equation of Forchheimer type coupled with a semilinear parabolic equation. The system describes a fluid-like driven system for active-passive pedestrian dynamics. The structure of the nonlinearity of the coupling allows us to prove the uniqueness of solutions. We provide also the stability estimate of solutions with respect to selected parameters.

When diffusion faces drift: Consequences of exclusion processes for bi-directional pedestrian ows.
Cirillo, E.; Colangeli, M.; Muntean, A.; and Thieu, T.
2020.

link bibtex abstract

link bibtex abstract

@misc{ title = {When diffusion faces drift: Consequences of exclusion processes for bi-directional pedestrian ows}, type = {misc}, year = {2020}, source = {arXiv}, keywords = {Occupation numbers,Particles current,Passive-active pedestrian ows,Simple exclusion process,Two species stochastic dynamics}, id = {a2dea75a-106d-31d8-8169-f91163b509f9}, created = {2020-11-03T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2020-11-06T11:05:58.368Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © 2020, arXiv, All rights reserved. Stochastic particle-based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of particles, mimicking pedestrians walking in a built environment, enter a room from two opposite sides. One population is passive - being unaware of the local environment; particles belonging to this group perform a symmetric random walk. The other population has information on the local geometry in the sense that as soon as particles enter a visibility zone, a drift activates them. Their self-propulsion leads them towards the exit. This second type of species is referred here as active. The assumed crowdedness corresponds to a near-jammed scenario. The main question we ask in this paper is: Can we induce modifications of the dynamics of the active particles to improve the outgoing current of the passive particles? To address this question, we compute occupation number profiles and currents for both populations in selected parameter ranges. Besides observing the more classical faster-is-slower effect, new features appear as prominent like the non-monotonicity of currents, self-induced phase separation within the active population, as well as acceleration of passive particles for large-drift regimes of active particles.MSC Codes 82C20, 82C80}, bibtype = {misc}, author = {Cirillo, E.N.M. and Colangeli, M. and Muntean, A. and Thieu, T.K.T.} }

Copyright © 2020, arXiv, All rights reserved. Stochastic particle-based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of particles, mimicking pedestrians walking in a built environment, enter a room from two opposite sides. One population is passive - being unaware of the local environment; particles belonging to this group perform a symmetric random walk. The other population has information on the local geometry in the sense that as soon as particles enter a visibility zone, a drift activates them. Their self-propulsion leads them towards the exit. This second type of species is referred here as active. The assumed crowdedness corresponds to a near-jammed scenario. The main question we ask in this paper is: Can we induce modifications of the dynamics of the active particles to improve the outgoing current of the passive particles? To address this question, we compute occupation number profiles and currents for both populations in selected parameter ranges. Besides observing the more classical faster-is-slower effect, new features appear as prominent like the non-monotonicity of currents, self-induced phase separation within the active population, as well as acceleration of passive particles for large-drift regimes of active particles.MSC Codes 82C20, 82C80

A moving boundary approach of capturing diffusants penetration into rubber: FEM approximation and comparison with laboratory measurements.
Nepal, S.; Meyer, R.; Kröger, N.; Aiki, T.; Muntean, A.; Wondmagegne, Y.; and Giese, U.
2020.

link bibtex abstract

link bibtex abstract

@misc{ title = {A moving boundary approach of capturing diffusants penetration into rubber: FEM approximation and comparison with laboratory measurements}, type = {misc}, year = {2020}, source = {arXiv}, keywords = {Absorption,Diffusion,Finite element method,Moving boundary problem,Rubber,Swelling}, id = {a702aa17-decf-3a8c-8c09-198763c1f783}, created = {2021-02-08T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2021-02-21T10:38:33.579Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {true}, abstract = {© 2020, CC BY. We propose a moving-boundary scenario to model the penetration of diffusants into dense and foamed rubbers. The presented modelling approach recovers experimental findings related to the diffusion of cyclohexane and the resulting swelling in a piece of material made of ethylene propylene diene monomer rubber (EPDM). The main challenge is to find out relatively simple model components which can mimic the mechanical behavior of the rubber. Such special structure is identified here so that the computed penetration depths of the diffusant concentration are within the range of experimental measurements. We investigate two cases: a dense rubber and a rubber foam, both made of the same matrix material. After a brief discussion of scaling arguments, we present a finite element approximation of the moving boundary problem. To overcome numerical difficulties due to the a priori unknown motion of the diffusants penetration front, we transform the governing model equations from the physical domain with moving unknown boundary to a fixed fictitious domain. We then solve the transformed equations by the finite element method and explore the robustness of our approximations with respect to relevant model parameters. Finally, we discuss numerical estimations of the expected large-time behavior of the material.}, bibtype = {misc}, author = {Nepal, S. and Meyer, R. and Kröger, N.H. and Aiki, T. and Muntean, A. and Wondmagegne, Y. and Giese, U.} }

© 2020, CC BY. We propose a moving-boundary scenario to model the penetration of diffusants into dense and foamed rubbers. The presented modelling approach recovers experimental findings related to the diffusion of cyclohexane and the resulting swelling in a piece of material made of ethylene propylene diene monomer rubber (EPDM). The main challenge is to find out relatively simple model components which can mimic the mechanical behavior of the rubber. Such special structure is identified here so that the computed penetration depths of the diffusant concentration are within the range of experimental measurements. We investigate two cases: a dense rubber and a rubber foam, both made of the same matrix material. After a brief discussion of scaling arguments, we present a finite element approximation of the moving boundary problem. To overcome numerical difficulties due to the a priori unknown motion of the diffusants penetration front, we transform the governing model equations from the physical domain with moving unknown boundary to a fixed fictitious domain. We then solve the transformed equations by the finite element method and explore the robustness of our approximations with respect to relevant model parameters. Finally, we discuss numerical estimations of the expected large-time behavior of the material.

2019
(10)

Local weak solvability of a moving boundary problem describing swelling along a halfline.
Kumazaki, K.; and Muntean, A.
*Networks and Heterogeneous Media*, 14(3). 2019.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Local weak solvability of a moving boundary problem describing swelling along a halfline}, type = {article}, year = {2019}, keywords = {A priori estimates,Flux boundary conditions,Moving boundary problem,Nonlinear initialboundary value problems for nonli,Swelling of pores}, volume = {14}, id = {0346d6e2-9478-33dc-9f1d-fad80cf9dd38}, created = {2019-08-23T19:37:40.239Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.239Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© American Institute of Mathematical Sciences. We obtain the local well-posedness of a moving boundary problem that describes the swelling of a pocket of water within an infinitely thin elongated pore (i.e. on [a,+∞), a > 0). Our result involves fine a priori estimates of the moving boundary evolution, Banach fixed point arguments as well as an application of the general theory of evolution equations governed by subdifferentials.}, bibtype = {article}, author = {Kumazaki, K. and Muntean, A.}, doi = {10.3934/nhm.2019018}, journal = {Networks and Heterogeneous Media}, number = {3} }

© American Institute of Mathematical Sciences. We obtain the local well-posedness of a moving boundary problem that describes the swelling of a pocket of water within an infinitely thin elongated pore (i.e. on [a,+∞), a > 0). Our result involves fine a priori estimates of the moving boundary evolution, Banach fixed point arguments as well as an application of the general theory of evolution equations governed by subdifferentials.

Fast drift effects in the averaging of a filtration combustion system: A periodic homogenization approach.
Ijioma, E.; and Muntean, A.
*Quarterly of Applied Mathematics*, 77(1). 2019.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Fast drift effects in the averaging of a filtration combustion system: A periodic homogenization approach}, type = {article}, year = {2019}, keywords = {Filtration combustion,Periodic homogenization,Thermal dispersion,Two-scale convergence with drift}, volume = {77}, id = {2c456351-6c2a-3ce4-88be-936265035b6e}, created = {2019-08-23T19:37:40.287Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.287Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2018 Brown University. We target the periodic homogenization of a semi-linear reaction-diffusionconvection system describing filtration combustion, where fast drifts are triggered by the competition between heat and mass transfer processes in an asymptotic regime of dominant convection. In addition, we consider the interplay between surface nonlinear chemical reactions and transport processes. To handle the oscillations occurring due to the heterogeneity of the medium, we rely on the concept of two-scale convergence with drift to obtain, for suitably scaled model parameters, the upscaled system of equations together with effective transport parameters. The main difficulty is to treat the case of a coupled multi-physics problem. We proceed by extending the results reported by G. Allaire et al. and other related papers in this context to the case of a coupled system of evolution equations pertinent to filtration combustion.}, bibtype = {article}, author = {Ijioma, E.R. and Muntean, A.}, doi = {10.1090/qam/1509}, journal = {Quarterly of Applied Mathematics}, number = {1} }

© 2018 Brown University. We target the periodic homogenization of a semi-linear reaction-diffusionconvection system describing filtration combustion, where fast drifts are triggered by the competition between heat and mass transfer processes in an asymptotic regime of dominant convection. In addition, we consider the interplay between surface nonlinear chemical reactions and transport processes. To handle the oscillations occurring due to the heterogeneity of the medium, we rely on the concept of two-scale convergence with drift to obtain, for suitably scaled model parameters, the upscaled system of equations together with effective transport parameters. The main difficulty is to treat the case of a coupled multi-physics problem. We proceed by extending the results reported by G. Allaire et al. and other related papers in this context to the case of a coupled system of evolution equations pertinent to filtration combustion.

Particle-based modelling of flows through obstacles.
Cirillo, E.; Muntean, A.; and van Santen, R.
2019.

link bibtex abstract

link bibtex abstract

@book{ title = {Particle-based modelling of flows through obstacles}, type = {book}, year = {2019}, source = {Complexity Science: An Introduction}, id = {ff972083-f3bb-39c9-bc50-a3725bd6542a}, created = {2019-08-23T19:37:41.007Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.007Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2019 by World Scientific Publishing Co. Pte. Ltd. Particle diffusion is modified by the presence of barriers. In cells macromolecules, behaving as obstacles, slow down the dynamics so that the meansquare displacement of molecules grows with time as a power law with exponent smaller than one. In different situations, such as grain and pedestrian dynamics, it can happen that an obstacle can accelerate the dynamics. In the framework of very basic models, we study the time needed by particles to cross a strip for different bulk dynamics and discuss the effect of obstacles. We find that in some regimes such a residence time is not monotonic with respect to the size and the position of the obstacles. We can then conclude that, even in very elementary systems where no interaction among particles is considered, obstacles can either slow down or accelerate the particle dynamics depending on their geometry and position.}, bibtype = {book}, author = {Cirillo, E.N.M. and Muntean, A. and van Santen, R.A.} }

© 2019 by World Scientific Publishing Co. Pte. Ltd. Particle diffusion is modified by the presence of barriers. In cells macromolecules, behaving as obstacles, slow down the dynamics so that the meansquare displacement of molecules grows with time as a power law with exponent smaller than one. In different situations, such as grain and pedestrian dynamics, it can happen that an obstacle can accelerate the dynamics. In the framework of very basic models, we study the time needed by particles to cross a strip for different bulk dynamics and discuss the effect of obstacles. We find that in some regimes such a residence time is not monotonic with respect to the size and the position of the obstacles. We can then conclude that, even in very elementary systems where no interaction among particles is considered, obstacles can either slow down or accelerate the particle dynamics depending on their geometry and position.

Effects of Environment Knowledge in Evacuation Scenarios Involving Fire and Smoke: A Multiscale Modelling and Simulation Approach.
Richardson, O.; Jalba, A.; and Muntean, A.
*Fire Technology*, 55(2). 2019.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Effects of Environment Knowledge in Evacuation Scenarios Involving Fire and Smoke: A Multiscale Modelling and Simulation Approach}, type = {article}, year = {2019}, keywords = {Crowd dynamics,Environment knowledge,Evacuation,Fire and smoke dynamics,Particle methods,Transport processes}, volume = {55}, id = {f372daa6-b7d3-3d46-bdeb-2ec4161041c3}, created = {2019-08-23T19:37:41.043Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.043Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2018, The Author(s). We study the evacuation dynamics of a crowd evacuating from a complex geometry in the presence of a fire as well as of a slowly spreading smoke curtain. The crowd is composed of two kinds of individuals: those who know the layout of the building, and those who do not and rely exclusively on potentially informed neighbors to identify a path towards the exit. We aim to capture the effect the knowledge of the environment has on the interaction between evacuees and their residence time in the presence of fire and evolving smoke. Our approach is genuinely multiscale—we employ a two-scale model that is able to distinguish between compressible and incompressible pedestrian flow regimes and allows for micro and macro pedestrian dynamics. Simulations illustrate the expected qualitative behavior of the model. We finish with observations on how mixing evacuees with different levels of knowledge impacts important evacuation aspects.}, bibtype = {article}, author = {Richardson, O. and Jalba, A. and Muntean, A.}, doi = {10.1007/s10694-018-0743-x}, journal = {Fire Technology}, number = {2} }

© 2018, The Author(s). We study the evacuation dynamics of a crowd evacuating from a complex geometry in the presence of a fire as well as of a slowly spreading smoke curtain. The crowd is composed of two kinds of individuals: those who know the layout of the building, and those who do not and rely exclusively on potentially informed neighbors to identify a path towards the exit. We aim to capture the effect the knowledge of the environment has on the interaction between evacuees and their residence time in the presence of fire and evolving smoke. Our approach is genuinely multiscale—we employ a two-scale model that is able to distinguish between compressible and incompressible pedestrian flow regimes and allows for micro and macro pedestrian dynamics. Simulations illustrate the expected qualitative behavior of the model. We finish with observations on how mixing evacuees with different levels of knowledge impacts important evacuation aspects.

Analysis of a projection method for the Stokes problem using an ε -Stokes approach.
Kimura, M.; Matsui, K.; Muntean, A.; and Notsu, H.
*Japan Journal of Industrial and Applied Mathematics*. 2019.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Analysis of a projection method for the Stokes problem using an ε -Stokes approach}, type = {article}, year = {2019}, keywords = {Asymptotic analysis,Finite element method,Pressure-Poisson equation,Stokes problem}, id = {a33a2b10-ba29-36e1-8ffe-df3a463ccf48}, created = {2019-08-23T19:37:41.653Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.653Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2019, The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature. We generalize pressure boundary conditions of an ε-Stokes problem. Our ε-Stokes problem connects the classical Stokes problem and the corresponding pressure-Poisson equation using one parameter ε> 0. For the Dirichlet boundary condition, it is proven in Matsui and Muntean (Adv Math Sci Appl, 27:181–191, 2018) that the solution for the ε-Stokes problem converges to the one for the Stokes problem as ε tends to 0, and to the one for the pressure-Poisson problem as ε tends to ∞. Here, we extend these results to the Neumann and mixed boundary conditions. We also establish error estimates in suitable norms between the solutions to the ε-Stokes problem, the pressure-Poisson problem and the Stokes problem, respectively. Several numerical examples are provided to show that several such error estimates are optimal in ε. Our error estimates are improved if one uses the Neumann boundary conditions. In addition, we show that the solution to the ε-Stokes problem has a nice asymptotic structure.}, bibtype = {article}, author = {Kimura, M. and Matsui, K. and Muntean, A. and Notsu, H.}, doi = {10.1007/s13160-019-00373-3}, journal = {Japan Journal of Industrial and Applied Mathematics} }

© 2019, The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature. We generalize pressure boundary conditions of an ε-Stokes problem. Our ε-Stokes problem connects the classical Stokes problem and the corresponding pressure-Poisson equation using one parameter ε> 0. For the Dirichlet boundary condition, it is proven in Matsui and Muntean (Adv Math Sci Appl, 27:181–191, 2018) that the solution for the ε-Stokes problem converges to the one for the Stokes problem as ε tends to 0, and to the one for the pressure-Poisson problem as ε tends to ∞. Here, we extend these results to the Neumann and mixed boundary conditions. We also establish error estimates in suitable norms between the solutions to the ε-Stokes problem, the pressure-Poisson problem and the Stokes problem, respectively. Several numerical examples are provided to show that several such error estimates are optimal in ε. Our error estimates are improved if one uses the Neumann boundary conditions. In addition, we show that the solution to the ε-Stokes problem has a nice asymptotic structure.

Modelling, simulation and parameter identification of active pollution reduction with photocatalytic asphalt.
Kruschwitz, J.; Lind, M.; Muntean, A.; Richardson, O.; and Wondmagegne, Y.
*Acta Polytechnica*, 59(1). 2019.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Modelling, simulation and parameter identification of active pollution reduction with photocatalytic asphalt}, type = {article}, year = {2019}, keywords = {Environmental modelling,Finite element simulation,Parameter identification,Pollution}, volume = {59}, id = {7b10523e-7eb6-327b-b2d6-e70690c11c3b}, created = {2019-08-23T19:37:42.006Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:42.006Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© Czech Technical University in Prague, 2019. We develop and implement a numerical model to simulate the effect of photocatalytic asphalt on reducing the concentration of nitrogen monoxide (NO) due to the presence of heavy traffic in an urban environment. The contributions in this paper are threefold: we model and simulate the spread and breakdown of pollution in an urban environment, we provide a parameter estimation process that can be used to find missing parameters, and finally, we train and compare this simulation with different data sets. We analyse the results and provide an outlook on further research.}, bibtype = {article}, author = {Kruschwitz, J. and Lind, M. and Muntean, A. and Richardson, O. and Wondmagegne, Y.}, doi = {10.14311/AP.2019.59.0051}, journal = {Acta Polytechnica}, number = {1} }

© Czech Technical University in Prague, 2019. We develop and implement a numerical model to simulate the effect of photocatalytic asphalt on reducing the concentration of nitrogen monoxide (NO) due to the presence of heavy traffic in an urban environment. The contributions in this paper are threefold: we model and simulate the spread and breakdown of pollution in an urban environment, we provide a parameter estimation process that can be used to find missing parameters, and finally, we train and compare this simulation with different data sets. We analyse the results and provide an outlook on further research.

A lattice model approach to the morphology formation from ternary mixtures during the evaporation of one component.
Cirillo, E.; Colangeli, M.; Moons, E.; Muntean, A.; Muntean, S.; and van Stam, J.
*European Physical Journal: Special Topics*, 228(1). 2019.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {A lattice model approach to the morphology formation from ternary mixtures during the evaporation of one component}, type = {article}, year = {2019}, volume = {228}, id = {7705667f-647e-3e1d-a1ea-0dd70f99b83a}, created = {2019-08-23T19:37:42.093Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:42.093Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2019, The Author(s). Stimulated by experimental evidence in the field of solution-born thin films, we study the morphology formation in a three state lattice system subjected to the evaporation of one component. The practical problem that we address is the understanding of the parameters that govern morphology formation from a ternary mixture upon evaporation, as is the case in the fabrication of thin films from solution for organic photovoltaics. We use, as a tool, a generalized version of the Potts and Blume-Capel models in 2D, with the Monte Carlo Kawasaki-Metropolis algorithm, to simulate the phase behaviour of a ternary mixture upon evaporation of one of its components. The components with spin 1, −1 and 0 in the Blume-Capel dynamics correspond to the electron-acceptor, electron-donor and solvent molecules, respectively, in a ternary mixture used in the preparation of the active layer films in an organic solar cell. Furthermore, we introduce parameters that account for the relative composition of the mixture, temperature, and interaction between the species in the system. We identify the parameter regions that are prone to facilitate the phase separation. Furthermore, we study qualitatively the types of formed configurations. We show that even a relatively simple model, as the present one, can generate key morphological features, similar to those observed in experiments, which proves the method valuable for the study of complex systems.}, bibtype = {article}, author = {Cirillo, E.N.M. and Colangeli, M. and Moons, E. and Muntean, A. and Muntean, S.-A. and van Stam, J.}, doi = {10.1140/epjst/e2019-800140-1}, journal = {European Physical Journal: Special Topics}, number = {1} }

© 2019, The Author(s). Stimulated by experimental evidence in the field of solution-born thin films, we study the morphology formation in a three state lattice system subjected to the evaporation of one component. The practical problem that we address is the understanding of the parameters that govern morphology formation from a ternary mixture upon evaporation, as is the case in the fabrication of thin films from solution for organic photovoltaics. We use, as a tool, a generalized version of the Potts and Blume-Capel models in 2D, with the Monte Carlo Kawasaki-Metropolis algorithm, to simulate the phase behaviour of a ternary mixture upon evaporation of one of its components. The components with spin 1, −1 and 0 in the Blume-Capel dynamics correspond to the electron-acceptor, electron-donor and solvent molecules, respectively, in a ternary mixture used in the preparation of the active layer films in an organic solar cell. Furthermore, we introduce parameters that account for the relative composition of the mixture, temperature, and interaction between the species in the system. We identify the parameter regions that are prone to facilitate the phase separation. Furthermore, we study qualitatively the types of formed configurations. We show that even a relatively simple model, as the present one, can generate key morphological features, similar to those observed in experiments, which proves the method valuable for the study of complex systems.

A pore-scale study of transport of inertial particles by water in porous media.
Endo Kokubun, M.; Muntean, A.; Radu, F.; Kumar, K.; Pop, I.; Keilegavlen, E.; and Spildo, K.
*Chemical Engineering Science*, 207. 2019.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {A pore-scale study of transport of inertial particles by water in porous media}, type = {article}, year = {2019}, keywords = {Clogging,Flow diversion,Inertial particles,Particles transport,Porous medium}, volume = {207}, id = {78a092cc-e13f-3b77-8351-0d3259de21c0}, created = {2019-08-23T19:37:42.124Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:42.124Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2019 Elsevier Ltd We study the transport of inertial particles in water flow in porous media. Our interest lies in understanding the accumulation of particles including the possibility of clogging. We propose that accumulation can be a result of hydrodynamic effects: the tortuous paths of the porous medium generate regions of dominating strain, which favour the accumulation of particles. Numerical simulations show that essentially two accumulation regimes are identified: for low and for high flow velocities. When particles accumulate at the entrance of a pore throat (high-velocity region), a clog is formed. This significantly modifies the flow, as the partial blockage of the pore causes a local redistribution of pressure, which diverts the upstream water flow into neighbouring pores. Moreover, we show that accumulation in high velocity regions occurs in heterogeneous media, but not in homogeneous media, where we refer to homogeneity with respect to the distribution of the pore throat diameters.}, bibtype = {article}, author = {Endo Kokubun, M.A. and Muntean, A. and Radu, F.A. and Kumar, K. and Pop, I.S. and Keilegavlen, E. and Spildo, K.}, doi = {10.1016/j.ces.2019.06.036}, journal = {Chemical Engineering Science} }

© 2019 Elsevier Ltd We study the transport of inertial particles in water flow in porous media. Our interest lies in understanding the accumulation of particles including the possibility of clogging. We propose that accumulation can be a result of hydrodynamic effects: the tortuous paths of the porous medium generate regions of dominating strain, which favour the accumulation of particles. Numerical simulations show that essentially two accumulation regimes are identified: for low and for high flow velocities. When particles accumulate at the entrance of a pore throat (high-velocity region), a clog is formed. This significantly modifies the flow, as the partial blockage of the pore causes a local redistribution of pressure, which diverts the upstream water flow into neighbouring pores. Moreover, we show that accumulation in high velocity regions occurs in heterogeneous media, but not in homogeneous media, where we refer to homogeneity with respect to the distribution of the pore throat diameters.

