Statistical-mechanical characteristics of dense planar granular systems
Statistical-mechanical characteristics of dense planar granular systems
复制标题
致密平面颗粒系统的统计力学特性
DOI：
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发表时间：
2012
期刊：
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通讯作者：
R. Blumenfeld
中科院分区：
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作者：
Rebecca Hihinashvili;R. Blumenfeld
我们演示了使用的结构和统计特性的方法对两种类型的平面光盘包。一个是平均配位数为5.20的非常密集的包，另一个是平均配位数为4.0的非常密集的包。除了限制后一种中的平均配位数之外，不同的包类型通过相同的沉积过程构造，并且具有相同的圆盘尺寸分布，用于公平的统计比较。我们表明，这两种类型的收敛极限统计量，这些极限统计量是不同的。我们分析的极限统计和比较两种类型的包，表明差异直接相关的平均配位数的差异。然后，我们定量地发现两种包类型的（逆）压缩性之间的差异：$${\frac{1}{X_{5.2}} - \frac{1}{X_{4}} = 1.5\pm 0.05}$$。这一明确的结果有力地支持了爱德华兹方法的有效性，并支持它作为一个有用的工具来定量地描述粒度系统。特别是，它也铺平了道路，量化难以捉摸的紧凑性。
We demonstrate the use of a structural and statistical characterisation method on two types of planar disc packs. One is a very dense pack of mean coordination number 5.20 and the other of mean coordination number 4.0. Except for constraining the mean coordination number in the latter one, the different pack types were constructed by the same deposition process and had the same disc size distribution, for a fair statistical comparison. We show that the two types converge to limit statistics and that these limit statistics are different. We analyse the limit statistics and compare between both types of packs, demonstrating that the differences are directly related to the difference in the mean coordination numbers. We then find quantitatively the difference between the (inverse) compactivities of the two pack types: $${\frac{1}{X_{5.2}} - \frac{1}{X_{4}} = 1.5\pm 0.05}$$ . This explicit result supports strongly the validity of Edwards approach and underpins it as a useful tool to characterise granular systems quantitatively. In particular, it also paves the way to quantify the elusive compactivity.