Study On Non-equilibrium Phase Transition Behaviors In Several Models Coupled With Asymmetric Exclusion Processes

Multiple exclusion processes are based on the common ASEP, which is also named as asymmetric simple exclusion process. However, it develops ASEP, since coupling with other models or considering the effect of Langmuir kinetics. Besides, tremendous physical or chemical phenomena can be revealed from it, since the physical insight or physical institution can be obtained. By the methods of mean-field analysis or exact solutions complemented by Monte-Carlo simulations, the multiple exclusion processes can be analyzed to obtain the corresponding non-equilibrium phase transitions.Actually, the multiple exclusion processes can be applied into the following phenomena in the areas of biology, chemistry and physics. Firstly, as for the field of biology, the protein motors (e. g. kinesins) using the energy surge of ATP can move along filaments in cells. Besides, they can also perform the attachment and detachment behavior, according to the nonlinear dynamics. Moreover, in the process of protein synthesis, the ribosome can diffuse in the cytoplasm. Secondly, when concerned about the chemical phenomena, some must be addressed. For example, in the preparation of thin films, particles (e. g. atoms) can diffuse between the interlayer of films. Besides, in the gel electrophoresis, the electrophoresis molecules (e. g. nucleic acid molecules) can migrate in the gel. Finally, the jamming and the following behavior of vehicles can also be investigated by the multiple exclusion processes. Besides, the clusters and the spontaneous symmetry breaking revealed from ants’ model are also extracted from the multiple exclusion processes. Therefore, many physical mechanisms can be obtained from them, such as the shock formation in driven diffusive systems, topological structures in corresponding phase diagrams, the spontaneous symmetry breaking, the current splitting, Langmuir kinetics et al. The research work is organized as follows:In Chapter two, bulk induced phase transitions are addressed. Asymmetric lane-changing rates are investigated. By studying the transitions among LLS, LS1H, SHH, LS2H, LCH, bulk induced phase transitions are confirmed to exist in the weak coupling system. Since the complexity of the phase diagram structures, one detailed case is displayed, in order to understand the physical institution of the bulk induced phase transitions. According to the current minimal theorem, two or more bulk induced shock can’t exist in the system. Besides, antishock and other formations are demonstrated in the chapter, in order to explain the specialty of the right solutions. In the next chapter, the model constituted by three-lane TASEPs with weak coupling is studied. Symmetric and asymmetric lane-changing rates are displayed. With varied ratios ΩB/ΩA, phase diagram structures are obtained.In Chapter four, a mesoscopic ring constituted by two-lane SEPs coupled with a common TASEP. Two subsystems compete with each other. Since the driven diffusive mechanism is controlled by some critical parameters, e. g. the global density np, the diffusivity D1,D2, the current splitting parameter θ. Therefore, varied phase diagram structures, density profiles and current profiles are calculated.In the next part, authors generalize the model to show the effect of the multiple diffusive channels. On one hand, if the topology of the system is symmetric, the phase boundaries of the driven part (TASEP) can be deduced. No crossing lines can be found in the phase diagram structures. Besides, if the global density np keeps constant, with the increase of the multiple diffusive channels, the low density parts in the phase diagrams shrink. When the parameter N is large enough, the LD-HD and the LD regions disappear. On the other hand, if the total number of particles in the system Np keeps constant, the high density parts in the phase diagrams shrink. When the parameter N is large enough, the LD-HD and the HD regions disappear. Actually, these conclusions can be extended to general cases.In Chapter six, a one-dimensional exclusion process is developed. The biased diffusive effect is investigated. The diffusive parameter δ is classified, in order to give a generalized investigation. Profound domain wall theory is promoted.In the next part, exact solutions of the multiple ASEPs coupled with asymmetric lane-changing rates are studied. The strictly mathematical derivations are deduced to illustrate the system with the effect of Langmuir kinetics.