**Papers Published**

- Degond, P; Herty, M; Liu, JG,
*Flow on sweeping networks*, Multiscale Modeling & Simulation, vol. 12 no. 2 (January, 2014), pp. 538-565, Society for Industrial & Applied Mathematics (SIAM), ISSN 1540-3459

(last updated on 2019/07/22)**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 during panic situations in a small corridor where the propagation of people in a part of the corridor can be either left- or right-going. Under the assumptions of propagation of chaos and mean-field limit, we derive a master equation and the corresponding mean-field kinetic and macroscopic models. Steady-states are computed and analyzed and exhibit the possibility of multiple metastable states and hysteresis. © 2014 Society for Industrial and Applied Mathematics.