Adiscretecontactmodelforcrowdmotion-BertrandMaury,创新.PDFVIP

A discrete contact model for crowd motion Bertrand Maury Juliette Venel Universit´e de Paris-Sud Universit´e de Paris-Sud UMR du CNRS 8628 UMR du CNRS 8628 F-91405 Orsay Cedex F-91405 Orsay Cedex bertrand.maury@math.u-psud.fr juliette.venel@math.u-psud.fr 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 term