Mathematikgebäude, Seminarraum M614/616 (6. Etage)

Microscopic rules for pedestrian traffic in a narrow street are discussed and the corresponding stochastic lattice system modeling the pedestrian bi-directional flow is introduced. Then the mesoscopic and macroscopic PDE models for the pedestrian density are derived. The macroscopic PDE model is a system of conservation laws which can change type depending on the strength of interaction between the pedestrian flows and initial conditions. Behavior of the stochastic and coarse-grained models is compared numerically for several different regimes and initial conditions. Finally, nonlinear diffusive corrections to the PDE model are derived systematically. Numerical simulations show that the diffusive terms can play a crucial role when the conservative coarse-grain PDE model becomes non-hyperbolic.

Prof. Ilya Timofeyev

University of Houston, USA