We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
KINETIC DESCRIPTION OF COLLISION AVOIDANCE IN PEDESTRIAN CROWDS BY SIDESTEPPING.
- Authors
Festa, Adriano; Tosin, Andrea; Wolfram, Marie-Therese
- 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.
- Subjects
PEDESTRIANS; TRAFFIC safety; BOLTZMANN'S equation; KINETIC energy; APPROXIMATION theory; HYDRODYNAMICS
- Publication
Kinetic & Related Models, 2018, Vol 11, Issue 3, p491
- ISSN
1937-5093
- Publication type
Article
- DOI
10.3934/krm.2018022