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

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

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.

Keywords: non equilibrium process spontaneous symmetry breaking mean-field approach Monte Carlo simulation

Received: 10 April 2012
Revised: 03 June 2012
Accepted manuscript online:

PACS:	05.70.Ln	(Nonequilibrium and irreversible thermodynamics)
	02.50.Ey	(Stochastic processes)
	05.60.Cd	(Classical transport)

Fund: 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).

Corresponding Authors: Li Shao-Da
E-mail: lisd@cdut.edu.cn

Cite this article:

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 2012 Chin. Phys. B 21 090510

[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

[1]	Abnormal magnetic behavior of prussian blue analogs modified with multi-walled carbon nanotubes Jia-Jun Mo(莫家俊), Pu-Yue Xia(夏溥越), Ji-Yu Shen(沈纪宇), Hai-Wen Chen(陈海文), Ze-Yi Lu(陆泽一), Shi-Yu Xu(徐诗语), Qing-Hang Zhang(张庆航), Yan-Fang Xia(夏艳芳), Min Liu(刘敏). Chin. Phys. B, 2023, 32(4): 047503.
[2]	Computational studies on magnetism and ferroelectricity Ke Xu(徐可), Junsheng Feng(冯俊生), and Hongjun Xiang(向红军). Chin. Phys. B, 2022, 31(9): 097505.
[3]	Steady-state and transient electronic transport properties of β-(Al_xGa_1-x)₂O₃/Ga₂O₃ heterostructures: An ensemble Monte Carlo simulation Yan Liu(刘妍), Ping Wang(王平), Ting Yang(杨婷), Qian Wu(吴茜), Yintang Yang(杨银堂), and Zhiyong Zhang(张志勇). Chin. Phys. B, 2022, 31(11): 117305.
[4]	Zero-field skyrmions in FeGe thin films stabilized through attaching a perpendicularly magnetized single-domain Ni layer Zi-Bo Zhang(张子博) and Yong Hu(胡勇). Chin. Phys. B, 2021, 30(7): 077503.
[5]	Monte Carlo simulations of electromagnetically induced transparency in a square lattice of Rydberg atoms Shang-Yu Zhai(翟尚宇) and Jin-Hui Wu(吴金辉). Chin. Phys. B, 2021, 30(7): 074206.
[6]	Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets Guangyu Sun(孙光宇), Nvsen Ma(马女森), Bowen Zhao(赵博文), Anders W. Sandvik, and Zi Yang Meng(孟子杨). Chin. Phys. B, 2021, 30(6): 067505.
[7]	Correlated insulating phases in the twisted bilayer graphene Yuan-Da Liao(廖元达), Xiao-Yan Xu(许霄琰), Zi-Yang Meng(孟子杨), and Jian Kang(康健). Chin. Phys. B, 2021, 30(1): 017305.
[8]	Existence of spontaneous symmetry breaking in two-lane totally asymmetric simple exclusion processes with an intersection Bo Tian(田波), Ping Xia(夏萍), Li Liu(刘莉), Meng-Ran Wu(吴蒙然), Shu-Yong Guo(郭树勇). Chin. Phys. B, 2020, 29(5): 050505.
[9]	Tunable deconfined quantum criticality and interplay of different valence-bond solid phases Bowen Zhao(赵博文), Jun Takahashi, Anders W. Sandvik. Chin. Phys. B, 2020, 29(5): 057506.
[10]	Magnetic properties of La₂CuMnO₆ double perovskite ceramic investigated by Monte Carlo simulations S Mtougui, I EL Housni, N EL Mekkaoui, S Ziti, S Idrissi, H Labrim, R Khalladi, L Bahmad. Chin. Phys. B, 2020, 29(5): 056101.
[11]	Two types of highly efficient electrostatic traps for single loading or multi-loading of polar molecules Bin Wei(魏斌), Hengjiao Guo(郭恒娇), Yabing Ji(纪亚兵), Shunyong Hou(侯顺永), Jianping Yin(印建平). Chin. Phys. B, 2020, 29(4): 043701.
[12]	Phase transition of DNA compaction in confined space: Effects of macromolecular crowding are dominant Erkun Chen(陈尔坤), Yangtao Fan(范洋涛), Guangju Zhao(赵光菊), Zongliang Mao(毛宗良), Haiping Zhou(周海平), Yanhui Liu(刘艳辉). Chin. Phys. B, 2020, 29(1): 018701.
[13]	Variational and diffusion Monte Carlo simulations of a hydrogen molecular ion in a spherical box Xuehui Xiao(肖学会), Kuo Bao(包括), Youchun Wang(王友春), Hui Xie(谢慧), Defang Duan(段德芳), Fubo Tian(田夫波), Tian Cui(崔田). Chin. Phys. B, 2019, 28(5): 056401.
[14]	Computational study of inverse ferrite spinels A EL Maazouzi, R Masrour, A Jabar, M Hamedoun. Chin. Phys. B, 2019, 28(5): 057504.
[15]	Phase diagrams and magnetic properties of the mixed spin-1 and spin-3/2 Ising ferromagnetic thin film:Monte Carlo treatment B Boughazi, M Boughrara, M Kerouad. Chin. Phys. B, 2019, 28(2): 027501.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention