Totally asymmetric exclusion processes on two intersected lattices with open and periodic boundaries

In this paper, we study TASEPs on two intersected lattices. One TASEP has an open boundary (lattice 1) and the other has a periodic boundary (lattice 2). Extensive Monte Carlo simulations are carried out. It is found that the system phase diagram structure depends on the density ρ on lattice 2. Three critical densities ρc = 1/3, 1/2 and 2/3 are identified and four phase diagram structures are observed. The density profiles corresponding to all stationary phases and the phase boundaries are calculated using mean-field analysis. The analytic results are in good agreement with the simulation results