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

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.

References in corpus (10)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Phase Coexistence in Driven One Dimensional Transport
• The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics
• Inhomogeneous exclusion processes with extended objects: The effect of defect locations
• Bottleneck-induced transitions in a minimal model for intracellular transport
• Far-from-equilibrium transport with constrained resources
• Feedback and Fluctuations in a Totally Asymmetric Simple Exclusion Process with Finite Resources
• Transport on a Lattice with Dynamical Defects
• Defect-induced phase transition in the asymmetric simple exclusion process
• Understanding the edge effect in TASEP with mean-field theoretic approaches