Hydrodynamic mean field solutions of 1D exclusion processes with spatially varying hopping rates

Abstract

We analyze the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean field limit. The mean field equations for particle densities are written in terms of Ricatti equations with the steady-state current $J$ as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents $J$ are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for $J$ from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.

12 pages, 4 figures

References in corpus (12)

• Phase transitions in an exactly soluble one-dimensional exclusion process
• Clustered bottlenecks in mRNA translation and protein synthesis
• The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics
• Shock formation in an exclusion process with creation and annihilation
• Representations of the quadratic Algebra and Partially Asymmetric Diffusion with Open Boundaries
• Partially Asymmetric Exclusion Process with Open Boundaries
• Ribosome recycling, diffusion, and mRNA loop formation in translational regulation
• A multi-species asymmetric simple exclusion process and its relation to traffic flow
• Kinetics and thermodynamics across single-file pores: solute permeability and rectified osmosis
• Relaxation times in the ASEP model using a DMRG method
• The nondeterministic Nagel-Schreckenberg traffic model with open boundary conditions
• Relaxation kinetics of biological dimer adsorption models

Cited by in corpus (12)

• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Characteristics of the asymmetric simple exclusion process in the presence of quenched spatial disorder
• Partially Asymmetric Exclusion Processes with Sitewise Disorder
• Dynamic Boundaries in Asymmetric Exclusion Processes
• Defect-induced phase transition in the asymmetric simple exclusion process
• Disordered driven lattice gases with boundary reservoirs and Langmuir kinetics
• Diffusion of tagged particles in a crowded medium
• Smoothly-varying hopping rates in driven flow with exclusion
• Steady states and phase transitions in heterogeneous asymmetric exclusion processes
• Collective transport of weakly interacting molecular motors with Langmuir kinetics
• Two-species active transport along cylindrical biofilaments is limited by emergent topological hindrance
• Spreading in narrow channels