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研究生: 曾煒軒
Tzeng, Wei-hsuan
論文名稱: 布朗粒子在狹窄通道中的傳輸行為-通道幾何形狀的影響
Transport of Brownian particle in narrow channel-Effect of channel geometry
指導教授: 杜其永
To, Ki-Wing
張宜仁
Chang, Yi-Ren
學位類別: 碩士
Master
系所名稱: 物理學系
Department of Physics
論文出版年: 2019
畢業學年度: 107
語文別: 中文
論文頁數: 75
中文關鍵詞: 布朗運動不對稱通道不均向性通道布朗引擎
英文關鍵詞: Brownian motion, Asymmetrical channel, Anisotropic channel, Brownian motor
DOI URL: http://doi.org/10.6345/NTNU201900104
論文種類: 學術論文
相關次數: 點閱:111下載:14
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  • 在非平衡態中,布朗粒子在有不對稱性與不均向性的通道中運動時,粒子的運動會出現往固定方向漂移的現象。我們以通道的寬度變化形成的腔室形狀不對稱來造成不對稱性,而不均向性則由通道底部溝槽產生。我們製作了風箏型與三角形腔室形狀的通道來比較型狀對漂移運動的影響。我們發現三角形相對於風箏型的通道反而使其中的粒子傳輸速度變慢。並且也較大程度的限制了粒子的隨機擴散,使擴散係數也較低。透過分析兩通道中粒子的瞬時速度分佈,我們發現能量在三角形通道中較難傳導到縱向的運動中。使得粒子的漂移與擴散都在三角形通道中都較慢。

    In non-equilibrium system, the drift motion happens as a Brownian particle moving in the channel with asymmetry and anisotropy. The asymmetry was given by asymmetrical shape of cells form the channel. Anisotropy was given by grooves built along the channel. We made two channels with different cell shapes, kite shape and triangle, to compare the effect on drift motion caused by geometry of channel. We found particle in triangular channel had slower drift and diffusion than particle in kite shape channel with the same energy input. By analysing the instantaneous velocity distribution, We found that it was more difficult to transfer energy from transverse direction to longitudinal direction for particle in triangular channel. With less energy, particle drifted slower in triangular channel than particle in kite shape channel.

    1緒論 1 1.1狹窄通道中的布朗運動 3 1.2布朗引擎 4 1.3研究回顧 5 1.4實驗簡介 6 1.5論文大綱 7 2實驗方法 9 2.1不對稱通道 10 2.1.1不對稱通道幾何形狀 10 2.1.2不均向性的底部 11 2.2實驗架設 12 2.3實驗步驟 12 2.4數據擷取與處理 13 2.4.1原始影像中的粒子位置擷取 13 2.4.2漂移速度與擴散係數的測量 14 2.4.3瞬時速度的測量 15 2.4.4位置分佈、逃脫時間的測量 15 2.5通道等效驅動力的測量 16 3實驗結果 27 3.1漂移速度、擴散係數與振動參數間對照關係 29 3.2橫向瞬時速度分佈與方均根速率與通道形狀無關 31 3.3橫向方均根速度與最大加速度成對數關係 31 3.4方均根速率與漂移速度、擴散係數無函數關係 33 3.5漂移速度、擴散係數、方均根速率和粒子分佈的關係 34 3.6逃脫時間的分佈符合馬可夫過程 35 3.7粒子在通道中所受驅動力 36 4討論與結論 55 4.1造成粒子漂移的來源 56 4.2漂移速度和擴散係數對熱速度的關係 58 4.3通道形狀與其中布朗粒子的受力 58 4.4結論 59 參考文獻 60 附錄A 65

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