Density profiles in the totally asymmetric exclusion processes with both local inhomogeneity and Langmuir kinetics

In this article, the density profiles in the totally asymmetric simple exclusion processes (TASEPs) with both Langmuir kinetics and the local inhomogeneity, have been investigated by Monte Carlo simulations and a mean-field theory. The model is relevant for the understanding of the biological and chemical phenomena. Unlike the density profiles of TASEPs with the local defect, computer simulations indicate that the low-density phase, the shock-wave phase and the high-density phase have been found in the two sublattices. Eight possible steady density profiles such as hp/hp, sp/sp, lp/lp, hp/sp, sp/hp, sp/lp, lp/sp and hp/lp are discovered in the phase diagram. Both the hopping rate p   and the kinetics rate ΩDΩD influence on the density profiles not only upward, but also downward the defect. An approximate mean-field theory is presented and used to calculate phase diagrams and particle profiles. The approximate results can only agree with Monte Carlo simulations in the special cases. The reason is that the flow limited by the defect, is neglected in considering the mean-field theory.