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