Flow on sweeping networks

Pierre Degond (1) , Michael Herty (2) , Jian-Guo Liu (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 RWTH - Rheinisch-Westfälische Technische Hochschule Aachen University
3 Duke Physics

We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the transported quantity in the neighboring cells. A motivation is pedestrian dynamics in a small corridor where the propagation of people in a part of the corridor can be either left or rightgoing. Under the assumptions of propagation of chaos and mean-field limit, we derive a master equation and the corresponding meanfield kinetic and macroscopic models. Steady--states are computed and analyzed analytically and exhibit the possibility of multiple meta-stable states and hysteresis.

Domaines: Physique mathématique [math-ph]

Pierre Degond, Michael Herty, Jian-Guo Liu. Flow on sweeping networks. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2014, 12, pp.538-565. ⟨hal-00839711⟩