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Time-dependent Ginzburg–Landau equation for lattice hydrodynamic model describing pedestrian flow |
| Ge Hong-Xia (葛红霞)a, Cheng Rong-Jun (程荣军)b, Lo Siu-Ming (卢兆明)c |
a Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China;
b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;
c Department of Civil and Architectural Engineering, City University of Hong Kong, Hong Kong, China |
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Abstract A thermodynamic theory is formulated to describe the phase transition and critical phenomena in pedestrian flow. Based on the extended lattice hydrodynamic pedestrian model taking the interaction of the next-nearest-neighbor persons into account, the time-dependent Ginzburg-Landau (TDGL) equation is derived to describe the pedestrian flow near the critical point through the nonlinear analysis method. And the corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line, and critical point are obtained by the first and second derivatives of the thermodynamic potential.
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Received: 10 September 2012
Revised: 12 January 2013
Accepted manuscript online:
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PACS:
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05.70.Fh
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(Phase transitions: general studies)
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89.40.+k
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05.90.+m
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(Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11072117 and 61074142), the Natural Science Foundation of ZheJiang Province, China (Grant No. Y6110007), the Scientific Research Fund of Zhejiang Provincial Education Department, China (Grant No. Z201119278), the Natural Science Foundation of Ningbo, China (Grant Nos. 2012A610152 and 2012A610038), the K. C. Wong Magna Fund in Ningbo University, China, and the Research Grant Council, Government of the Hong Kong Administrative Region, China (Grant Nos. CityU9041370 and CityU9041499). |
Corresponding Authors:
Ge Hong-Xia
E-mail: gehongxia@nbu.edu.cn
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Cite this article:
Ge Hong-Xia (葛红霞), Cheng Rong-Jun (程荣军), Lo Siu-Ming (卢兆明) Time-dependent Ginzburg–Landau equation for lattice hydrodynamic model describing pedestrian flow 2013 Chin. Phys. B 22 070507
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