Improving the density of jammed disordered packings using ellipsoids
Improving the density of jammed disordered packings using ellipsoids
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DOI：
10.1126/science.1093010
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发表时间：
2004-02-13
期刊：
影响因子：
56.9
通讯作者：
Chaikin, PM
中科院分区：
文献类型：
--
作者：
Donev, A;Cisse, I;Chaikin, PM
包装问题，如如何密集的对象可以填补一个体积，是最古老的和持久的问题在数学和科学。对于相等的球面，最近才证明面心立方晶格具有最高可能的堆积分数φ =pi/root 18，约为0.74。众所周知，某些无规（无定形）堵塞填料的φ约为0.64。在这里，我们通过实验和一个新的模拟算法表明，椭球体可以随机包装更密集的高达φ =0.68至0.71的椭球体的纵横比接近的M&M的椭圆形，甚至接近φ approximate到0.74的椭球体与其他纵横比。我们认为，更高的密度是直接相关的每个颗粒的自由度的数量更高，因此，机械稳定的包装所需的颗粒接触的数量更大。我们测量了每个颗粒的接触数，对于我们的球体，Z约为10，而对于球体，Z约为6。我们的结果对广泛的科学学科具有影响，包括颗粒介质和陶瓷的性质、玻璃形成和离散几何。
Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction phi=pi/root18approximate to0.74. It is also well known that certain random (amorphous) jammed packings have phiapproximate to0.64. Here, we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely-up to phi=0.68 to 0.71 for spheroids with an aspect ratio close to that of M&M's Candies-and even approach phiapproximate to0.74 for ellipsoids with other aspect ratios. We suggest that the higher density is directly related to the higher number of degrees of freedom per particle and thus the larger number of particle contacts required to mechanically stabilize the packing. We measured the number of contacts per particle Zapproximate to10 for our spheroids, as compared to Zapproximate to6 for spheres. Our results have implications for a broad range of scientific disciplines, including the properties of granular media and ceramics, glass formation, and discrete geometry.