Séance Séminaire

Colloquium de Mathématiques

Microscopic and macroscopic crowd motion models Microscopic and macroscopic crowd motion models

The modeling of crowd motions has motivated a huge activity in the last 3 decades. Most models are based on principles which pertain to classical mechanics: individuals are considered as particles or grains, and those virtual entities are submitted to forces which encode individual and collective tendencies. We shall detail a model of the granular type, dedicated to highly congested crowds at the microscopic and macroscopic scales. This approach is inspired by the sweeping process introduced by J.J. Moreau in the late 70’s, and we shall present how Moreau’s framework extends to the Wasserstein setting (for macroscopic versions of this approach). We will also explore to which extend those models fit in the general framework of gradient flows, and to which extend this framework is suited to the modeling of social phenomena.