Homogenization of a pseudo-parabolic system via a spatial-temporal decoupling: upscaling and corrector estimates for perforated domains.
Vromans, A.; van de Ven, F.; and Muntean, A.
2019.

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@misc{ title = {Homogenization of a pseudo-parabolic system via a spatial-temporal decoupling: upscaling and corrector estimates for perforated domains}, type = {misc}, year = {2019}, source = {arXiv}, keywords = {Corrector estimates,Mixture theory,Perforated domains,Periodic homogenization,Pseudo-parabolic system,Upscaled system}, id = {52773457-02a2-313b-bf16-2e63998713fb}, created = {2020-10-27T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2020-10-30T08:41:13.900Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © 2019, arXiv, All rights reserved. In this paper, we determine the convergence speed of an upscaling of a pseudo-parabolic system containing drift terms with scale separation of size ǫ ≪ 1. Both the upscaling and convergence speed determination exploit a natural spatial-temporal decomposition, which splits the pseudo-parabolic system into a spatial elliptic partial differential equation and a temporal ordinary differential equation. We extend the applicability to space-time domains that are a product of spatial and temporal domains, such as a time-independent perforated spatial domain. Finally, for special cases we show convergence speeds for global times, i.e. t ∈ R+, by using time intervals that converge to R+ as ǫ ↓ 0.35B27, 35K70, 35A35, 40A30}, bibtype = {misc}, author = {Vromans, A.J. and van de Ven, F. and Muntean, A.} }

Copyright © 2019, arXiv, All rights reserved. In this paper, we determine the convergence speed of an upscaling of a pseudo-parabolic system containing drift terms with scale separation of size ǫ ≪ 1. Both the upscaling and convergence speed determination exploit a natural spatial-temporal decomposition, which splits the pseudo-parabolic system into a spatial elliptic partial differential equation and a temporal ordinary differential equation. We extend the applicability to space-time domains that are a product of spatial and temporal domains, such as a time-independent perforated spatial domain. Finally, for special cases we show convergence speeds for global times, i.e. t ∈ R+, by using time intervals that converge to R+ as ǫ ↓ 0.35B27, 35K70, 35A35, 40A30

Weak solvability a fluid-like driven system for active-passive pedestrian dynamics.
Thieu, T.; Colangeli, M.; and Muntean, A.
2019.

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@misc{ title = {Weak solvability a fluid-like driven system for active-passive pedestrian dynamics}, type = {misc}, year = {2019}, source = {arXiv}, keywords = {Double non-linear parabolic equation,Forchheimer flows,Nonlinear coupling,Pedestrian flows}, id = {d122d20b-53f8-31ba-820f-805bcdb9b53a}, created = {2020-11-03T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2020-11-05T11:25:38.854Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © 2019, arXiv, All rights reserved. We study the question of weak solvability for a nonlinear coupled parabolic system that models the evolution of a complex pedestrian flow. The main feature is that the ow is composed of a mix of densities of active and passive pedestrians that are moving with different velocities. We rely on special energy estimates and on the use a Schauder's fixed point argument to tackle the existence of solutions to our evolution problem.MSC Codes 34B60, 34D20, 35Q35, 35K55, 35K65, 76S05, 76S99}, bibtype = {misc}, author = {Thieu, T.K.T. and Colangeli, M. and Muntean, A.} }

Copyright © 2019, arXiv, All rights reserved. We study the question of weak solvability for a nonlinear coupled parabolic system that models the evolution of a complex pedestrian flow. The main feature is that the ow is composed of a mix of densities of active and passive pedestrians that are moving with different velocities. We rely on special energy estimates and on the use a Schauder's fixed point argument to tackle the existence of solutions to our evolution problem.MSC Codes 34B60, 34D20, 35Q35, 35K55, 35K65, 76S05, 76S99

2018
(10)

Preface.
Muntean, A.
*Applicable Analysis*, 97(1). 2018.

doi link bibtex

doi link bibtex

@article{ title = {Preface}, type = {article}, year = {2018}, volume = {97}, id = {a5b0c67e-802c-3860-a386-20ebad5d31de}, created = {2019-08-23T19:37:40.110Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.110Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, bibtype = {article}, author = {Muntean, A.}, doi = {10.1080/00036811.2017.1397317}, journal = {Applicable Analysis}, number = {1} }

Corrector estimates for a thermodiffusion model with weak thermal coupling.
Muntean, A.; and Reichelt, S.
*Multiscale Modeling and Simulation*, 16(2). 2018.

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doi link bibtex abstract

@article{ title = {Corrector estimates for a thermodiffusion model with weak thermal coupling}, type = {article}, year = {2018}, keywords = {Composite media,Corrector estimates,Gradient folding operator,Homogenization,Perforated domain,Periodic unfolding,Reaction-diffusion systems,Thermodiffusion}, volume = {16}, id = {6faf656d-14bf-3b91-9611-897b3fe81f19}, created = {2019-08-23T19:37:40.335Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.335Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermodiffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast microstructures. The term \weak thermal coupling" refers here to the variable scaling in terms of the small homogenization parameter " of the heat conduction-diffusion interaction terms, while the \high-contrast" is considered particularly in terms of the heat conduction properties of the composite material. As a main target, we justify the first-order terms of the multiscale asymptotic expansions in the presence of coupled fluxes, induced by the joint contribution of Sorret and Dufour-like effects. The contrasting heat conduction combined with cross coupling leads to the main mathematical difficulty in the system. Our approach relies on the method of periodic unfolding combined with "-independent estimates for the thermal and concentration fields and for their coupled fluxes.}, bibtype = {article}, author = {Muntean, A. and Reichelt, S.}, doi = {10.1137/16M109538X}, journal = {Multiscale Modeling and Simulation}, number = {2} }

Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermodiffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast microstructures. The term \weak thermal coupling" refers here to the variable scaling in terms of the small homogenization parameter " of the heat conduction-diffusion interaction terms, while the \high-contrast" is considered particularly in terms of the heat conduction properties of the composite material. As a main target, we justify the first-order terms of the multiscale asymptotic expansions in the presence of coupled fluxes, induced by the joint contribution of Sorret and Dufour-like effects. The contrasting heat conduction combined with cross coupling leads to the main mathematical difficulty in the system. Our approach relies on the method of periodic unfolding combined with "-independent estimates for the thermal and concentration fields and for their coupled fluxes.

Asymptotics of diffusion-limited fast reactions.
Seidman, T.; and Muntean, A.
*Quarterly of Applied Mathematics*, 76(2). 2018.

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@article{ title = {Asymptotics of diffusion-limited fast reactions}, type = {article}, year = {2018}, keywords = {Asymptotics,Compactness,Energy method,Fast reaction,Reaction-diffusion systems}, volume = {76}, id = {f92c3b36-8923-39a7-9f80-aacf75777bb4}, created = {2019-08-23T19:37:40.342Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.342Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2017 Brown University. We are concerned with the fast-reaction asymptotics λ→∞ for a semilinear coupled diffusion-limited reaction system in contact with infinite reservoirs of reactants. We derive the system of limit equations and prove the uniqueness of its solutions for equal diffusion coefficients. Additionally, we emphasize the structure of the limit free boundary problem. The key tools of our analysis include (uniform with respect to λ) L1-estimates for both fluxes and products of reaction and a balanced formulation, where combinations of the original components which balance the fast reaction are used.}, bibtype = {article}, author = {Seidman, T.I. and Muntean, A.}, doi = {10.1090/qam/1496}, journal = {Quarterly of Applied Mathematics}, number = {2} }

© 2017 Brown University. We are concerned with the fast-reaction asymptotics λ→∞ for a semilinear coupled diffusion-limited reaction system in contact with infinite reservoirs of reactants. We derive the system of limit equations and prove the uniqueness of its solutions for equal diffusion coefficients. Additionally, we emphasize the structure of the limit free boundary problem. The key tools of our analysis include (uniform with respect to λ) L1-estimates for both fluxes and products of reaction and a balanced formulation, where combinations of the original components which balance the fast reaction are used.

A Priori Feedback Estimates for Multiscale Reaction-Diffusion Systems.
Lind, M.; and Muntean, A.
*Numerical Functional Analysis and Optimization*, 39(4). 2018.

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doi link bibtex abstract

@article{ title = {A Priori Feedback Estimates for Multiscale Reaction-Diffusion Systems}, type = {article}, year = {2018}, keywords = {Feedback finite element method,Galerkin approximation,micro–macro coupling,multiscale reaction–diffusion systems}, volume = {39}, id = {57a12052-0bc5-3096-ba16-5e0887c92723}, created = {2019-08-23T19:37:40.385Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.385Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2017 Taylor & Francis. We study the approximation of a multiscale reaction–diffusion system posed on both macroscopic and microscopic space scales. The coupling between the scales is done through micro–macro flux conditions. Our target system has a typical structure for reaction–diffusion flow problems in media with distributed microstructures (also called, double porosity materials). Besides ensuring basic estimates for the convergence of two-scale semi-discrete Galerkin approximations, we provide a set of a priori feedback estimates and a local feedback error estimator that help in designing a distributed-high-errors strategy to allow for a computationally eﬃcient zooming in and out from microscopic structures. The error control on the feedback estimates relies on two-scale-energy, regularity, and interpolation estimates as well as on a fine bookeeping of the sources responsible with the propagation of the (multiscale) approximation errors. The working technique based on a priori feedback estimates is in principle applicable to a large class of systems of PDEs with dual structure admitting strong solutions.}, bibtype = {article}, author = {Lind, M. and Muntean, A.}, doi = {10.1080/01630563.2017.1369996}, journal = {Numerical Functional Analysis and Optimization}, number = {4} }

© 2017 Taylor & Francis. We study the approximation of a multiscale reaction–diffusion system posed on both macroscopic and microscopic space scales. The coupling between the scales is done through micro–macro flux conditions. Our target system has a typical structure for reaction–diffusion flow problems in media with distributed microstructures (also called, double porosity materials). Besides ensuring basic estimates for the convergence of two-scale semi-discrete Galerkin approximations, we provide a set of a priori feedback estimates and a local feedback error estimator that help in designing a distributed-high-errors strategy to allow for a computationally eﬃcient zooming in and out from microscopic structures. The error control on the feedback estimates relies on two-scale-energy, regularity, and interpolation estimates as well as on a fine bookeeping of the sources responsible with the propagation of the (multiscale) approximation errors. The working technique based on a priori feedback estimates is in principle applicable to a large class of systems of PDEs with dual structure admitting strong solutions.

Well-posedness and inverse Robin estimate for a multiscale elliptic/parabolic system.
Lind, M.; Muntean, A.; and Richardson, O.
*Applicable Analysis*, 97(1). 2018.

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doi link bibtex abstract

@article{ title = {Well-posedness and inverse Robin estimate for a multiscale elliptic/parabolic system}, type = {article}, year = {2018}, keywords = {Upscaled porous media,inverse micro–macro Robin problem,two-scale PDE}, volume = {97}, id = {1d1bee53-ca93-3784-98c9-a778c2ddd424}, created = {2019-08-23T19:37:41.054Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.054Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2017 Informa UK Limited, trading as Taylor & Francis Group. We establish the well-posedness of a coupled micro–macro parabolic–elliptic system modeling the interplay between two pressures in a gas–liquid mixture close to equilibrium that is filling a porous media with distributed microstructures. Additionally, we prove a local stability estimate for the inverse micro–macro Robin problem, potentially useful in identifying quantitatively a micro–macro interfacial Robin transfer coefficient given microscopic measurements on accessible fixed interfaces. To tackle the solvability issue we use two-scale energy estimates and two-scale regularity/compactness arguments cast in the Schauder’s fixed point theorem. A number of auxiliary problems, regularity, and scaling arguments are used in ensuring the suitable Fréchet differentiability of the solution and the structure of the inverse stability estimate.}, bibtype = {article}, author = {Lind, M. and Muntean, A. and Richardson, O.M.}, doi = {10.1080/00036811.2017.1364366}, journal = {Applicable Analysis}, number = {1} }

© 2017 Informa UK Limited, trading as Taylor & Francis Group. We establish the well-posedness of a coupled micro–macro parabolic–elliptic system modeling the interplay between two pressures in a gas–liquid mixture close to equilibrium that is filling a porous media with distributed microstructures. Additionally, we prove a local stability estimate for the inverse micro–macro Robin problem, potentially useful in identifying quantitatively a micro–macro interfacial Robin transfer coefficient given microscopic measurements on accessible fixed interfaces. To tackle the solvability issue we use two-scale energy estimates and two-scale regularity/compactness arguments cast in the Schauder’s fixed point theorem. A number of auxiliary problems, regularity, and scaling arguments are used in ensuring the suitable Fréchet differentiability of the solution and the structure of the inverse stability estimate.

Modelling interactions between active and passive agents moving through heterogeneous environments.
Colangeli, M.; Muntean, A.; Richardson, O.; and Thieu, T.
2018.

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doi link bibtex abstract

@book{ title = {Modelling interactions between active and passive agents moving through heterogeneous environments}, type = {book}, year = {2018}, source = {Modeling and Simulation in Science, Engineering and Technology}, keywords = {Crowd dynamics,Fire and smoke dynamics,Heterogeneous domains,Lattice gas model,Particle methods}, id = {71212f4d-5b7a-3ee6-b67c-662e71e9c3f8}, created = {2019-08-23T19:37:41.693Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.693Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© Springer Nature Switzerland AG 2018. We study the dynamics of interacting agents from two distinct intermixed populations: one population includes active agents that follow a predetermined velocity field, while the second population contains exclusively passive agents, i.e., agents that have no preferred direction of motion. The orientation of their local velocity is affected by repulsive interactions with the neighboring agents and environment. We present two models that allow for a qualitative analysis of these mixed systems. We show that the residence times of this type of systems containing mixed populations is strongly affected by the interplay between these two populations. After showing our modelling and simulation results, we conclude with a couple of mathematical aspects concerning the well-posedness of our models.}, bibtype = {book}, author = {Colangeli, M. and Muntean, A. and Richardson, O. and Thieu, T.K.T.}, doi = {10.1007/978-3-030-05129-7_8} }

© Springer Nature Switzerland AG 2018. We study the dynamics of interacting agents from two distinct intermixed populations: one population includes active agents that follow a predetermined velocity field, while the second population contains exclusively passive agents, i.e., agents that have no preferred direction of motion. The orientation of their local velocity is affected by repulsive interactions with the neighboring agents and environment. We present two models that allow for a qualitative analysis of these mixed systems. We show that the residence times of this type of systems containing mixed populations is strongly affected by the interplay between these two populations. After showing our modelling and simulation results, we conclude with a couple of mathematical aspects concerning the well-posedness of our models.

Free to move or trapped in your group: Mathematical modeling of information overload and coordination in crowded populations.
Ciallella, A.; Cirillo, E.; Curşeu, P.; and Muntean, A.
*Mathematical Models and Methods in Applied Sciences*, 28(9). 2018.

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@article{ title = {Free to move or trapped in your group: Mathematical modeling of information overload and coordination in crowded populations}, type = {article}, year = {2018}, keywords = {Balance of measures,Coordination,Evacuation,Groups,Information overload,Pedestrian flows,Stochastic interacting particle systems}, volume = {28}, id = {c7eda7f1-50d8-3cf9-9e89-75c829182046}, created = {2019-08-23T19:37:41.697Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.697Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© World Scientific Publishing Company. We present modeling strategies that describe the motion and interaction of groups of pedestrians in obscured spaces.We start off with an approach based on balance equations in terms of measures and then we exploit the descriptive power of a probabilistic cellular automaton model. Based on a variation of the simple symmetric random walk on the square lattice, we test the interplay between population size and an interpersonal attraction parameter for the evacuation of confined and darkened spaces. We argue that information overload and coordination costs associated with information processing in small groups are two key processes that influence the evacuation rate. Our results show that substantial computational resources are necessary to compensate for incomplete information - the more individuals in (information processing) groups the higher the exit rate for low population size. For simple social systems, it is likely that the individual representations are not redundant and large group sizes ensure that this non-redundant information is actually available to a substantial number of individuals. For complex social systems, information redundancy makes information evaluation and transfer inefficient and, as such, group size becomes a drawback rather than a benefit. The effect of group sizes on outgoing fluxes, evacuation times and wall effects is carefully studied with a Monte Carlo framework accounting also for the presence of an internal obstacle.}, bibtype = {article}, author = {Ciallella, A. and Cirillo, E.N.M. and Curşeu, P.L. and Muntean, A.}, doi = {10.1142/S0218202518400079}, journal = {Mathematical Models and Methods in Applied Sciences}, number = {9} }

© World Scientific Publishing Company. We present modeling strategies that describe the motion and interaction of groups of pedestrians in obscured spaces.We start off with an approach based on balance equations in terms of measures and then we exploit the descriptive power of a probabilistic cellular automaton model. Based on a variation of the simple symmetric random walk on the square lattice, we test the interplay between population size and an interpersonal attraction parameter for the evacuation of confined and darkened spaces. We argue that information overload and coordination costs associated with information processing in small groups are two key processes that influence the evacuation rate. Our results show that substantial computational resources are necessary to compensate for incomplete information - the more individuals in (information processing) groups the higher the exit rate for low population size. For simple social systems, it is likely that the individual representations are not redundant and large group sizes ensure that this non-redundant information is actually available to a substantial number of individuals. For complex social systems, information redundancy makes information evaluation and transfer inefficient and, as such, group size becomes a drawback rather than a benefit. The effect of group sizes on outgoing fluxes, evacuation times and wall effects is carefully studied with a Monte Carlo framework accounting also for the presence of an internal obstacle.

A semidiscrete Galerkin scheme for a two-scale coupled elliptic-parabolic system: Well-posedness and convergence approximation rates.
Lind, M.; Muntean, A.; and Richardson, O.
2018.

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@misc{ title = {A semidiscrete Galerkin scheme for a two-scale coupled elliptic-parabolic system: Well-posedness and convergence approximation rates}, type = {misc}, year = {2018}, source = {arXiv}, keywords = {Distributed microstructures,Elliptic-parabolic system,Error analysis,Galerkin approx-imations,Macroscopic mesh refinement strategy,Weak solutions}, id = {35f88e65-e0ca-30ea-805a-2ddf6e07697c}, created = {2020-10-27T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2020-10-30T15:47:51.349Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © 2018, arXiv, All rights reserved. In this paper, we study the evolution of a gas-liquid mixture via a cou- pled system of elliptic-parabolic equations posed on two separated spatial scales. The model equations describe the interplay between macroscopic and microscopic pressures in an unsaturated heterogeneous medium with distributed microstructures. Besides ensuring the well-posedness of our two-scale model, we design two-scale convergent numerical approxima- tions and prove a priori error estimates and propose an a posteriori error estimator. Finally, we propose a macroscopic mesh refinement strategy that ensures a redistribution of the local macroscopic errors until an over- all error reduction is achieved.MSC Codes 35K58, 65N30, 65N15}, bibtype = {misc}, author = {Lind, M. and Muntean, A. and Richardson, O.} }

Copyright © 2018, arXiv, All rights reserved. In this paper, we study the evolution of a gas-liquid mixture via a cou- pled system of elliptic-parabolic equations posed on two separated spatial scales. The model equations describe the interplay between macroscopic and microscopic pressures in an unsaturated heterogeneous medium with distributed microstructures. Besides ensuring the well-posedness of our two-scale model, we design two-scale convergent numerical approxima- tions and prove a priori error estimates and propose an a posteriori error estimator. Finally, we propose a macroscopic mesh refinement strategy that ensures a redistribution of the local macroscopic errors until an over- all error reduction is achieved.MSC Codes 35K58, 65N30, 65N15

Driven particle flux through a membrane: Two-scale asymptotics of a diffusion equation with polynomial drift.
Cirillo, E.; de Bonis, I.; Muntean, A.; and Richardson, O.
2018.

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@misc{ title = {Driven particle flux through a membrane: Two-scale asymptotics of a diffusion equation with polynomial drift}, type = {misc}, year = {2018}, source = {arXiv}, keywords = {Convection-diffusion,Derivation of transmission boundary conditions,Dimension reduction,Upscaling}, id = {c3786162-5a13-3462-8d5a-ba106c4f5b5a}, created = {2020-10-27T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2020-10-31T14:22:25.993Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © 2018, arXiv, All rights reserved. Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one–directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the structure of heterogeneities is observable the obstacle line has an inherent thickness. Assuming the heterogeneity to be made of an array of periodically arranged microstructures (e.g. impenetrable solid rectangles), two scaling regimes are identified: the characteristic size of the microstructure is either significantly smaller than the thickness of the obstacle line or it is of the same order of magnitude. We scale up the convection-diffusion model and compute the effective diffusion and drift tensorial coefficients for both scaling regimes. The upscaling procedure combines ideas of two-scale asymptotics homogenization with dimension reduction arguments. Consequences of these results for the construction of more general transmission boundary conditions are discussed. We numerically illustrate the behavior of the upscaled membrane in the finite thickness regime and apply it to describe the transport of CO2 through paperboard.35B27, 76M50, 76M45}, bibtype = {misc}, author = {Cirillo, E.N.M. and de Bonis, I. and Muntean, A. and Richardson, O.} }

Copyright © 2018, arXiv, All rights reserved. Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one–directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the structure of heterogeneities is observable the obstacle line has an inherent thickness. Assuming the heterogeneity to be made of an array of periodically arranged microstructures (e.g. impenetrable solid rectangles), two scaling regimes are identified: the characteristic size of the microstructure is either significantly smaller than the thickness of the obstacle line or it is of the same order of magnitude. We scale up the convection-diffusion model and compute the effective diffusion and drift tensorial coefficients for both scaling regimes. The upscaling procedure combines ideas of two-scale asymptotics homogenization with dimension reduction arguments. Consequences of these results for the construction of more general transmission boundary conditions are discussed. We numerically illustrate the behavior of the upscaled membrane in the finite thickness regime and apply it to describe the transport of CO2 through paperboard.35B27, 76M50, 76M45

Periodic homogenization of a pseudo-parabolic equation via a spatial-temporal decomposition.
Vromans, A.; Van De Ven, F.; and Muntean, A.
2018.

