博碩士論文 962202009 詳細資訊




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姓名 黃冠華(Kuan-Hua Huang)  查詢紙本館藏   畢業系所 物理學系
論文名稱 剛體球在不對稱垂直震盪系統中的動力學行為
(Hard Spheres Dynamics in Asymmetrical Vertical Vibrating Systems)
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摘要(中) 我們觀察鋼球在三種不同的不對稱且垂直震盪的環形容器中的行為。首先,這個環形的容器底部被刻鑿了放射狀的不對稱溝槽,使得球會往一個方向移動。我們測量了在不同的震盪振幅與頻率下的平均角速度。減掉平均速度之後的速度分佈符合Gaussian 分佈,而減掉平均速度之後的位置平方與時間的關係,使我們獲得了擴散係數。假設底板給球的推進力為Fd,而此力所建立的位能場為U=Fd Rθ當記錄球位置的分佈機率,再用Maxwell-Boltzmann 與它匹配,我們便可知道這個力的大小。搭配上之前求出的平均速度我們可以得到溫度與摩擦係數的比值。將這個比值與擴散係數做比較,可得知此實驗系統符合Einstein-Smoluchowski 理論。我們也將許多顆球放入系統中,用磁場改變球的密度,它們集體的行為,例如等效的溫度等,將會因為密度的不同而改變。在其他的實驗中,鋼球將被放入不對稱邊界的容器中,平均速度與震動振幅的關係將會被記錄下來。而當鋼球被放入有不對稱位能場的容器中時,它的動力學行為隨著振幅的增加有三個步驟,從被困住,前進,到隨機移動。移動的軌跡顯示,其主要的原因是磁場可以幫助改變方向,使它可以在容器中移動較長的距離,而這個機制在兩個方向是不對稱的,這使得球可以朝某個特定方向移動。在這三種不對稱的系統中,球的速度都不會因提高振動的振幅而無限量的增加。
摘要(英) We observe the dynamics of steel spheres in three kinds of asymmetric annular cells vibrated vertically. First, the annular cell is carved with asymmetric troughs in the bottom and the spheres are continuously driven to move in one direction. The average angular velocities of the spheres in different vibration frequencies and amplitudes are measured. The velocity distribution of the deviation from the average velocity is shown to follow the Gaussian distribution. According to the displacement deviation from the average velocity, the diffusion constant is obtained. When the spheres are confined in one region of the cell, we assume the potential isU=Fd Rθand fit the density distribution with Boltzmann distribution to get the driving force Fd. Using the driving force and the average velocity, we can get the ratio of the effective temperature and the drag coefficient. Comparing this ratio with the diffusion constant, the behavior fit Einstein-Smoluchowski theory. We put multiple spheres in the cell and add magnet under the cell to control the magnetic field which change the density distribution of the spheres. It is found that the collective behaviors like effective temperature change in different densities. The relation between the average angular velocity and the non-uniform density is also reported. In other experiments, the sphere is put in the asymmetrical boundary systems. The sphere transports. The relation of the vibrate amplitudes and the average velocity is brought up. When we add asymmetrical magnetic field on a symmetrical system. The behavior of the sphere change from trapped, transport, to moving randomly. The trajectories of the sphere show how the magnetic field change the sphere’s direction. This mechanism is asymmetrical in two direction which makes the sphere move in one direction. The transport velocity can’t increase infinite in these three methods.
關鍵字(中) ★ 複雜流體
★ 粒狀流體
★ 垂直震盪
★ 不對稱系統
關鍵字(英) ★ granular fluid
★ complex fluid
★ vertical vibrate
★ asymmetrical system
論文目次 1 Introduction 1
1.1 Maxwell-Boltzmann distribution. . . . . . . . . . . . . . . . . 3
1.2 Einstein-Smoluchowski theory . . . . . . . . . . . . . . . . . . 5
2 Apparatus and experiment 8
2.1 Whole apparatus . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Composition of the cells . . . . . . . . . . . . . . . . . . . . . 8
2.3 The measurement of the experiment . . . . . . . . . . . . . . 13
2.3.1 In symmetric container . . . . . . . . . . . . . . . . . . 13
2.3.2 In asymmetric bottom container . . . . . . . . . . . . 13
2.3.3 Confined region in asymmetric bottom container . . . 15
2.3.4 Horizontal calibration . . . . . . . . . . . . . . . . . . 16
3 Result and Discussion 19
3.1 One sphere in the asymmetrical bottom system . . . . . . . . 19
3.2 Multiple spheres in the asymmetrical bottom system . . . . . 23
3.3 Multiple spheres in the asymmetrical bottom and potential
system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4 The asymmetrical boundary system . . . . . . . . . . . . . . . 27
3.5 The asymmetrical potential system . . . . . . . . . . . . . . . 29
4 Conclusion 43
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指導教授 陳培亮(Peilong Chen) 審核日期 2010-8-5
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