中国物理B ›› 2011, Vol. 20 ›› Issue (8): 80509-080509.doi: 10.1088/1674-1056/20/8/080509

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The time-dependent Ginzburg–Landau equation for the two-velocity difference model

程荣军1, 吴淑贞2, 葛红霞2   

  1. (1)Department of Fundamental Course, Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China; (2)Faculty of Science, Ningbo University, Ningbo 315211, China
  • 收稿日期:2010-11-02 修回日期:2011-02-23 出版日期:2011-08-15 发布日期:2011-08-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11072117, 10802042, and 60904068), the Natural Science Foundation of Zhejiang Province of China (Grant No. Y6100023), the Natural Science Foundation of Ningbo City (Grant No. 2009B21003), and K. C. Wong Magna Fund in Ningbo University.

The time-dependent Ginzburg–Landau equation for the two-velocity difference model

Wu Shu-Zhen(吴淑贞)a),Cheng Rong-Jun(程荣军)b),and Ge Hong-Xia(葛红霞)a)†   

  1. a Faculty of Science, Ningbo University, Ningbo 315211, China; b Department of Fundamental Course, Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China
  • Received:2010-11-02 Revised:2011-02-23 Online:2011-08-15 Published:2011-08-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11072117, 10802042, and 60904068), the Natural Science Foundation of Zhejiang Province of China (Grant No. Y6100023), the Natural Science Foundation of Ningbo City (Grant No. 2009B21003), and K. C. Wong Magna Fund in Ningbo University.

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摘要： A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow. Based on the two-velocity difference model, the time-dependent Ginzburg—Landau (TDGL) equation under certain condition is derived to describe the traffic flow near the critical point through the nonlinear analytical 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. The modified Korteweg de Vries (mKdV) equation around the critical point is derived by using the reductive perturbation method and its kink—antikink solution is also obtained. The relation between the TDGL equation and the mKdV equation is shown. The simulation result is consistent with the nonlinear analytical result.

关键词: traffic flow, two-velocity difference model, TDGL equation, mKdV equation

Abstract: A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow. Based on the two-velocity difference model, the time-dependent Ginzburg—Landau (TDGL) equation under certain condition is derived to describe the traffic flow near the critical point through the nonlinear analytical 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. The modified Korteweg de Vries (mKdV) equation around the critical point is derived by using the reductive perturbation method and its kink—antikink solution is also obtained. The relation between the TDGL equation and the mKdV equation is shown. The simulation result is consistent with the nonlinear analytical result.

Key words: traffic flow, two-velocity difference model, TDGL equation, mKdV equation

中图分类号:  (Phase transitions: general studies)

  • 05.70.Fh
05.70.Jk (Critical point phenomena)