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@misc{ title = {Periodic homogenization of a pseudo-parabolic equation via a spatial-temporal decomposition}, type = {misc}, year = {2018}, source = {arXiv}, id = {499e8145-7595-3d76-9be4-91d8b8910b0d}, created = {2020-11-03T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2020-11-04T16:50:13.186Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © 2018, arXiv, All rights reserved. Pseudo-parabolic equations have been used to model unsaturated fluid flow in porous media. In this paper it is shown how a pseudo-parabolic equation can be upscaled when using a spatio-temporal decomposition employed in the Peszyńska-Showalter-Yi paper [8]. The spatial-temporal decomposition transforms the pseudo-parabolic equation into a system containing an elliptic partial differential equation and a temporal ordinary differential equation. To strengthen our argument, the pseudo-parabolic equation has been given advection/convection/drift terms. The upscaling is done with the technique of periodic homogenization via two-scale convergence. The well-posedness of the extended pseudo-parabolic equation is shown as well. Moreover, we argue that under certain conditions, a non-local-in-time term arises from the elimination of an unknown.MSC Codes 35B27, 40A10}, bibtype = {misc}, author = {Vromans, A.J. and Van De Ven, F. and Muntean, A.} }

Copyright © 2018, arXiv, All rights reserved. Pseudo-parabolic equations have been used to model unsaturated fluid flow in porous media. In this paper it is shown how a pseudo-parabolic equation can be upscaled when using a spatio-temporal decomposition employed in the Peszyńska-Showalter-Yi paper [8]. The spatial-temporal decomposition transforms the pseudo-parabolic equation into a system containing an elliptic partial differential equation and a temporal ordinary differential equation. To strengthen our argument, the pseudo-parabolic equation has been given advection/convection/drift terms. The upscaling is done with the technique of periodic homogenization via two-scale convergence. The well-posedness of the extended pseudo-parabolic equation is shown as well. Moreover, we argue that under certain conditions, a non-local-in-time term arises from the elimination of an unknown.MSC Codes 35B27, 40A10

2017
(14)

Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources.
De Bonis, I.; and Muntean, A.
*Electronic Journal of Differential Equations*, 2017. 2017.

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@article{ title = {Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources}, type = {article}, year = {2017}, keywords = {Reaction-diffusion systems,Singular parabolic equations,Weak solutions}, volume = {2017}, id = {34ff6c5f-08e2-3aed-aa36-46e525b5d170}, created = {2019-08-23T19:37:40.389Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.389Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2017 Texas State University. We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i) the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii) the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.}, bibtype = {article}, author = {De Bonis, I. and Muntean, A.}, journal = {Electronic Journal of Differential Equations} }

© 2017 Texas State University. We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i) the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii) the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.

Large-time behavior of solutions to a thermo-diffusion system with Smoluchowski interactions.
Aiki, T.; and Muntean, A.
*Journal of Differential Equations*, 263(5). 2017.

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@article{ title = {Large-time behavior of solutions to a thermo-diffusion system with Smoluchowski interactions}, type = {article}, year = {2017}, keywords = {Gradient estimates,Large-time behavior,Sorret and Dufour effects,Thermo-diffusion}, volume = {263}, id = {200551cc-a79b-3bb5-917d-609a3476f8ad}, created = {2019-08-23T19:37:40.424Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.424Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2017 Elsevier Inc. We prove the large time behavior of solutions to a coupled thermo-diffusion arising in the modeling of the motion of hot colloidal particles in porous media. Additionally, we also ensure the uniqueness of solutions of the target problem. The main mathematical difficulty is due to the presence in the right-hand side of the equations of products between temperature and concentration gradients. Such terms mimic the so-called thermodynamic Soret and Dufour effects. These are cross-coupling terms emphasizing in this context a strong interplay between heat conduction and molecular diffusion.}, bibtype = {article}, author = {Aiki, T. and Muntean, A.}, doi = {10.1016/j.jde.2017.04.024}, journal = {Journal of Differential Equations}, number = {5} }

© 2017 Elsevier Inc. We prove the large time behavior of solutions to a coupled thermo-diffusion arising in the modeling of the motion of hot colloidal particles in porous media. Additionally, we also ensure the uniqueness of solutions of the target problem. The main mathematical difficulty is due to the presence in the right-hand side of the equations of products between temperature and concentration gradients. Such terms mimic the so-called thermodynamic Soret and Dufour effects. These are cross-coupling terms emphasizing in this context a strong interplay between heat conduction and molecular diffusion.

Corrector estimates for the homogenization of a two-scale thermoelasticity problem with a priori known phase transformations.
Eden, M.; and Muntean, A.
*Electronic Journal of Differential Equations*, 2017. 2017.

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@article{ title = {Corrector estimates for the homogenization of a two-scale thermoelasticity problem with a priori known phase transformations}, type = {article}, year = {2017}, keywords = {Corrector estimates,Distributed microstructures,Homogenization,Time-dependent domains,Two-phase thermoelasticity}, volume = {2017}, id = {8eee6ca7-e8a5-3de6-b946-29fc85c4e8da}, created = {2019-08-23T19:37:40.428Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.428Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2017 Texas State University. We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in [11] by two-scale convergence arguments. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing a priori known phase transformations. While such estimates seem not to be obtainable in the fully coupled setting, we show that for some simplified scenarios optimal convergence rates can be proven rigorously. The main technique for the proofs are energy estimates using special reconstructions of two-scale functions and particular operator estimates for periodic functions with zero average. Here, additional regularity results for the involved functions are necessary.}, bibtype = {article}, author = {Eden, M. and Muntean, A.}, journal = {Electronic Journal of Differential Equations} }

© 2017 Texas State University. We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in [11] by two-scale convergence arguments. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing a priori known phase transformations. While such estimates seem not to be obtainable in the fully coupled setting, we show that for some simplified scenarios optimal convergence rates can be proven rigorously. The main technique for the proofs are energy estimates using special reconstructions of two-scale functions and particular operator estimates for periodic functions with zero average. Here, additional regularity results for the involved functions are necessary.

Homogenization of a fully coupled thermoelasticity problem for a highly heterogeneous medium with a priori known phase transformations.
Eden, M.; and Muntean, A.
*Mathematical Methods in the Applied Sciences*, 40(11). 2017.

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@article{ title = {Homogenization of a fully coupled thermoelasticity problem for a highly heterogeneous medium with a priori known phase transformations}, type = {article}, year = {2017}, keywords = {distributed microstructures,homogenization,time-dependent domains,two-phase thermoelasticity,two-scale convergence}, volume = {40}, id = {54259f2f-2b5c-3e71-aca4-042289006494}, created = {2019-08-23T19:37:40.464Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.464Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © 2017 John Wiley & Sons, Ltd. We investigate a linear, fully coupled thermoelasticity problem for a highly heterogeneous, two-phase medium. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing an a priori known interface movement because of phase transformations. After transforming the moving geometry to an ϵ-periodic, fixed reference domain, we establish the well-posedness of the model and derive a number of ϵ-independent a priori estimates. Via a two-scale convergence argument, we then show that the ϵ-dependent solutions converge to solutions of a corresponding upscaled model with distributed time-dependent microstructures. Copyright © 2017 John Wiley & Sons, Ltd.}, bibtype = {article}, author = {Eden, M. and Muntean, A.}, doi = {10.1002/mma.4276}, journal = {Mathematical Methods in the Applied Sciences}, number = {11} }

Copyright © 2017 John Wiley & Sons, Ltd. We investigate a linear, fully coupled thermoelasticity problem for a highly heterogeneous, two-phase medium. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing an a priori known interface movement because of phase transformations. After transforming the moving geometry to an ϵ-periodic, fixed reference domain, we establish the well-posedness of the model and derive a number of ϵ-independent a priori estimates. Via a two-scale convergence argument, we then show that the ϵ-dependent solutions converge to solutions of a corresponding upscaled model with distributed time-dependent microstructures. Copyright © 2017 John Wiley & Sons, Ltd.

Trapping in bottlenecks: Interplay between microscopic dynamics and large scale effects.
Cirillo, E.; Colangeli, M.; and Muntean, A.
*Physica A: Statistical Mechanics and its Applications*, 488. 2017.

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@article{ title = {Trapping in bottlenecks: Interplay between microscopic dynamics and large scale effects}, type = {article}, year = {2017}, keywords = {Condensation,Interacting particle systems,Pedestrian flows through bottlenecks,Stochastic modeling,Trapping}, volume = {488}, id = {5bddeb33-2abc-3f0e-b1c5-3ad2adb10e68}, created = {2019-08-23T19:37:41.095Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.095Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2017 Elsevier B.V. We investigate the appearance of trapping states in pedestrian flows through bottlenecks as a result of the interplay between the geometry of the system and the microscopic stochastic dynamics. We model the flow through a bottleneck via a Zero Range Process on a one-dimensional periodic lattice. Particle are removed from the lattice sites with rates proportional to the local occupation numbers. The bottleneck is modeled by a particular site of the lattice whose updating rate saturates to a constant value as soon as the local occupation number exceeds a fixed threshold. We show that for any finite value of the threshold the stationary particle current saturates to the limiting bottleneck rate when the total particle density in the system exceeds a critical value corresponding to the bottleneck rate itself.}, bibtype = {article}, author = {Cirillo, E.N.M. and Colangeli, M. and Muntean, A.}, doi = {10.1016/j.physa.2017.07.001}, journal = {Physica A: Statistical Mechanics and its Applications} }

© 2017 Elsevier B.V. We investigate the appearance of trapping states in pedestrian flows through bottlenecks as a result of the interplay between the geometry of the system and the microscopic stochastic dynamics. We model the flow through a bottleneck via a Zero Range Process on a one-dimensional periodic lattice. Particle are removed from the lattice sites with rates proportional to the local occupation numbers. The bottleneck is modeled by a particular site of the lattice whose updating rate saturates to a constant value as soon as the local occupation number exceeds a fixed threshold. We show that for any finite value of the threshold the stationary particle current saturates to the limiting bottleneck rate when the total particle density in the system exceeds a critical value corresponding to the bottleneck rate itself.

Weak solutions to Allen-Cahn-like equations modelling consolidation of porous media.
Harris, P.; Cirillo, E.; and Muntean, A.
*IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)*, 82(1). 2017.

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@article{ title = {Weak solutions to Allen-Cahn-like equations modelling consolidation of porous media}, type = {article}, year = {2017}, keywords = {Consolidation of porous media,Cross-diffusion system,Energy method,Finite differences,Leray-schauder fixed-point theorem,Weak solutions}, volume = {82}, id = {cbeb3579-0f6f-3c85-8af6-0143d76da316}, created = {2019-08-23T19:37:41.127Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.127Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© The authors 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. We study the weak solvability of a system of coupled Allen-Cahn-like equations resembling crossdiffusion which arises as a model for the consolidation of saturated porous media. Besides using energylike estimates, we cast the special structure of the system in the framework of the Leray-Schauder fixedpoint principle and ensure in this way the local existence of strong solutions to a regularized version of our system. Furthermore, weak convergence techniques ensure the existence of weak solutions to the original consolidation problem. The uniqueness of global-in-Time solutions is guaranteed in a particular case. Moreover, we use a finite difference scheme to show the negativity of the vector of solutions.}, bibtype = {article}, author = {Harris, P.A. and Cirillo, E.N.M. and Muntean, A.}, doi = {10.1093/imamat/hxw013}, journal = {IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)}, number = {1} }

© The authors 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. We study the weak solvability of a system of coupled Allen-Cahn-like equations resembling crossdiffusion which arises as a model for the consolidation of saturated porous media. Besides using energylike estimates, we cast the special structure of the system in the framework of the Leray-Schauder fixedpoint principle and ensure in this way the local existence of strong solutions to a regularized version of our system. Furthermore, weak convergence techniques ensure the existence of weak solutions to the original consolidation problem. The uniqueness of global-in-Time solutions is guaranteed in a particular case. Moreover, we use a finite difference scheme to show the negativity of the vector of solutions.

Discrete and continuum links to a nonlinear coupled transport problem of interacting populations.
Duong, M.; Muntean, A.; and Richardson, O.
*European Physical Journal: Special Topics*, 226(10). 2017.

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@article{ title = {Discrete and continuum links to a nonlinear coupled transport problem of interacting populations}, type = {article}, year = {2017}, volume = {226}, id = {11a1c76d-e736-3328-90a3-eb32817be333}, created = {2019-08-23T19:37:41.137Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.137Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2017, The Author(s). We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.}, bibtype = {article}, author = {Duong, M.H. and Muntean, A. and Richardson, O.M.}, doi = {10.1140/epjst/e2017-70009-y}, journal = {European Physical Journal: Special Topics}, number = {10} }

© 2017, The Author(s). We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.

Fluctuations around mean walking behaviors in diluted pedestrian flows.
Corbetta, A.; Lee, C.; Benzi, R.; Muntean, A.; and Toschi, F.
*Physical Review E*, 95(3). 2017.

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@article{ title = {Fluctuations around mean walking behaviors in diluted pedestrian flows}, type = {article}, year = {2017}, volume = {95}, id = {6460fc45-0696-3eaf-a97e-f1ab7d9aa61e}, created = {2019-08-23T19:37:42.042Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:42.042Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2017 American Physical Society. Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of a crowd is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviors. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviors. To understand quantitatively crowd stochasticity, we study the real-life dynamics of a large ensemble of pedestrians walking undisturbed, and we perform a statistical analysis of the fully resolved pedestrian trajectories obtained by a yearlong high-resolution measurement campaign. Our measurements have been carried out in a corridor of the Eindhoven University of Technology via a combination of Microsoft Kinect 3D range sensor and automatic head-tracking algorithms. The temporal homogeneity of our large database of trajectories allows us to robustly define and separate average walking behaviors from fluctuations parallel and orthogonal with respect to the average walking path. Fluctuations include rare events when individuals suddenly change their minds and invert their walking directions. Such tendency to invert direction has been poorly studied so far, even if it may have important implications on the functioning and safety of facilities. We propose a model for the dynamics of undisturbed pedestrians, based on stochastic differential equations, that provides a good agreement with our field observations, including the occurrence of rare events.}, bibtype = {article}, author = {Corbetta, A. and Lee, C.-M. and Benzi, R. and Muntean, A. and Toschi, F.}, doi = {10.1103/PhysRevE.95.032316}, journal = {Physical Review E}, number = {3} }

© 2017 American Physical Society. Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of a crowd is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviors. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviors. To understand quantitatively crowd stochasticity, we study the real-life dynamics of a large ensemble of pedestrians walking undisturbed, and we perform a statistical analysis of the fully resolved pedestrian trajectories obtained by a yearlong high-resolution measurement campaign. Our measurements have been carried out in a corridor of the Eindhoven University of Technology via a combination of Microsoft Kinect 3D range sensor and automatic head-tracking algorithms. The temporal homogeneity of our large database of trajectories allows us to robustly define and separate average walking behaviors from fluctuations parallel and orthogonal with respect to the average walking path. Fluctuations include rare events when individuals suddenly change their minds and invert their walking directions. Such tendency to invert direction has been poorly studied so far, even if it may have important implications on the functioning and safety of facilities. We propose a model for the dynamics of undisturbed pedestrians, based on stochastic differential equations, that provides a good agreement with our field observations, including the occurrence of rare events.

Existence of weak solutions for a pseudo-parabolic system coupling chemical reactions, diffusion and momentum equations^{∗}.
Vromans, A.; van de Ven, F.; and Muntean, A.
2017.

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@misc{ title = {Existence of weak solutions for a pseudo-parabolic system coupling chemical reactions, diffusion and momentum equations<sup>∗</sup>}, type = {misc}, year = {2017}, source = {arXiv}, keywords = {Existence,Reaction-diffusion,Rothe method,System of nonlinear parabolic and pseudo-parabolic,Weak solutions}, id = {5062951d-eeed-3a40-a26e-ba5e1ad8b508}, created = {2020-10-27T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2020-10-28T20:43:47.938Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © 2017, arXiv, All rights reserved. We study the weak solvability of a nonlinearly coupled system of parabolic and pseudo-parabolic equations describing the interplay between mechanics, chemical reactions, diffusion and flow in a mixture theory framework. Our approach relies on suitable discrete-in-time energy-like estimates and discrete Gronwall inequalities. In selected parameter regimes, these estimates ensure the convergence of the Rothe method for the discretized partial differential equations.35A01, 35K51 (Primary) 35D30, 35K70, 74D05, 74F10, 74F20, 74F25 (Secondary)}, bibtype = {misc}, author = {Vromans, A.J. and van de Ven, F. and Muntean, A.} }

Copyright © 2017, arXiv, All rights reserved. We study the weak solvability of a nonlinearly coupled system of parabolic and pseudo-parabolic equations describing the interplay between mechanics, chemical reactions, diffusion and flow in a mixture theory framework. Our approach relies on suitable discrete-in-time energy-like estimates and discrete Gronwall inequalities. In selected parameter regimes, these estimates ensure the convergence of the Rothe method for the discretized partial differential equations.35A01, 35K51 (Primary) 35D30, 35K70, 74D05, 74F10, 74F20, 74F25 (Secondary)

Corrector homogenization estimates for a non-stationary Stokes-Nernst-Planck-Poisson system in perforated domains.
Khoa, V.; and Muntean, A.
2017.

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@misc{ title = {Corrector homogenization estimates for a non-stationary Stokes-Nernst-Planck-Poisson system in perforated domains}, type = {misc}, year = {2017}, source = {arXiv}, keywords = {Corrector estimates,Homogenization asymptotics,Perforated domain,Stokes-Nernst-Planck-Poisson system,Two-scale convergence,Variable scalings}, id = {baab7582-fac3-3ceb-9c91-b9af9cc77e25}, created = {2020-10-27T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2020-10-29T09:49:13.633Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © 2017, arXiv, All rights reserved. We consider a non-stationary Stokes-Nernst-Planck-Poisson system posed in perforated domains. Our aim is to justify rigorously the homogenization limit for the upscaled system derived by means of two-scale convergence in [28]. In other words, we wish to obtain the so-called corrector homogenization estimates that specify the error obtained when upscaling the microscopic equations. Essentially, we control in terms of suitable norms differences between the micro- and macro-concentrations and between the corresponding micro- and macro-concentration gradients. The major challenges that we face are the coupled flux structure of the system, the nonlinear drift terms and the presence of the microstructures. Employing various energy-like estimates, we discuss several scalings choices and boundary conditions.35B27, 35C20, 35D30, 65M15}, bibtype = {misc}, author = {Khoa, V.A. and Muntean, A.} }

Copyright © 2017, arXiv, All rights reserved. We consider a non-stationary Stokes-Nernst-Planck-Poisson system posed in perforated domains. Our aim is to justify rigorously the homogenization limit for the upscaled system derived by means of two-scale convergence in [28]. In other words, we wish to obtain the so-called corrector homogenization estimates that specify the error obtained when upscaling the microscopic equations. Essentially, we control in terms of suitable norms differences between the micro- and macro-concentrations and between the corresponding micro- and macro-concentration gradients. The major challenges that we face are the coupled flux structure of the system, the nonlinear drift terms and the presence of the microstructures. Employing various energy-like estimates, we discuss several scalings choices and boundary conditions.35B27, 35C20, 35D30, 65M15

Colloidal transport in locally periodic evolving porous media - An upscaling exercise.
Muntean, A.; and Nikolopoulos, C.
2017.

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@misc{ title = {Colloidal transport in locally periodic evolving porous media - An upscaling exercise}, type = {misc}, year = {2017}, source = {arXiv}, keywords = {Asymptotic homogenization,Clogging,Colloidal dynamics,Evolving porous media,Numerical simulations,Storage capacity}, id = {00d202aa-ec3c-33e6-8267-1ee0703c1a9a}, created = {2020-10-27T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2020-10-29T12:02:39.011Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © 2017, arXiv, All rights reserved. We derive an upscaled model describing the aggregation and deposition of colloidal particles within a porous medium allowing for the possibility of local clogging of the pores. At the level of the pore scale, we extend an existing model for colloidal dynamics including the evolution of free interfaces separating colloidal particles deposited on solid boundaries (solid spheres) from the colloidal particles transported through the gaseous parts of the porous medium. As a result of deposition, the solid spheres grow reducing therefore the space available for transport in the gaseous phase. Upscaling procedures are applied and several classes of macroscopic models together with effective transport tensors are obtained, incorporating explicitly the local growth of the solid spheres. The resulting models are solved numerically and various simulations are presented. In particular, they are able to detect clogging regions, and therefore, can provide estimates on the storage capacity of the porous matrix.35B27, 76M50, 76R50, 76VXX, 76M10}, bibtype = {misc}, author = {Muntean, A. and Nikolopoulos, C.V.} }

Copyright © 2017, arXiv, All rights reserved. We derive an upscaled model describing the aggregation and deposition of colloidal particles within a porous medium allowing for the possibility of local clogging of the pores. At the level of the pore scale, we extend an existing model for colloidal dynamics including the evolution of free interfaces separating colloidal particles deposited on solid boundaries (solid spheres) from the colloidal particles transported through the gaseous parts of the porous medium. As a result of deposition, the solid spheres grow reducing therefore the space available for transport in the gaseous phase. Upscaling procedures are applied and several classes of macroscopic models together with effective transport tensors are obtained, incorporating explicitly the local growth of the solid spheres. The resulting models are solved numerically and various simulations are presented. In particular, they are able to detect clogging regions, and therefore, can provide estimates on the storage capacity of the porous matrix.35B27, 76M50, 76R50, 76VXX, 76M10

Effects of environment knowledge in evacuation scenarios involving fire and smoke - a multiscale modelling and simulation approach.
Richardson, O.; Jalbay, A.; and Muntean, A.
2017.

