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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

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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
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
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:
DateEvent
1 June 2018Published
March 2018Available
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:
Project/Grant IDRIOXX Funder NameFunder ID
New Frontiers Grant NST 0001 Österreichischen Akademie der Wissenschaftenhttp://dx.doi.org/10.13039/501100001822
UNSPECIFIEDCompagnia di San Paolohttp://dx.doi.org/10.13039/100007388
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