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

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