臺灣博碩士論文加值系統

受力的布朗粒子在通道中的傳輸是我們所要探討的主題。若傳輸的外在幾何限制隨著位置而改變，其效果就相當於對運動加上一道熵壘，相較於能量壘的情形，此時的傳輸過程會展現出相當不同的特徵行為，包括一種特有的標尺體制的出現。本文的主要工作是提出一個簡單的隨機行走模型，對熵壘傳輸過程作了離散化的描述後，再以數值方法檢驗那些從連續性描述得到有關熵壘傳輸的結論。我們的結果顯示，這類空間受限的傳輸，在離散化的描述下，除了會繼續保有部分已知的熵壘傳輸特徵之外，還另外具有在連續描述下所看不到的獨特行為，如粒子流會因受力程度的不同而對溫度有截然不同的相依關係，及粒子的遷移率對外力也不再是單調地依賴，而是存在一個最大值。此外，結果也顯示離散化的作法會導致標尺體制的破壞，然而透過降低模型的離散性，則可以得到一個關於標尺體制是如何地在連續化的過程中突現的簡單描述。

It''s a known fact that driven Brownian transport through a geometrical landscape exhibits characteristic dependence of current and diffusion upon both temperature and a driving force as well as a remarkable existence of a scaling regime. From a different standpoint, this paper has investigated a neat random-walk model aiming at uniformly-driven transports under geometrical confinement and yet subject to discrete description. The results show that in this discrete modeling, some of those representative characteristcs of entropic transport retain while the others, such as scaling behavior, don''t. In addition, two characteristics are observed which do not exist in the continuous model: a reverse dependence of current on noise strengths, and the existence of mobility optimization.

1 緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 簡介與背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 熵壘傳輸的連續描述、方法及主要結果. . . . . . . . . . . . . . . . . . 2
2 隨機行走模型及其傳輸性質. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 模型設定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 基本傳輸性質. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.1 平坦邊界的傳輸行為. . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 變化邊界的傳輸行為. . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2.1 粒子流遷移率. . . . . . . . . . . . . . . . . . . . . . 10
2.3.2.2 擴散係數. . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.2.3 不同的邊界條件的影響. . . . . . . . . . . . . . . . . 17
3 標尺體制. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1 引言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 連續與離散模型的對應. . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 標尺體制的數值檢驗. . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.1 總結. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2 討論與展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
A 數值計算描述. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
A.1 一般性討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
A.2 計算與數值檢驗. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
B 反射邊界條件的數值結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

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