Reservoir crowding in a totally asymmetric simple exclusion process with Langmuir Kinetics

TL;DR

This paper investigates a modified asymmetric exclusion process with reservoir crowding and Langmuir kinetics, revealing phase diagram changes and novel back-and-forth transitions, validated by Monte Carlo simulations.

Contribution

It introduces a new model incorporating reservoir crowding into ASEP with Langmuir kinetics and analyzes its phase behavior and density profiles.

Findings

Phase diagram topology changes near filling factor μ=1.

Reservoir crowding induces back-and-forth transitions.

Theoretical results are validated by Monte Carlo simulations.

Abstract

We study a totally asymmetric simple exclusion process equipped with Langmuir kinetics with boundaries connected to a common reservoir. The total number of particles in the system is conserved and controlled by filling factor $\mu$. Additionally, crowding of reservoir is taken into account which regulates the entry and exit of particles from both boundary as well as bulk. In the framework of mean-field approximation, we express the density profiles in terms of Lambert-W functions and obtain phase diagrams in $\alpha-\beta$ parameter space. Further, we elucidate the variation of phase diagram with respect to filling factor and Langmuir kinetics. In particular, the topology of the phase diagram is found to change in the vicinity of $\mu=1$. Moreover, the interplay between reservoir crowding and Langmuir kinetics develops a novel feature in the form of back-and-forth transition. The theoretical phase boundaries and density profiles are validated through extensive Monte Carlo simulations.% We performed Monte Carlo simulations to validate our theoretical findings.