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

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.

Symmetry phases of asymmetric simple exclusion processes on two lanes with an intersection

“…α > β 1 and β 1 < 0.5, α 1 < β and α 1 < 0.5, α > β 2 and β 2 < 0.5, α 2 < β and α 2 < 0.5. (11) The currents of upstream and downstream of lane 1 are equal, i.e., J 1 = J 2 . Then…”

“…Despite its simplicity, the model has been used as a basis for many generalizations, such as dense media polymer dynamics, [3] dynamics of motor proteins moving along rigid filaments, [4,5] membrane channels diffusion, [6] gel electrophoresis, [7] traffic flow, [8][9][10] and information flow. [11] In many realistic situations, transportation is complex. For example, transport along some parallel or intersect lanes is very common in vehicular traffic or intracellular transport.…”

Existence of spontaneous symmetry breaking in two-lane totally asymmetric simple exclusion processes with an intersection*

“…[1] The ASEP was first introduced in the description of kinetics of biopolymerization. [2] Despite its simplicity, the model has been extensively applied in descriptions of protein synthesis, [3] dense media polymer dynamics, [4] gel electrophoresis, [5] membrane channels diffusion, [6] traffic flow, [7][8][9][10][11] information flow, [12,13] and so on.…”

Spurious symmetry-broken phase in a bidirectional two-lane ASEP with narrow entrances

“…To understand the basic statistical properties of non-equilibrium systems, many paradigmatic models have been proposed. As one of the paradigmatic models of non-equilibrium systems, the asymmetric simple exclusion process (ASEP) has been widely used to study many physical, chemical, and biological systems, [1][2][3][4][5] such as biopolymerization, [6] gel electrophoresis, [7] the kinetics of synthesis of proteins, [8][9][10] biological transport, [11][12][13][14][15][16] polymer dynamics in dense media, [17] diffusion through membrane channels, [18] surface growth, [19,20] glassy dynamics, [21,22] traffic flow, [23][24][25][26] information flow, [27][28][29] and so on.…”