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研究生： 陳泓伸
Chen, Hung-Shen
論文名稱： Mean-field theory of sandpile model with two-site correlation
指導教授： 吳玉書
Wu, George Yu-Shu
口試委員:
學位類別： 碩士
Master
系所名稱： 電機資訊學院 - 電子工程研究所
Institute of Electronics Engineering
論文出版年： 2009
畢業學年度： 97
語文別： 英文
論文頁數： 36
中文關鍵詞： 平均場理論 、沙堆模型 、關聯函數
外文關鍵詞： mean-field theory, sandpile model, correlation function
相關次數： 點閱：2  下載：0 
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    • In the thesis, we apply mean-field theory to discuss the critical phenomena in two-dimensional sandpile model. With the concept of mean-field theory, every site in the system is assumed to be independent of each other. Following the investigation of A. Vespignani and S. Zapperi[5], we have derived higher-order correction to various single-site densities of sand grains.
    In the calculation, we include the two-site correlation function between two nearest-neighbor sites, which contributes to the higher-order correction to the previous calculated densities. Last of all, we discuss the correction to critical exponents due to the higher-order correction of densities.

    1. Introduction 1 1.1 Introduction to self-organized criticality 1 1.2 Motivation 11 1.3 Thesis work 12 2. Higher-order correction in the single-site approximation 13 2.1 The two-dimensional BTW sandpile model 13 2.2 Higher-order correction 13 2.3 Toppling mechanism 22 3. Two-site approximation 23 3.1 The dynamical equations involving two-site correlations 23 3.2 The calculation within the two-site approximation 25 3.3 The correction to the critical exponents due to the two-site correlations 31 Appendices 33 A. Dynamical equations of two-site densities 33 B. Solutions of two-site correlations 35 Reference 36

    [1] Shang-Keng Ma, Statistical Mechanics (World Scientific, 1985).

    [2] 楊朝順, 沙堆模型之自組臨界性的理論與數值分析 (2005).

    [3] P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. A 38, 364 (1988).

    [4] A. van der Ziel, Physica 16, 359 (1950).

    [5] A. Vespignani, S. Zapperi, Phys. Rev. E 57, 6345 (1998).

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