Flow on sweeping networks

Pierre Degond Institut de Math´ematiques de Toulouse Michael Herty RWTH Aachen Universit Jian-Guo Liu Duke University

Analysis of PDEs mathscidoc:1702.03035

MULTISCALE MODEL. SIMUL, 12, (2), 538–565, 2014.2
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.
. cellular automata, pedestrian dynamics, networks, master equation, kinetic model, hydrodynamical model, multiple metastable states, hysteresis
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@inproceedings{pierre2014flow,
  title={Flow on sweeping networks},
  author={Pierre Degond, Michael Herty, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208103158902972309},
  booktitle={MULTISCALE MODEL. SIMUL},
  volume={12},
  number={2},
  pages={538–565},
  year={2014},
}
Pierre Degond, Michael Herty, and Jian-Guo Liu. Flow on sweeping networks. 2014. Vol. 12. In MULTISCALE MODEL. SIMUL. pp.538–565. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208103158902972309.
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