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Study on Spontaneous Symmetry Breaking in Bidirectional Two-channel Asymmetric Simple Exclusion Process

Author: SunZhiHu
Tutor: JiangRui；WuQingSong
School: University of Science and Technology of China
Course: Thermal Power Engineering
Keywords: One-dimensional traffic flow TASEP model Mean Field Theory Monte Carlo simulation
CLC: O411.3
Type: Master's thesis
Year: 2011
Downloads: 14
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Abstract


In nature and human society, there is a wide variety of material movement process. Such as urban vehicular traffic system in vivo molecular motor movement. In the course of these campaigns, the most common and simple one-dimensional course of the campaign. In the 1960s and 1970s, have been proposed a theoretical model used to simulate the dynamics of biopolymers mechanism, this model is asymmetric simple exclusion process (ASEP - asymmetric simple exclusion processes) model. The ASEP model described having a string containing N lattice and certain particles composed of one-dimensional system of particles in the lattice string movement, the particles in the original lattice may be a certain probability jumps to the both sides of the lattice, but ASEP model , a grid can only accommodate a particle, so that the particles can not jump into the particles occupy the lattice. If the probability of particle motion in one direction only movement in the other direction, then known as asymmetric simple exclusion process - TASEP (totally asymmetric simple Exclusion processes). Because the TASEP model more in line with the actual course of the campaign, TASEP model has been more attention. Later, scientists have proposed a variety of the TASEP model expansion model to describe more complex course of the campaign. In the the TASEP expansion model study, the emergence of many one-dimensional system does not have the balance, a variety of physical phenomena, spontaneous symmetry breaking is one of them. The second chapter of this paper, we study the parallel update rules, the particles jump probability is less than 1, a narrow inlet conditions bidirectional dual-channel asymmetric simple exclusion process system. Particles in the two lane moving in the opposite direction, respectively, and are not allowed to change lanes. Narrowly defined inlet conditions: when another trail at the outlet of the particle, the particle can not jump from the outside world into the inlet grid points. We consider in the aisle particles to determine the probability leap forward. The phase diagram of the model, the system density and flow using the mean field theory analysis showed that two symmetry breaking phase. By the phase diagram, we can see that the jump probability of structural changes in the phase diagram of the system had a significant impact. By Monte Carlo simulation, we found that the analysis results of the simulation results with the mean-field theory varied, this is because the correlation of the system are not considered in the theoretical analysis. The third chapter of this paper, in order to solve the inconsistencies of the previous chapter, the Monte Carlo simulation and mean field theory, we propose an improved mean field theory to analyze two-way dual-channel TASEP model with a narrow inlet conditions. The improvements mean field theory, consider the interaction of the system at the end side of the vertical lattice string two grid points, which are included in the vertical lattice the string grid point correlation, thus obtained theoretical results than the simple mean-field theory phase diagram more in line with the results of Monte Carlo simulations. The fourth chapter of this paper, we studied the dual-channel TASEP model with a narrow export conditions. Narrowly defined export: another trail entrance to the particles, the particles can not jump out from the exit grid point system. We use a simple mean-field theory, improved mean field theory and Monte Carlo simulation are three ways to study the model, the results showed improved mean field theory closer to the Monte Carlo simulation results than the simple mean-field theory, but compared to the simple mean-field theory, improved mean field theory applies to a lesser extent.

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CLC: > Mathematical sciences and chemical > Physics > Theoretical Physics > Mathematical methods of physics > Physical simulation,physical simulation
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