Local inhomogeneity in totally asymmetric simple exclusion processes with different hopping rates

Local inhomogeneity in totally asymmetric simple exclusion processes (TASEPs) with different hopping rates was studied. Many biological and chemical phenomena can be described by these non-equilibrium processes. A simple approximate theory and extensive Monte Carlo computer simulations were used to calculate the steady-state phase diagrams and bulk densities. It is found that the phase diagram for local inhomogeneity in TASEP with different hopping rates p is qualitatively similar to homogeneous models. Interestingly, there is a saturation point pair (alpha*, beta*) for the system, which is decided by parameters p and q. There are three stationary phases in the system, when parameter p is fixed (i.e., p=0.8), with the increase of the parameter q, the region of LD/LD and HD/HD phase increases and the HD/LD is the only phase which the region shrinks. The analytical results are in good agreement with simulations.