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Bruna, Maria, Burger, Martin, Pietschmann, Jan-Frederik and Wolfram, Marie-Therese (2021) Active crowds. In: Bellomo, Nicola and Carrillo, Antonio and Tadmor, Eitan, (eds.) Active Particles : Advances in Theory, Models, and Applications. Modeling and Simulation in Science, Engineering and Technology, 3 . Cham, Switzerland: Birkhaeuser, pp. 35-73. ISBN 9783030933012
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Official URL: https://doi.org/10.1007/978-3-030-93302-9_2
Abstract
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential equations for the particle density. The macroscopic models share common features, such as cross diffusion or degenerate mobilities. We then take the diversity of macroscopic models to a uniform structure and work out potential similarities and differences. Moreover, we discuss boundary effects and possible applications in life and social sciences. This is complemented by numerical simulations that highlight the effects of different boundary conditions.
Item Type: | Book Item | |||||||||||||||||||||
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Subjects: | H Social Sciences > HM Sociology Q Science > QA Mathematics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Crowds -- Mathematical models, Collective behavior -- Mathematical models | |||||||||||||||||||||
Series Name: | Modeling and Simulation in Science, Engineering and Technology | |||||||||||||||||||||
Publisher: | Birkhaeuser | |||||||||||||||||||||
Place of Publication: | Cham, Switzerland | |||||||||||||||||||||
ISBN: | 9783030933012 | |||||||||||||||||||||
Book Title: | Active Particles : Advances in Theory, Models, and Applications | |||||||||||||||||||||
Editor: | Bellomo, Nicola and Carrillo, Antonio and Tadmor, Eitan | |||||||||||||||||||||
Official Date: | 7 December 2021 | |||||||||||||||||||||
Dates: |
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Volume: | 3 | |||||||||||||||||||||
Page Range: | pp. 35-73 | |||||||||||||||||||||
DOI: | 10.1007/978-3-030-93302-9_2 | |||||||||||||||||||||
Status: | Peer Reviewed | |||||||||||||||||||||
Publication Status: | Published | |||||||||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||||||||
Date of first compliant deposit: | 10 January 2022 | |||||||||||||||||||||
Date of first compliant Open Access: | 7 December 2023 | |||||||||||||||||||||
RIOXX Funder/Project Grant: |
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