Marschler, Christian3; Starke, Jens3; Liu, Ping4; Kevrekidis, Ioannis G.4
1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Dynamical Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Dynamical systems, Department of Mathematics, Technical University of Denmark4 Princeton University
Interacting particle systems constitute the dynamic model of choice in a variety of application areas. A prominent example is pedestrian dynamics, where good design of escape routes for large buildings and public areas can improve evacuation in emergency situations, avoiding exit blocking and the ensuing panic. Here we employ diffusion maps to study the coarse-grained dynamics of two pedestrian crowds trying to pass through a door from opposite sides. These macroscopic variables and the associated smooth embeddings lead to a better description and a clearer understanding of the nature of the transition to oscillatory dynamics. We also compare the results to those obtained through intuitively chosen macroscopic variables.
Physical Review E (statistical, Nonlinear, and Soft Matter Physics), 2014, Vol 89, Issue 1