Phase Diagram, Density, And Current Density Profiles Of Totally Asymmetric Simple Exclusion Process For A Junction With Two Entrances and Two Exits

Abstract

A dynamical model called the totally asymmetric simple exclusion process (TASEP) in one dimension (1D) is a widely-held particle hopping model which has developed into a reference model for studying non-equilibrium driven systems in particular transport phenomena. In this study, the TASEP is extended for a case of a junction with two entrances and two exits. The model is specified by a dynamical rule and boundary conditions. The dynamical rule determines the movement of particles and in this case the sequential updating dynamics is applied. The boundary condition used is the open boundary conditions, where particles may enter or exit the lattice sites. The density of the TASEP is governed by a continuity equation, which is solved numerically, such that a phase diagram and the current density profiles are obtained. The result shows that there are ten density phases produced, viz.: low density, high density, coexistence phase, maximal current, low density-low density, high density-high density, high density-maximal current, low density-maximal current, maximal current-high density, and maximal current-low density. The current density is generally constant throughout the lattice sites, except at the junction where a spike occurs.

Keywords: current density profile, density profile, open boundary condition, phase diagram, sequential updating dynamics.