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@misc{ title = {Effects of environment knowledge in evacuation scenarios involving fire and smoke - a multiscale modelling and simulation approach}, type = {misc}, year = {2017}, source = {arXiv}, id = {6c0ee74c-60bb-3c98-a412-0164e8b36bbe}, created = {2020-10-27T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2020-10-30T16:22:05.772Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © 2017, arXiv, All rights reserved. We study the evacuation dynamics of a crowd evacuating from a com- plex geometry in the presence of a fire as well as of a slowly spreading smoke curtain. The crowd is composed of two kinds of individuals: those who know the layout of the building, and those who do not and rely ex- clusively on potentially informed neighbors to identify a path towards the flexit. We aim to capture the effect the knowledge of the environment has on the interaction between evacuees and their residence time in the presence of fire and evolving smoke. Our approach is genuinely multiscale - we employ a two-scale model that is able to distinguish between compress- ible and incompressible pedestrian flow regimes and allows for micro and macro pedestrian dynamics. Simulations illustrate the expected qualita- tive behavior of the model. We finish with observations on how mixing evacuees with different levels of knowledge impacts important evacuation aspects.655Z05, 82C70, 91E30}, bibtype = {misc}, author = {Richardson, O. and Jalbay, A. and Muntean, A.} }

Copyright © 2017, arXiv, All rights reserved. We study the evacuation dynamics of a crowd evacuating from a com- plex geometry in the presence of a fire as well as of a slowly spreading smoke curtain. The crowd is composed of two kinds of individuals: those who know the layout of the building, and those who do not and rely ex- clusively on potentially informed neighbors to identify a path towards the flexit. We aim to capture the effect the knowledge of the environment has on the interaction between evacuees and their residence time in the presence of fire and evolving smoke. Our approach is genuinely multiscale - we employ a two-scale model that is able to distinguish between compress- ible and incompressible pedestrian flow regimes and allows for micro and macro pedestrian dynamics. Simulations illustrate the expected qualita- tive behavior of the model. We finish with observations on how mixing evacuees with different levels of knowledge impacts important evacuation aspects.655Z05, 82C70, 91E30

Correctors justification for a Smoluchowski-Soret-Dufour model posed in perforated domains.
Khoa, V.; and Muntean, A.
2017.

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link bibtex abstract

@misc{ title = {Correctors justification for a Smoluchowski-Soret-Dufour model posed in perforated domains}, type = {misc}, year = {2017}, source = {arXiv}, id = {d6d83497-d7ae-362a-8d39-d3711ecf3cb8}, created = {2020-11-03T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2020-11-06T13:55:57.231Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © 2017, arXiv, All rights reserved. We study a coupled thermo-diffusion system that accounts for the dynamics of hot colloids in periodically heterogeneous media. Our model describes the joint evolution of temperature and colloidal concentrations in a saturated porous structure, where the Smoluchowski interactions are responsible for aggregation and fragmentation processes in the presence of Soret-Dufour type effects. Additionally, we allow for deposition and depletion on internal micro-surfaces. In this work, we derive corrector estimates quantifying the rate of convergence of the periodic homogenization limit process performed in [24] via two-scale convergence arguments. The major technical difficulties in the proof are linked to the estimates between nonlinear processes of aggregation and deposition and to the convergence arguments of the a priori information of the oscillating weak solutions and cell functions in high dimensions. Essentially, we circumvent the arisen difficulties by a suitable use of the energy method and of fine integral estimates controlling interactions at the level of micro-surfaces.MSC Codes 35B27, 35C20, 35D30, 65M15}, bibtype = {misc}, author = {Khoa, V.A. and Muntean, A.} }

Copyright © 2017, arXiv, All rights reserved. We study a coupled thermo-diffusion system that accounts for the dynamics of hot colloids in periodically heterogeneous media. Our model describes the joint evolution of temperature and colloidal concentrations in a saturated porous structure, where the Smoluchowski interactions are responsible for aggregation and fragmentation processes in the presence of Soret-Dufour type effects. Additionally, we allow for deposition and depletion on internal micro-surfaces. In this work, we derive corrector estimates quantifying the rate of convergence of the periodic homogenization limit process performed in [24] via two-scale convergence arguments. The major technical difficulties in the proof are linked to the estimates between nonlinear processes of aggregation and deposition and to the convergence arguments of the a priori information of the oscillating weak solutions and cell functions in high dimensions. Essentially, we circumvent the arisen difficulties by a suitable use of the energy method and of fine integral estimates controlling interactions at the level of micro-surfaces.MSC Codes 35B27, 35C20, 35D30, 65M15

Asymptotic analysis of an ε-Stokes problem connecting Stokes and pressure-Poisson problems.
Matsui, K.; and Muntean, A.
2017.

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link bibtex abstract

@misc{ title = {Asymptotic analysis of an ε-Stokes problem connecting Stokes and pressure-Poisson problems}, type = {misc}, year = {2017}, source = {arXiv}, keywords = {Asymptotic analysis,Pressure-Poisson equation,Stokes problem}, id = {8a9533b8-f85f-39c7-9cbc-b0160657ae2f}, created = {2020-11-04T23:59:00.000Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2020-11-10T18:16:26.303Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © 2017, arXiv, All rights reserved. In this Note, we prepare an ε-Stokes problem connecting the Stokes problem and the corresponding pressure-Poisson equation using one parameter ε > 0. We prove that the solution to the ε-Stokes problem, convergences as ε tends to 0 or ∞ to the Stokes and pressure-Poisson problem, respectively.MSC Codes 76D03 (Primary), 35Q35, 35B40 (Secondary)}, bibtype = {misc}, author = {Matsui, K. and Muntean, A.} }

Copyright © 2017, arXiv, All rights reserved. In this Note, we prepare an ε-Stokes problem connecting the Stokes problem and the corresponding pressure-Poisson equation using one parameter ε > 0. We prove that the solution to the ε-Stokes problem, convergences as ε tends to 0 or ∞ to the Stokes and pressure-Poisson problem, respectively.MSC Codes 76D03 (Primary), 35Q35, 35B40 (Secondary)

2016
(8)

Asymptotic analysis of a semi-linear elliptic system in perforated domains: Well-posedness and correctors for the homogenization limit.
Khoa, V.; and Muntean, A.
*Journal of Mathematical Analysis and Applications*, 439(1). 2016.

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@article{ title = {Asymptotic analysis of a semi-linear elliptic system in perforated domains: Well-posedness and correctors for the homogenization limit}, type = {article}, year = {2016}, keywords = {Corrector estimates,Elliptic systems,Homogenization,Perforated domains}, volume = {439}, id = {76de500b-8969-31f9-9082-74d62a4f930b}, created = {2019-08-23T19:37:40.508Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.508Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2016 Elsevier Inc. In this study, we prove results on the weak solvability and homogenization of a microscopic semi-linear elliptic system posed in perforated media. The model presented here explores the interplay between stationary diffusion and both surface and volume chemical reactions in porous media. Our interest lies in deriving homogenization limits (upscaling) for alike systems and particularly in justifying rigorously the obtained averaged descriptions. Essentially, we prove the well-posedness of the microscopic problem ensuring also the positivity and boundedness of the involved concentrations and then use the structure of the two scale expansions to derive corrector estimates delimitating this way the convergence rate of the asymptotic approximates to the macroscopic limit concentrations. Our techniques include Moser-like iteration techniques, a variational formulation, two-scale asymptotic expansions as well as energy-like estimates.}, bibtype = {article}, author = {Khoa, V.A. and Muntean, A.}, doi = {10.1016/j.jmaa.2016.02.068}, journal = {Journal of Mathematical Analysis and Applications}, number = {1} }

© 2016 Elsevier Inc. In this study, we prove results on the weak solvability and homogenization of a microscopic semi-linear elliptic system posed in perforated media. The model presented here explores the interplay between stationary diffusion and both surface and volume chemical reactions in porous media. Our interest lies in deriving homogenization limits (upscaling) for alike systems and particularly in justifying rigorously the obtained averaged descriptions. Essentially, we prove the well-posedness of the microscopic problem ensuring also the positivity and boundedness of the involved concentrations and then use the structure of the two scale expansions to derive corrector estimates delimitating this way the convergence rate of the asymptotic approximates to the macroscopic limit concentrations. Our techniques include Moser-like iteration techniques, a variational formulation, two-scale asymptotic expansions as well as energy-like estimates.

A note on iterations-based derivations of high-order homogenization correctors for multiscale semi-linear elliptic equations.
Khoa, V.; and Muntean, A.
*Applied Mathematics Letters*, 58. 2016.

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@article{ title = {A note on iterations-based derivations of high-order homogenization correctors for multiscale semi-linear elliptic equations}, type = {article}, year = {2016}, keywords = {Corrector estimates,Elliptic systems,Homogenization,Perforated domains}, volume = {58}, id = {7bcdcd94-92db-36b5-a2ae-8e15cdf16387}, created = {2019-08-23T19:37:40.514Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.514Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2016 Elsevier Ltd. All rights reserved. This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working technique relies on monotone iterations combined with formal two-scale homogenization asymptotics. It can be adapted to handle more complex scenarios including for instance nonlinearities posed at the boundary of perforations and the vectorial case, when the model equations are coupled only through the nonlinear production terms.}, bibtype = {article}, author = {Khoa, V.A. and Muntean, A.}, doi = {10.1016/j.aml.2016.02.009}, journal = {Applied Mathematics Letters} }

© 2016 Elsevier Ltd. All rights reserved. This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working technique relies on monotone iterations combined with formal two-scale homogenization asymptotics. It can be adapted to handle more complex scenarios including for instance nonlinearities posed at the boundary of perforations and the vectorial case, when the model equations are coupled only through the nonlinear production terms.

Blockage-induced condensation controlled by a local reaction.
Cirillo, E.; Colangeli, M.; and Muntean, A.
*Physical Review E*, 94(4). 2016.

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@article{ title = {Blockage-induced condensation controlled by a local reaction}, type = {article}, year = {2016}, volume = {94}, id = {4098e573-9dac-3eb8-a8c5-8f7866409d1d}, created = {2019-08-23T19:37:41.166Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.166Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2016 American Physical Society. We consider the setup of stationary zero range models and discuss the onset of condensation induced by a local blockage on the lattice. We show that the introduction of a local feedback on the hopping rates allows us to control the particle fraction in the condensed phase. This phenomenon results in a current versus blockage parameter curve characterized by two nonanalyticity points.}, bibtype = {article}, author = {Cirillo, E.N.M. and Colangeli, M. and Muntean, A.}, doi = {10.1103/PhysRevE.94.042116}, journal = {Physical Review E}, number = {4} }

© 2016 American Physical Society. We consider the setup of stationary zero range models and discuss the onset of condensation induced by a local blockage on the lattice. We show that the introduction of a local feedback on the hopping rates allows us to control the particle fraction in the condensed phase. This phenomenon results in a current versus blockage parameter curve characterized by two nonanalyticity points.

Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities.
Evers, J.; Hille, S.; and Muntean, A.
*SIAM Journal on Mathematical Analysis*, 48(3). 2016.

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@article{ title = {Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities}, type = {article}, year = {2016}, keywords = {Measure-valued equations,Mild solutions,Nonlinearities,Particle systems,Time discretization,Ux boundary con-dition}, volume = {48}, id = {068b7d6e-d666-39c1-b198-d90cbabc23ec}, created = {2019-08-23T19:37:41.175Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.175Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© by SIAM. In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and ux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of an earlier paper [J. Differential Equations, 259 (2015), pp. 1068-1097] to settings where the dynamics are driven by interactions. In a forward-Euler-like approach, we construct a time-discretized version of the original problem and employ those results as a building block within each subinterval. A limit solution is obtained as the mesh size of the time discretization goes to zero. Moreover, the limit is independent of the specific way of partitioning the time interval [0; T]. This paper is partially based on results presented in Chapter 5 of [Evolution Equations for Systems Governed by Social Interactions, Ph.D. thesis, Eindhoven University of Technology, 2015], while a number of issues that were still open there are now resolved.}, bibtype = {article}, author = {Evers, J.H.M. and Hille, S.C. and Muntean, A.}, doi = {10.1137/15M1031655}, journal = {SIAM Journal on Mathematical Analysis}, number = {3} }

© by SIAM. In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and ux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of an earlier paper [J. Differential Equations, 259 (2015), pp. 1068-1097] to settings where the dynamics are driven by interactions. In a forward-Euler-like approach, we construct a time-discretized version of the original problem and employ those results as a building block within each subinterval. A limit solution is obtained as the mesh size of the time discretization goes to zero. Moreover, the limit is independent of the specific way of partitioning the time interval [0; T]. This paper is partially based on results presented in Chapter 5 of [Evolution Equations for Systems Governed by Social Interactions, Ph.D. thesis, Eindhoven University of Technology, 2015], while a number of issues that were still open there are now resolved.

Effects of communication efficiency and exit capacity on fundamental diagrams for pedestrian motion in an obscure tunnel|a particle system approach.
Cirillo, E.; Colangeli, M.; and Muntean, A.
*Multiscale Modeling and Simulation*, 14(2). 2016.

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@article{ title = {Effects of communication efficiency and exit capacity on fundamental diagrams for pedestrian motion in an obscure tunnel|a particle system approach}, type = {article}, year = {2016}, keywords = {Continuity equation,Evacuation scenario,Fundamental diagrams,Hydrodynamic limits,Lattice model,Pedestrian transport in the dark,Porous media equation}, volume = {14}, id = {257d256b-5e59-3a84-b453-a27f2fe92d60}, created = {2019-08-23T19:37:41.204Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.204Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2016 Society for Industrial and Applied Mathematics. Fundamental diagrams describing the relation between pedestrians' speed and density are key points in understanding pedestrian dynamics. Experimental data evidence the onset of complex behaviors in which the velocity decreases with the density, and different logistic regimes are identified. This paper addresses the issue of pedestrian transport and of fundamental diagrams for a scenario involving the motion of pedestrians escaping from an obscure tunnel. We capture the effects of communication eficiency and exit capacity by means of two thresholds controlling the rate at which particles (walkers, pedestrians) move on the lattice. Using a particle system model, we show that in the absence of limitation in communication among pedestrians, we reproduce with good accuracy the standard fundamental diagrams, whose basic behaviors can be interpreted in terms of exit capacity limitation. When the effect of limited communication ability is considered, then interesting nonintuitive phenomena occur. In particular, we shed light on the loss of monotonicity of the typical speed-density curves, revealing the existence of a pedestrian density optimizing the escape. We study both the discrete particle dynamics and the corresponding hydrodynamic limit (a porous medium equation and a transport (continuity) equation). We also point out the dependence of the effective transport coeffcients on the two thresholds|the essence of the microstructure information.}, bibtype = {article}, author = {Cirillo, E.N.M. and Colangeli, M. and Muntean, A.}, doi = {10.1137/15M1030960}, journal = {Multiscale Modeling and Simulation}, number = {2} }

© 2016 Society for Industrial and Applied Mathematics. Fundamental diagrams describing the relation between pedestrians' speed and density are key points in understanding pedestrian dynamics. Experimental data evidence the onset of complex behaviors in which the velocity decreases with the density, and different logistic regimes are identified. This paper addresses the issue of pedestrian transport and of fundamental diagrams for a scenario involving the motion of pedestrians escaping from an obscure tunnel. We capture the effects of communication eficiency and exit capacity by means of two thresholds controlling the rate at which particles (walkers, pedestrians) move on the lattice. Using a particle system model, we show that in the absence of limitation in communication among pedestrians, we reproduce with good accuracy the standard fundamental diagrams, whose basic behaviors can be interpreted in terms of exit capacity limitation. When the effect of limited communication ability is considered, then interesting nonintuitive phenomena occur. In particular, we shed light on the loss of monotonicity of the typical speed-density curves, revealing the existence of a pedestrian density optimizing the escape. We study both the discrete particle dynamics and the corresponding hydrodynamic limit (a porous medium equation and a transport (continuity) equation). We also point out the dependence of the effective transport coeffcients on the two thresholds|the essence of the microstructure information.

Stationary Currents in Particle Systems with Constrained Hopping Rates.
Cirillo, E.; Colangeli, M.; and Muntean, A.
*Journal of Non-Equilibrium Thermodynamics*, 41(2). 2016.

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@article{ title = {Stationary Currents in Particle Systems with Constrained Hopping Rates}, type = {article}, year = {2016}, keywords = {stationary currents,stochastic particle systems,threshold effects}, volume = {41}, id = {029487e5-f3aa-344c-9426-ebe8b1bc8589}, created = {2019-08-23T19:37:41.216Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.216Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2016 by De Gruyter Mouton. We study the effect on the stationary currents of constraints affecting the hopping rates in stochastic particle systems. In the framework of zero range processes with drift within a finite volume, we discuss how the current is reduced by the presence of the constraint and deduce exact formulae, fully explicit in some cases. The model discussed here has been introduced by Cirillo et al. (Does communication enhance pedestrians transport in the dark? To appear in C. R. Mécanique 344 (2016), 19-23) and is relevant for the description of pedestrian motion in elongated dark corridors, where the constraint on the hopping rates can be related to limitations on the interaction distance among pedestrians, but finds also applications in the modeling of various transport phenomena.}, bibtype = {article}, author = {Cirillo, E.N.M. and Colangeli, M. and Muntean, A.}, doi = {10.1515/jnet-2015-0066}, journal = {Journal of Non-Equilibrium Thermodynamics}, number = {2} }

© 2016 by De Gruyter Mouton. We study the effect on the stationary currents of constraints affecting the hopping rates in stochastic particle systems. In the framework of zero range processes with drift within a finite volume, we discuss how the current is reduced by the presence of the constraint and deduce exact formulae, fully explicit in some cases. The model discussed here has been introduced by Cirillo et al. (Does communication enhance pedestrians transport in the dark? To appear in C. R. Mécanique 344 (2016), 19-23) and is relevant for the description of pedestrian motion in elongated dark corridors, where the constraint on the hopping rates can be related to limitations on the interaction distance among pedestrians, but finds also applications in the modeling of various transport phenomena.

Does communication enhance pedestrians transport in the dark?.
Cirillo, E.; Colangeli, M.; and Muntean, A.
*Comptes Rendus - Mecanique*, 344(1). 2016.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Does communication enhance pedestrians transport in the dark?}, type = {article}, year = {2016}, keywords = {Dynamics of crowd motions,Evacuation scenario,Lattice model,Thresholds}, volume = {344}, id = {2eccbf33-5cee-3cff-a04c-c18783e1a73a}, created = {2019-08-23T19:37:41.249Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.249Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2015 Académie des sciences. We study the motion of pedestrians through an obscure tunnel where the lack of visibility hides the exits. Using a lattice model, we explore the effects of communication on the effective transport properties of the crowd of pedestrians. More precisely, we study the effect of two thresholds on the structure of the effective nonlinear diffusion coefficient. One threshold models pedestrian communication efficiency in the dark, while the other one describes the tunnel capacity. Essentially, we note that if the evacuees show a maximum trust (leading to a fast communication), they tend to quickly find the exit and hence the collective action tends to prevent the occurrence of disasters.}, bibtype = {article}, author = {Cirillo, E.N.M. and Colangeli, M. and Muntean, A.}, doi = {10.1016/j.crme.2015.09.004}, journal = {Comptes Rendus - Mecanique}, number = {1} }

© 2015 Académie des sciences. We study the motion of pedestrians through an obscure tunnel where the lack of visibility hides the exits. Using a lattice model, we explore the effects of communication on the effective transport properties of the crowd of pedestrians. More precisely, we study the effect of two thresholds on the structure of the effective nonlinear diffusion coefficient. One threshold models pedestrian communication efficiency in the dark, while the other one describes the tunnel capacity. Essentially, we note that if the evacuees show a maximum trust (leading to a fast communication), they tend to quickly find the exit and hence the collective action tends to prevent the occurrence of disasters.

Lattice model of reduced jamming by a barrier.
Cirillo, E.; Krehel, O.; Muntean, A.; and Van Santen, R.
*Physical Review E*, 94(4). 2016.

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doi link bibtex abstract

@article{ title = {Lattice model of reduced jamming by a barrier}, type = {article}, year = {2016}, volume = {94}, id = {4fb73663-9a1b-3dee-a9a2-289c349280c9}, created = {2019-08-23T19:37:41.735Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.735Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2016 American Physical Society. We study an asymmetric simple exclusion process in a strip in the presence of a solid impenetrable barrier. We focus on the effect of the barrier on the residence time of the particles, namely, the typical time needed by the particles to cross the whole strip. We explore the conditions for reduced jamming when varying the environment (different drifts, reservoir densities, horizontal diffusion walks, etc.). In particular, we discover an interesting nonmonotonic behavior of the residence time as a function of the barrier length. Besides recovering by means of both the lattice dynamics and the mean-field model well-known aspects like the faster-is-slower effect and the intermittence of the flow, we propose also a birth-and-death process and a reduced one-dimensional (1D) model with variable barrier permeability to capture the behavior of the residence time with respect to the parameters.}, bibtype = {article}, author = {Cirillo, E.N.M. and Krehel, O. and Muntean, A. and Van Santen, R.}, doi = {10.1103/PhysRevE.94.042115}, journal = {Physical Review E}, number = {4} }

© 2016 American Physical Society. We study an asymmetric simple exclusion process in a strip in the presence of a solid impenetrable barrier. We focus on the effect of the barrier on the residence time of the particles, namely, the typical time needed by the particles to cross the whole strip. We explore the conditions for reduced jamming when varying the environment (different drifts, reservoir densities, horizontal diffusion walks, etc.). In particular, we discover an interesting nonmonotonic behavior of the residence time as a function of the barrier length. Besides recovering by means of both the lattice dynamics and the mean-field model well-known aspects like the faster-is-slower effect and the intermittence of the flow, we propose also a birth-and-death process and a reduced one-dimensional (1D) model with variable barrier permeability to capture the behavior of the residence time with respect to the parameters.

2015
(9)

Continuum Modeling: An Approach Through Practical Examples.
Muntean, A.
2015.

doi link bibtex abstract

doi link bibtex abstract

@book{ title = {Continuum Modeling: An Approach Through Practical Examples}, type = {book}, year = {2015}, source = {Continuum Modeling: An Approach Through Practical Examples}, id = {9446884f-d40e-32ae-b349-8676cec56e89}, created = {2019-08-23T19:37:40.111Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.111Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {This book develops continuum modeling skills and approaches the topic from three sides: (1) derivation of global integral laws together with the associated local differential equations, (2) design of constitutive laws and (3) modeling boundary processes. The focus of this presentation lies on many practical examples covering aspects such as coupled flow, diffusion and reaction in porous media or microwave heating of a pizza, as well as traffic issues in bacterial colonies and energy harvesting from geothermal wells. The target audience comprises primarily graduate students in pure and applied mathematics as well as working practitioners in engineering who are faced by nonstandard rheological topics like those typically arising in the food industry. The Author(s) 2015. All rights are reserved.}, bibtype = {book}, author = {Muntean, A.}, doi = {10.1007/978-3-319-22132-8} }

This book develops continuum modeling skills and approaches the topic from three sides: (1) derivation of global integral laws together with the associated local differential equations, (2) design of constitutive laws and (3) modeling boundary processes. The focus of this presentation lies on many practical examples covering aspects such as coupled flow, diffusion and reaction in porous media or microwave heating of a pizza, as well as traffic issues in bacterial colonies and energy harvesting from geothermal wells. The target audience comprises primarily graduate students in pure and applied mathematics as well as working practitioners in engineering who are faced by nonstandard rheological topics like those typically arising in the food industry. The Author(s) 2015. All rights are reserved.

