CONSERVATION LAWS AND UNDERCOMPRESSIVE SHOCKS: THEORY AND APPLICATIONS TO PEDESTRIAN FLOWS
Massimiliano Daniele ROSSINI
Department of Mathematics and Computer Science, University of Ferrara, Ferrara, I-44121, ItalyIn the first part of the talk we briefly introduce basic concepts and properties of crowd dynamics. After a short overview of the state of the art of modelling crowd dynamics at different scales of description, we describe more in detail the macroscopic approach. In particular, we show that the classical theory for conservation laws is not appropriate to describe, for instance, the onset of collective panic behaviour and the flow through bottlenecks. Then we introduce the non classical theory for conservation laws and show the analytical results obtained for non classical shocks related to panic and for constrained conservation laws.
In the second part of the talk we highlight everyday real life experiences that require the theoretical set up of non classical conservation laws. We show then how to apply this theory to crowd dynamics. In particular, we show how it is possible to reproduce counter-intuitive phenomena such as Braess’s paradox, faster is slower effect and capacity drop.