Analytical investigation of the boundary-triggered phase transition dynamics in a cellular automata model with a slow-to-start rule

doi:10.1088/1674-1056/21/10/100206

中国物理B ›› 2012, Vol. 21 ›› Issue (10): 100206-100206.doi: 10.1088/1674-1056/21/10/100206

Analytical investigation of the boundary-triggered phase transition dynamics in a cellular automata model with a slow-to-start rule

贾宁, 马寿峰, 钟石泉

Institute of Systems Engineering, Tianjin University, Tianjin 300072, China

收稿日期:2012-02-20 修回日期:2012-03-15 出版日期:2012-09-01 发布日期:2012-09-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 70971094 and 50908155) and the Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT).

Analytical investigation of the boundary-triggered phase transition dynamics in a cellular automata model with a slow-to-start rule

Jia Ning (贾宁), Ma Shou-Feng (马寿峰), Zhong Shi-Quan (钟石泉)

Institute of Systems Engineering, Tianjin University, Tianjin 300072, China

Received:2012-02-20 Revised:2012-03-15 Online:2012-09-01 Published:2012-09-01
Contact: Jia Ning E-mail:jianing.BLGT@gmail.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 70971094 and 50908155) and the Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT).

摘要/Abstract

摘要： Previous studies suggest that there are three different jam phases in the cellular automata automaton model with a slow-to-start rule under open boundaries. In the present paper, the dynamics of each free-flow-jam phase transition is studied. By analysing the microscopic behaviour of the traffic flow, we obtain analytical results on the phase transition dynamics. Our results can describe the detailed time evolution of the system during phase transition, while they provide good approximation for the numerical simulation data. These findings can perfectly explain the microscopic mechanism and details of the boundary-triggered phase transition dynamics.

关键词: traffic flow, boundary-triggered phase transition, cellular automata, time evolution, analytical solution

Abstract: Previous studies suggest that there are three different jam phases in the cellular automata automaton model with a slow-to-start rule under open boundaries. In the present paper, the dynamics of each free-flow-jam phase transition is studied. By analysing the microscopic behaviour of the traffic flow, we obtain analytical results on the phase transition dynamics. Our results can describe the detailed time evolution of the system during phase transition, while they provide good approximation for the numerical simulation data. These findings can perfectly explain the microscopic mechanism and details of the boundary-triggered phase transition dynamics.

Key words: traffic flow, boundary-triggered phase transition, cellular automata, time evolution, analytical solution

中图分类号: (Probability theory, stochastic processes, and statistics)

02.50.-r

05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 45.70.-n (Granular systems)

贾宁, 马寿峰, 钟石泉. Analytical investigation of the boundary-triggered phase transition dynamics in a cellular automata model with a slow-to-start rule[J]. 中国物理B, 2012, 21(10): 100206-100206.

Jia Ning (贾宁), Ma Shou-Feng (马寿峰), Zhong Shi-Quan (钟石泉). Analytical investigation of the boundary-triggered phase transition dynamics in a cellular automata model with a slow-to-start rule[J]. Chin. Phys. B, 2012, 21(10): 100206-100206.

参考文献 15

[1]	Huang P H, Kong L J and Liu M R 2002 Chin. Phys. 11 678
[2]	Qian Y S, Shi P J, Zeng Q, Ma C X, Lin F, Sun P and Wang H L 2010 Chin. Phys. B 19 048201
[3]	Hu S X, Gao K, Wang B H and Lu Y F 2008 Chin. Phys. B 17 1863
[4]	Zheng L, Ma S F and Jia N 2010 Acta Phys. Sin. 59 4490 (in Chinese)
[5]	Nagel K and Schreckenberg M 1992 J. Phys. I (France) 2 2221
[6]	Cheybani S, Kertesz J and Schreckenberg M 2000 Phys. Rev. E 63 016107
[7]	Cheybani S, Kertesz J and Schreckenberg M 2000 Phys. Rev. E 63 016108
[8]	Jiang R and Wu Q S 2002 Phys. Rev. E 66 036104
[9]	Jia B, Jiang R and Wu Q S 2004 Phys. Rev. E 69 056105
[10]	Neumann T and Wagner P 2008 Eur. Phys. J. B 63 255
[11]	Huang D W and Huang W N 2002 Physica A 312 597
[12]	Barlovic R, Huisinga T, Schadschneider A and Schreckenberg M 2002 Phys. Rev. E 66 046113
[13]	Huang D W 2008 Physica A 387 587
[14]	Jia N and Ma S F 2009 Phys. Rev. E 79 031115
[15]	Jia N and Ma S F 2009 Phys. Rev. E 80 041105

Analytical investigation of the boundary-triggered phase transition dynamics in a cellular automata model with a slow-to-start rule

Analytical investigation of the boundary-triggered phase transition dynamics in a cellular automata model with a slow-to-start rule

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