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研究生： 黃士誠
Huang, Shi-cheng
論文名稱： 布朗馬達在週期勢能下受非平衡溫度影響之運動分析
The Kinetic Analysis of Brownian Motor Suffered a Periodic Potential in Nonuniform Temperature
指導教授： 黃明哲
Huang, Ming-Jer
學位類別： 碩士
Master
系所名稱： 工學院 - 工程科學系
Department of Engineering Science
論文出版年： 2009
畢業學年度： 97
語文別： 中文
論文頁數： 52
中文關鍵詞： 非平衡溫度 、布朗運動
外文關鍵詞： nonuniform temperature, Fokker-Planck equation, Brownian motion
相關次數： 點閱：73  下載：1 
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    • 利用擾動分析來解釋分子馬達的運動行為，在之前已經有很多的研究。然而考慮一個非平衡溫度的條件是比較少被提出來的。因此提出一個擾動分析，而馬達的運動是處在一個非平衡溫度上。
    本文使用Fokker-Planck equation 為運動方程式，解出在非平衡溫度下的或然率或機率流，再利用文獻[11] Robust 數值演算法計算切換過程中的運動模式。
    採用MATLAB 7 軟體計算上述方程式和數值分析。求得在耦合一個週期性的勢能和一個非平衡溫度下的布朗運動行為，並與文獻[6]之結果比較，有很高的一致性。並討論平均速度和隨機性的影響。再利用改變振幅、溫差和粒子移動距離的模型，來探討每個模型對布朗馬
    達運動的平均速度和隨機性的影響。

    There are many researches regarding using fluctuation analysis to explain the movement of molecular motor. However there are not so many studies being presented by considering the condition of nonuniform temperature. Therefore provide a fluctuation analysis with the motor
    movement which is running under nonuniform temperature.
    The Fokker-Planck equation is the governing equation in this paper,it can be used to slove the probability and the probability fiux and it also can be used on calculating working model with potential energy switches between on and off state by Robust numerical algorithm in the reference[11].

    This paper used MATLAB7.0 to calculate the equations and the numerical algorithm to analyze.The behavior of Brownian motion in the case of coupling a periodic potential to a nonuniform temperature foeld is further investigated.The results of this study are highly consistent with this of previous studies for the reference[6].Discuss the average velocities and randomness of Brownian motions.By changing the molds of amplitude,temperature difference and particle moves distance to discussthe effects of molds which are average velocities and randomness to Brownian motor kinetic.

    摘要................................................I 英文摘要............................. .............II 誌謝..............................................III 目錄...............................................IV 圖目錄............................................VII 符號說明...........................................IX 第一章 緒論.........................................1 1-1 前言...........................................1 1-2 文獻回顧.......................................2 1-3 研究動機與目的.................................4 1-4 本文架構.......................................4 第二章 布朗馬達原理簡介.............................6 2-1 布朗運動.......................................6 2-1-1 布朗運動的或然率描述........................7 2-1-2 史摩勒丘司基-費曼棘輪.......................8 2-2 布朗馬達.......................10 2-2-1 布朗棘輪................10 2-2-2 Flashing ratchet...........................11 2-2-3 Diffusion ratchet..........................12 2-3 隨機性........................................12 2-3-1 Rate-limiting..............................13 2-3-2 隨機過程...................................13 第三章 布朗馬達理論模型的建立......................15 3-1 基本原理......................................15 3-2 模型建立......................................15 3-3 數學理論......................................17 3-4 數值演算法....................................18 第四章 結果與討論..................................24 4-1 振幅對運動的影響..............................24 4-1-1 平均速度...................................24 4-1-2 隨機性.....................................25 4-2 非對稱勢能對運動的影響........................25 4-2-1 平均速度...................................25 4-2-2 隨機性.....................................26 4-2-3 加入外力的影響.............................26 4-2-4 不同振幅對的影響...........................27 4-3 溫差對運動的影響..............................27 4-3-1 平均速度...................................27 4-3-2 隨機性.....................................28 4-3-3 不同勢能的影響.............................29 4-4 溫度對運動的影響..............................29 4-4-1 平均速度...................................29 4-4-2 隨機性.....................................30 4-5 滑動距離對運動的影響..........................30 4-5-1 平均速度...................................30 4-5-2 隨機性.....................................32 第五章 結論與未來研究方向..........................33 5-1 結論..........................................33 5-2 未來研究方向..................................34 参考文獻...........................................35 自述...............................................52 圖目錄 圖2-1史摩勒丘司基-費曼棘輪裝置圖...................38 圖2-2布朗棘輪示意圖................................38 圖2-3位能切換之Flashing ratchet....................39 圖2-4溫數變化與週期性位能函數耦合的擴散棘輪........39 圖3-1鋸齒狀傾斜勢能................................40 圖3-2空間離散化的馬可夫鏈..........................40 圖4-1改變振幅 的平均速度...........................41 圖4-2改變振幅 的隨機性.............................41 圖4-3 勢能改變示意圖...............................42 圖4-4改變勢能 的平均速度...........................43 圖4-5改變勢能 的隨機性.............................43 圖4-6加入不同外力的平均速度........................44 圖4-7加入不同外力的隨機性..........................44 圖4-8不同 下比較的平均速度.........................45 圖4-9不同 下比較的隨機性...........................45 圖4-10改變溫差 的平均速度..........................46 圖4-11改變溫差 的隨機性............................46 圖4-12不同 的平均速度..............................47 圖4-13不同 的隨機性................................47 圖4-14改變低溫 的平均速度..........................48 圖4-15改變低溫 的隨機性............................48 圖4-16勢能移動一個 距離示意圖......................49 圖4-17低溫高溫對平均速度的影響.....................49 圖4-18高溫低溫對平均速度的影響.....................50 圖4-19低溫高溫對隨機性的影響.......................50 圖4-20高溫低溫對隨機性的影響.......................51

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