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Freezing transition in the mean-field approximation model of pedestrian counter flow

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  • Nagatani, Takashi

Abstract

We study the freezing transition in the counter flow of pedestrians within the channel numerically and analytically. We present the mean-field approximation (MFA) model for the pedestrian counter flow. The model is described in terms of a couple of nonlinear difference equations. The excluded-volume effect and bi-directionality are taken into account. The fundamental diagrams (current–density diagrams) are derived. When pedestrian density is higher than a critical value, the dynamical phase transition occurs from the free flow to the freezing (stopping) state. The critical density is derived by using the linear stability analysis. Also, the velocity and current (flow) at the steady state are derived analytically. The analytical result is consistent with that obtained by the numerical simulation.

Suggested Citation

  • Nagatani, Takashi, 2009. "Freezing transition in the mean-field approximation model of pedestrian counter flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(24), pages 4973-4978.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:24:p:4973-4978
    DOI: 10.1016/j.physa.2009.08.031
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    Cited by:

    1. Guo, Wei & Wang, Xiaolu & Zheng, Xiaoping, 2015. "Lane formation in pedestrian counterflows driven by a potential field considering following and avoidance behaviours," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 87-101.

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