Collective dynamics of an inhomogeneous two-channel exclusion process: Theory and Monte Carlo simulations

TL;DR

This paper introduces a hybrid theoretical approach combined with simulations to analyze how localized bottlenecks affect the phase behavior and density profiles in a two-channel exclusion process with Langmuir kinetics.

Contribution

A novel hybrid method integrating singular perturbation techniques to study bottleneck effects in a coupled exclusion process with detailed phase diagram analysis.

Findings

Identification of bottleneck-induced shock, phase, and Meissner phase

Critical bottleneck rates for phase diagram topology changes

Lane-changing and unequal rates weaken bottleneck effects

Abstract

This work is devoted to the development of a novel theoretical approach, named hybrid approach, to handle a localized bottleneck in a symmetrically coupled two-channel totally asymmetric simple exclusion process with Langmuir kinetics. The hybrid approach is combined with singular perturbation technique to get steady-state phase diagrams and density profiles. We have thoroughly examined the role played by the strength of bottleneck, binding constant and lane-changing rate in the system dynamics. The appearances of bottleneck-induced shock, a bottleneck phase and Meissner phase are explained. Further, the critical values of bottleneck rate are identified, which signify the changes in the topology of phase diagram. It is also found that increase in lane-changing rate as well as unequal attachment, detachment rates weaken the bottleneck effect. Our theoretical arguments are in good agreement with extensively performed Monte Carlo simulations.