臺灣博碩士論文加值系統

我們將短顆粒鍊置於可讓其作繞行與垂直運動的準二維環形軌道中，施加垂直振動場於其上，同時以兩台正交的攝影機側錄顆粒鍊的運動。我們發現，短顆粒鍊在垂直振動場下的水平運動與其形狀有密切的關聯：當顆粒鍊在震動週期中維持棒狀均勻地直上直下時，其位移為緩慢的隨機漫步；當顆粒鍊在震動週期中一端翹起時，其會沿著翹起端的方向以定速前行；而當顆粒鍊在震動週期中兩端皆翹起時，其運動為超擴散運動，且其週期與週期間的運動有相當程度的關聯性。此外，顆粒鍊三形態的水平運動特性隨著實驗控制參數的改變大致相同。

We put a short granular chain in a qusai-2D circular channel and apply a vertical sinusoidal vibration on it. We set up 2 side-viewing cameras with orthogonal orientation to record the motion of the chain and discover that the horizontal motion of a short granular chain is closely related with its shape in vibrating cycles. When the chain keeps rod-like shape during vibration cycles, it behaves like small step random walk; when one of the ends rises up during vibration cycles, the chain moves ballistically; when both of the ends rise up, the chain behaves as a larger step random walk, but its horizontal motions of adjacent vibration cycles are related. Moreover, the character of the horizontal motion of 3 states keep consistent while the control parameters change.

論文口試委員審定書 II
誌謝 III
中文摘要 iv
Abstract v
目錄 vi
圖片錄目 ix
表格錄目 x
符號說明 xi
Chapter 1 緒論 1
1.1 隨機漫步介紹 1
1.2 歷史回顧 2
1.3 結構安排說明 7
Chapter 2 實驗架設與影像分析 9
2.1 實驗架設 9
2.1.1 系統設置 10
2.1.2 影像錄製 11
2.2 顆粒鍊定位 13
2.2.1 顆粒鍊的位置及位移 13
2.2.2 影像尺度量測 14
2.2.3 攝影重疊區域的銜接 16
2.2.4 空間精確度討論 17
2.3 形態（State）及區段（Interval）定義 19
2.3.1 形態（State）定義 19
2.3.2 區段（Interval）定義 21
2.3.3 顆粒鍊行為概述 21
Chapter 3 水平運動與形態之關聯 24
3.1 基本分析 24
3.1.1 顆粒鍊軌跡（Trajectories） 24
3.1.2 位移分佈直方圖（Histogram） 25
3.1.3 方均位移（Mean Square Displacement, MSD） 25
3.2 形態0的研究 27
3.2.1 顆粒鍊軌跡 27
3.2.2 位移分佈 28
3.2.3 方均位移 29
3.3 形態1的研究 31
3.3.1 顆粒鍊軌跡 31
3.3.2 位移分佈 32
3.3.3 方均位移 34
3.4 形態2的研究 35
3.4.1 顆粒鍊軌跡 35
3.4.2 位移分佈 36
3.4.3 方均位移 37
3.5 其他分析 38
3.5.1 位移延滯圖（Lag plot） 38
3.5.2 位移與顆粒鍊兩端高度差關聯探討 40
3.5.3 位移－時距之散佈圖（Scatter Plot） 42
3.6 小結 45
Chapter 4 控制參數的角色及其他評估 48
4.1 振動強度（Γ） 48
4.1.1 Γ對形態區段長度的影響 48
4.1.2 Γ對位移分佈的影響 51
4.1.3 Γ對方均位移的影響 52
4.2 顆粒數（N） 53
4.2.1 顆粒數對形態分佈的影響 54
4.2.2 顆粒數對位移分佈的影響 55
4.2.3 顆粒數對方均位移的影響 57
4.3 系統不對稱性的影響評估 58
4.3.1 基板水平的影響評估 58
4.3.2 顆粒鍊的不對稱性 60
4.4 小結 60
Chapter 5 結果與討論 63
參考資料 64
附錄 66
附錄一 hcut對形態判定的影響 66
附錄二 線上附錄 67

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