Research Over Percolation Model Based On Monte Carlo Simulation

There is a class of common and unique phenomenon is common in nature, such as rock flow of oil, coffee soaked, forest fires occurred, the spread of disease, these problems have one thing in common: there are two different macro-state, such as oil nonconducting to conducting, coffee does not penetrate to penetrate, after part of the forest fire to extinguish all forest fire, after the termination of spread of the disease to some people the disease broke out in the crowd. Like there are different macroscopic state is subject to a microscopic parameters such as particle occupation probability or percentage concentration of factors such as control, such natural phenomena are reflected in the gradual penetration of the substance through the process, this process is called percolation phenomenon. For the study of such phenomena percolation simulation created mathematical or physical model was percolation model.Statistical physics standpoint, the percolation model in two macroscopic state of the system is considered to be a two-phase, when the microscopic parameters occupation probability f or particle concentration increases that exceed a certain value when fc, macroscopic state of the system to change from one phase to another phase, this phenomenon is called phase change(phase transition), the value of a particular state change occurs understood as the phase transition point. Thus, although the initial percolation model is presented as a purely mathematical model, but then more as a physical model was used to study. The results can help people more in-depth understanding of the nature of the physical properties of phase transitions and critical phenomena. Although percolation model change the rules seem simple, but in fact it was not easy to study. So far, through simulation and analytical studies to obtain accurate solutions of the percolation model is rare, especially in the three-dimensional reality. In this context, the numerical study of percolation become the focus of research dependence, especially Monte Carlo Simulation.This paper focuses on metal- transport properties of the conductive insulator or semiconductor particle complex medium percolation model, the main work and research results are as follows:(1)Study the percolation model by means of Monte Carlo random walk simulation, computer software to construct a two-dimensional orientation point and three-dimensional simple cubic lattice square on the percolation model in order to simulate study insulator- metal transition phase change. The results show that: effective conductivity decreases as the concentration of the metal component decreases when the concentration of f to achieve effective conductivity hours a critical value fc; when the concentration is less than the critical value, the entire system is not conductive; when the concentration of f equal to the critical value, the entire system of the metal- insulator transition. Two-dimensional conductive phase change point fc≈0.69, three-dimensional conductive phase change point fc≈0.43.(2)Percolation threshold depends not only on the nature of the size of each component of the granular composite itself, but also on the geometry of the conducting component. In this paper, the effective medium theory, the combination of different degradation factors study found that particles of different shapes of the larger particle size, the lower the percolation threshold.(3)The temperature influence on the percolation threshold: research and analysis in this article were made on the two cases, one is hopping conductivity between the particles generated by the temperature, conductance by localized electrons into localized states from a jump another localized state, while producing jump probability proportional to the conductance jump probability and thus the formation of the relationship between temperature, conductivity using the basic model T-1/2 rate when simulation analysis, the conclusion is obtained by hopping conductance of the conductive network threshold percolation model becomes small, two-dimensional grid network model threshold by a 0.69 decreased to 0.6, three-dimensional cubic lattice network model threshold from 0.43 lowered to 0.32, indicating that the temperature impact of hopping conductivity so that the percolation threshold is reduced. On the other hand is the resistivity of metals and semiconductors will occur with increasing temperature different changes, using effective medium model, the effective resistance of the composite medium as the temperature changes after showing steady rise gradually declining trends, while effective resistance the rate of change will inevitably affect the effective conductivity and thresholds after data fitting showed that the critical threshold point of the conductive percolation network model will decrease as the temperature rises.