# 臺灣博碩士論文加值系統

(34.239.167.149) 您好！臺灣時間：2022/06/29 18:56

:::

### 詳目顯示

:

• 被引用:0
• 點閱:267
• 評分:
• 下載:0
• 書目收藏:0
 本篇論文簡單介紹了展透理論的概念及將其應用到隨機阻抗網絡問題上
 In this thesis, we briefly review the percolation theory and apply it to random resistor network problem. We start with reviewing site percolation, bond percolation, percolation quantities and critical exponents. It has been conjectured that there exists a universal scaling law between critical exponents. We examine the scaling law by carrying out numerical simulation and use the finite-size scaling analysis to evaluate the various critical exponents. To study the problem of random resistor network, we use real-space renormalization to work out the exact critical exponents of 3*3 bond square lattice and 2*2*2 bond simple cubic lattice. Although the exact renormalization solutions are not the exact solutions, we got reasonable approximations. In the case of square lattice, the fixed point of probability is equal to the exact percolation threshold and so we got very good estimates of other critical exponents. In the case of simple cubic lattice, renormalization method offers us a quicker approach of critical exponents. However, the results are not so good because the fixed point is not very close to percolation threshold. If we use the best numerical estimate of percolation threshold as the fixed point, we also can get very good approximations of critical exponents. In addition, we show the numerical solutions of percolation threshold by Monte Carlo Renormalization Method. It is found to be a good method to derive more precise estimate of percolation threshold. The new contribution of this thesis is the exact renormalization results of 3*3 bond square lattice and 2*2*2 simple cubic lattice. We list all configurations in Appendix A and B. In two-dimensional lattice, we also work out the fixed-point p* and for several small lattices.
 Symbol Table i Abstract ii Chapter 1 Introduction 1 Chapter 2 Percolation Theory 4 2.1 Introduction4 2.2 What is Percolation 4 2.3 Percolation Quantities5 2.4 Exact Solution of Percolation10 2.5 The Universal Scaling Laws13 2.6 Numerical Solution of Percolation18 Chapter 3 Renormalization Approach to Percolation25 3.1 Introduction25 3.2 Small Cell Renormalization25 3.3 Large Call Renormalization33 Chalper 4 Application to Conductivity35 4.1 Introduction35 4.2 Random Resistor Network35 4.3 Critical Exponents36 4.4 Renormalization Approach to Critical Exponents38 Conclusion45 Future research46 References47 Appendix50 Appendix A51 Appendix B91
 Bernasconi, J. (1978) Real-space Renormalization of Bond-Disordered Conductance Lattices. Phys. Rev. B. 18, 2185-2191.Broadbent, S.R. & Hammersley, J.M. (1957) Percolation Processes. Proc. Camb. Philos. Soc. 53, 629.Conway, A.R. & Guttmann, A.J. (1995) On Two-dimensional Percolation. J. Phys. A. 28, 891-904.Derrida, B., Zabolitzky, J.G., Vannimenus, J., & Stauffer, D. (1984) A Transfer Matrix Program to Calculate the Conductivity of Random Resistor Networks. J. Stat. Phys. 36, 31-42.Deutscher, G., Entin-Wohlman, O., Fishman, S. & Shapira, Y. (1980) Percolation Description of Granular Superconductors. Phys.Rev. B. 21, 5041-5047.Eggarter, T.P. & Cohen, M.H. (1970) Simple Model for Density of States and Mobility of an Electron in a Gas of Hard-Core Scatterers. Phys. Rev. Lett. 25, 807.Fisher, M.E. (1971) In Critical Phenomena: Enrico Fermi Summer School, edited by M.S. Green, New York, Academic Press.Flory, P.J. (1941) Molecular Size Distribution in Three Dimensional Polymers. J. Am. Chem. Soc. 63, 3083-3090.Frisch, H.L., Sonnenblick,E., Vyssotsky, V.A., & Hammersley, J.M. (1961) Critical Percolation Probabilities (Site