Recent developments in totally asymmetric simple exclusion processes with local inhomogeneity

Mingzhe Liu,Xianguo Tuo,Rui Jiang,Ruili Wang

doi:10.1007/s11434-011-4449-4

Abstract

A totally asymmetric simple exclusion process (TASEP) has become an essential tool in modeling and analyzing non-equilibrium systems. A wide variety of TASEP models have been developed that are motivated by real-world traffic, biological transport and by the dynamics of the process itself. This paper provides an overview of recent developments in TASEP with inhomogeneity. Some important generalizations and extensions of inhomogeneous TASEP models are reviewed, and several popular mean-field techniques used to analyze the inhomogeneous TASEP models are summarized. A comparison between similar TASEP models under different updating procedures is given. Phase separations in such disordered systems have been identified. The present status of the inhomogeneous TASEP models and areas for future investigations are also described.

Highlights

A totally asymmetric simple exclusion process (TASEP) has been acknowledged as a paradigmatic model for nonequilibrium systems
The maximal currents are the same for the TASEP with zoned inhomogeneities. Another conclusion that can be drawn is that the maximal current of the TASEP with single inhomogeneity is larger than that of the TASEP with extended inhomogeneities because p/(1 + p) > (1 − 1 − p)/2 for p < 1
Note that such models with random update have been studied by Xiao et al. [30]

Summary

Introduction

A totally asymmetric simple exclusion process (TASEP) has been acknowledged as a paradigmatic model for nonequilibrium systems. TASEP was introduced originally in 1968 as a theoretical model for describing ribosome motion along mRNA [1]. A wide variety of TASEP models have found natural applications in biology, physics, and chemistry [2, 3] such as gel electrophoresis [4], protein synthesis [5, 6], mRNA translation [7], motion of molecular motors along cytoskeletal filaments [8], and the depolymerization of. Several review articles on TASEP models have been published from the perspective of applied biophysics [12, 13] as well as from a purely theoretical viewpoint [14, 15]. TASEP variants have been successfully applied to modeling real-world complex systems in biology, physics and chemistry. We refer the reader to review articles [12, 13] and references therein for biological transport, and review articles [10, 11] and references therein for vehicular traffic

TASEP with local inhomogeneities

TASEP with single inhomogeneity

TASEP with multiple inhomogeneities

Summary and conclusions β