Math @ Duke

Publications [#246849] of JianGuo Liu
Papers Published
 Degond, P; Herty, M; Liu, JG, Flow on sweeping networks,
Multiscale Modeling & Simulation, vol. 12 no. 2
(January, 2014),
pp. 538565, Society for Industrial & Applied Mathematics (SIAM), ISSN 15403459 [doi]
(last updated on 2019/05/22)
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 rightgoing. Under the assumptions of propagation of chaos and meanfield limit, we derive a master equation and the corresponding meanfield kinetic and macroscopic models. Steadystates are computed and analyzed and exhibit the possibility of multiple metastable states and hysteresis. © 2014 Society for Industrial and Applied Mathematics.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