Problem). Phys. Rev. 124, 1021-1022.George, H.W. (1994) Contemporary Problems in Statistical Physics. Society for Industrial and Applied Mathematics, Philadelphia.Hong, D.C. & Stanley, H.E. (1983) Cumulant Renormalization Group and Its Application to the Incipient Infinite Cluster in Percolation. J. Phys. A: Math. Gen. 16, L525-529.Hoshen, J. & Kopelman, R. (1976) Percolation and Cluster Distribution. Phys. Rev. B 14, 3428-3445.Hovi, J.P. and Aharony, A. (1997) Different Self-Avoiding Walks on Percolation Clusters: A Small-Cell Real-Space Renormalization-Group Study. J. Stat. Phys. 86, 1163-1178.Kirkpatrick, S. (1973) Percolation and Conduction. Rev. Mod. Phys. 45, 574-588.Last, B.J. & Thouless, D.J. (1971) Percolation Theory and Electrical Conductivity.Phys. Rev. Lett. 27, 1719-1721.Larson, R.G., Scriven, L.E., & Davis, H.T. (1977) Percolation Theory of Residual Phases in Porous Media. Nature. 268, 409-413.Lobb, C.J. & Frank, D.J. (1979) A Large-Cell Renormalization Group Calculation of the Percolation Conduction Critical Exponent. J. Phys. C: Solid St. Phys. 12, L8270-830.Lobb, C.J. & Karasek, K.R. (1982) Critical Exponents for Two —Dimensional Bond Percolation. Phys. Rev. B. 25, 492-495.Magalhaes, Tsallis, C., & Schwachheim, G. (1980) Probability Renormalization Group Treatment of Bond Percolation in Square, Cubic and Hypercubic Lattices. J. Phys. C: Solid St. Phys. 13, 321-330.Redelmeier, D.H. (1981) Counting Polyominoes: Yet Another Attack. Discrete Math. 36,191-203.Reynolds, P.J., Stanley, H.E., & Klein, W. (1978) Percolation by Position-Space Renormalization Group with Large Cells. J. Phys. A: Math. Gen. 11, L199-207.Reynolds, P.J., Stanley, H.E., & Klein, W. (1980) Large-Cell Monte Carlo Renormalization Group for Percolation. Phys. Rev. B 21, 1223-1245.Sahimi, M. (1994) Applications of Percolation Theory. Taylor & Francis, London.Stanley, H.E. (1977) Cluster Shapes at the Percolation Threshold. J. Phys. A 10, L211-220.Seiden, P.E. & Schulman, L.S. (1990) Percolation Model of Galactic Structure. Adv. Phys. 39, 1-54.Staufer, D. & Aharony, A. (1992) Introduction to Percolation Theory. Taylor & Francis, London.Stockmayer, W.H. (1943) Theory of Molecular Size Distribution and Gel Formation in Branched-Chain Polymers. J.Chem.Phys. 11, 45-55.Sykes, M.F. & Essam, J.W. (1963) Some Exact Critical Percolation Probabilities for Bond and Site Problems in Two Dimensions. Phys. Rev. Lett. 10, 3.Sykes, M.F. & Essam, J.W. (1964) Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions. J. Math. Phys. 5, 1117-1127.Vyssotsky, V.A., Gordon, S.B., Frisch, H.L., & Hammersley, J.M. (1961) Critical Percolation Probabilities (Bond Problem). Phys. Rev. 123, 1566-1567.Webman, I., Jortner, J., & Cohen, M.H. (1975) Numerical Simulation of Electrical Conductivity in Microscopically Inhomogeneous Materials. Phys. Rev. B. 11, 2885-2892.Webman, I., Jortner, J., & Cohen, M.H. (1977) Critical Exponents for Percolation Conductivity in Resistor Networks. Phys. Rev. B. 16, 2593-2596.Wilson, K.G. (1971) Renormalization Group and Critical Phenomena. Phys. Rev. B 4, 3184-3205.Ziman, J.M. (1968) The Localization of Electrons in Ordered and Disordered Systems. J. Phys. C: Proc. Phys. Soc., London 1, 1532-1538.
 國圖紙本論文
 推文當script無法執行時可按︰推文 網路書籤當script無法執行時可按︰網路書籤 推薦當script無法執行時可按︰推薦 評分當script無法執行時可按︰評分 引用網址當script無法執行時可按︰引用網址 轉寄當script無法執行時可按︰轉寄

 無相關論文

 無相關期刊

 1 翼尖小翼近地效應之實驗與數值模擬分析 2 以機器學習方法訓練二維凡德瓦異質結構之分子勢場 3 初探大氣紊流模式與風機性能之評估 4 優化具嵌入擋板之矩形流道的電滲流流量 5 聲射流之熱、磁效應 6 瞬間起動球體流場之研究 7 液滴撞擊液膜之飛濺臨界邊界研究 8 微機械光學調變元件之研究 9 感應式耦合電漿源之電磁模型與氣體動力論分析 10 非接觸式遺傳演算法樑裂縫偵測 11 以相位重建技術研製三維電子斑點干涉儀 12 多功光學顯微系統:設計與研製具橢偏儀功能之凌尼克干涉顯微鏡 13 多探頭裂縫掃描之研究 14 CMOS立體微電感之設計與製作 15 電子構裝中錫球接合之偵測及反算

 簡易查詢 | 進階查詢 | 熱門排行 | 我的研究室