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Phase Transitions And The Korteweg-De Vries Equation In The Density Difference Lattice Hydrodynamic Model Of Traffic Flow

Author

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  • JUN-FANG TIAN

    (MOE Key Laboratory for Urban Transportation, Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing, 100044, P. R. China)

  • ZHEN-ZHOU YUAN

    (MOE Key Laboratory for Urban Transportation, Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing, 100044, P. R. China)

  • BIN JIA

    (MOE Key Laboratory for Urban Transportation, Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing, 100044, P. R. China)

  • HONG-QIANG FAN

    (MOE Key Laboratory for Urban Transportation, Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing, 100044, P. R. China)

Abstract

We investigate the phase transitions and the Korteweg-de Vries (KdV) equation in the density difference lattice hydrodynamic (DDLM) model, which shows a close connection with the gas-kinetic-based model and the microscopic car following model. The KdV equation near the neutral stability line is derived and the corresponding soliton solution describing the density waves is obtained. Numerical simulations are conducted in two aspects. On the one hand, under periodic conditions perturbations are applied to demonstrate the nonlinear analysis result. On the other hand, the open boundary condition with random fluctuations is designed to explore the empirical congested traffic patterns. The phase transitions among the free traffic (FT), widening synchronized flow pattern (WSP), moving localized cluster (MLC), oscillatory congested traffic (OCT) and homogeneous congested traffic (HCT) occur by varying the amplitude of the fluctuations. To our knowledge, it is the first research showing that the lattice hydrodynamic model could reproduce so many congested traffic patterns.

Suggested Citation

  • Jun-Fang Tian & Zhen-Zhou Yuan & Bin Jia & Hong-Qiang Fan, 2013. "Phase Transitions And The Korteweg-De Vries Equation In The Density Difference Lattice Hydrodynamic Model Of Traffic Flow," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(03), pages 1-9.
    • Handle: RePEc:wsi:ijmpcx:v:24:y:2013:i:03:n:s0129183113500162
    DOI: 10.1142/S0129183113500162
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    Cited by:

    1. Wang, Qingying & Ge, Hongxia, 2019. "An improved lattice hydrodynamic model accounting for the effect of “backward looking” and flow integral," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 438-446.
    2. Liu, Hui & Sun, Dihua & Liu, Weining, 2016. "Lattice hydrodynamic model based traffic control: A transportation cyber–physical system approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 795-801.

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