A discrete contact model for crowd motion

Bertrand Maury; Juliette Venel

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

  • Volume: 45, Issue: 1, page 145-168
  • ISSN: 0764-583X

Abstract

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The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here the underlying mathematical framework, and we explain how recent results by J.F. Edmond and L. Thibault on the sweeping process by uniformly prox-regular sets can be adapted to handle this situation in terms of well-posedness. We propose a numerical scheme for this contact dynamics model, based on a prediction-correction algorithm. Numerical illustrations are finally presented and discussed.

How to cite

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Maury, Bertrand, and Venel, Juliette. "A discrete contact model for crowd motion." ESAIM: Mathematical Modelling and Numerical Analysis 45.1 (2011): 145-168. <http://eudml.org/doc/197528>.

@article{Maury2011,
abstract = { The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here the underlying mathematical framework, and we explain how recent results by J.F. Edmond and L. Thibault on the sweeping process by uniformly prox-regular sets can be adapted to handle this situation in terms of well-posedness. We propose a numerical scheme for this contact dynamics model, based on a prediction-correction algorithm. Numerical illustrations are finally presented and discussed. },
author = {Maury, Bertrand, Venel, Juliette},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Crowd motion model; contact dynamics; convex analysis; differential inclusion; prox-regularity; crowd motion model},
language = {eng},
month = {1},
number = {1},
pages = {145-168},
publisher = {EDP Sciences},
title = {A discrete contact model for crowd motion},
url = {http://eudml.org/doc/197528},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Maury, Bertrand
AU - Venel, Juliette
TI - A discrete contact model for crowd motion
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2011/1//
PB - EDP Sciences
VL - 45
IS - 1
SP - 145
EP - 168
AB - The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here the underlying mathematical framework, and we explain how recent results by J.F. Edmond and L. Thibault on the sweeping process by uniformly prox-regular sets can be adapted to handle this situation in terms of well-posedness. We propose a numerical scheme for this contact dynamics model, based on a prediction-correction algorithm. Numerical illustrations are finally presented and discussed.
LA - eng
KW - Crowd motion model; contact dynamics; convex analysis; differential inclusion; prox-regularity; crowd motion model
UR - http://eudml.org/doc/197528
ER -

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