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

Source: [Reservoir crowding in a totally asymmetric simple exclusion process with Langmuir Kinetics](<https://www.sota2.com/research/paper/68fa406f1e209131ce8f3593>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:54:28.448Z

Authors: Bipasha Pal, Arvind Kumar Gupta

Published: 2021-03-08T06:13:57.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2103.05470>)

[PDF](<https://arxiv.org/pdf/2103.05470.pdf>)