| ASEP(asymmetric simple exclusion processes)was first introduced in 1968 to describe the kinetics of biopolymerization..In this model,the stochaastic dynamics of multi-particle transport across one-dimensional lattice in which particles interact only through a hard core exclusion potential is described. Although these dynamic rules are very simple,they lead to a very rich and complex dynamic phase behaviour.There are non-equilibrium phase transitions between the stationary states of the system,included by boundary processes.So ,in recent years it has been applied successfully to investigate many processes in chemistry,physics and biology.,this model provides the first crucial steps towards the modeling of realistic processes,such as proteins synthesis,surface growth,the motion of motor proteins along cytoskeleton filaments and vehicular traffic.when particles move only in one direction the model is the simplest limit of an ASEP,which is called a totally asymmetric simple exclusion processes.In order to describe some more complex realistic processes,a considerable effort has been devoted to the study of extension of the TASEP,in this paper,we will study one of the extended TASEP which is called the coupled TASEP.In chapter 2,we investigate totally asymmetric simple exclusion processes on lattices with junctions,considering random particle attachment and detachment in the bulk.Particles ranomly attach to the bulk with the rateωA and detach from the bulk with the rateωD.Setting K =ωA /ωD,we study three cases: K > 1, K < 1 and K = 1.It is found that different phase diagram structures arise in the three cases.While only four stationary phases, LD-LD,LD-S,S-HD and HD-HD,could be found in the case of K > 1,additional phases are observed in the case of K≤1.When K = 1 , LD-(LD-MC),LD-(LD-MC-HD),(LD-MC-HD)-HD,(MC-HD)-HD,and eight MC related phases could be observed.When K < 1,four HD-LD telated phases could be observed.It is also shown that at a fixed K ,the phase diagram structure changes with the increase ofΩD.Continuum mean-field calculations are performed,and the analytic results are in good agreement with Monte Carlo simulations for all three cases.In chapter 3,we investigate N -channel simple exclusion processes.In this model,the system consists of N equal-size channels and each channel contains L sites.,particles can move across N parallel lattices and jump fuuly asymmetrically between the channels.Monte Carlo simulations are carried out to investigate the phase diagrams and density profiles of the system.It is shown that the phase diagram structure changes with increase of N .Moreover,hou the phase diagram depends on N is obtained. A vertical cluster mean-field analysis is carried out;it shows good agreement with simulations.In chapter 4,we investigate two-channel simple exclusion processes where particles can move along two parallel lattices and jump between the channels. We consider the case with asymmetric coupling, where the particles in the first channel could jump to the second channel with the rateω1 ,while the opposite motion has the rate ofω2,andω1≠ω2.We consider the system with periodic boundaries and open boundaries respectively.Monte Carlo simulations and the vertical cluster mean-field analysis are carried out to investigate the phase diagrams and density profiles of the system,and it is shown that they are in good agreement.
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