臺灣博碩士論文加值系統

在這篇論文，我們用最大熵值法來研究加以震盪的氣態粒狀系統的速度分佈。這類系統的速度分佈偏離傳統的馬克斯威-波茲曼，其一般特性是具有較多高能量粒子。我們選擇適當的系統約束量以應用最大熵值法，並試圖給這種分佈一個物理解釋。分佈的形式是P(v)=Cexp[-av⁴-bv-cv-dv]，至於係數a, b, c 和 d 我們只能決定他們的比例關係。而與模擬的結果相比之下還無法得到好的驗證。除此之外，我們也觀察到速度分佈和顆粒大小、單位體積粒子數和恢復係數有關，並且在某個程度下與外界的振盪頻率及振盪振幅無關。我們也探討了粒狀物體在位能井中的空間分佈表現。

The velocity distribution function of a granular gas system driven by the vibrating boundary is studied with maximum entropy principle. It is a well-known result that the velocity distribution of such system deviated from the Maxwell-Boltzmann one and had a characteristic over-populated high energy tail. We applied maximum entropy principle with suitable chosen constraints to give a possible explanation of this phenomenon. The distribution is given by P(v)=Cexp[-av⁴-bv³-cv²-dv] where only the ratio of these parameters can be determined. Yet, agreement with simulation data was not certain. Besides this, the velocity distribution depends on the size of granular particles, number density, and the coefficient of restitution but not on external driving frequency and amplitude. The spatial distribution of granules in a potential well is also investigated.

1 Introduction . . . 1
2 Kinetic Theory and Maximum Entropy Formalism . . . 4
2.1 Homogeneous Enskog-Boltzmann equation . . . . . . 4
2.2 MaximumEntropy Formalism . . . . . . 6
3 Molecular Dynamics simulation . . . 8
4 MEF Estimate . . . 10
4.1 Calculation of deltaE/deltaT . . . . . . 10
4.1.1 Near-elastic approximation . . . . . . 13
4.1.2 A crude approximation for inelastic cases . . . . . . 18
4.1.3 Asymptotic behavior for deltaE/deltaT at high energy tails . . . . . . 24
5 Discussion on inelasticity, driving frequency, particle size, number
density and granules in a potential well . . . 26
5.1 Driving frequency and amplitude . . . . . . 26
5.2 Inelasticity . . . . . . 26
5.3 Number Density . . . . . . 28
5.4 Particle size . . . . . . 30
5.5 Granules in a potential well . . . . . . 35
6 Conclusions . . . 43

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