Flow on sweeping networks

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Degond, P; Herty, M; Liu, JG

Published Date

  • January 1, 2014

Published In

Volume / Issue

  • 12 / 2

Start / End Page

  • 538 - 565

Electronic International Standard Serial Number (EISSN)

  • 1540-3467

International Standard Serial Number (ISSN)

  • 1540-3459

Digital Object Identifier (DOI)

  • 10.1137/130927061

Citation Source

  • Scopus