Large-time behavior of a two-scale semilinear reaction-diffusion system for concrete sulfatation.
Aiki, T.; and Muntean, A.
*Mathematical Methods in the Applied Sciences*, 38(7). 2015.

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@article{ title = {Large-time behavior of a two-scale semilinear reaction-diffusion system for concrete sulfatation}, type = {article}, year = {2015}, keywords = {concrete corrosion,homogenization,large-time asymptotics,reaction-diffusion system,two-scale system}, volume = {38}, id = {03e915c6-719d-3ca7-937b-91b47fe71b43}, created = {2019-08-23T19:37:40.468Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.468Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2014 John Wiley and Sons, Ltd. We study the large-time behavior of (weak) solutions to a two-scale reaction-diffusion system coupled with a nonlinear ordinary differential equations modeling the partly dissipative corrosion of concrete (or cement)-based materials with sulfates. We prove that as t → ∞ , the solution to the original two-scale system converges to the corresponding two-scale stationary system. To obtain the main result, we make use essentially of the theory of evolution equations governed by subdifferential operators of time-dependent convex functions developed combined with a series of two-scale energy-like time-independent estimates.}, bibtype = {article}, author = {Aiki, T. and Muntean, A.}, doi = {10.1002/mma.3161}, journal = {Mathematical Methods in the Applied Sciences}, number = {7} }

© 2014 John Wiley and Sons, Ltd. We study the large-time behavior of (weak) solutions to a two-scale reaction-diffusion system coupled with a nonlinear ordinary differential equations modeling the partly dissipative corrosion of concrete (or cement)-based materials with sulfates. We prove that as t → ∞ , the solution to the original two-scale system converges to the corresponding two-scale stationary system. To obtain the main result, we make use essentially of the theory of evolution equations governed by subdifferential operators of time-dependent convex functions developed combined with a series of two-scale energy-like time-independent estimates.

Multiscale modeling of colloidal dynamics in porous media including aggregation and deposition.
Krehel, O.; Muntean, A.; and Knabner, P.
*Advances in Water Resources*, 86. 2015.

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@article{ title = {Multiscale modeling of colloidal dynamics in porous media including aggregation and deposition}, type = {article}, year = {2015}, keywords = {Aggregation,Colloidal transport,Deposition,Multiscale coefficients,Periodic homogenization}, volume = {86}, id = {19295097-0ce8-3fd5-b49d-7a509ca0c8f7}, created = {2019-08-23T19:37:41.259Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.259Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2015 Elsevier Ltd. We investigate the influence of aggregation and deposition on the colloidal dynamics in a saturated porous medium. On the pore scale, the aggregation of colloids is modeled by the Smoluchowski equation. Essentially, the colloidal mass splits into different size clusters and we treat clusters as different species involved in a diffusion-reaction mechanism. This modeling procedure allows for different material properties to be varied between the different species, specifically the diffusion rate, which changes due to size as described by the Stokes-Einstein relation, and the deposition rate. The periodic homogenization procedure is applied to obtain a macroscopic model. The resulting model is illustrated by numerical computations that capture the colloidal transport with and without aggregation.}, bibtype = {article}, author = {Krehel, O. and Muntean, A. and Knabner, P.}, doi = {10.1016/j.advwatres.2015.10.005}, journal = {Advances in Water Resources} }

© 2015 Elsevier Ltd. We investigate the influence of aggregation and deposition on the colloidal dynamics in a saturated porous medium. On the pore scale, the aggregation of colloids is modeled by the Smoluchowski equation. Essentially, the colloidal mass splits into different size clusters and we treat clusters as different species involved in a diffusion-reaction mechanism. This modeling procedure allows for different material properties to be varied between the different species, specifically the diffusion rate, which changes due to size as described by the Stokes-Einstein relation, and the deposition rate. The periodic homogenization procedure is applied to obtain a macroscopic model. The resulting model is illustrated by numerical computations that capture the colloidal transport with and without aggregation.

Mild solutions to a measure-valued mass evolution problem with flux boundary conditions.
Evers, J.; Hille, S.; and Muntean, A.
*Journal of Differential Equations*, 259(3). 2015.

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@article{ title = {Mild solutions to a measure-valued mass evolution problem with flux boundary conditions}, type = {article}, year = {2015}, keywords = {Boundary layer asymptotics,Convergence rate,Flux boundary condition,Measure-valued equations,Mild solutions,Singular limit}, volume = {259}, id = {d48a7304-9b1b-3a73-9d0c-34484230c78b}, created = {2019-08-23T19:37:41.294Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.294Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2015 Elsevier Inc. We investigate the well-posedness and approximation of mild solutions to a class of linear transport equations on the unit interval [0, 1] endowed with a linear discontinuous production term, formulated in the space M([0,1]) of finite Borel measures. Our working technique includes a detailed boundary layer analysis in terms of a semigroup representation of solutions in spaces of measures able to cope with the passage to the singular limit where thickness of the layer vanishes. We obtain not only a suitable concept of solutions to the chosen measure-valued evolution problem, but also derive convergence rates for the approximation procedure and get insight in the structure of flux boundary conditions for the limit problem.}, bibtype = {article}, author = {Evers, J.H.M. and Hille, S.C. and Muntean, A.}, doi = {10.1016/j.jde.2015.02.037}, journal = {Journal of Differential Equations}, number = {3} }

© 2015 Elsevier Inc. We investigate the well-posedness and approximation of mild solutions to a class of linear transport equations on the unit interval [0, 1] endowed with a linear discontinuous production term, formulated in the space M([0,1]) of finite Borel measures. Our working technique includes a detailed boundary layer analysis in terms of a semigroup representation of solutions in spaces of measures able to cope with the passage to the singular limit where thickness of the layer vanishes. We obtain not only a suitable concept of solutions to the chosen measure-valued evolution problem, but also derive convergence rates for the approximation procedure and get insight in the structure of flux boundary conditions for the limit problem.

Parameter estimation of social forces in pedestrian dynamics models via a probabilistic method.
Corbetta, A.; Muntean, A.; and Vafayi, K.
*Mathematical Biosciences and Engineering*, 12(2). 2015.

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@article{ title = {Parameter estimation of social forces in pedestrian dynamics models via a probabilistic method}, type = {article}, year = {2015}, keywords = {Bayes theorem,Crowd dynamics,Data analysis,Models classification,Parameter estimation}, volume = {12}, id = {82d7a6f2-6e24-31dc-ba01-89c1f38b9ab1}, created = {2019-08-23T19:37:41.302Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.302Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Focusing on a specific crowd dynamics situation, including real life experiments and measurements, our paper targets a twofold aim: (1) we present a Bayesian probabilistic method to estimate the value and the uncertainty (in the form of a probability density function) of parameters in crowd dynamic models from the experimental data; and (2) we introduce a fitness measure for the models to classify a couple of model structures (forces) according to their fitness to the experimental data, preparing the stage for a more general model-selection and validation strategy inspired by probabilistic data analysis. Finally, we review the essential aspects of our experimental setup and measurement technique.}, bibtype = {article}, author = {Corbetta, A. and Muntean, A. and Vafayi, K.}, doi = {10.3934/mbe.2015.12.337}, journal = {Mathematical Biosciences and Engineering}, number = {2} }

Focusing on a specific crowd dynamics situation, including real life experiments and measurements, our paper targets a twofold aim: (1) we present a Bayesian probabilistic method to estimate the value and the uncertainty (in the form of a probability density function) of parameters in crowd dynamic models from the experimental data; and (2) we introduce a fitness measure for the models to classify a couple of model structures (forces) according to their fitness to the experimental data, preparing the stage for a more general model-selection and validation strategy inspired by probabilistic data analysis. Finally, we review the essential aspects of our experimental setup and measurement technique.

Modelling with measures: Approximation of a mass-emitting object by a point source.
Evers, J.; Hille, S.; and Muntean, A.
*Mathematical Biosciences and Engineering*, 12(2). 2015.

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@article{ title = {Modelling with measures: Approximation of a mass-emitting object by a point source}, type = {article}, year = {2015}, keywords = {Boundary exchange,Diffusion,Model reduction,Modelling with measures,Point source,Quantitative flux estimates}, volume = {12}, id = {09bfaf44-071e-32ad-8f52-1213cff4b24b}, created = {2019-08-23T19:37:41.337Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.337Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We consider a linear diffusion equation on Ω := ℝ2 \ (Formula presented.), where ΩO is a bounded domain. The time-dependent flux on the boundary F := ∂ΩO is prescribed. The aim of the paper is to approximate the dynamics by the solution of the diffusion equation on the whole of ℝ2 with a measure-valued point source in the origin and provide estimates for the quality of approximation. For all time t, we derive an L2 ([0; t]; L2 (F))-bound on the difference in flux on the boundary. Moreover, we derive for all t > 0 an L2 (Ω)-bound and an L2 ([0; t]; H1 (Ω))-bound for the difference of the solutions to the two models.}, bibtype = {article}, author = {Evers, J.H.M. and Hille, S.C. and Muntean, A.}, doi = {10.3934/mbe.2015.12.357}, journal = {Mathematical Biosciences and Engineering}, number = {2} }

We consider a linear diffusion equation on Ω := ℝ2 \ (Formula presented.), where ΩO is a bounded domain. The time-dependent flux on the boundary F := ∂ΩO is prescribed. The aim of the paper is to approximate the dynamics by the solution of the diffusion equation on the whole of ℝ2 with a measure-valued point source in the origin and provide estimates for the quality of approximation. For all time t, we derive an L2 ([0; t]; L2 (F))-bound on the difference in flux on the boundary. Moreover, we derive for all t > 0 an L2 (Ω)-bound and an L2 ([0; t]; H1 (Ω))-bound for the difference of the solutions to the two models.

Effect of material anisotropy on the fingering instability in reverse smoldering combustion.
Ijioma, E.; Muntean, A.; and Ogawa, T.
*International Journal of Heat and Mass Transfer*, 81. 2015.

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@article{ title = {Effect of material anisotropy on the fingering instability in reverse smoldering combustion}, type = {article}, year = {2015}, keywords = {Anisotropy,Combustion instability,Fingering pattern,Homogenization,Reverse smoldering}, volume = {81}, id = {170f937b-f07b-30ea-99d8-dec95bb4fdf4}, created = {2019-08-23T19:37:41.391Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.391Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2014 Elsevier Ltd. All rights reserved. It is well known from experiments that a sample of thin porous material burning against an oxidizing air under microgravity exhibits various finger-like char patterns. The patterns are classified into three distinct types depending on the oxidizer flow rate. (I) Sparse fingers; (II) tip-splitting fingers; (III) connected front. We presently extend our modeling strategy based on the homogenization approach, which has been applied for the case of isotropic porous media, to analyze the pattern behavior on anisotropic porous media. In order to understand the characteristic features of the patterns based on the influence of the local structure, we simply rely on fixed anisotropic two-dimensional geometries representative of the microstructure of interest. Thus, we illustrate numerically the consequence of the material anisotropy on the fingering patterns based on effective diffusion tensors calculated using the homogenization method and the mechanism of thermal-diffusion instability. Besides revealing new insights on the experimental observations, our numerical results show that material anisotropy can influence the uniformity on the patterns, but the distinct fingering regimes are independent of the local microstructure of materials. This effect is consistent with the qualitative experimental findings from Zik and Moses (1999).}, bibtype = {article}, author = {Ijioma, E.R. and Muntean, A. and Ogawa, T.}, doi = {10.1016/j.ijheatmasstransfer.2014.11.021}, journal = {International Journal of Heat and Mass Transfer} }

© 2014 Elsevier Ltd. All rights reserved. It is well known from experiments that a sample of thin porous material burning against an oxidizing air under microgravity exhibits various finger-like char patterns. The patterns are classified into three distinct types depending on the oxidizer flow rate. (I) Sparse fingers; (II) tip-splitting fingers; (III) connected front. We presently extend our modeling strategy based on the homogenization approach, which has been applied for the case of isotropic porous media, to analyze the pattern behavior on anisotropic porous media. In order to understand the characteristic features of the patterns based on the influence of the local structure, we simply rely on fixed anisotropic two-dimensional geometries representative of the microstructure of interest. Thus, we illustrate numerically the consequence of the material anisotropy on the fingering patterns based on effective diffusion tensors calculated using the homogenization method and the mechanism of thermal-diffusion instability. Besides revealing new insights on the experimental observations, our numerical results show that material anisotropy can influence the uniformity on the patterns, but the distinct fingering regimes are independent of the local microstructure of materials. This effect is consistent with the qualitative experimental findings from Zik and Moses (1999).

Preface to "modeling with measures".
Ackleh, A.; Colombo, R.; Hille, S.; and Muntean, A.
*Mathematical Biosciences and Engineering*, 12(2). 2015.

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doi link bibtex

@article{ title = {Preface to "modeling with measures"}, type = {article}, year = {2015}, volume = {12}, id = {f27c26a7-512b-3edf-91a3-fe0ae21c26d9}, created = {2019-08-23T19:37:41.785Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.785Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, bibtype = {article}, author = {Ackleh, A.S. and Colombo, R.M. and Hille, S.C. and Muntean, A.}, doi = {10.3934/mbe.2015.12.2i}, journal = {Mathematical Biosciences and Engineering}, number = {2} }

Residence time estimates for asymmetric simple exclusion dynamics on strips.
Cirillo, E.; Krehel, O.; Muntean, A.; Van Santen, R.; and Sengar, A.
*Physica A: Statistical Mechanics and its Applications*, 442. 2015.

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@article{ title = {Residence time estimates for asymmetric simple exclusion dynamics on strips}, type = {article}, year = {2015}, keywords = {Complexity,Deposition model,Residence time,Self-organization,Simple exclusion random walks}, volume = {442}, id = {b7b91e05-20d6-37d2-8045-b401ce0db994}, created = {2019-08-23T19:37:42.050Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:42.050Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2015 Elsevier B.V. The target of our study is to approximate numerically and, in some particular physically relevant cases, also analytically, the residence time of particles undergoing an asymmetric simple exclusion dynamics on a two-dimensional vertical strip. The sources of asymmetry are twofold: (i) the choice of boundary conditions (different reservoir levels) and (ii) the strong anisotropy from a drift nonlinear in density with prescribed directionality. We focus on the effect of the choice of anisotropy on residence time. We analyze our results by means of two theoretical models, a Mean Field and a one-dimensional Birth and Death one. For positive drift we find a striking agreement between Monte Carlo and theoretical results. In the zero drift case we still find agreement as long as particles can freely escape the strip through the bottom boundary. Otherwise, the two models give different predictions and their ability to reproduce numerical results depends on the horizontal displacement probability. The topic is relevant for situations occurring in pedestrian flows or biological transport in crowded environments, where lateral displacements of the particles occur predominantly affecting therefore in an essentially way the efficiency of the overall transport mechanism.}, bibtype = {article}, author = {Cirillo, E.N.M. and Krehel, O. and Muntean, A. and Van Santen, R. and Sengar, A.}, doi = {10.1016/j.physa.2015.09.037}, journal = {Physica A: Statistical Mechanics and its Applications} }

© 2015 Elsevier B.V. The target of our study is to approximate numerically and, in some particular physically relevant cases, also analytically, the residence time of particles undergoing an asymmetric simple exclusion dynamics on a two-dimensional vertical strip. The sources of asymmetry are twofold: (i) the choice of boundary conditions (different reservoir levels) and (ii) the strong anisotropy from a drift nonlinear in density with prescribed directionality. We focus on the effect of the choice of anisotropy on residence time. We analyze our results by means of two theoretical models, a Mean Field and a one-dimensional Birth and Death one. For positive drift we find a striking agreement between Monte Carlo and theoretical results. In the zero drift case we still find agreement as long as particles can freely escape the strip through the bottom boundary. Otherwise, the two models give different predictions and their ability to reproduce numerical results depends on the horizontal displacement probability. The topic is relevant for situations occurring in pedestrian flows or biological transport in crowded environments, where lateral displacements of the particles occur predominantly affecting therefore in an essentially way the efficiency of the overall transport mechanism.

2014
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Preface.
Muntean, A.; and Toschi, F.
Volume 553 2014.

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@book{ title = {Preface}, type = {book}, year = {2014}, source = {CISM International Centre for Mechanical Sciences, Courses and Lectures}, volume = {553}, id = {db5dc39a-6735-3461-a199-92a859b8e1e4}, created = {2019-08-23T19:37:40.300Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.300Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, bibtype = {book}, author = {Muntean, A. and Toschi, F.} }

Preface to "The mathematics of concrete".
Muntean, A.; and Aiki, T.
*Networks and Heterogeneous Media*, 9(4). 2014.

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@article{ title = {Preface to "The mathematics of concrete"}, type = {article}, year = {2014}, volume = {9}, id = {5c2dfe49-1428-33db-bd3f-e80ece6a79f3}, created = {2019-08-23T19:37:40.557Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.557Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, bibtype = {article}, author = {Muntean, A. and Aiki, T.}, doi = {10.3934/nhm.2014.9.4i}, journal = {Networks and Heterogeneous Media}, number = {4} }

Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence.
Fatima, T.; and Muntean, A.
*Nonlinear Analysis: Real World Applications*, 15(1). 2014.

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@article{ title = {Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence}, type = {article}, year = {2014}, keywords = {Multiscale system,Periodic homogenization,Periodic unfolding method,Semi-linear partially dissipative system,Sulfate corrosion of concrete,Two-scale convergence}, volume = {15}, id = {66fb6fbf-c73a-342b-9f89-67f53d9d6f3e}, created = {2019-08-23T19:37:40.561Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.561Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We explore the homogenization limit and rigorously derive upscaled equations for a microscopic reaction-diffusion system modeling sulfate corrosion in sewer pipes made of concrete. The system, defined in a periodically- perforated domain, is semi-linear, partially dissipative and weakly coupled via a non-linear ordinary differential equation posed on the solid-water interface at the pore level. First, we show the well-posedness of the microscopic model. We then apply homogenization techniques based on two-scale convergence for a uniformly periodic domain and derive upscaled equations together with explicit formulas for the effective diffusion coefficients and reaction constants. We use a boundary unfolding method to pass to the homogenization limit in the non-linear ordinary differential equation. Finally, we give the strong formulation of the upscaled system. © 2011 Elsevier Ltd. All rights reserved.}, bibtype = {article}, author = {Fatima, T. and Muntean, A.}, doi = {10.1016/j.nonrwa.2012.01.019}, journal = {Nonlinear Analysis: Real World Applications}, number = {1} }

We explore the homogenization limit and rigorously derive upscaled equations for a microscopic reaction-diffusion system modeling sulfate corrosion in sewer pipes made of concrete. The system, defined in a periodically- perforated domain, is semi-linear, partially dissipative and weakly coupled via a non-linear ordinary differential equation posed on the solid-water interface at the pore level. First, we show the well-posedness of the microscopic model. We then apply homogenization techniques based on two-scale convergence for a uniformly periodic domain and derive upscaled equations together with explicit formulas for the effective diffusion coefficients and reaction constants. We use a boundary unfolding method to pass to the homogenization limit in the non-linear ordinary differential equation. Finally, we give the strong formulation of the upscaled system. © 2011 Elsevier Ltd. All rights reserved.

Upscaling of dislocation walls in finite domains.
Van Meurs, P.; Muntean, A.; and Peletier, M.
*European Journal of Applied Mathematics*, 25(6). 2014.

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@article{ title = {Upscaling of dislocation walls in finite domains}, type = {article}, year = {2014}, keywords = {74Q05, 74C05, 82B21, 49J45, 82D35,Discrete-to-continuum limit,Multiscale,Plasticity,Straight edge-dislocations,Γ-convergence}, volume = {25}, id = {5f40284c-951e-3063-83c0-25d89ac3f124}, created = {2019-08-23T19:37:41.084Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.084Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Copyright © 2014 Cambridge University Press. We wish to understand the macroscopic plastic behaviour of metals by upscaling the micro-mechanics of dislocations. We consider a highly simplified dislocation network, which allows our discrete model to be a one dimensional particle system, in which the interactions between the particles (dislocation walls) are singular and non-local. As a first step towards treating realistic geometries, we focus on finite-size effects rather than considering an infinite domain as typically discussed in the literature. We derive effective equations for the dislocation density by means of Γ-convergence on the space of probability measures. Our analysis yields a classification of macroscopic models, in which the size of the domain plays a key role.}, bibtype = {article}, author = {Van Meurs, P. and Muntean, A. and Peletier, M.A.}, doi = {10.1017/S0956792514000254}, journal = {European Journal of Applied Mathematics}, number = {6} }

Copyright © 2014 Cambridge University Press. We wish to understand the macroscopic plastic behaviour of metals by upscaling the micro-mechanics of dislocations. We consider a highly simplified dislocation network, which allows our discrete model to be a one dimensional particle system, in which the interactions between the particles (dislocation walls) are singular and non-local. As a first step towards treating realistic geometries, we focus on finite-size effects rather than considering an infinite domain as typically discussed in the literature. We derive effective equations for the dislocation density by means of Γ-convergence on the space of probability measures. Our analysis yields a classification of macroscopic models, in which the size of the domain plays a key role.

Homogenization of a thermo-diffusion system with smoluchowski interactions.
Krehel, O.; Aiki, T.; and Muntean, A.
*Networks and Heterogeneous Media*, 9(4). 2014.

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@article{ title = {Homogenization of a thermo-diffusion system with smoluchowski interactions}, type = {article}, year = {2014}, keywords = {Colloids,Combustion,Crossdiffusion,Homogenization,Thermal-diffusion,Well-posedness}, volume = {9}, id = {6990dd89-a0a8-3246-baa4-8172b527fb38}, created = {2019-08-23T19:37:41.341Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.341Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© American Institute of Mathematical Sciences. We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via twoscale convergence techniques, allows the investigation of deposition effects in porous materials in the presence of thermal gradients.}, bibtype = {article}, author = {Krehel, O. and Aiki, T. and Muntean, A.}, doi = {10.3934/nhm.2014.9.739}, journal = {Networks and Heterogeneous Media}, number = {4} }

© American Institute of Mathematical Sciences. We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via twoscale convergence techniques, allows the investigation of deposition effects in porous materials in the presence of thermal gradients.

