Parallel Coupling of Symmetric and Asymmetric Exclusion Processes

Abstract

A system consisting of two parallel coupled channels where particles in one of them follow the rules of totally asymmetric exclusion processes (TASEP) and in another one move as in symmetric simple exclusion processes (SSEP) is investigated theoretically. Particles interact with each other via hard-core exclusion potential, and in the asymmetric channel they can only hop in one direction, while on the symmetric lattice particles jump in both directions with equal probabilities. Inter-channel transitions are also allowed at every site of both lattices. Stationary state properties of the system are solved exactly in the limit of strong couplings between the channels. It is shown that strong symmetric couplings between totally asymmetric and symmetric channels lead to an effective partially asymmetric simple exclusion process (PASEP) and properties of both channels become almost identical. However, strong asymmetric couplings between symmetric and asymmetric channels yield an effective TASEP with nonzero particle flux in the asymmetric channel and zero flux on the symmetric lattice. For intermediate strength of couplings between the lattices a vertical cluster mean-field method is developed. This approximate approach treats exactly particle dynamics during the vertical transitions between the channels and it neglects the correlations along the channels. Our calculations show that in all cases there are three stationary phases defined by particle dynamics at entrances, at exits or in the bulk of the system, while phase boundaries depend on the strength and symmetry of couplings between the channels. Extensive Monte Carlo computer simulations strongly support our theoretical predictions.

16 pages

References in corpus (24)

• Traffic and Related Self-Driven Many-Particle Systems
• Statistical Physics of Vehicular Traffic and Some Related Systems
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Phase Coexistence in Driven One Dimensional Transport
• The totally asymmetric exclusion process with extended objects, a model for protein synthesis
• Clustered bottlenecks in mRNA translation and protein synthesis
• Traffic of molecular motors through tube-like compartments
• Intra-cellular transport of single-headed molecular motors KIF1A
• Partially Asymmetric Exclusion Process with Open Boundaries
• Entropy-driven pumping across zeolites and biological channels
• Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
• Local Inhomogeneity in Asymmetric Simple Exclusion Processes with Extended Objects
• Two-Channel Totally Asymmetric Simple Exclusion Processes
• Spontaneous Symmetry Breaking in Two-Channel Asymmetric Exclusion Processes with Narrow Entrances
• Symmetry breaking and phase coexistence in a driven diffusive two-channel system
• Asymmetric Coupling in Two-Channel Simple Exclusion Processes
• Exclusion Processes with Internal States
• Theoretical Investigation of Totally Asymmetric Exclusion Processes on Lattices with Junctions
• Traffic jams induced by rare switching events in two-lane transport
• Weakly coupled, antiparallel, totally asymmetric simple exclusion processes
• Movements of molecular motors: Ratchets, random walks and traffic phenomena
• Inhomogeneous Coupling in Two-Channel Asymmetric Simple Exclusion Processes
• Particle redistribution and slow decay of correlations in hard-core fluids on a half-driven ladder

Cited by in corpus (10)

• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Intracellular transport driven by cytoskeletal motors: General mechanisms and defects
• Modelling cytoskeletal traffic: an interplay between passive diffusion and active transport
• Phase diagram of two-lane driven diffusive systems
• Diffusion with Local Resetting and Exclusion
• Non-equilibrium phase transitions in tubulation by molecular motors
• Driven Transport on Parallel Lanes with Particle Exclusion and Obstruction
• Dynamics at barriers in bidirectional two-lane exclusion processes
• Self-organized system-size oscillation of a stochastic lattice-gas model
• An interface phase transition induced by a driven line in 2D