逾渗模型的蒙特卡罗模拟

发布时间：2019-01-05 06:41

【摘要】：有一类普遍现象常见于自然界中,如疾病传播,液体流动,火灾蔓延等,共同特点是:有两种宏观状态,如石油不导通至导通,咖啡不浸透至浸透,森林部分着火后熄灭至森林全部着火,疾病传染部分人后终止至疾病在人群中全面爆发。此类自然现象均体现了某种物质逐渐渗透穿越的过程,此过程被称为逾渗(percolation)现象。为研究此类逾渗现象而模拟创建的各种数学的或物理的模型则为逾渗模型。逾渗模型中,当占据概率或粒子浓度f逐渐增大以至超越阈值fc时,模型中的两种宏观状态改变,系统的宏观状态将从一相改变为另一相,这样的变化就是相变现象,发生状态改变的特定值理解为相变点。通过逾渗理论及模型的研究和应用,更多的物理转变现象能够被人们认识和理解。虽然逾渗模型变化规则看似简单,但在研究开展工作中有很多困难。迄今,在三维现实环境下,模拟构建并获得准确阈值的逾渗模型的很少。蒙特卡罗模拟(Monte Carlo Simulation)是逾渗过程中中非常有效的数值研究方式。本文重点研究了金属-绝缘体(半导体)颗粒复合介质逾渗模型的导电输运性质,主要工作和研究成果如下:(1)借助蒙特卡罗随机行走模拟方法研究了逾渗模型,计算机软件构造出二维平方和三维简单立方格子上的定向点逾渗模型,以此用来模拟研究绝缘体-金属转变的相变。模拟结果表明:当金属组分浓度小于这个临界值fc,整个系统不导电;随着金属组分的浓度的增大有效电导率也逐渐增大;当浓度f等于临界阈值时,整个系统发生了绝缘体至金属的转变。二维导电性相变点fc≈0.69,三维导电性相变点fc≈0.43。(2)复合体系的介质组分性质会影响逾渗阈值的大小,同时颗粒的几何形状和大小同样会对阈值带来影响。本文利用了有效介质理论,结合不同形状颗粒的退化因子的不同,研究发现颗粒的粒径越大,逾渗阈值越低。文中分别用圆球颗粒和不同大小的椭球颗粒为例,模拟出其对应的阈值情况。(3)温度条件对逾渗阈值的影响:本文中分别就两种情况作了研究分析,一方面是颗粒间受温度影响而产生的跳跃电导,电导通过局域化的电子从一个局域态跳转进入另一个局域态,同时产生跳跃概率,电导正比于跳跃概率进而形成与温度的关系,模拟时使用电导T-1/2率的基本模型进行分析,获得结论是因跳跃电导的影响,导电网络逾渗模型的阈值变小,二维方格网络模型阈值由0.69降低为0.6,三维立方点格网络模型阈值由0.43降低为0.32,表明温度影响产生的跳变电导使得逾渗阈值减小了。另一方面是金属和半导体的电阻率会随着温度的升高发生不同的变化,利用有效介质模型,复合介质的有效电阻率随着温度变化呈现逐步上升后稳健下降的趋势变化,同时有效电阻率变化必然影响有效电导率和阈值,经过数据拟合,结果显示导电网络逾渗模型的阈值临界点会因为温度的升高而减小。
[Abstract]:A common phenomenon is common in nature, such as disease transmission, liquid flow, fire spreading and the like, and is characterized in that there are two macroscopic states, such as the oil is not communicated to the air guide, the coffee is not saturated to the saturation, and the forest part is extinguished until all the forests are on fire after the fire, The disease infects a part of the population and then terminates until the disease breaks out in the crowd. Such natural phenomena are a process of gradual penetration of some kind of material, which is known as the percolation phenomenon. The various mathematical or physical models that are simulated for the study of such percolation are more than the percolation model. In the percolation model, when the occupancy probability or the particle concentration f is gradually increased to exceed the threshold value fc, the two macroscopic states in the model change, and the macroscopic state of the system will change from one phase to the other, such that the change is the phase change phenomenon, and the specific value of the change of the occurrence state is understood as the phase change point. Through the research and application of percolation theory and model, more physical transformation can be recognized and understood. Although the percolation model change rule appears to be simple, there are many difficulties in the study. So far, in a three-dimensional realistic environment, there are few percolation models that simulate the build-up and get the exact threshold. Monte Carlo Simulation (Monte Carlo Simulation) is a very effective numerical method in the percolation process. In this paper, the conductive transport properties of a metal-insulator (semi-conductor) particle composite medium percolation model are studied. The main work and research results are as follows: (1) The percolation model is studied by means of the Monte-Carlo random walk simulation method. Computer software constructs the directional point percolation model on the three-dimensional simple cubic lattice of the two-dimensional sum of squares, which is used to simulate the transition of the insulator-metal transition. The simulation results show that when the concentration of the metal component is less than the critical value, the whole system is not conductive, and the effective conductivity is increased with the increase of the concentration of the metal component; when the concentration f is equal to the critical threshold, the whole system has the transition of the insulator to the metal. the two-dimensional conductive phase change point fc = 0.69, the three-dimensional conductive phase change point fc = 0.43. (2) The nature of the medium component of the composite system will affect the size of the percolation threshold, and the geometry and size of the particles will also affect the threshold. In this paper, the effective medium theory is used to study the difference of the degradation factors of different shape particles. The larger the particle size and the lower the percolation threshold are found. In this paper, spherical particles and spherical particles with different sizes are used as examples to simulate the corresponding threshold condition. (3) The effect of the temperature condition on the percolation threshold: In this paper, the two cases are studied and analyzed, on the one hand, the jump conductance generated by the temperature influence among the particles, the conductance is changed from a local state to the other local state by the localized electrons, and the jump probability is generated. the conductance is directly proportional to the jump probability and then the relationship with the temperature is formed, the basic model of the conductivity t-1/ 2 ratio is used for analysis in the simulation, the conclusion is that the threshold of the percolation model of the conductive network is reduced due to the influence of the jump conductance, the threshold of the two-dimensional grid network model is reduced from 0.69 to 0.6, The three-dimensional cubic lattice network model threshold is reduced from 0.43 to 0.32, indicating that the jump conductance resulting from the temperature influence reduces the percolation threshold. on the other hand, the resistivity of the metal and the semiconductor can change with the increase of the temperature, At the same time, the effective resistivity change inevitably affects the effective conductivity and the threshold, and through the data fitting, the result shows that the critical point of the percolation model of the conductive network is reduced due to the increase of the temperature.
【学位授予单位】：南京邮电大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O471;O242.2

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