A continuum model for hierarchical fibril assembly.
Van Lith, B.; Muntean, A.; and Storm, C.
*EPL*, 106(6). 2014.

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@article{ title = {A continuum model for hierarchical fibril assembly}, type = {article}, year = {2014}, volume = {106}, id = {9188d5b6-76f2-3af2-aa25-b46a63aa41c7}, created = {2019-08-23T19:37:41.397Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.397Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Most of the biological polymers that make up our cells and tissues are hierarchically structured. For biopolymers ranging from collagen, to actin, to fibrin and amyloid fibrils this hierarchy provides vitally important versatility. The structural hierarchy must be encoded in the self-assembly process, from the earliest stages onward, in order to produce the appropriate substructures. In this letter, we explore the kinetics of multistage self-assembly processes in a model system which allows comparison to bulk probes such as light scattering. We apply our model to recent turbidimetry data on the self-assembly of collagen fibrils. Our analysis suggests a connection between diffusion-limited aggregation kinetics and fibril growth, supported by slow, power-law growth at very long time scales. © CopyrightEPLA, 2014.}, bibtype = {article}, author = {Van Lith, B.S. and Muntean, A. and Storm, C.}, doi = {10.1209/0295-5075/106/68004}, journal = {EPL}, number = {6} }

Most of the biological polymers that make up our cells and tissues are hierarchically structured. For biopolymers ranging from collagen, to actin, to fibrin and amyloid fibrils this hierarchy provides vitally important versatility. The structural hierarchy must be encoded in the self-assembly process, from the earliest stages onward, in order to produce the appropriate substructures. In this letter, we explore the kinetics of multistage self-assembly processes in a model system which allows comparison to bulk probes such as light scattering. We apply our model to recent turbidimetry data on the self-assembly of collagen fibrils. Our analysis suggests a connection between diffusion-limited aggregation kinetics and fibril growth, supported by slow, power-law growth at very long time scales. © CopyrightEPLA, 2014.

Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions.
Evers, J.; Hille, S.; and Muntean, A.
*Comptes Rendus Mathematique*, 352(1). 2014.

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@article{ title = {Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions}, type = {article}, year = {2014}, volume = {352}, id = {540155c8-a935-3cab-8238-11bf35ba9293}, created = {2019-08-23T19:37:41.438Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.438Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {This Note deals with imposing a flux boundary condition on a non-conservative measure-valued mass evolution problem posed on a bounded interval. To establish the well-posedness of the problem, we exploit particle system approximations of the mass accumulation in a thin layer near the active boundary. We derive the convergence rate for the approximation procedure as well as the structure of the flux boundary condition in the limit problem. © 2013 Académie des sciences.}, bibtype = {article}, author = {Evers, J. and Hille, S.C. and Muntean, A.}, doi = {10.1016/j.crma.2013.11.012}, journal = {Comptes Rendus Mathematique}, number = {1} }

This Note deals with imposing a flux boundary condition on a non-conservative measure-valued mass evolution problem posed on a bounded interval. To establish the well-posedness of the problem, we exploit particle system approximations of the mass accumulation in a thin layer near the active boundary. We derive the convergence rate for the approximation procedure as well as the structure of the flux boundary condition in the limit problem. © 2013 Académie des sciences.

Pedestrians moving in the dark: Balancing measures and playing games on lattices.
Muntean, A.; Cirillo, E.; Krehel, O.; and Böhm, M.
Volume 553 2014.

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@book{ title = {Pedestrians moving in the dark: Balancing measures and playing games on lattices}, type = {book}, year = {2014}, source = {CISM International Centre for Mechanical Sciences, Courses and Lectures}, keywords = {Cellular Automaton Model,Dual Phase Steel,Interact Particle System,Pedestrian Motion,Porous Medium}, volume = {553}, id = {d551b054-0034-379f-beb0-a3aee18b7d9e}, created = {2019-08-23T19:37:41.739Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.739Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2014, CISM, Udine. We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors: (i) a Becker-Döring-type dynamics and (ii) a probabilistic cellular automaton model. In both models the group formation is affected by a threshold. The pedestrians are supposed to have very limited knowledge about their current position and their neighborhood; they can form groups up to a certain size and they can leave them. Their main goal is to find the exit of the corridor. Although being of mathematically different character, the discussion of both models shows that it seems to be a disadvantage for the individual to adhere to larger groups. We illustrate this effect numerically by solving both model systems. Finally we list some of our main open questions and conjectures.}, bibtype = {book}, author = {Muntean, A. and Cirillo, E.N.M. and Krehel, O. and Böhm, M.}, doi = {10.1007/978-3-7091-1785-9_3} }

© 2014, CISM, Udine. We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors: (i) a Becker-Döring-type dynamics and (ii) a probabilistic cellular automaton model. In both models the group formation is affected by a threshold. The pedestrians are supposed to have very limited knowledge about their current position and their neighborhood; they can form groups up to a certain size and they can leave them. Their main goal is to find the exit of the corridor. Although being of mathematically different character, the discussion of both models shows that it seems to be a disadvantage for the individual to adhere to larger groups. We illustrate this effect numerically by solving both model systems. Finally we list some of our main open questions and conjectures.

High statistics measurements of pedestrian dynamics.
Corbetta, A.; Bruno, L.; Muntean, A.; and Toschi, F.
In *Transportation Research Procedia*, volume 2, 2014.

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@inproceedings{ title = {High statistics measurements of pedestrian dynamics}, type = {inproceedings}, year = {2014}, keywords = {high statistics measurements,pedestrian dynamics,pedestrian tracking,statistical mechanics}, volume = {2}, id = {9963e2d9-7ef6-3b0e-a471-ce7b9c98f8dc}, created = {2019-08-23T19:37:41.778Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.778Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2014 The Authors. Aiming at a quantitative understanding of basic aspects of pedestrian dynamics, extensive and high-accuracy measurements of real-life pedestrian trajectories have been performed. A measurement strategy based on Microsoft KinectTM has been used. Specifically, more than 100.000 pedestrians have been tracked while walking along a trafficked corridor at the Eindhoven University of Technology, The Netherlands. The obtained trajectories have been analyzed as ensemble data. The main result consists of a statistical descriptions of pedestrian characteristic kinematic quantities such as positions and fundamental diagrams, possibly conditioned to the local crowd flow (e.g. co-flow or counter-flow).}, bibtype = {inproceedings}, author = {Corbetta, A. and Bruno, L. and Muntean, A. and Toschi, F.}, doi = {10.1016/j.trpro.2014.09.013}, booktitle = {Transportation Research Procedia} }

© 2014 The Authors. Aiming at a quantitative understanding of basic aspects of pedestrian dynamics, extensive and high-accuracy measurements of real-life pedestrian trajectories have been performed. A measurement strategy based on Microsoft KinectTM has been used. Specifically, more than 100.000 pedestrians have been tracked while walking along a trafficked corridor at the Eindhoven University of Technology, The Netherlands. The obtained trajectories have been analyzed as ensemble data. The main result consists of a statistical descriptions of pedestrian characteristic kinematic quantities such as positions and fundamental diagrams, possibly conditioned to the local crowd flow (e.g. co-flow or counter-flow).

Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers.
Fatima, T.; Ijioma, E.; Ogawa, T.; and Muntean, A.
*Networks and Heterogeneous Media*, 9(4). 2014.

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@article{ title = {Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers}, type = {article}, year = {2014}, keywords = {Anisotropic singular perturbations,Dimension reduction,Filtration combustion,Homogenization,Thin layers,Two-scale convergence}, volume = {9}, id = {076509db-566b-36a4-a74d-abdd4b5e77b1}, created = {2019-08-23T19:37:41.826Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.826Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© American Institute of Mathematical Sciences. We study the homogenization of a reaction-diffusion-convection system posed in an ε-periodic δ-thin layer made of a two-component (solid-air) composite material. The microscopic system includes heat ow, diffusion and convection coupled with a nonlinear surface chemical reaction. We treat two distinct asymptotic scenarios: (1) For a fixed width δ > 0 of the thin layer, we homogenize the presence of the microstructures (the classical periodic homogenization limit ε → 0); (2) In the homogenized problem, we pass to δ → 0 (the vanishing limit of the layer's width). In this way, we are preparing the stage for the simultaneous homogenization (ε → 0) and dimension reduction limit (δ → 0) with δ = δ(ε). We recover the reduced macroscopic equations from [25] with precise formulas for the effective transport and reaction coefficients. We complement the analytical results with a few simulations of a case study in smoldering combustion. The chosen multiscale scenario is relevant for a large variety of practical applications ranging from the forecast of the response to fire of refractory concrete, the microstructure design of resistanceto-heat ceramic-based materials for engines, to the smoldering combustion of thin porous samples under microgravity conditions.}, bibtype = {article}, author = {Fatima, T. and Ijioma, E. and Ogawa, T. and Muntean, A.}, doi = {10.3934/nhm.2014.9.709}, journal = {Networks and Heterogeneous Media}, number = {4} }

© American Institute of Mathematical Sciences. We study the homogenization of a reaction-diffusion-convection system posed in an ε-periodic δ-thin layer made of a two-component (solid-air) composite material. The microscopic system includes heat ow, diffusion and convection coupled with a nonlinear surface chemical reaction. We treat two distinct asymptotic scenarios: (1) For a fixed width δ > 0 of the thin layer, we homogenize the presence of the microstructures (the classical periodic homogenization limit ε → 0); (2) In the homogenized problem, we pass to δ → 0 (the vanishing limit of the layer's width). In this way, we are preparing the stage for the simultaneous homogenization (ε → 0) and dimension reduction limit (δ → 0) with δ = δ(ε). We recover the reduced macroscopic equations from [25] with precise formulas for the effective transport and reaction coefficients. We complement the analytical results with a few simulations of a case study in smoldering combustion. The chosen multiscale scenario is relevant for a large variety of practical applications ranging from the forecast of the response to fire of refractory concrete, the microstructure design of resistanceto-heat ceramic-based materials for engines, to the smoldering combustion of thin porous samples under microgravity conditions.

Cognitive distance, absorptive capacity and group rationality: A simulation study.
Curşeu, P.; Krehel, O.; Evers, J.; and Muntean, A.
*PLoS ONE*, 9(10). 2014.

doi link bibtex abstract

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@article{ title = {Cognitive distance, absorptive capacity and group rationality: A simulation study}, type = {article}, year = {2014}, volume = {9}, id = {c977c879-d0cf-3e1b-8f2e-7e4714591723}, created = {2019-08-23T19:37:41.826Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.826Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2014 Curşeu et al. We report the results of a simulation study in which we explore the joint effect of group absorptive capacity (as the averageindividual rationality of the group members) and cognitive distance (as the distance between the most rational group member and the rest of the group) on the emergence of collective rationality in groups. We start from empirical results reported in the literature on group rationality as collective group level competence and use data on real-life groups of four and five to validate a mathematical model. We then use this mathematical model to predict group level scores from a variety of possible group configurations (varying both in cognitive distance and average individual rationality). Our results show that both group competence and cognitive distance are necessary conditions for emergent group rationality. Group configurations, in which the groups become more rational than the most rational group member, are groups scoring low on cognitive distance and scoring high on absorptive capacity.}, bibtype = {article}, author = {Curşeu, P.L. and Krehel, O. and Evers, J.H.M. and Muntean, A.}, doi = {10.1371/journal.pone.0109359}, journal = {PLoS ONE}, number = {10} }

© 2014 Curşeu et al. We report the results of a simulation study in which we explore the joint effect of group absorptive capacity (as the averageindividual rationality of the group members) and cognitive distance (as the distance between the most rational group member and the rest of the group) on the emergence of collective rationality in groups. We start from empirical results reported in the literature on group rationality as collective group level competence and use data on real-life groups of four and five to validate a mathematical model. We then use this mathematical model to predict group level scores from a variety of possible group configurations (varying both in cognitive distance and average individual rationality). Our results show that both group competence and cognitive distance are necessary conditions for emergent group rationality. Group configurations, in which the groups become more rational than the most rational group member, are groups scoring low on cognitive distance and scoring high on absorptive capacity.

Is adding charcoal to soil a good method for CO2 sequestration? - Modeling a spatially homogeneous soil.
Bourne, D.; Fatima, T.; Van Meurs, P.; and Muntean, A.
*Applied Mathematical Modelling*, 38(9-10). 2014.

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@article{ title = {Is adding charcoal to soil a good method for CO<inf>2</inf> sequestration? - Modeling a spatially homogeneous soil}, type = {article}, year = {2014}, keywords = {Biochar,Equilibria and steady states,Modeling chemical kinetics in fertile soils,Simulation,Solvability of a nonlinear ODE system}, volume = {38}, id = {a25e6120-a5dd-3767-81c0-fc5c4eed7b42}, created = {2019-08-23T19:37:41.867Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.867Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {Carbon sequestration is the process of capture and long-term storage of atmospheric carbon dioxide (CO2) with the aim to avoid dangerous climate change. In this paper, we propose a simple mathematical model (a coupled system of nonlinear ODEs) to capture some of the dynamical effects produced by adding charcoal to fertile soils. The main goal is to understand to which extent charcoal is able to lock up carbon in soils. Our results are preliminary in the sense that we do not solve the CO2 sequestration problem. Instead, we do set up a flexible modeling framework in which the interaction between charcoal and soil can be tackled by means of mathematical tools.We show that our model is well-posed and has interesting large-time behaviour. Depending on the reference parameter range (e.g., type of soil) and chosen time scale, numerical simulations suggest that adding charcoal typically postpones the release of CO2. © 2013 Elsevier Inc.}, bibtype = {article}, author = {Bourne, D. and Fatima, T. and Van Meurs, P. and Muntean, A.}, doi = {10.1016/j.apm.2013.10.064}, journal = {Applied Mathematical Modelling}, number = {9-10} }

Carbon sequestration is the process of capture and long-term storage of atmospheric carbon dioxide (CO2) with the aim to avoid dangerous climate change. In this paper, we propose a simple mathematical model (a coupled system of nonlinear ODEs) to capture some of the dynamical effects produced by adding charcoal to fertile soils. The main goal is to understand to which extent charcoal is able to lock up carbon in soils. Our results are preliminary in the sense that we do not solve the CO2 sequestration problem. Instead, we do set up a flexible modeling framework in which the interaction between charcoal and soil can be tackled by means of mathematical tools.We show that our model is well-posed and has interesting large-time behaviour. Depending on the reference parameter range (e.g., type of soil) and chosen time scale, numerical simulations suggest that adding charcoal typically postpones the release of CO2. © 2013 Elsevier Inc.

Analysis of non-equilibrium evolution problems: Selected topics in material and life sciences.
Aiki, T.; Hulshof, J.; Kenmochi, N.; and Muntean, A.
*Discrete and Continuous Dynamical Systems - Series S*, 7(1). 2014.

doi link bibtex

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@article{ title = {Analysis of non-equilibrium evolution problems: Selected topics in material and life sciences}, type = {article}, year = {2014}, volume = {7}, id = {9ab38a68-24ce-3e43-bf91-a2495ec93e24}, created = {2019-08-23T19:37:41.871Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.871Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, bibtype = {article}, author = {Aiki, T. and Hulshof, J. and Kenmochi, N. and Muntean, A.}, doi = {10.3934/dcdss.2014.7.1}, journal = {Discrete and Continuous Dynamical Systems - Series S}, number = {1} }

2013
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Corrector estimates for the homogenization of a locally periodic medium with areas of low and high diffusivity.
Muntean, A.; and Van Noorden, T.
*European Journal of Applied Mathematics*, 24(5). 2013.

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@article{ title = {Corrector estimates for the homogenization of a locally periodic medium with areas of low and high diffusivity}, type = {article}, year = {2013}, keywords = {Homogenization,Key words: Corrector estimates,Micro-macro transport,Reaction-diffusion system in heterogeneous materia,Transmission condition}, volume = {24}, id = {8ff6e6bf-98c9-3c79-bb88-eb99142e2c76}, created = {2019-08-23T19:37:40.663Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.663Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We prove an upper bound for the convergence rate of the homogenization limit Î → 0 for a linear transmission problem for a advection-diffusion(-reaction) system posed in areas with low and high diffusivity, where Î is a suitable scale parameter. In this way we rigorously justify the formal homogenization asymptotics obtained in [37] (van Noorden, T. and Muntean, A. (2011) Homogenization of a locally-periodic medium with areas of low and high diffusivity. Eur. J. Appl. Math. 22, 493-516). We do this by providing a corrector estimate. The main ingredients for the proof of the correctors include integral estimates for rapidly oscillating functions with prescribed average, properties of the macroscopic reconstruction operators, energy bounds, and extra two-scale regularity estimates. The whole procedure essentially relies on a good understanding of the analysis of the limit two-scale problem. Copyright © Cambridge University Press 2013 A ̂.}, bibtype = {article}, author = {Muntean, A. and Van Noorden, T.L.}, doi = {10.1017/S0956792513000090}, journal = {European Journal of Applied Mathematics}, number = {5} }

We prove an upper bound for the convergence rate of the homogenization limit Î → 0 for a linear transmission problem for a advection-diffusion(-reaction) system posed in areas with low and high diffusivity, where Î is a suitable scale parameter. In this way we rigorously justify the formal homogenization asymptotics obtained in [37] (van Noorden, T. and Muntean, A. (2011) Homogenization of a locally-periodic medium with areas of low and high diffusivity. Eur. J. Appl. Math. 22, 493-516). We do this by providing a corrector estimate. The main ingredients for the proof of the correctors include integral estimates for rapidly oscillating functions with prescribed average, properties of the macroscopic reconstruction operators, energy bounds, and extra two-scale regularity estimates. The whole procedure essentially relies on a good understanding of the analysis of the limit two-scale problem. Copyright © Cambridge University Press 2013 A ̂.

Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry's law and time-dependent Dirichlet data.
Aiki, T.; and Muntean, A.
*Nonlinear Analysis, Theory, Methods and Applications*, 93. 2013.

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@article{ title = {Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry's law and time-dependent Dirichlet data}, type = {article}, year = {2013}, keywords = {Concrete carbonation,Free boundary problem,Henry's law,Large-time behavior,Time-dependent Dirichlet data}, volume = {93}, id = {f0f9ad7a-263e-3203-a779-ec84b4c97c85}, created = {2019-08-23T19:37:40.670Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.670Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the t-behavior of reaction penetration depths by including nonlinear effects due to deviations from the classical Henry's law and time-dependent Dirichlet data. © 2013 The Authors. Published by Elsevier Ltd. All rights reserved.}, bibtype = {article}, author = {Aiki, T. and Muntean, A.}, doi = {10.1016/j.na.2013.07.002}, journal = {Nonlinear Analysis, Theory, Methods and Applications} }

We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the t-behavior of reaction penetration depths by including nonlinear effects due to deviations from the classical Henry's law and time-dependent Dirichlet data. © 2013 The Authors. Published by Elsevier Ltd. All rights reserved.

A free-boundary problem for concrete carbonation: Front nucleation and rigorous justification of the pt -law of propagation.
Aiki, T.; and Muntean, A.
*Interfaces and Free Boundaries*, 15(2). 2013.

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@article{ title = {A free-boundary problem for concrete carbonation: Front nucleation and rigorous justification of the pt -law of propagation}, type = {article}, year = {2013}, keywords = {Concrete carbonation,Free-boundary problem,Integral estimates,Large-time behavior}, volume = {15}, id = {dc441ae0-1c0a-389e-a7ae-680ba74a2671}, created = {2019-08-23T19:37:40.713Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.713Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We study a one-dimensional free-boundary problem describing the penetration of carbonation fronts (free reaction-triggered interfaces) in concrete. Using suitable integral estimates for the free boundary and involved concentrations, we reach a twofold aim: (1) We fill a fundamental gap by justifying rigorously the experimentally guessed pt asymptotic behavior. Previously we obtained the upper bound s.t / 6 C0pt for some constant C0; now we show the optimality of the rate by proving the right nontrivial lower estimate, i.e., there exists C00 > 0 such that s.t / > C00pt . (2) We obtain weak solutions to the free-boundary problem for the case when the measure of the initial domain vanishes. In this way, we allow for the nucleation of the moving carbonation front -a scenario that until now was open from the mathematical analysis point of view. © European Mathematical Society 2013.}, bibtype = {article}, author = {Aiki, T. and Muntean, A.}, doi = {10.4171/IFB/299}, journal = {Interfaces and Free Boundaries}, number = {2} }

We study a one-dimensional free-boundary problem describing the penetration of carbonation fronts (free reaction-triggered interfaces) in concrete. Using suitable integral estimates for the free boundary and involved concentrations, we reach a twofold aim: (1) We fill a fundamental gap by justifying rigorously the experimentally guessed pt asymptotic behavior. Previously we obtained the upper bound s.t / 6 C0pt for some constant C0; now we show the optimality of the rate by proving the right nontrivial lower estimate, i.e., there exists C00 > 0 such that s.t / > C00pt . (2) We obtain weak solutions to the free-boundary problem for the case when the measure of the initial domain vanishes. In this way, we allow for the nucleation of the moving carbonation front -a scenario that until now was open from the mathematical analysis point of view. © European Mathematical Society 2013.

Dynamics of pedestrians in regions with no visibility - A lattice model without exclusion.
Cirillo, E.; and Muntean, A.
*Physica A: Statistical Mechanics and its Applications*, 392(17). 2013.

