Time-dependent Ginzburg-Landau equation for lattice hydrodynamic model describing pedestrian flow |
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| Affiliation: | [1]Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China [2]Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China [3]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. 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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| Keywords: | pedestrian flow lattice hydrodynamic model time-dependent Ginzburg–Landau equation |
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