Study Of Totally Asymmetric Simple Exclusion Process On Lattices With Branches And Junctions

Asymmetric Simple Exclusion Process ( ASEP ) is a lattice model of particles hopping stochastically and interacting through hard-core exclusion. The unusual dynamic properties and rich phase behaviours of ASEP have stimulated many theoretical studies. In recent years ASEP has become an important tool of investigation for many processes in chemistry, physics and biology. It has been applied to understand the kinetics of gel electrophoresis, interface growth, biopolymerization, and synthesis of proteins. Also recently, ASEP has been succesfully used in traffic flow modelling.In this paper, we investigate Totally Asymmetric Simple Exclusion Process (TASEP) where particles (vehicle or molecular motor) move on a single-chain lattice which diverges into two parallel lattice branches. This kind of geometry can be observed in the traffic of molecular motors or vehicles. At the branching point, the particles choose one of the two branches with equal rate . Here could model (i) the delay of vehicle drivers at the divergence because they need to slow down to consider which route to choose; (ii) the slow down of leading molecular motors due to additional frictions exerted on them. The effective injection and removal rates for each chain are introduced and the model can be mapped into three coupled exactly solved single-chain TASEP. We study the possible phase structures of the system in terms of these rates by using mean field approximation and Monte Carlo simulation. The structure of phase diagram depends on . A threshold rc = 2? 2 is identified. In cases of r > rc and r < rc, the phase diagram exhibits qualitatively di?erent phases. The analytical results of phase structure and density profiles are in good agreement with simulations except on a phase coexistence line. It reveals that the correlations is unnegligible in this case. The domain wall theory is adopted to calculate the density profile in this case and the results agree well with Monte Carlo simulations. The mean field approximation theory and the domain wall theory thus provide a reasonable way of analyzing TASEP with inhomogeneous geographic structure.Lattices with a junction, in which two or more parallel lattice branches combine into a single one, is important for complex biological and vehicular transport phenomena. For instance, the junction of protofilaments might lead to motor protein crowding phenomena that are responsible for many human diseases and the road junction might lead to serious traffic congestions. Take it into consideration, we investigate TASEP on lattices with a junction under unequal injection rates. The phase diagram, density profile of the stationary phases and phase boundaries are obtained in detail by using Monte Carlo simulation, mean field approximation, and domain wall theory. The analytical results are in good agreement with simulation results.The research introduced above has been summarized into two papers. One of them has been accepted by Int.J.Mod.Phys.B. The other is submitted to Int.J.Mod.Phys.C.