布朗運動時顆粒體的能量均分現象

Abstract

我們研究宏觀下被釐米大小的顆粒氣體(視為分子)所環繞的物體(公分大小)之布朗運動(Brownian motion)行為，當振動台給予系統垂直振動時，我們利用高速攝影技術來追蹤物體在水平面之位置、速度、方向及角速度。藉由這些影像，我們測量物體在水平面之兩個方向的移動及轉動的平均動能，令人驚訝的是，我們發現在誤差範圍下物體的移動自由度和轉動自由度的平均動能是相同的，即在非平衡態下的顆粒體系統中物體是遵守能量均分定律的。之後，我們做了二維分子動力學模擬，但是發現除非粒子的表面極度粗糙否則粒子無法有能量均分現象。We study the Brownian motion of a macroscopic (centimeter size) granular object surrounded by a granular gas composed of millimeter size spheres acting as the molecules. While the system is vibrated vertically by an electromagnetic shaker, we use a fast camera to capture the temporal variations of the horizontal position and the orientation from above. From the captured image sequences, we manage to measure the translational and the rotational velocities in the horizontal plan. Suprisingly, we find that the average kinetic energies carried by the translational degrees of freedom and the rotational degree of freedom of the disk are the same within experimental uncertainty. Hence energy equipartition is found to valid even for nonequilibrium granular systems. We find granular object obey Equipartition law. Then, we do the two dimentional molecular dynamic simulation and we find granular object won’t obey Equipartition law unless the granular object surface is extremely rough.