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Abstract: The aim of this paper is to develop a crowd motion model designed to handlehighly packed situations. The model we propose rests on two principles: Wefirst define a spontaneous velocity which corresponds to the velocity eachindividual would like to have in the absence of other people; The actualvelocity is then computed as the projection of the spontaneous velocity ontothe set of admissible velocities i.e. velocities which do not violate thenon-overlapping constraint. We describe here the underlying mathematicalframework, and we explain how recent results by J.F. Edmond and L. Thibault onthe sweeping process by uniformly prox-regular sets can be adapted to handlethis situation in terms of well-posedness. We propose a numerical scheme forthis contact dynamics model, based on a prediction-correction algorithm.Numerical illustrations are finally presented and discussed.



Author: Bertrand Maury LM-Orsay, Juliette Venel LM-Orsay

Source: https://arxiv.org/







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