逾滲模型的蒙特卡羅模擬
發(fā)布時(shí)間：2019-01-05 06:41
【摘要】：有一類普遍現(xiàn)象常見于自然界中,如疾病傳播,液體流動(dòng),火災(zāi)蔓延等,共同特點(diǎn)是:有兩種宏觀狀態(tài),如石油不導(dǎo)通至導(dǎo)通,咖啡不浸透至浸透,森林部分著火后熄滅至森林全部著火,疾病傳染部分人后終止至疾病在人群中全面爆發(fā)。此類自然現(xiàn)象均體現(xiàn)了某種物質(zhì)逐漸滲透穿越的過程,此過程被稱為逾滲(percolation)現(xiàn)象。為研究此類逾滲現(xiàn)象而模擬創(chuàng)建的各種數(shù)學(xué)的或物理的模型則為逾滲模型。逾滲模型中,當(dāng)占據(jù)概率或粒子濃度f逐漸增大以至超越閾值fc時(shí),模型中的兩種宏觀狀態(tài)改變,系統(tǒng)的宏觀狀態(tài)將從一相改變?yōu)榱硪幌?這樣的變化就是相變現(xiàn)象,發(fā)生狀態(tài)改變的特定值理解為相變點(diǎn)。通過逾滲理論及模型的研究和應(yīng)用,更多的物理轉(zhuǎn)變現(xiàn)象能夠被人們認(rèn)識和理解。雖然逾滲模型變化規(guī)則看似簡單,但在研究開展工作中有很多困難。迄今,在三維現(xiàn)實(shí)環(huán)境下,模擬構(gòu)建并獲得準(zhǔn)確閾值的逾滲模型的很少。蒙特卡羅模擬(Monte Carlo Simulation)是逾滲過程中中非常有效的數(shù)值研究方式。本文重點(diǎn)研究了金屬-絕緣體(半導(dǎo)體)顆粒復(fù)合介質(zhì)逾滲模型的導(dǎo)電輸運(yùn)性質(zhì),主要工作和研究成果如下:(1)借助蒙特卡羅隨機(jī)行走模擬方法研究了逾滲模型,計(jì)算機(jī)軟件構(gòu)造出二維平方和三維簡單立方格子上的定向點(diǎn)逾滲模型,以此用來模擬研究絕緣體-金屬轉(zhuǎn)變的相變。模擬結(jié)果表明:當(dāng)金屬組分濃度小于這個(gè)臨界值fc,整個(gè)系統(tǒng)不導(dǎo)電;隨著金屬組分的濃度的增大有效電導(dǎo)率也逐漸增大;當(dāng)濃度f等于臨界閾值時(shí),整個(gè)系統(tǒng)發(fā)生了絕緣體至金屬的轉(zhuǎn)變。二維導(dǎo)電性相變點(diǎn)fc≈0.69,三維導(dǎo)電性相變點(diǎn)fc≈0.43。(2)復(fù)合體系的介質(zhì)組分性質(zhì)會(huì)影響逾滲閾值的大小,同時(shí)顆粒的幾何形狀和大小同樣會(huì)對閾值帶來影響。本文利用了有效介質(zhì)理論,結(jié)合不同形狀顆粒的退化因子的不同,研究發(fā)現(xiàn)顆粒的粒徑越大,逾滲閾值越低。文中分別用圓球顆粒和不同大小的橢球顆粒為例,模擬出其對應(yīng)的閾值情況。(3)溫度條件對逾滲閾值的影響:本文中分別就兩種情況作了研究分析,一方面是顆粒間受溫度影響而產(chǎn)生的跳躍電導(dǎo),電導(dǎo)通過局域化的電子從一個(gè)局域態(tài)跳轉(zhuǎn)進(jìn)入另一個(gè)局域態(tài),同時(shí)產(chǎn)生跳躍概率,電導(dǎo)正比于跳躍概率進(jìn)而形成與溫度的關(guān)系,模擬時(shí)使用電導(dǎo)T-1/2率的基本模型進(jìn)行分析,獲得結(jié)論是因跳躍電導(dǎo)的影響,導(dǎo)電網(wǎng)絡(luò)逾滲模型的閾值變小,二維方格網(wǎng)絡(luò)模型閾值由0.69降低為0.6,三維立方點(diǎn)格網(wǎng)絡(luò)模型閾值由0.43降低為0.32,表明溫度影響產(chǎn)生的跳變電導(dǎo)使得逾滲閾值減小了。另一方面是金屬和半導(dǎo)體的電阻率會(huì)隨著溫度的升高發(fā)生不同的變化,利用有效介質(zhì)模型,復(fù)合介質(zhì)的有效電阻率隨著溫度變化呈現(xiàn)逐步上升后穩(wěn)健下降的趨勢變化,同時(shí)有效電阻率變化必然影響有效電導(dǎo)率和閾值,經(jīng)過數(shù)據(jù)擬合,結(jié)果顯示導(dǎo)電網(wǎng)絡(luò)逾滲模型的閾值臨界點(diǎn)會(huì)因?yàn)闇囟鹊纳叨鴾p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.
【學(xué)位授予單位】：南京郵電大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：O471;O242.2
[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.
【學(xué)位授予單位】：南京郵電大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：O471;O242.2
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