Asymmetric simple exclusion processes with complex lattice geometries: A review of models and phenomena

doi:10.1088/1674-1056/21/9/090510

中国物理B ›› 2012, Vol. 21 ›› Issue (9): 90510-090510.doi: 10.1088/1674-1056/21/9/090510

Asymmetric simple exclusion processes with complex lattice geometries: A review of models and phenomena

刘明哲^a, 李少达^b, Wang Rui-Li^c

a State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, China;
b College of Earth Science, Chengdu University of Technology, Chengdu 610059, China;
c School of Engineering and Advanced Technology, Massey University, Palmerston North, New Zealand

收稿日期:2012-04-10 修回日期:2012-06-03 出版日期:2012-08-01 发布日期:2012-08-01
基金资助:
Project supported by the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, China (Grant No. 2011Z006) and the Chengdu University of Technology, China (Grant Nos. HY0084 and HG0092).

Asymmetric simple exclusion processes with complex lattice geometries: A review of models and phenomena

Liu Ming-Zhe (刘明哲)^a, Li Shao-Da (李少达)^b, Wang Rui-Li^c

a State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, China;
b College of Earth Science, Chengdu University of Technology, Chengdu 610059, China;
c School of Engineering and Advanced Technology, Massey University, Palmerston North, New Zealand

Received:2012-04-10 Revised:2012-06-03 Online:2012-08-01 Published:2012-08-01
Contact: Li Shao-Da E-mail:lisd@cdut.edu.cn
Supported by:
Project supported by the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, China (Grant No. 2011Z006) and the Chengdu University of Technology, China (Grant Nos. HY0084 and HG0092).

摘要/Abstract

摘要： We summarize the findings of a large number of researches concerning the totally asymmetric simple exclusion process (TASEP) with complex lattice geometries. The TASEP has been recognized as a paradigm in modeling and analyzing non-equilibrium traffic systems. The paper surveys both the observed physical phenomena and several popular mean-field approaches used to analyze the extended TASEP models. Several interesting physical phenomena, such as phase separation, spontaneous symmetry breaking, and finite-size effect, have been identified and explained. The future investigations of the extended TASEP with complex lattice geometries are also introduced. This paper may help to obtain a better understanding of non-equilibrium systems.

关键词: non equilibrium process, spontaneous symmetry breaking, mean-field approach, Monte Carlo simulation

Abstract: We summarize the findings of a large number of researches concerning the totally asymmetric simple exclusion process (TASEP) with complex lattice geometries. The TASEP has been recognized as a paradigm in modeling and analyzing non-equilibrium traffic systems. The paper surveys both the observed physical phenomena and several popular mean-field approaches used to analyze the extended TASEP models. Several interesting physical phenomena, such as phase separation, spontaneous symmetry breaking, and finite-size effect, have been identified and explained. The future investigations of the extended TASEP with complex lattice geometries are also introduced. This paper may help to obtain a better understanding of non-equilibrium systems.

Key words: non equilibrium process, spontaneous symmetry breaking, mean-field approach, Monte Carlo simulation

中图分类号: (Nonequilibrium and irreversible thermodynamics)

05.70.Ln

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

刘明哲, 李少达, Wang Rui-Li. Asymmetric simple exclusion processes with complex lattice geometries: A review of models and phenomena[J]. 中国物理B, 2012, 21(9): 90510-090510.

Liu Ming-Zhe (刘明哲), Li Shao-Da (李少达), Wang Rui-Li. Asymmetric simple exclusion processes with complex lattice geometries: A review of models and phenomena[J]. Chin. Phys. B, 2012, 21(9): 90510-090510.

