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Kinetic description of collision avoidance in pedestrian crowds by sidestepping
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Festa, Adriano, Tosin, Andrea and Wolfram, Marie-Therese (2018) Kinetic description of collision avoidance in pedestrian crowds by sidestepping. Kinetic and Related Models, 11 (3). pp. 491-520. doi:10.3934/krm.2018022 ISSN 1937-5093.
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Official URL: http://dx.doi.org/10.3934/krm.2018022
Abstract
In this paper we study a kinetic model for pedestrians, who are assumed to adapt their motion towards a desired direction while avoiding collisions with others by stepping aside. These minimal microscopic interaction rules lead to complex emergent macroscopic phenomena, such as velocity alignment in unidirectional flows and lane or stripe formation in bidirectional flows. We start by discussing collision avoidance mechanisms at the microscopic scale, then we study the corresponding Boltzmann-type kinetic description and its hydrodynamic mean-field approximation in the grazing collision limit. In the spatially homogeneous case we prove directional alignment under specific conditions on the sidestepping rules for both the collisional and the mean-field model. In the spatially inhomogeneous case we illustrate, by means of various numerical experiments, the rich dynamics that the proposed model is able to reproduce.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Pedestrian traffic flow -- Mathematical models, Maxwell-Boltzmann distribution law , Mean field theory | |||||||||
| Journal or Publication Title: | Kinetic and Related Models | |||||||||
| Publisher: | American Institute of Mathematical Sciences | |||||||||
| ISSN: | 1937-5093 | |||||||||
| Official Date: | 1 June 2018 | |||||||||
| Dates: |
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| Volume: | 11 | |||||||||
| Number: | 3 | |||||||||
| Page Range: | pp. 491-520 | |||||||||
| DOI: | 10.3934/krm.2018022 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | The following article appeared in Festa, Adriano, Tosin, Andrea and Wolfram, Marie-Therese (2018) Kinetic description of collision avoidance in pedestrian crowds by sidestepping. Kinetic and Related Models, 11 (3). pp. 491-520. and may be found at doi:10.3934/krm.2018022 | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 30 October 2019 | |||||||||
| Date of first compliant Open Access: | 30 October 2019 | |||||||||
| RIOXX Funder/Project Grant: |
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| Open Access Version: |
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