Two-channel totally asymmetric simple exclusion process with Langmuir kinetics: The role of coupling constant

Department of Mathematics, Indian Institute of Technology Ropar - Rupnagar-140001, Punjab, India

^(a) akgupta@iitrpr.ac.in

Received: 27 May 2014
Accepted: 26 June 2014

Abstract

In this letter, we study the dynamics of a coupled two-channel totally asymmetric simple exclusion process with particle attachment and detachment in the bulk. The coupling constant C, which signifies the ratio of lane-changing rates, is introduced and the steady-state dynamics of the system are analyzed for different values of C. Singular perturbation technique is used on continuum mean-field equations to construct the phase diagrams, which have been characterized in terms of C for all possible orders of lane-changing rates. It is found that for lower orders of lane-changing rates, the effect of C is minor; while the effect is significant for higher orders. A critical value of is identified, above which the disappearance as well as the appearance of certain phases is observed. Moreover, synchronization of shocks also occurs for . We have also analyzed the effect of the system size on the Monte Carlo simulation results. Our theoretical arguments are in good agreement with Monte Carlo simulation results.