顆粒物質在自然界是極為常見的，小到海邊的沙粒，大到冰洋中的浮冰等，都屬於顆粒物質的範疇。在農業上，顆粒物質的性質對倉儲與輸送的過程與效率等，都具有決定性的影響。但到目前為止，其物理性質還有許多尚未被人們清楚了解的地方。我們利用透明壓克力製成薄盒子，並在裡面放入塑膠球後，放在震動台上垂直震動，來探究類二維顆粒氣體在水平投影的動力行為。使用高速攝影機與影像處理軟體，我們追蹤到每顆球的位置，並進一步分析其與出發點的平均平方位移、速度分佈與過程中的碰撞次數等。我們發現球本身呈現出隨機行走與擴散的行為。進一步的探究發現在中低密度時，不管是擴散係數或其方均根速度都隨著密度增加而增加。此一結果不同於高密度時，與理想氣體下的氣體動力論預測的變化接近。我們進一步的分析與考量球與球碰撞中的能量耗散行為，試著去提出一個簡單模型，將不同種類的複雜碰撞行為簡化為兩種不同溫度的熱浴，並且成功的計算出我們的實驗結果。這暗示了儘管跳躍球系統的能量是非守恆態，但引進能量守恆時的物理定律來簡化系統的描述是可能的。

[1] Heinrich M. Jaeger, Sand, Jams and Jets, Physics World 18, 34-39 December (2005)
[2] Duran, J., Reisinger A., Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials, Springer-Verlag New York, Inc., New York, ISBN 0-387-98656-1, November (2000)
[3] Richard, P, Slow relaxation and compaction of granular systems, Nature Materials 4, 121–128, February (2005)
[4] Rodhes, M, Principles of powder technology, Wiley, Chichester, England; New York, ISBN 0-471-92422-9, (1990)
[5] Happel, J. and Brenner H., Low Reynolds number hydrodynamics, Prentice-Hall, (1965)
[6] Heinrich M. Jaeger and Sidney R. Nagel, Granular solids, liquids, and gases, Rev. Mod. Phys. 68, 1259 – 1273, (1996)
[7] Florence Rouyer and Narayanan Menon, Velocity Fluctuations in a Homogeneous 2D Granular Gas in Steady State, Phys. Rev. Lett. 85, 3676 - 3679 (2000)
[8] W. Losert, D. G. W. Cooper, and J. Delour, A. Kudrolli and J. P. Gollub, Velocity statistics in excited granular media, Chaos 9, 682 (1999)
[9] J. S. Olafsen and J. S. Urbach, Velocity distributions and density fluctuations in a granular gas, Physical Review E Volume 60, Number 3, September (2000)
[10] Klebert Feitosa and Narayanan Menon, Breakdown of Energy Equipartition in 2D Binary Vibrated Granular Gas, Phys. Rev. Lett. 88, 198301 (2002)
[11] Baxter and Olafsen, The temperature of a vibrated granular gas, Granular Matter 9:135–139 (2007)
[12] 0. Zik and J. Stavans, Self-Diffusion in Granular Flows, Europhys. Lett., 16 (3), pp. 255-258, (1991)
[13] Nikolai V. B., Thorsten P., Self-diffusion in granular gases, Physical Review E Volume 61, Number 2, February (2000)
[14] Jaehyuk Choi, Arshad Kudrolli, Rodolfo R. Rosales, and Martin Z. Bazant, Diffusion and Mixing in Gravity-Driven Dense Granular Flows, Physical Review Letters, Volume 92, Number 17, 30 April (2004)
[15] R. D. Wildman, J. M. Huntley, and J.-P. Hansen, Self-diffusion of grains in a two-dimensional vibrofluidized bed, Physical Review E Volume 60, Number 6, December (1999)
[16] V. V. R. Natarajan , M. L. Hunt and E. D. Taylor, Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow, Journal of Fluid Mechanics, 304: 1-25 Cambridge University Press (1995)
[17] Hsiau S. S. ; Hunt M. L., Kinetic theory analysis of flow-induced particle diffusion and thermal conduction in granular material flows, Journal of heat transfer, vol. 115, no3, pp. 541-548 (1993)
[18] P. M. Reis,* R. A. Ingale, and M. D. Shattuck, Caging Dynamics in a Granular Fluid, Phys. Rev. Lett. 98, 188301 (2007)
[19] P. M. Reis,* R. A. Ingale, and M. D. Shattuck, Forcing independent velocity distributions in an experimental granular fluid, Phys. Rev. E 75, 051311 (2007)