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
Author: M. Za’im and W. S. B. Dwandaru
Journal Code: jpfisikagg140019
