Totally asymmetric exclusion processes at constrained m-input n-output junction points

doi:10.1088/1674-1056/22/6/060512

中国物理B ›› 2013, Vol. 22 ›› Issue (6): 60512-060512.doi: 10.1088/1674-1056/22/6/060512

Totally asymmetric exclusion processes at constrained m-input n-output junction points

李少达^{a b}, 刘明哲^a, 裴向军^a

a State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, China;
b College of Earth Sciences, Chengdu University of Technology, Chengdu 610059, China

收稿日期:2012-09-28 修回日期:2012-11-06 出版日期:2013-05-01 发布日期:2013-05-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 41274109), the Special Fund of the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, China (Grant No. 2011Z006), the Scientific and Technological Support Program of Sichuan Province, China (Grant Nos. 2013FZ0021 and 2013FZ0022), and the Creative Team Program of Chengdu University of Technology, China (Grant No. KYTD201301).

Totally asymmetric exclusion processes at constrained m-input n-output junction points

Li Shao-Da (李少达)^{a b}, Liu Ming-Zhe (刘明哲)^a, Pei Xiang-Jun (裴向军)^a

a State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, China;
b College of Earth Sciences, Chengdu University of Technology, Chengdu 610059, China

Received:2012-09-28 Revised:2012-11-06 Online:2013-05-01 Published:2013-05-01
Contact: Liu Ming-Zhe E-mail:liumz@cdut.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 41274109), the Special Fund of the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, China (Grant No. 2011Z006), the Scientific and Technological Support Program of Sichuan Province, China (Grant Nos. 2013FZ0021 and 2013FZ0022), and the Creative Team Program of Chengdu University of Technology, China (Grant No. KYTD201301).

摘要/Abstract

摘要： Totally asymmetric exclusion processes at constrained m-input n-output junction points under random update are studied by theoretical calculation and computer simulation in this paper. At the junction points, the hopping rate of particles from m-input parallel lattices to n-output parallel lattices is assumed to be equal to r/n (0 < r < 1). The mean-field approach and Monte Carlo simulations show that the phase diagram can be classified into three regions at any value of r. More interestingly, there is a threshold r_c = n( 1-√1-m/n)/m. In the cases of r > r_c and r < r_c, qualitatively different phases exist in the system. With the increase of the value of m/n, the regions of (LD, LD) and (MC, LD) or (HD, LD) decrease, and the (HD, HD) is the only phase that increases in the region (LD stands for low density, HD stands for high density, and MC for maximal current). Stationary current and density profiles are calculated, showing that they are in good agreement with Monte Carlo simulations.

关键词: exclusion process, mean-field approximation, phase diagram, Monte Carlo simulations

Abstract: Totally asymmetric exclusion processes at constrained m-input n-output junction points under random update are studied by theoretical calculation and computer simulation in this paper. At the junction points, the hopping rate of particles from m-input parallel lattices to n-output parallel lattices is assumed to be equal to r/n (0 < r < 1). The mean-field approach and Monte Carlo simulations show that the phase diagram can be classified into three regions at any value of r. More interestingly, there is a threshold r_c = n( 1-√1-m/n)/m. In the cases of r > r_c and r < r_c, qualitatively different phases exist in the system. With the increase of the value of m/n, the regions of (LD, LD) and (MC, LD) or (HD, LD) decrease, and the (HD, HD) is the only phase that increases in the region (LD stands for low density, HD stands for high density, and MC for maximal current). Stationary current and density profiles are calculated, showing that they are in good agreement with Monte Carlo simulations.

Key words: exclusion process, mean-field approximation, phase diagram, Monte Carlo simulations

中图分类号: (Nonequilibrium and irreversible thermodynamics)

05.70.Ln

02.50.Ey (Stochastic processes) 05.60.Cd (Classical transport)

李少达, 刘明哲, 裴向军. Totally asymmetric exclusion processes at constrained m-input n-output junction points[J]. 中国物理B, 2013, 22(6): 60512-060512.

Li Shao-Da (李少达), Liu Ming-Zhe (刘明哲), Pei Xiang-Jun (裴向军). Totally asymmetric exclusion processes at constrained m-input n-output junction points[J]. Chin. Phys. B, 2013, 22(6): 60512-060512.

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Totally asymmetric exclusion processes at constrained m-input n-output junction points

Totally asymmetric exclusion processes at constrained m-input n-output junction points

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