Synchronous asymmetric exclusion processes with an extended defect

Abstract

In this Letter, we investigate a total asymmetric simple exclusion process (TASEP) with an extended defect in parallel update under open boundary conditions by theoretical analysis and extensive simulations. The extended defect is a group of successive cells with reduced hopping probability. Two cases (i.e., Cases V and W) of lattice geometries are studied. In Case V, the system is divided into two subsystems (i.e., the left and right subsystems); the left subsystem is a normal TASEP, while the right subsystem is an extend defect. Case W is an extension of Case V, and it has three subsystems (i.e., the left, middle and right subsystems). The left and right subsystems have the same hopping probability, while the middle subsystem is an extended defect. Exact phase diagrams, stationary current, and density profiles are obtained. Case W shows a more complex system behaviour than Case V. The maximal-current regions (in the phase diagram) of the systems with different numbers of successive defect cells are compared. With the same p value, the area of the maximal-current region in Case W is larger than that in Case V under the same parameters. This indicates that the introduction of the third subsystem in Case W can enhance the current in some conditions.