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Discrete and continuum links to a nonlinear coupled transport problem of interacting populations
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Duong, Manh Hong, Muntean, Adrian and Richardson, Omar (2017) Discrete and continuum links to a nonlinear coupled transport problem of interacting populations. The European Physical Journal Special Topics, 226 (10). pp. 2345-2357. ISSN 1951-6355.
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Official URL: http://www.springer.com/materials/journal/11734
Abstract
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.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QC Physics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Particles, Transport theory, Hydrodynamics | ||||||||
Journal or Publication Title: | The European Physical Journal Special Topics | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 1951-6355 | ||||||||
Official Date: | July 2017 | ||||||||
Dates: |
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Volume: | 226 | ||||||||
Number: | 10 | ||||||||
Page Range: | pp. 2345-2357 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 21 July 2017 | ||||||||
Date of first compliant Open Access: | 21 July 2017 | ||||||||
Funder: | European Research Council (ERC) | ||||||||
Grant number: | Starting Grant 335120 | ||||||||
Open Access Version: |
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