Theoretical analysis and simulation of phase separation in a driven bidirectional two-lane system

The two-lane driven system is a type of important model to research some transport systems, and also a powerful tool to investigate properties of nonequilibrium state systems. This paper presents a driven bidirectional two-lane model. The dynamic characteristics of the model with periodic boundary are investigated by Monte Carlo simulation, simple mean field, and cluster mean field methods, respectively. By simulations, phase separations are observed in the system with some values of model parameters. When the phase separation does not occur, cluster mean field results are in good agreement with simulation results. According to the cluster mean field analysis and simulations, a conjecture about the condition that the phase separation happens is proposed. Based on the conjecture, the phase boundary distinguishing phase separation state and homogeneous state is determined, and a corresponding phase diagram is drawn. The conjecture is validated through observing directly the spatiotemporal diagram and investigating the coarsening process of the system by simulation, and a possible mechanism causing the phase separation is also discussed. These outcomes maybe contribute to understand deeply transport systems including the congestion and efficiency of the transport, and enrich explorations of nonequilibrium state systems.