布朗馬達 (Brownian motors) 的概念可用來解釋受熱擾力而作機械化學耦合運動的分子馬達如何達成具方向性的運動。其機械化學耦合是利用 ATP 的水解和鍵結來改變分子馬達構形，造成位能的改變而產生機械運動。為了讓布朗馬達產生單方向運動，並且讓速度有效提升，本文採用 Flashing ratchet 和 Diffusion ratchet 耦合的運動模型來模擬布朗馬達的運動情況。
本文使用 Fokker-Planck equation 為運動方程式，解出在變溫情況下的或然率與機率流，再利用文獻[17] Robust 數值演算法計算位能切換過程中的運作模式。此演算法涵蓋精細平衡 (Detailed balance) ，可用來描述具有連續馬可夫過程 (Continuous Markov process) 之性質的跳躍過程(Jump process) 與跳躍率 (Jump rate)，進而求解布朗馬達的運動性質。
採用MATLAB 6.5軟體計算以上描述之方程式及數值演算法，分析布朗馬達在何種變溫模型的運動速度最大，並且討論增加位能振幅和施予外作用力對布朗馬達的平均速度、等效擴散係數與隨機性三種參數的影響。結果顯示布朗馬達於不同變溫情況之位能振幅、外作用力與狀態切換率皆會影響其參數的大小。本文假設四種溫度分布模型，其中的第三種溫度分布模型，即狀態一週期性變溫(低高溫順序)與狀態二高溫之模型的平均速度為四種模型中最大一種，而且平均速度會隨高溫與低溫的溫度比值增加而遞增；由此可知，溫度的變化對於布朗馬達平均速度的大小有所影響。

The concept of Brownian motors may use for to explain how molecular motors take mechanochemistry coupling of the motion to achieve the directive movement when it subjects to thermal fluctuation. The conformation of molecular motors is changed by the mechanochemistry coupling of the motion with hydrolysis of ATP and the binding of ATP. It means that molecular motors generate the change of potential energy and mechanical motion. In order to Brownian motors produce motion in one direction, and increasing the average velocity effectively. This paper uses the coupling model of flashing ratchet and diffusion ratchet to simulate the movement situation of Brownian motors.

The Fokker-Planck equation is the governing equation in this paper, it can be used to solve the probability and the probability flux in different temperature conditions and it also used to calculate working model with potential energy switches between an on and an off state by Robust numerical algorithm in the reference[17]. In the algorithm a continuous Markov process is discretized as a jump process and the jump rates are derived from local solution of the continuous systems which contain the property of detailed balance.

This paper used MATLAB 6.5 to calculate the equations and the numerical algorithm to analyze what kinds of different temperature conditions influences the average velocities of Brownian motors to achieve the maximum value, and to discuss the average velocities, the effective diffusion coefficients and the randomness parameters of Brownian motors with increasing the amplitude of potential energy under external force. The results show that the amplitude of potential energy, the external force and chemical transitions in different temperature conditions influence the values of parameters. This paper assumes four kinds of models of temperature distributions, the average velocity of the third temperature distribution is the miximum value. And the average velocity will increase with increasing temperature ratio. In other words, it will effect the average velocities of Brownian motors in different temperature conditions.

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