Structural characterization and statistical properties of two-dimensional granular systems.
Structural characterization and statistical properties of two-dimensional granular systems.
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二维颗粒系统的结构表征和统计特性。
DOI：
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发表时间：
2008
期刊：
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通讯作者：
P. King
中科院分区：
文献类型：
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作者：
G. Frenkel;R. Blumenfeld;Zdenek Grof;P. King
最近开发的方法用于分析平面无序颗粒组件的结构。在此方法中，组件被划分为与晶粒或称为四边形的更基本元素相关的体积元素。我们的第一个目标是比较四元或晶粒描述对于熵表征的相对有用性。第二个目标是使用该方法更好地理解摩擦以及晶粒形状和尺寸分布在确定无序结构中的不同作用。我们的第三个目标是量化用于熵分析的基本体积的统计数据。我们报告以下结果。 (1) 作为熵形式主义的基本“准粒子”，四元组比晶粒更有用。 (2) 晶粒和四边形体积分布都显示出不平凡的峰和肩。这些只能在特定条件分布的四元组背景下才能理解。 (3) 正如预期的那样，增加摩擦力会增加平均单元尺寸，但不会影响条件分布，这在基本层面上得到了解释。我们得出的结论是，颗粒尺寸和形状分布决定了条件分布，而它们的相对重量则由摩擦力和堆积形成过程决定。这清楚地区分了摩擦力和颗粒形状分布所起的不同作用。 (4) 四元体体积的分析表明，伽玛分布被认为可以很好地描述泡沫状结构，但对于一般颗粒系统来说过于简单化。 (5) 获得了四方体“态密度”和晶粒体积的一系列定量结果，并演示了结构特性期望值的计算。将颗粒系统的结构特征与数值生成的泡沫状狄利克雷-沃罗诺伊结构进行比较。
A recently developed method is used for the analysis of structures of planar disordered granular assemblies. Within this method, the assemblies are partitioned into volume elements associated either with grains or with more basic elements called quadrons. Our first aim is to compare the relative usefulness of description by quadrons or by grains for entropic characterization. The second aim is to use the method to gain better understanding of the different roles of friction and grain shape and size distributions in determining the disordered structure. Our third aim is to quantify the statistics of basic volumes used for the entropic analysis. We report the following results. (1) Quadrons are more useful than grains as basic ''quasiparticles'' for the entropic formalism. (2) Both grain and quadron volume distributions show nontrivial peaks and shoulders. These can be understood only in the context of the quadrons in terms of particular conditional distributions. (3) Increasing friction increases the mean cell size, as expected, but does not affect the conditional distributions, which is explained on a fundamental level. We conclude that grain size and shape distributions determine the conditional distributions, while their relative weights are dominated by friction and by the pack formation process. This separates sharply the different roles that friction and grain shape distributions play. (4) The analysis of the quadron volumes shows that Gamma distributions, which are accepted to describe foamlike structures well, are too simplistic for general granular systems. (5) A range of quantitative results is obtained for the ''density of states'' of quadron and grain volumes and calculations of expectation values of structural properties are demonstrated. The structural characteristics of granular systems are compared with numerically generated foamlike Dirichlet-Voronoi constructions.