How to push one's way through a dense crowd

¹ Univ. Grenoble Alpes, CNRS, LIPhy - 38000 Grenoble, France
² Institut de Recherche Mathématique Avancée - 67000 Strasbourg, France

Received: 9 February 2018
Accepted: 9 April 2018

Abstract

Moving through a dense crowd to help someone can be a tough task for emergency services as well as for security agents willing to ease a star to cross a crowd of fans. High densities reduce the mobility of an individual who wants to move and cross a crowd by pushing their way through. In this work, we study two situations. The first considers a person who moves through a static crowd while the second reports on a moving person (e.g., a star) who crosses a crowd of fans. Despite the simplicity of the mechanical model we use to describe a moving person who pushes apart the people of the crowd or tries to avoid them, we obtain some non-trivial results. Depending on the rigidity of a static crowd or on the aggressiveness of fans we extract quantities like the average velocity of a person moving across a crowd or the critical number of fans above which any motion of a star is impossible.