## Flow on sweeping networks

Publication ,  Journal Article
Degond, P; Herty, M; Liu, JG
Published in: Multiscale Modeling and Simulation
January 1, 2014

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.

## Published In

Multiscale Modeling and Simulation

1540-3467

1540-3459

January 1, 2014

12

2

538 / 565

## Related Subject Headings

• Applied Mathematics
• 4901 Applied mathematics
• 0102 Applied Mathematics

### Citation

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Chicago
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MLA
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Degond, P., Herty, M., & Liu, J. G. (2014). Flow on sweeping networks. Multiscale Modeling and Simulation, 12(2), 538–565. https://doi.org/10.1137/130927061
Degond, P., M. Herty, and J. G. Liu. “Flow on sweeping networks.” Multiscale Modeling and Simulation 12, no. 2 (January 1, 2014): 538–65. https://doi.org/10.1137/130927061.
Degond P, Herty M, Liu JG. Flow on sweeping networks. Multiscale Modeling and Simulation. 2014 Jan 1;12(2):538–65.
Degond, P., et al. “Flow on sweeping networks.” Multiscale Modeling and Simulation, vol. 12, no. 2, Jan. 2014, pp. 538–65. Scopus, doi:10.1137/130927061.
Degond P, Herty M, Liu JG. Flow on sweeping networks. Multiscale Modeling and Simulation. 2014 Jan 1;12(2):538–565.

## Published In

Multiscale Modeling and Simulation

1540-3467

1540-3459

January 1, 2014

12

2

538 / 565

## Related Subject Headings

• Applied Mathematics
• 4901 Applied mathematics
• 0102 Applied Mathematics