参考文献 50

[1]	Boccara N 2004 Modeling Complex Systems (Berlin: Springer-verlag) p. 6
[2]	Derrida B, Domany E and Mukamel D 1992 J. Stat. Phys. 69 667
[3]	Schütz G M 2001 Phase Transitions and Critical Phenomena 19 (edited by Domb C and Lebowitz J L) (San Diego: Academic Press)
[4]	Widom B, Viovy J L and Defontaines A D 1991 J. Phys. I 1 1759
[5]	Schütz G M 1997 Int. J. Mod. Phys. B 11 197
[6]	Shaw L B, Zia R K P and Lee K H 2003 Phys. Rev. E 68 021910
[7]	Chou T 2003 Biophys. J. 85 755
[8]	Klumpp S and Lipowsky R 2003 J. Stat. Phys. 113 233
[9]	Klein G A, Kruse K and Cuniberti G 2005 Phys. Rev. Lett. 94 108102
[10]	Chowdhury D, Santen L and Schadschneider A 2000 Phys. Rep. 329 199
[11]	Helbing D 2001 Rev. Mod. Phys. 73 1067
[12]	Pronina E and Kolomeisky A B 2004 J. Phys. A 37 9907
[13]	Pronina E and Kolomeisky A B 2006 Physica A 372 12
[14]	Juhász R 2007 Phys. Rev. E 76 021117
[15]	Cai Z P, Yuan Y M, Jiang R, Hu M B and Wu Q S 2008 J. Stat. Mech. P07016
[16]	Tsekouras K and Kolomeisky A B 2008 J. Phys. A 41 095002
[17]	Melbinger A, Reichenbach T, Franosch T and Frey E 2011 Phys. Rev. E 83 031923
[18]	Mitsudo T and Hayakawa H 2005 J. Phys. A 38 3087
[19]	Jiang R, Wang R and Wu Q S 2007 Physica A 375 247
[20]	Wang R, Jiang R, Liu M Z, Liu J and Wu Q S 2007 Int. J. Mod. Phys. C 18 1483
[21]	Jiang R, Hu M B, Wu Y H and Wu Q S 2008 Phys. Rev. E 77 041128
[22]	Evans M R, Kafri Y, Sugden K E P and Tailleur J 2011 J. Stat. Mech. P06009
[23]	Reichenbach T, Franosch T and Frey E 2006 Phys. Rev. Lett. 97 050603
[24]	Jiang R, Nishinari K, Hu M B, Wu Y H and Wu Q S 2009 J. Stat. Phys. 136 73
[25]	Pronina E and Kolomeisky A B 2005 J. Stat. Mech. P07010
[26]	Kolomeisky A B, Schütz G M, Kolomeisky E B and Straley J P 1998 J. Phys. A 31 6911
[27]	Xiao S, Liu M Z, Wang J J and Wang H 2011 Chin. Phys. B 20 060509
[28]	Wang R, Liu M Z and Jiang R 2008 Phys. Rev. E 77 051108
[29]	Liu M Z and Wang R 2009 Physica A 388 4068
[30]	Cai Z P, Yuan Y M, Jiang R, Nishinari K and Wu Q S 2009 J. Stat. Mech. P02050
[31]	Popkov V, Evans M R and Mukamel D 2008 J. Phys. A 41 432002
[32]	http://www.nature.com/news/2008/081007/full/news.2008.1155.html
[33]	Evans M R, Foster D P, Godreche C and Mukamel D 1995 Phys. Rev. Lett. 74 208
[34]	Gupta S, Mukamel D and Schütz G M 2009 J. Phys. A: Math. Theor. 42 485002
[35]	Popkov V and Peschel I 2001 Phys. Rev. E 64 026126
[36]	Pronina E and Kolomeisky A B 2007 J. Phys. A 40 2275
[37]	Jiang R, Wang R, Hu M B, Jia B and Wu Q S 2007 J. Phys. A 40 9213
[38]	Zhu K X, Wang N, Hao Q Y, Liu Q Y and Jiang R 2012 Phys. Rev. E 85 041132
[39]	Yuan Y M, Jiang R, Wang R L, Wu Q S and Zhang J Q 2008 J. Phys. A 41 035003
[40]	Jiang R, Hu M B, Jia B, Wang R and Wu Q S 2007 Phys. Rev. E 76 036116
[41]	Wang R, Kolomeisky A B and Liu M Z 2011 Phys. Lett. A 375 318
[42]	Liu M Z, Wang R L and Jiang R 2010 Int. J. Mod. Phys. C 21 825
[43]	Arndt P F, Heinzel T and Rittenberg V 1998 J. Stat. Phys. 90 783
[44]	Erickson D W, Pruessner G, Schmittmann B and Zia R K P 2005 J. Phys. A 38 L659
[45]	Clincy M, Evans M R and Mukamel D 2001 J. Phys. A 34 9923
[46]	Levine E and Willmann R D 2004 J. Phys. A 37 3333
[47]	Liu M Z, Hawick K, Marsland S and Jiang R 2010 Physica A 389 3870
[48]	Neri I, Kern N and Parmeggiani A 2011 Phys. Rev. Lett. 107 068702
[49]	Embley B, Parmeggiani A and Kern N 2009 Phys. Rev. E 80 041128
[50]	Basu M and Mohanty P K 2010 J. Stat. Mech. P10014

Asymmetric simple exclusion processes with complex lattice geometries: A review of models and phenomena

Asymmetric simple exclusion processes with complex lattice geometries: A review of models and phenomena

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