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Jamming transition of high-dimensional traffic dynamics

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  • Nagatani, Takashi

Abstract

Phase transition and critical phenomenon are investigated in high-dimensional traffic flow numerically and analytically. The two-dimensional lattice traffic model is extended to the three- and d-dimensional traffic flows. It is shown that the phase transition among the freely moving phase, the coexisting phase, and the uniformly congested phase occurs below the critical point in the two-, three-, and four-dimensional traffic simulations. The phase separation line and the critical point of the d-dimensional traffic are consistent with those of the one-dimensional traffic. The time-dependent Ginzburg–Landau (TDGL) equation for the d-dimensional traffic is derived by the use of the nonlinear analysis. The phase separation line, the spinodal line, and the critical point are calculated from the TDGL equation. It is found that the phase transition and critical phenomenon are independent of the space dimension.

Suggested Citation

  • Nagatani, Takashi, 1999. "Jamming transition of high-dimensional traffic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(3), pages 592-611.
    • Handle: RePEc:eee:phsmap:v:272:y:1999:i:3:p:592-611
    DOI: 10.1016/S0378-4371(99)00296-4
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    Cited by:

    1. Tu, Lihua & Zhou, Jie, 2019. "Memory’s effect on bidirectional pedestrian flow based on lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    2. Cen, Bing-ling & Xue, Yu & Zhang, Yi-cai & Wang, Xue & He, Hong-di, 2020. "A feedback control method with consideration of the next-nearest-neighbor interactions in a lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).

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