Granular Dynamics in Uniform and Non-Uniform Potential Fields

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姓名

蕭義霖(YI-LIN HSIAO) 查詢紙本館藏

畢業系所

生物物理研究所

論文名稱

(Granular Dynamics in Uniform and Non-Uniform Potential Fields)

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摘要(中)

在我們的實驗中，研究在垂直震盪系統中單一顆粒體的布朗運動(Brownian Motion)。在有規則粗糙的底板上給予不同的震盪條件，顆粒體的速度分佈會符合高斯分佈(Gaussian distribution)且會均勻分散在整個環形範圍內(360 度)。我們選擇單一顆粒體和鐵棒做為實驗對象。捨棄了顆粒體之間的交互作用，才能更明確的研究位能場對於布朗運動的影響。
在對稱的位能場中，鋼體球的分佈密度和位能場關係是符合馬克士威－波茲曼統計(Maxwell-Boltzmann statistics)。如果考慮熱力學系統，位能場是相對於磁場，而有效溫度是相對於速度平方。結論一樣會符合馬克士威－波茲曼統計。其次，脫離位能井的行為也一併被記錄下來。其脫離位能井的時間在克拉瑪脫離理論(Kramer Escape Theory)下跟有效溫度是相關的。我們還針對鋼體球攀爬位能井的行為做討論。再來，我們把鋼體球放入不對稱的位能場中，剛體球的分佈密度和位能場的關係一樣是符合馬克士威－波茲曼統計。在鋼體球攀爬位能井的觀察中，我們分別記錄了在攀爬不同梯度的位能壁其所需要的時間，和定量的時間下成功攀爬上去的次數。最後，我們使用了圓柱形的實驗顆粒來做跟位能場有關的實驗。圓柱相對於磁場的位置和其旋轉的位置將被記錄下來，並且描述其運動行為。

摘要(英)

Brownian motion which is excited by the vertical vibration is studied with a single particle in our experiment. The particle’s probability velocity distributions match the Gaussian distribution and the position distribution is homogeneous with different vibration condition in the annular container on a regular rough bottom. We setup a single hard sphere and iron bar to do the experiment. Without interaction between the particles, the effect of the potential field in Brownian motion is observed directly.
In a symmetric potential field, we find that the hard sphere’s density and the magnetic field are correlated with the Maxwell-Boltzmann statistics. Following the thermodynamics, the potential energy E is related to the intensity of magnetic field B and the effective temperature kT is related to the average velocity . The Maxwell-Boltzmann statistics is also used in this discussion. Second, we record the escape behavior in the potential well. The escape time T is related to the effective temperature kT under the Kramer escape theory. We also try to find the relation between the climbing behavior and potential field. Next, we put the single hard sphere in an asymmetric potential field. The sphere’s behavior is also correlated with the Maxwell-Boltzmann statistics. With climbing the asymmetric potential field, we record the time and quantity that the sphere climbs the asymmetric potential well that the distance is defined by the location or the magnetic field. Finally, the cylinder is used to do the experiment with potential field. The relation between position and orientation is recorded and the real motion behavior is described.

關鍵字(中)

★ 顆粒體動力學
★ 不對稱位能場
★ 垂直震盪
★ 複雜系統

關鍵字(英)

★ Granular dynamics
★ asymmetric potential field
★ vertical vibrate
★ complex system

論文目次

1 Introduction 1
1.1 Maxwell-Boltzmann Statistics . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Kramer Escape Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Apparatus and Methods 5
2.1 Experiment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Vibrate contain . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Magnetic eld . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Measure of Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 General Brownian Motion . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 Eect of Magnetic Field - Sphere . . . . . . . . . . . . . . . . . 12
2.2.3 Rod Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Results and Discussions 18
3.1 Single Sphere in the Symmetric Potential Field . . . . . . . . . . . . . . 18
3.2 Single Sphere in the Asymmetric Potential Field . . . . . . . . . . . . . 28
3.3 The Rod in the Symmetric Potential Field . . . . . . . . . . . . . . . . 34
4 Conclusion 38
Bibliography 40

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指導教授

陳培亮(PEI-LONG CHEN)

審核日期

2013-7-29

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