Scientific Computation and Applied & Industrial Mathematics Seminar: Marie-Therese Wolfram

The dynamic motion of large human crowds is an ubiquitous phenomena in everyday life. First empirical studies on crowd motion started in the late 1950ties and spread into different fields like transportation research, psychology or urban and regional planning. Recently there has been a strong interest in crowd motion within the mathematical community, which initiated a lot of research on mathematical models, their analysis and simulations.
 

 

In this talk we focus on a fast exit scenario and consider a group, which wants to leave a room as quickly as possible. We present different modeling approaches, starting on the microscopic level and working our way up to the appropriate continuum limits. In particular we focus on Hughes model for pedestrian flow and give an interpretation from the mean field game perspective. Finally we discuss different challenges in the analysis and numerical simulations and illustrate the behaviour of the presented models with numerical simulations.