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@article{ title = {Dynamics of pedestrians in regions with no visibility - A lattice model without exclusion}, type = {article}, year = {2013}, keywords = {Crowd dynamics,Lattice models,Motion in regions with no visibility,Non-exclusion processes,Pedestrians evacuation}, volume = {392}, id = {e7fc18d7-3d1e-361a-bd96-eaa1ad5c5844}, created = {2019-08-23T19:37:40.724Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.724Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We investigate the motion of pedestrians through obscure corridors where the lack of visibility (due to smoke, fog, darkness, etc.) hides the precise position of the exits. We focus our attention on a set of basic mechanisms, which we assume to be governing the dynamics at the individual level. Using a lattice model, we explore the effects of non-exclusion on the overall exit flux (evacuation rate). More precisely, we study the effect of the buddying threshold (of no-exclusion per site) on the dynamics of the crowd and investigate to which extent our model confirms the following pattern revealed by investigations on real emergencies: If the evacuees tend to cooperate and act altruistically, then their collective action tends to favor the occurrence of disasters. The research reported here opens many fundamental questions and should be seen therefore as a preliminary investigation of the very complex behavior of the people and their motion in dark regions. © 2013 Elsevier B.V. All rights reserved.}, bibtype = {article}, author = {Cirillo, E.N.M. and Muntean, A.}, doi = {10.1016/j.physa.2013.04.029}, journal = {Physica A: Statistical Mechanics and its Applications}, number = {17} }

We investigate the motion of pedestrians through obscure corridors where the lack of visibility (due to smoke, fog, darkness, etc.) hides the precise position of the exits. We focus our attention on a set of basic mechanisms, which we assume to be governing the dynamics at the individual level. Using a lattice model, we explore the effects of non-exclusion on the overall exit flux (evacuation rate). More precisely, we study the effect of the buddying threshold (of no-exclusion per site) on the dynamics of the crowd and investigate to which extent our model confirms the following pattern revealed by investigations on real emergencies: If the evacuees tend to cooperate and act altruistically, then their collective action tends to favor the occurrence of disasters. The research reported here opens many fundamental questions and should be seen therefore as a preliminary investigation of the very complex behavior of the people and their motion in dark regions. © 2013 Elsevier B.V. All rights reserved.

Crowds reaching targets by maximizing entropy: A Clausius-Duhem inequality approach.
Evers, J.; Muntean, A.; and Van De Ven, F.
In *IFAC Proceedings Volumes (IFAC-PapersOnline)*, volume 1, 2013.

doi link bibtex abstract

doi link bibtex abstract

@inproceedings{ title = {Crowds reaching targets by maximizing entropy: A Clausius-Duhem inequality approach}, type = {inproceedings}, year = {2013}, keywords = {Crowd dynamics,Entropy,First-order systems,Steady states,Thermodynamics,View angles,Walking}, volume = {1}, issue = {PART 1}, id = {aefa1d80-d145-312f-8497-036b288c2a83}, created = {2019-08-23T19:37:41.434Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.434Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {In this paper we propose the use of concepts from thermodynamics in the study of crowd dynamics. Our continuous model consists of the continuity equation for the density of the crowd and a kinetic equation for the velocity field. The latter includes a nonlocal term that models interactions between individuals. To support our modelling assumptions, we introduce an inequality that resembles the Second Law of Thermodynamics, containing an entropy-like functional. We show that its time derivative equals a positive dissipation term minus a corrector term. The latter term should be small for the time derivative of the entropy to be positive. In case of isotropic interactions the corrector term is absent. For the anisotropic case, we support the claim that the corrector term is small by simulations for the corresponding particle system. They reveal that this term is sufficiently small for the entropy still to increase. Moreover, we show that the entropy converges in time towards a limit value. © IFAC.}, bibtype = {inproceedings}, author = {Evers, J. and Muntean, A. and Van De Ven, F.}, doi = {10.3182/20130925-3-FR-4043.00006}, booktitle = {IFAC Proceedings Volumes (IFAC-PapersOnline)} }

In this paper we propose the use of concepts from thermodynamics in the study of crowd dynamics. Our continuous model consists of the continuity equation for the density of the crowd and a kinetic equation for the velocity field. The latter includes a nonlocal term that models interactions between individuals. To support our modelling assumptions, we introduce an inequality that resembles the Second Law of Thermodynamics, containing an entropy-like functional. We show that its time derivative equals a positive dissipation term minus a corrector term. The latter term should be small for the time derivative of the entropy to be positive. In case of isotropic interactions the corrector term is absent. For the anisotropic case, we support the claim that the corrector term is small by simulations for the corresponding particle system. They reveal that this term is sufficiently small for the entropy still to increase. Moreover, we show that the entropy converges in time towards a limit value. © IFAC.

Corrigendum to "Pattern formation in reverse smouldering combustion: A homogenisation approach" (Combust. Theor. Model, (2013), 17, 2, (185-223)).
Ijioma, E.; Muntean, A.; and Ogawa, T.
*Combustion Theory and Modelling*, 17(3). 2013.

doi link bibtex

doi link bibtex

@article{ title = {Corrigendum to "Pattern formation in reverse smouldering combustion: A homogenisation approach" (Combust. Theor. Model, (2013), 17, 2, (185-223))}, type = {article}, year = {2013}, volume = {17}, id = {2080a68a-45a6-3e3b-8aec-026c10fa8519}, created = {2019-08-23T19:37:41.488Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.488Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, bibtype = {article}, author = {Ijioma, E.R. and Muntean, A. and Ogawa, T.}, doi = {10.1080/13647830.2013.808878}, journal = {Combustion Theory and Modelling}, number = {3} }

Stratified turbulent Bunsen flames: flame surface analysis and flame surface density modelling.
Ijioma, E.; Muntean, A.; and Ogawa, T.
*Combustion Theory and Modelling*, 17(2). 2013.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Stratified turbulent Bunsen flames: flame surface analysis and flame surface density modelling}, type = {article}, year = {2013}, keywords = {combustion instability,fingering pattern,multiscale modelling,periodic homogenisation,reverse combustion}, volume = {17}, id = {d5b4c3b7-7eb3-3143-9437-2f8a26628a1d}, created = {2019-08-23T19:37:41.490Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.490Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {The development of fingering char patterns on the surface of porous thin materials has been investigated in the framework of reverse combustion. This macroscopic characteristic feature of combustible media has also been studied experimentally and through the use of phenomenological models. However, not much attention has been given to the behaviour of the emerging patterns based on characteristic material properties. Starting from a microscopic description of the combustion process, macroscopic models of reverse combustion that are derived by the application of the homogenisation technique are presented. Using proper scaling by means of a small scale parameter εlunate, the results of the formal asymptotic procedure are justified by qualitative multiscale numerical simulations at the microscopic and macroscopic levels. We consider two equilibrium models that are based on effective conductivity contrasts, in a simple adiabatic situation, to investigate the formation of unstable fingering patterns on the surface of a charred material. The behaviour of the emerging patterns is analysed using primarily the Péclet and Lewis numbers as control parameters. © 2013 Copyright Taylor and Francis Group, LLC.}, bibtype = {article}, author = {Ijioma, E.R. and Muntean, A. and Ogawa, T.}, doi = {10.1080/13647830.2012.734860}, journal = {Combustion Theory and Modelling}, number = {2} }

The development of fingering char patterns on the surface of porous thin materials has been investigated in the framework of reverse combustion. This macroscopic characteristic feature of combustible media has also been studied experimentally and through the use of phenomenological models. However, not much attention has been given to the behaviour of the emerging patterns based on characteristic material properties. Starting from a microscopic description of the combustion process, macroscopic models of reverse combustion that are derived by the application of the homogenisation technique are presented. Using proper scaling by means of a small scale parameter εlunate, the results of the formal asymptotic procedure are justified by qualitative multiscale numerical simulations at the microscopic and macroscopic levels. We consider two equilibrium models that are based on effective conductivity contrasts, in a simple adiabatic situation, to investigate the formation of unstable fingering patterns on the surface of a charred material. The behaviour of the emerging patterns is analysed using primarily the Péclet and Lewis numbers as control parameters. © 2013 Copyright Taylor and Francis Group, LLC.

The effect of perception anisotropy on particle systems describing pedestrian flows in corridors.
Gulikers, L.; Evers, J.; Muntean, A.; and Lyulin, A.
*Journal of Statistical Mechanics: Theory and Experiment*, 2013(4). 2013.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {The effect of perception anisotropy on particle systems describing pedestrian flows in corridors}, type = {article}, year = {2013}, keywords = {interacting agent models,pattern formation (theory),self-propelled particles,traffic and crowd dynamics}, volume = {2013}, id = {413c1c01-317b-32ed-91a6-e990bd864caa}, created = {2019-08-23T19:37:41.909Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.909Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We consider a microscopic model (a system of self-propelled particles) to study the behaviour of a large group of pedestrians walking in a corridor. Our point of interest is the effect of anisotropic interactions on the global behaviour of the crowd. The anisotropy we have in mind reflects the fact that people do not perceive (i.e. see, hear, feel or smell) their environment equally well in all directions. The dynamics of the individuals in our model follow from a system of Newton-like equations in the overdamped limit. The instantaneous velocity is modelled in such a way that it accounts for the angle at which an individual perceives another individual. We investigate the effects of this perception anisotropy by means of simulations, very much in the spirit of molecular dynamics. We define a number of characteristic quantifiers (including the polarization index and Morisita index) that serve as measures, for example, for organization and clustering, and we use these indices to investigate the influence of anisotropy on the global behaviour of the crowd. The goal of the paper is to investigate the potential of this model; extensive statistical analysis of simulation data and reproducing any specific real-life situation are beyond its scope. © 2013 IOP Publishing Ltd and SISSA Medialab srl.}, bibtype = {article}, author = {Gulikers, L. and Evers, J. and Muntean, A. and Lyulin, A.}, doi = {10.1088/1742-5468/2013/04/P04025}, journal = {Journal of Statistical Mechanics: Theory and Experiment}, number = {4} }

We consider a microscopic model (a system of self-propelled particles) to study the behaviour of a large group of pedestrians walking in a corridor. Our point of interest is the effect of anisotropic interactions on the global behaviour of the crowd. The anisotropy we have in mind reflects the fact that people do not perceive (i.e. see, hear, feel or smell) their environment equally well in all directions. The dynamics of the individuals in our model follow from a system of Newton-like equations in the overdamped limit. The instantaneous velocity is modelled in such a way that it accounts for the angle at which an individual perceives another individual. We investigate the effects of this perception anisotropy by means of simulations, very much in the spirit of molecular dynamics. We define a number of characteristic quantifiers (including the polarization index and Morisita index) that serve as measures, for example, for organization and clustering, and we use these indices to investigate the influence of anisotropy on the global behaviour of the crowd. The goal of the paper is to investigate the potential of this model; extensive statistical analysis of simulation data and reproducing any specific real-life situation are beyond its scope. © 2013 IOP Publishing Ltd and SISSA Medialab srl.

A mixed finite element discretization scheme for a concrete carbonation model with concentration-dependent porosity.
Radu, F.; Muntean, A.; Pop, I.; Suciu, N.; and Kolditz, O.
*Journal of Computational and Applied Mathematics*, 246. 2013.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {A mixed finite element discretization scheme for a concrete carbonation model with concentration-dependent porosity}, type = {article}, year = {2013}, keywords = {Carbonation,Convergence analysis,Coupled reactive transport}, volume = {246}, id = {1707d60a-547e-3391-8719-75a5e99df01d}, created = {2019-08-23T19:37:42.083Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:42.083Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {© 2012 Elsevier B.V. All rights reserved. We investigate a prototypical reaction-diffusion-flow problem in saturated/unsaturated porous media. The special features of our problem are twofold: the reaction produces water and therefore the flow and transport are coupled in both directions and moreover, the reaction may alter the microstructure. This means we have a variable porosity in our model. For the spatial discretization we propose a mass conservative scheme based on the mixed finite element method (MFEM). The scheme is semi-implicit in time. Error estimates are obtained for some particular cases. We apply our finite element methodology for the case of concrete carbonation - one of the most important physico-chemical processes affecting the durability of concrete.}, bibtype = {article}, author = {Radu, F.A. and Muntean, A. and Pop, I.S. and Suciu, N. and Kolditz, O.}, doi = {10.1016/j.cam.2012.10.017}, journal = {Journal of Computational and Applied Mathematics} }

© 2012 Elsevier B.V. All rights reserved. We investigate a prototypical reaction-diffusion-flow problem in saturated/unsaturated porous media. The special features of our problem are twofold: the reaction produces water and therefore the flow and transport are coupled in both directions and moreover, the reaction may alter the microstructure. This means we have a variable porosity in our model. For the spatial discretization we propose a mass conservative scheme based on the mixed finite element method (MFEM). The scheme is semi-implicit in time. Error estimates are obtained for some particular cases. We apply our finite element methodology for the case of concrete carbonation - one of the most important physico-chemical processes affecting the durability of concrete.

2012
(8)

Can cooperation slow down emergency evacuations?.
Cirillo, E.; and Muntean, A.
*Comptes Rendus - Mecanique*, 340(9). 2012.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Can cooperation slow down emergency evacuations?}, type = {article}, year = {2012}, keywords = {Dynamics of crowd motions,Evacuation scenario,Granular media,Lattice model}, volume = {340}, id = {bbe22e49-0fb6-3d65-b853-4682c2574ccd}, created = {2019-08-23T19:37:40.762Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.762Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We study the motion of pedestrians through obscure corridors where the lack of visibility hides the precise position of the exits. Using a lattice model, we explore the effects of cooperation on the overall exit flux (evacuation rate). More precisely, we study the effect of the buddying threshold (of no exclusion per site) on the dynamics of the crowd. In some cases, we note that if the evacuees tend to cooperate and act altruistically, then their collective action tends to favor the occurrence of disasters. © 2012 Académie des sciences.}, bibtype = {article}, author = {Cirillo, E.N.M. and Muntean, A.}, doi = {10.1016/j.crme.2012.09.003}, journal = {Comptes Rendus - Mecanique}, number = {9} }

We study the motion of pedestrians through obscure corridors where the lack of visibility hides the precise position of the exits. Using a lattice model, we explore the effects of cooperation on the overall exit flux (evacuation rate). More precisely, we study the effect of the buddying threshold (of no exclusion per site) on the dynamics of the crowd. In some cases, we note that if the evacuees tend to cooperate and act altruistically, then their collective action tends to favor the occurrence of disasters. © 2012 Académie des sciences.

Semi-discrete finite difference multiscale scheme for a concrete corrosion model: A priori estimates and convergence.
Chalupecký, V.; and Muntean, A.
*Japan Journal of Industrial and Applied Mathematics*, 29(2). 2012.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Semi-discrete finite difference multiscale scheme for a concrete corrosion model: A priori estimates and convergence}, type = {article}, year = {2012}, keywords = {Approximation of weak solutions,Concrete corrosion,Convergence,Multiscale reaction-diffusion equations,Two-scale finite difference method}, volume = {29}, id = {1b591c58-09a9-3775-8534-405dccbf617a}, created = {2019-08-23T19:37:40.772Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.772Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We study a semi-discrete finite difference multiscale scheme for a concrete corrosion model consisting of a system of two-scale reaction-diffusion equations coupled with an ordinary differential equation. We prove energy and regularity estimates and use them to get the necessary compactness of the approximate solutions. Finally, we illustrate numerically the behavior of the two-scale finite difference approximation of the solution to our system. © The JJIAM Publishing Committee and Springer 2012.}, bibtype = {article}, author = {Chalupecký, V. and Muntean, A.}, doi = {10.1007/s13160-012-0060-6}, journal = {Japan Journal of Industrial and Applied Mathematics}, number = {2} }

We study a semi-discrete finite difference multiscale scheme for a concrete corrosion model consisting of a system of two-scale reaction-diffusion equations coupled with an ordinary differential equation. We prove energy and regularity estimates and use them to get the necessary compactness of the approximate solutions. Finally, we illustrate numerically the behavior of the two-scale finite difference approximation of the solution to our system. © The JJIAM Publishing Committee and Springer 2012.

Single and two-scale sharp-interface models for concrete carbonation - Asymptotics and numerical approximation.
Evans, J.; Fernández, A.; and Muntean, A.
*Multiscale Modeling and Simulation*, 10(3). 2012.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Single and two-scale sharp-interface models for concrete carbonation - Asymptotics and numerical approximation}, type = {article}, year = {2012}, keywords = {Concrete carbonation,Fast-reaction asymptotics,Matched asymptotics,Numerical approximation of reaction fronts,Reaction layer analysis,Two-scale sharp-interface models}, volume = {10}, id = {9ce5a75b-f6b5-322a-8b2d-967083709765}, created = {2019-08-23T19:37:41.527Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.527Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We investigate the fast-reaction asymptotics for a one-dimensional reaction-diffusion system describing the penetration of the carbonation reaction in concrete. The technique of matchedasymptotics is used to show that the reaction-diffusion system leads to two distinct classes of sharpinterface models. These correspond to different scalings of a small parameter ε representing the fast-reaction and defined here as the ratio between the characteristic scale of diffusion for the fastest species and the characteristic scale of the carbonation reaction. We explore three conceptually different diffusion regimes in terms of the behavior of the effective diffusivities for the driving chemical species. The limiting models include one-phase and two-phase generalized Stefan moving-boundary problems as well as a nonstandard two-scale (micro-macro) moving-boundary problem - the main result of the paper. Numerical results, supporting the asymptotics, illustrate the behavior of the concentration profiles for relevant parameter regimes. © 2012 Society for Industrial and Applied Mathematics.}, bibtype = {article}, author = {Evans, J.D. and Fernández, A. and Muntean, A.}, doi = {10.1137/110859701}, journal = {Multiscale Modeling and Simulation}, number = {3} }

We investigate the fast-reaction asymptotics for a one-dimensional reaction-diffusion system describing the penetration of the carbonation reaction in concrete. The technique of matchedasymptotics is used to show that the reaction-diffusion system leads to two distinct classes of sharpinterface models. These correspond to different scalings of a small parameter ε representing the fast-reaction and defined here as the ratio between the characteristic scale of diffusion for the fastest species and the characteristic scale of the carbonation reaction. We explore three conceptually different diffusion regimes in terms of the behavior of the effective diffusivities for the driving chemical species. The limiting models include one-phase and two-phase generalized Stefan moving-boundary problems as well as a nonstandard two-scale (micro-macro) moving-boundary problem - the main result of the paper. Numerical results, supporting the asymptotics, illustrate the behavior of the concentration profiles for relevant parameter regimes. © 2012 Society for Industrial and Applied Mathematics.

On a one-dimensional shape-memory alloy model in its fast-temperature- activation limit.
Aiki, T.; Muntean, A.; and Anthonissen, M.
*Discrete and Continuous Dynamical Systems - Series S*, 5(1). 2012.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {On a one-dimensional shape-memory alloy model in its fast-temperature- activation limit}, type = {article}, year = {2012}, keywords = {Existence and uniqueness of weak solutions,Modeling,Nonlinear elliptic equation,Shape-memory alloys}, volume = {5}, id = {743b83db-0429-3a76-be6c-03597344a6a4}, created = {2019-08-23T19:37:41.531Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.531Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We study a one-dimensional model describing the motion of a shape-memory alloy spring at a small characteristic time scale, called here fast-temperature-activation limit. At this level, the standard Falk's model reduces to a nonlinear elliptic partial differential equation (PDE) with Newton boundary condition. We show existence and uniqueness of a bounded weak solution and approximate this numerically. Interestingly, in spite of the nonlinearity of the model, the approximate solution exhibits nearly a linear profile. Finally, we extend the reduced model to the simplest PDE system for shape memory alloys that can capture oscillations and then damp out these oscillations numerically. The numerical results for both limiting cases show excellent agreement. The graphs show that the valve opens in an instant, which is realistic behavior of the free boundary. © 2000 Mathematics Subject Classification.}, bibtype = {article}, author = {Aiki, T. and Muntean, A. and Anthonissen, M.}, doi = {10.3934/dcdss.2012.5.15}, journal = {Discrete and Continuous Dynamical Systems - Series S}, number = {1} }

We study a one-dimensional model describing the motion of a shape-memory alloy spring at a small characteristic time scale, called here fast-temperature-activation limit. At this level, the standard Falk's model reduces to a nonlinear elliptic partial differential equation (PDE) with Newton boundary condition. We show existence and uniqueness of a bounded weak solution and approximate this numerically. Interestingly, in spite of the nonlinearity of the model, the approximate solution exhibits nearly a linear profile. Finally, we extend the reduced model to the simplest PDE system for shape memory alloys that can capture oscillations and then damp out these oscillations numerically. The numerical results for both limiting cases show excellent agreement. The graphs show that the valve opens in an instant, which is realistic behavior of the free boundary. © 2000 Mathematics Subject Classification.

Analysis and Approximation of Microstructure Models.
Muntean, A.; Ptashnyk, M.; and Showalter, R.
*Applicable Analysis*, 91(6). 2012.

doi link bibtex

doi link bibtex

@article{ title = {Analysis and Approximation of Microstructure Models}, type = {article}, year = {2012}, volume = {91}, id = {82316f6d-7254-3a86-b7ab-12c2b384561e}, created = {2019-08-23T19:37:41.567Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.567Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, bibtype = {article}, author = {Muntean, A. and Ptashnyk, M. and Showalter, R.E.}, doi = {10.1080/00036811.2012.689094}, journal = {Applicable Analysis}, number = {6} }

Unfolding-based corrector estimates for a reaction-diffusion system predicting concrete corrosion.
Fatima, T.; Muntean, A.; and Ptashnyk, M.
*Applicable Analysis*, 91(6). 2012.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Unfolding-based corrector estimates for a reaction-diffusion system predicting concrete corrosion}, type = {article}, year = {2012}, keywords = {corrector estimates,homogenization,periodic unfolding,reaction-diffusion systems,sulphate corrosion of concrete}, volume = {91}, id = {109ccb54-743d-357b-b5c1-fd91c77094d7}, created = {2019-08-23T19:37:41.571Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.571Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We use the periodic unfolding technique to derive corrector estimates for a reaction-diffusion system describing concrete corrosion penetration in the sewer pipes. The system, defined in a periodically perforated domain, is semi-linear, partially dissipative and coupled to a nonlinear ordinary differential equation posed on the solid-water interface at the pore level. After discussing the solvability of the pore scale model, we apply the periodic unfolding techniques (adapted to treat the presence of perforations) not only to derive macroscopic (upscaled) model equations, but also to prepare a proper framework for obtaining a convergence rate (corrector estimates) of the averaging procedure. © 2012 Copyright Taylor and Francis Group, LLC.}, bibtype = {article}, author = {Fatima, T. and Muntean, A. and Ptashnyk, M.}, doi = {10.1080/00036811.2011.625016}, journal = {Applicable Analysis}, number = {6} }

We use the periodic unfolding technique to derive corrector estimates for a reaction-diffusion system describing concrete corrosion penetration in the sewer pipes. The system, defined in a periodically perforated domain, is semi-linear, partially dissipative and coupled to a nonlinear ordinary differential equation posed on the solid-water interface at the pore level. After discussing the solvability of the pore scale model, we apply the periodic unfolding techniques (adapted to treat the presence of perforations) not only to derive macroscopic (upscaled) model equations, but also to prepare a proper framework for obtaining a convergence rate (corrector estimates) of the averaging procedure. © 2012 Copyright Taylor and Francis Group, LLC.

