Analysis And Simulation Of Several Extended Models Of Asymmetric Simple Exclusion Process

Asymmetric Simple Exclusion Process (ASEP) is applied to describe the motion characteristics of particles with hard-core effects in one-dimensional grid model. Although the rules of ASEP are very simple, ASEP can reproduce rich and complex non-equilibrium phenomena, such as the boundary induced phase transition, single-defect induced phase transition, shock formation, spontaneous symmetry breaking, etc. Recently, ASEP has attracted scientists'huge interest, and gradually becomes an important tool for research in biological, physical, chemical and traffic flow issues.This article has a discussion on several extended Totally Asymmetric Simple Exclusion Processes (TASEPs) by theoretical analysis and numerical simulation. Firstly, on the basis of cross-roads, a TASEP model is introduced with two intersected lattices; secondly, there will be vehicles entering or leaving on some locations of road. So a TASEP model coupled with TASEP and Langmiur Kinetic (LK) rules is studied. Then, as the background of ribosome hoppong forward rate is affected by limitation of the amino acids-transfer RNA (aa-tRNAs) resources, a TASEP model is discussed that considers the effect of the corelation between particle hopping rate and system density on the relationship between the steady-state flux and density. The simulation and mathematical analysis of the above problems reveals the characteristics of non-equilibrium state. The main contents are as follows:In the second chapter, the TASEPs on two intersection lattices are studied, in which the horizontal direction is under open boundary conditions, and the vertical direction is under periodic boundary conditions. The model is analyzed by using the extended Monte-Carlo simulations and Mean-Field analysis. Approximate solutions of the system are obtained. Results show that: the characteristics of the phase diagram of the model depends on the density ? of the TASEP with periodic boundary. In order to identify the exact relationship between them, three critical density (ρc=1/3, 1/2, 2/3) are obtained. Then, four phase diagram and eight steady-state phase (LL-LD, LL-HD, LL-LH, HH-LD, HH-LH, HL-LD, HL-HD, HL-LH) are presented. The analytical and simulation results are in good agreement.In the third chapter, the dynamic characteristics of model coupled with TASEP and LK rules are investigated. For theoretical analysis, a method is applied which divides a full time step into two sub-time steps. Then Monte Carlo and the Mean Field methods are used. The density distribution and the system phase diagram are obtained. For better understanding of the characteristics, further analysis is made on the form and characteristics of the shock in the system.In the fourth chapter, we discussed the effect of the corelation between particle hopping rate and system density on the relationship between the system steady-state flux and density. The extended model of TASEP is proposed, in which the particle's hopping rate is a function of the system density. Monte Carlo simulations and Mean Field method are used to analysis the system. For example, we introduce a particle's hopping rate function with an extreme point and found that with the constraints of the hopping rate function, the continuity of the system density is broken. And two critical density and the phase boundary are identified.The summarization and prospect of following research work are presented in the fifth Chapter.