Flow on sweeping networks
Cellular Automata and Lattice Gases
2013-07-02 v1
Abstract
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.
Cite
@article{arxiv.1307.0093,
title = {Flow on sweeping networks},
author = {Pierre Degond and Michael Herty and Jian-Guo Liu},
journal= {arXiv preprint arXiv:1307.0093},
year = {2013}
}