Emergence of Gamma distributions in granular materials and packing models
Emergence of Gamma distributions in granular materials and packing models
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DOI：
10.1103/physreve.77.021309
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发表时间：
2008-02-01
影响因子：
2.4
通讯作者：
Di Matteo, T.
中科院分区：
文献类型：
--
作者：
Aste, T.;Di Matteo, T.
我们研究了在实验和数值模拟中，用不同方法制备的等尺寸球形填料的体积涨落分布。我们发现，局部体积（Voronoi细胞）的分布，也是全球体积（整个样本）的分布遵循非常好的移位和重新缩放的伽玛分布，我们命名为一个k-Gamma分布。这种协议是强大的，在广泛的包装馏分，它是观察到几个不同的系统。该分布的特征在于平均填充分数和形状参数“k”，其对结构组织的变化非常敏感。统计力学方法预测这样的k-Gamma分布在统计平衡，它链接的参数k的数量的基本细胞在系统准备过程中交换体积。本文还讨论了k的当量及其与“颗粒温度”的关系。
We study the distribution of volume fluctuations in experiments and numerical simulations concerning equal-sized sphere packings prepared with different techniques. We show that the distribution of the local volumes (Voronoi cells) and also the distributions of the global volumes (whole samples) follow remarkably well a shifted and rescaled Gamma distribution that we name a k-Gamma distribution. Such agreement is robust over a broad range of packing fractions and it is observed for several distinct systems. This distribution is characterized by the average packing fraction and a shape parameter "k" which is very sensitive to changes in the structural organization. A statistical mechanics approach predicts such k-Gamma distribution at statistical equilibrium and it links the parameter k with the number of elementary cells which are exchanging volume during the system preparation. The thermodynamical equivalent of k and its relation with the "granular temperature" are also discussed.