Rigorous homogenization of a Stokes-Nernst-Planck-Poisson system.
Ray, N.; Muntean, A.; and Knabner, P.
*Journal of Mathematical Analysis and Applications*, 390(1). 2012.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Rigorous homogenization of a Stokes-Nernst-Planck-Poisson system}, type = {article}, year = {2012}, keywords = {Colloidal transport,Homogenization,Porous media,Stokes-Nernst-Planck-Poisson system,Two-scale convergence}, volume = {390}, id = {d358b0bc-90ee-36ce-98f2-79adfffd2f1a}, created = {2019-08-23T19:37:41.605Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.605Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We perform the periodic homogenization (i.e ε → 0) of a non-stationary Stokes-Nernst-Planck-Poisson system using two-scale convergence, where ε is a suitable scale parameter. The objective is to investigate the influence of different boundary conditions and variable choices of scalings in ε of the microscopic system of partial differential equations on the structure of the (upscaled) limit model equations. Due to the specific nonlinear coupling of the underlying equations, special attention has to be paid when passing to the limit in the electrostatic drift term. As a direct result of the homogenization procedure, various classes of upscaled model equations are obtained. © 2012 Elsevier Inc.}, bibtype = {article}, author = {Ray, N. and Muntean, A. and Knabner, P.}, doi = {10.1016/j.jmaa.2012.01.052}, journal = {Journal of Mathematical Analysis and Applications}, number = {1} }

We perform the periodic homogenization (i.e ε → 0) of a non-stationary Stokes-Nernst-Planck-Poisson system using two-scale convergence, where ε is a suitable scale parameter. The objective is to investigate the influence of different boundary conditions and variable choices of scalings in ε of the microscopic system of partial differential equations on the structure of the (upscaled) limit model equations. Due to the specific nonlinear coupling of the underlying equations, special attention has to be paid when passing to the limit in the electrostatic drift term. As a direct result of the homogenization procedure, various classes of upscaled model equations are obtained. © 2012 Elsevier Inc.

Preface.
Aiki, T.; Hilhorst, D.; Mimura, M.; and Muntean, A.
*Discrete and Continuous Dynamical Systems - Series S*, 5(1). 2012.

doi link bibtex

doi link bibtex

@article{ title = {Preface}, type = {article}, year = {2012}, volume = {5}, id = {1b719097-cb2d-3710-ac1b-464754b39b5a}, created = {2019-08-23T19:37:41.913Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.913Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, bibtype = {article}, author = {Aiki, T. and Hilhorst, D. and Mimura, M. and Muntean, A.}, doi = {10.3934/dcdss.2012.5.1i}, journal = {Discrete and Continuous Dynamical Systems - Series S}, number = {1} }

2011
(6)

Homogenisation of a locally periodic medium with areas of low and high diffusivity.
Van Noorden, T.; and Muntean, A.
*European Journal of Applied Mathematics*, 22(5). 2011.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Homogenisation of a locally periodic medium with areas of low and high diffusivity}, type = {article}, year = {2011}, keywords = {Heterogeneous porous materials,Locally periodic homogenisation,Micro-macro transport,Reaction-diffusion system,Two-scale model,Weak solvability}, volume = {22}, id = {64b43ff6-65a8-3ebb-8fca-71a694c20dc8}, created = {2019-08-23T19:37:40.821Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.821Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We aim at understanding transport in porous materials consisting of regions with both high and low diffusivities. We apply a formal homogenisation procedure to the case where the heterogeneities are not arranged in a strictly periodic manner. The result is a two-scale model formulated in x-dependent Bochner spaces. We prove the weak solvability of the limit two-scale model for a prototypical advection-diffusion system of minimal size. A special feature of our analysis is that most of the basic estimates (positivity, L ∈-bounds, uniqueness, energy inequality) are obtained in the x-dependent Bochner spaces. © 2011 Cambridge University Press.}, bibtype = {article}, author = {Van Noorden, T.L. and Muntean, A.}, doi = {10.1017/S0956792511000209}, journal = {European Journal of Applied Mathematics}, number = {5} }

We aim at understanding transport in porous materials consisting of regions with both high and low diffusivities. We apply a formal homogenisation procedure to the case where the heterogeneities are not arranged in a strictly periodic manner. The result is a two-scale model formulated in x-dependent Bochner spaces. We prove the weak solvability of the limit two-scale model for a prototypical advection-diffusion system of minimal size. A special feature of our analysis is that most of the basic estimates (positivity, L ∈-bounds, uniqueness, energy inequality) are obtained in the x-dependent Bochner spaces. © 2011 Cambridge University Press.

Modeling micro-macro pedestrian counter flow in heterogeneous domains.
Evers, J.; and Muntean, A.
*Nonlinear Phenomena in Complex Systems*, 14(1). 2011.

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link bibtex abstract

@article{ title = {Modeling micro-macro pedestrian counter flow in heterogeneous domains}, type = {article}, year = {2011}, keywords = {Crowd dynamics,Mass measures,Porosity measure,Social networks}, volume = {14}, id = {ffa36bd0-8279-3ff5-86dd-1fa490e9fb51}, created = {2019-08-23T19:37:40.823Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.823Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We present a micro-macro strategy able to describe the dynamics of crowds in heterogeneous spatial domains. Herein we focus on the example of pedestrian counter flow. The main working tools include the use of mass and porosity measures together with their transport as well as suitable application of a version of Radon-Nikodym Theorem formulated for finite measures. Finally, we illustrate numerically our microscopic model and emphasize the effects produced by an implicitly defined social velocity.}, bibtype = {article}, author = {Evers, J. and Muntean, A.}, journal = {Nonlinear Phenomena in Complex Systems}, number = {1} }

We present a micro-macro strategy able to describe the dynamics of crowds in heterogeneous spatial domains. Herein we focus on the example of pedestrian counter flow. The main working tools include the use of mass and porosity measures together with their transport as well as suitable application of a version of Radon-Nikodym Theorem formulated for finite measures. Finally, we illustrate numerically our microscopic model and emphasize the effects produced by an implicitly defined social velocity.

On uniqueness of a weak solution of one-dimensional concrete carbonation problem.
Aiki, T.; and Muntean, A.
*Discrete and Continuous Dynamical Systems*, 29(4). 2011.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {On uniqueness of a weak solution of one-dimensional concrete carbonation problem}, type = {article}, year = {2011}, keywords = {Dual equation method,Free boundary problem,Uniqueness}, volume = {29}, id = {72157574-c730-3410-8019-44e12f9b4190}, created = {2019-08-23T19:37:40.859Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.859Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {In our previous works we studied a one-dimensional free-boundary model related to the aggressive penetration of gaseous carbon dioxide in unsaturated concrete. Essentially, global existence and uniqueness of weak solutions to the model were obtained when the initial functions are bounded on the domain. In this paper we investigate the well-posedness of the problem for the case when the initial functions belong to a L2-class. Specifically, the uniqueness of weak solutions is proved by applying the dual equation method.}, bibtype = {article}, author = {Aiki, T. and Muntean, A.}, doi = {10.3934/dcds.2011.29.1345}, journal = {Discrete and Continuous Dynamical Systems}, number = {4} }

In our previous works we studied a one-dimensional free-boundary model related to the aggressive penetration of gaseous carbon dioxide in unsaturated concrete. Essentially, global existence and uniqueness of weak solutions to the model were obtained when the initial functions are bounded on the domain. In this paper we investigate the well-posedness of the problem for the case when the initial functions belong to a L2-class. Specifically, the uniqueness of weak solutions is proved by applying the dual equation method.

Oscillatory pulses in FitzHugh-Nagumo type systems with cross-diffusion.
Zemskov, E.; Epstein, I.; and Muntean, A.
*Mathematical Medicine and Biology*, 28(2). 2011.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Oscillatory pulses in FitzHugh-Nagumo type systems with cross-diffusion}, type = {article}, year = {2011}, keywords = {Cross-diffusion,Pattern formation,Pulse solutions,Reaction-diffusion systems}, volume = {28}, id = {98e02da4-9c04-3808-a812-414f4a3a3e7b}, created = {2019-08-23T19:37:41.610Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.610Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We study FitzHugh-Nagumo type reaction-diffusion systems with linear cross-diffusion terms. Based on an analytical description using piecewise linear approximations of the reaction functions, we completely describe the occurrence and properties of wavy pulses, patterns of relevance in several biological contexts, in two prototypical systems. The pulse wave profiles arising in this treatment contain oscillatory tails similar to those in travelling fronts. We find a fundamental, intrinsic feature of pulse dynamics in crossdiffusive systems-the appearance of pulses in the bistable regime when two fixed points exist. © The author 2010. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.}, bibtype = {article}, author = {Zemskov, E.P. and Epstein, I.R. and Muntean, A.}, doi = {10.1093/imammb/dqq012}, journal = {Mathematical Medicine and Biology}, number = {2} }

We study FitzHugh-Nagumo type reaction-diffusion systems with linear cross-diffusion terms. Based on an analytical description using piecewise linear approximations of the reaction functions, we completely describe the occurrence and properties of wavy pulses, patterns of relevance in several biological contexts, in two prototypical systems. The pulse wave profiles arising in this treatment contain oscillatory tails similar to those in travelling fronts. We find a fundamental, intrinsic feature of pulse dynamics in crossdiffusive systems-the appearance of pulses in the bistable regime when two fixed points exist. © The author 2010. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Moving carbonation fronts in concrete: A moving-sharp-interface approach.
Muntean, A.; Böhm, M.; and Kropp, J.
*Chemical Engineering Science*, 66(3). 2011.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Moving carbonation fronts in concrete: A moving-sharp-interface approach}, type = {article}, year = {2011}, keywords = {Carbonation,FEM,Fast reaction,Finite element method,Large-time behavior,Modeling,Moving-interface problem,Ode,Pde,RD}, volume = {66}, id = {0df9852f-6b56-3bd8-91df-b74c1b02eff7}, created = {2019-08-23T19:37:41.648Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.648Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We present a new modeling strategy for predicting the penetration of carbonation reaction fronts in concrete. The approach relies on the assumption that carbonation reaction concentrates macroscopically on an a priori unknown narrow strip (called reaction front) moving into concrete gradually changing its mechanical and chemical properties. We propose a moving-interface model to forecast the maximum penetration depth of gaseous CO2 in the porous concrete matrix. The main questions driving this research are: How fast does the carbonation front move? and How long does it take until the front reaches the reinforcement?. As model output, we determine simultaneously the position of the carbonation front and the profiles of the active concentrations. The model equations are solved using a specially tailored finite element scheme and are validated relying on experimental data from the Ph.D. thesis by D. Bunte Zum Karbonatisierungsbedingten Verlust der Dauerhaftigkeit von Außenbauteilen aus Stahlbeton, Ph.D. thesis, TU Braunschweig (1994). Our approach should be viewed as an alternative to the standard carbonation models. © 2010 Elsevier Ltd.}, bibtype = {article}, author = {Muntean, A. and Böhm, M. and Kropp, J.}, doi = {10.1016/j.ces.2010.11.011}, journal = {Chemical Engineering Science}, number = {3} }

We present a new modeling strategy for predicting the penetration of carbonation reaction fronts in concrete. The approach relies on the assumption that carbonation reaction concentrates macroscopically on an a priori unknown narrow strip (called reaction front) moving into concrete gradually changing its mechanical and chemical properties. We propose a moving-interface model to forecast the maximum penetration depth of gaseous CO2 in the porous concrete matrix. The main questions driving this research are: How fast does the carbonation front move? and How long does it take until the front reaches the reinforcement?. As model output, we determine simultaneously the position of the carbonation front and the profiles of the active concentrations. The model equations are solved using a specially tailored finite element scheme and are validated relying on experimental data from the Ph.D. thesis by D. Bunte Zum Karbonatisierungsbedingten Verlust der Dauerhaftigkeit von Außenbauteilen aus Stahlbeton, Ph.D. thesis, TU Braunschweig (1994). Our approach should be viewed as an alternative to the standard carbonation models. © 2010 Elsevier Ltd.

Homogenization of a reaction-diffusion system modeling sulfate corrosion of concrete in locally periodic perforated domains.
Fatima, T.; Arab, N.; Zemskov, E.; and Muntean, A.
*Journal of Engineering Mathematics*, 69(2). 2011.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Homogenization of a reaction-diffusion system modeling sulfate corrosion of concrete in locally periodic perforated domains}, type = {article}, year = {2011}, keywords = {Asymptotic homogenization,Locally periodic perforated media,Nonlinear Robin-type boundary conditions,Semi-linear PDE-ODE system,Sulfate corrosion}, volume = {69}, id = {49c7fe26-fc83-3637-b9a7-44fa265a4879}, created = {2019-08-23T19:37:41.956Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:41.956Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {A reaction-diffusion system modeling concrete corrosion in sewer pipes is discussed. The system is coupled, semi-linear, and partially dissipative. It is defined on a locally periodic perforated domain with nonlinear Robin-type boundary conditions at water-air and solid-water interfaces. Asymptotic homogenization techniques are applied to obtain upscaled reaction-diffusion models together with explicit formulae for the effective transport and reaction coefficients. It is shown that the averaged system contains additional terms appearing due to the deviation of the assumed geometry from a purely periodic distribution of perforations for two relevant parameter regimes: (a) all diffusion coefficients are of order of O(1) and (b) all diffusion coefficients are of order of O(ε 2 ) except the one for H 2 S(g) which is of order of O(1). In case (a) a set of macroscopic equations is obtained, while in case (b) a two-scale reaction-diffusion system is derived that captures the interplay between microstructural reaction effects and the macroscopic transport. © 2010 The Author(s).}, bibtype = {article}, author = {Fatima, T. and Arab, N. and Zemskov, E.P. and Muntean, A.}, doi = {10.1007/s10665-010-9396-6}, journal = {Journal of Engineering Mathematics}, number = {2} }

A reaction-diffusion system modeling concrete corrosion in sewer pipes is discussed. The system is coupled, semi-linear, and partially dissipative. It is defined on a locally periodic perforated domain with nonlinear Robin-type boundary conditions at water-air and solid-water interfaces. Asymptotic homogenization techniques are applied to obtain upscaled reaction-diffusion models together with explicit formulae for the effective transport and reaction coefficients. It is shown that the averaged system contains additional terms appearing due to the deviation of the assumed geometry from a purely periodic distribution of perforations for two relevant parameter regimes: (a) all diffusion coefficients are of order of O(1) and (b) all diffusion coefficients are of order of O(ε 2 ) except the one for H 2 S(g) which is of order of O(1). In case (a) a set of macroscopic equations is obtained, while in case (b) a two-scale reaction-diffusion system is derived that captures the interplay between microstructural reaction effects and the macroscopic transport. © 2010 The Author(s).

2010
(2)

Large time behavior of solutions to a moving-interface problem modeling concrete carbonation.
Aiki, T.; and Muntean, A.
*Communications on Pure and Applied Analysis*, 9(5). 2010.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Large time behavior of solutions to a moving-interface problem modeling concrete carbonation}, type = {article}, year = {2010}, keywords = {Free boundary problem,Large time behavior,Maximum principle}, volume = {9}, id = {3695e796-9648-3551-995d-b3866d8b1f9b}, created = {2019-08-23T19:37:40.867Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.867Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We study the large time behavior of the weak solutions to a onephase moving sharp-interface PDE system describing the aggressive penetration of gaseous carbon dioxide in unsaturated concrete. The key of the proof is a global uniform estimate for solutions obtained by using the maximum principle. The analysis reported here relies on the global existence and uniqueness of solutions that we have proved previously.}, bibtype = {article}, author = {Aiki, T. and Muntean, A.}, doi = {10.3934/cpaa.2010.9.1117}, journal = {Communications on Pure and Applied Analysis}, number = {5} }

We study the large time behavior of the weak solutions to a onephase moving sharp-interface PDE system describing the aggressive penetration of gaseous carbon dioxide in unsaturated concrete. The key of the proof is a global uniform estimate for solutions obtained by using the maximum principle. The analysis reported here relies on the global existence and uniqueness of solutions that we have proved previously.

A multiscale Galerkin approach for a class of nonlinear coupled reaction-diffusion systems in complex media.
Muntean, A.; and Neuss-Radu, M.
*Journal of Mathematical Analysis and Applications*, 371(2). 2010.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {A multiscale Galerkin approach for a class of nonlinear coupled reaction-diffusion systems in complex media}, type = {article}, year = {2010}, keywords = {Galerkin approximation,Gas-liquid reactions,Henry's law,Multiscale reaction-diffusion systems,Nonlinear coupling,Structured porous media}, volume = {371}, id = {d3d04f6c-969c-3386-bf86-19696aba7fba}, created = {2019-08-23T19:37:40.903Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.903Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {A Galerkin approach for a class of multiscale reaction-diffusion systems with nonlinear coupling between the microscopic and macroscopic variables is presented. This type of models are obtained e.g. by upscaling of processes in chemical engineering (particularly in catalysis), biochemistry, or geochemistry. Exploiting the special structure of the models, the functions spaces used for the approximation of the solution are chosen as tensor products of spaces on the macroscopic domain and on the standard cell associated to the microstructure. Uniform estimates for the finite dimensional approximations are proven. Based on these estimates, the convergence of the approximating sequence is shown. This approach can be used as a basis for the numerical computation of the solution. © 2010 Elsevier Inc.}, bibtype = {article}, author = {Muntean, A. and Neuss-Radu, M.}, doi = {10.1016/j.jmaa.2010.05.056}, journal = {Journal of Mathematical Analysis and Applications}, number = {2} }

A Galerkin approach for a class of multiscale reaction-diffusion systems with nonlinear coupling between the microscopic and macroscopic variables is presented. This type of models are obtained e.g. by upscaling of processes in chemical engineering (particularly in catalysis), biochemistry, or geochemistry. Exploiting the special structure of the models, the functions spaces used for the approximation of the solution are chosen as tensor products of spaces on the macroscopic domain and on the standard cell associated to the microstructure. Uniform estimates for the finite dimensional approximations are proven. Based on these estimates, the convergence of the approximating sequence is shown. This approach can be used as a basis for the numerical computation of the solution. © 2010 Elsevier Inc.

2009
(5)

Continuity with respect to data and parameters of weak solutions to a Stefan-like problem.
Muntean, A.
*Acta Mathematica Universitatis Comenianae*, 78(2). 2009.

link bibtex abstract

link bibtex abstract

@article{ title = {Continuity with respect to data and parameters of weak solutions to a Stefan-like problem}, type = {article}, year = {2009}, keywords = {Concrete corrosion,Moving-boundary problem,Reaction-diffusion system}, volume = {78}, id = {14d61004-0500-316f-a134-7ecadc26aadd}, created = {2019-08-23T19:37:40.151Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.151Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We study a reaction-diffusion system with moving boundary describing a prototypical fast reaction-diffusion scenario arising in the chemical corrosion of concrete-based materials. We prove the continuity with respect to data and parame-ters of weak solutions to the resulting moving-boundary system of partial differential equations.}, bibtype = {article}, author = {Muntean, A.}, journal = {Acta Mathematica Universitatis Comenianae}, number = {2} }

We study a reaction-diffusion system with moving boundary describing a prototypical fast reaction-diffusion scenario arising in the chemical corrosion of concrete-based materials. We prove the continuity with respect to data and parame-ters of weak solutions to the resulting moving-boundary system of partial differential equations.

Well-posedness of a moving-boundary problem with two moving reaction strips.
Muntean, A.
*Nonlinear Analysis: Real World Applications*, 10(4). 2009.

doi link bibtex abstract

doi link bibtex abstract

@article{ title = {Well-posedness of a moving-boundary problem with two moving reaction strips}, type = {article}, year = {2009}, keywords = {A priori estimates,Kinetic condition,Moving boundary,Stefan problem,Strip-concentrated reaction,Weak solutions,Well-posedness}, volume = {10}, id = {fd50d254-ac02-3e54-a8d7-e099ada4aa29}, created = {2019-08-23T19:37:40.154Z}, file_attached = {false}, profile_id = {b73905ef-6774-3e9d-ac7e-8d5666c2a46e}, last_modified = {2019-08-23T19:37:40.154Z}, read = {false}, starred = {false}, authored = {true}, confirmed = {false}, hidden = {false}, private_publication = {false}, abstract = {We deal with a one-dimensional coupled system of semi-linear reaction-diffusion equations in two a priori unknown moving phases driven by a non-local kinetic condition. The PDEs system models the penetration of gaseous carbon dioxide in unsaturated porous materials (like concrete). The main issue is that the strong competition between carbon dioxide diffusion and the fast reaction of carbon dioxide with calcium hydroxide-which are the main active reactants-leads to a sudden drop in the alkalinity of concrete near the steel reinforcement. This process-called concrete carbonation-facilitates chemical corrosion and drastically influences the lifetime of the material. We present details of a class of moving-boundary models with kinetic condition at the moving boundary and address the local existence, uniqueness and stability of positive weak solutions. We also point out our concept of global solvability. The application of such moving-boundary systems to the prediction of carbonation penetration into ordinary concrete samples is illustrated numerically. © 2008 Elsevier Ltd. All rights reserved.}, bibtype = {article}, author = {Muntean, A.}, doi = {10.1016/j.nonrwa.2008.05.010}, journal = {Nonlinear Analysis: Real World Applications}, number = {4} }

We deal with a one-dimensional coupled system of semi-linear reaction-diffusion equations in two a priori unknown moving phases driven by a non-local kinetic condition. The PDEs system models the penetration of gaseous carbon dioxide in unsaturated porous materials (like concrete). The main issue is that the strong competition between carbon dioxide diffusion and the fast reaction of carbon dioxide with calcium hydroxide-which are the main active reactants-leads to a sudden drop in the alkalinity of concrete near the steel reinforcement. This process-called concrete carbonation-facilitates chemical corrosion and drastically influences the lifetime of the material. We present details of a class of moving-boundary models with kinetic condition at the moving boundary and address the local existence, uniqueness and stability of positive weak solutions. We also point out our concept of global solvability. The application of such moving-boundary systems to the prediction of carbonation penetration into ordinary concrete samples is illustrated numerically. © 2008 Elsevier Ltd. All rights reserved.

On the interplay between fast reaction and slow diffusion in the concrete carbonation process: A matched-asymptotics approach.
Muntean, A.
*Meccanica*, 44(1). 2009.