Fundamental structural characteristics of planar granular assemblies: Self-organization and scaling away friction and initial state.
Fundamental structural characteristics of planar granular assemblies: Self-organization and scaling away friction and initial state.
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平面颗粒组件的基本结构特征：自组织和缩放摩擦和初始状态。
DOI：
10.1103/physreve.95.032905
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Matsushima T
中科院分区：
文献类型：
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作者：
Matsushima T
颗粒系统的微观组织是其宏观行为的最重要的决定因素。在这里，我们确定的基本因素，确定这样的微观结构的统计，使用数值实验，以获得一个普遍的理解。实验包括制备和压实各向同性的多分散摩擦盘的二维颗粒集合体和分析出现的统计性质的四边形颗粒固体的基本结构元素。对四边形的关注是因为已经发现它们的体积的统计显示出有趣的普适特征[T。Matsushima和R. Blumenfeld，Phys. Rev. Lett. 112，098003（2014）PRLTAO0031-900710.1103/PhysRevLett.112.098003]。的结构和包装分数的晶间摩擦和初始状态的依赖性进行了分析，并发现了一些有意义的结果。（i）的平均四边形体积的解析公式推导出的三个宏观量：平均配位数，包装分数，和rattlers分数。(ii)我们推导出一个独特的，初始状态独立的平均配位数和无响尾蛇包装分数之间的关系。该关系在一系列不同的系统中得到数值支持。(iii)我们崩溃的四分之一体积分布从所有系统到一条曲线上，我们验证，他们都有一个指数尾。(iv)的性质的四边形体积分布的分解成条件分布的体积给定的细胞顺序，我们发现，这些也崩溃到一个单一的曲线。(v)我们发现，平均四边形体积随颗粒间摩擦系数的增加而减小，这种效应在高阶细胞中是突出的。我们认为，这种现象是由于稳定的不规则形状的细胞的概率增加，我们测试这一点使用一个由此开发的自由细胞分析模型。我们的结论是，在原则上，微观结构特征主要由包装程序，而晶间摩擦和初始状态的影响是可以缩放的细节。然而，机械稳定性约束稍微抑制了小四边形体积的发生，这种效果的大小确实取决于摩擦。我们详细量化这种依赖性和偏差，它导致这些细胞从一个确切的崩溃。(vi)我们认为，我们的研究结果强烈支持的观点，系综颗粒统计力学不满足传统的统计力学的统一测量假设。结果（i）-（iv）已在上述参考文献中报道，并在此进行回顾和阐述。
The microstructural organization of a granular system is the most important determinant of its macroscopic behavior. Here we identify the fundamental factors that determine the statistics of such microstructures, using numerical experiments to gain a general understanding. The experiments consist of preparing and compacting isotropically two-dimensional granular assemblies of polydisperse frictional disks and analyzing the emergent statistical properties of quadrons—the basic structural elements of granular solids. The focus on quadrons is because the statistics of their volumes have been found to display intriguing universal-like features [T. Matsushima and R. Blumenfeld, Phys. Rev. Lett. 112, 098003 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.098003]. The dependence of the structures and of the packing fraction on the intergranular friction and the initial state is analyzed, and a number of significant results are found. (i) An analytical formula is derived for the mean quadron volume in terms of three macroscopic quantities: the mean coordination number, the packing fraction, and the rattlers fraction. (ii) We derive a unique, initial-state-independent relation between the mean coordination number and the rattler-free packing fraction. The relation is supported numerically for a range of different systems. (iii) We collapse the quadron volume distributions from all systems onto one curve, and we verify that they all have an exponential tail. (iv) The nature of the quadron volume distribution is investigated by decomposition into conditional distributions of volumes given the cell order, and we find that each of these also collapses onto a single curve. (v) We find that the mean quadron volume decreases with increasing intergranular friction coefficients, an effect that is prominent in high-order cells. We argue that this phenomenon is due to an increased probability of stable irregularly shaped cells, and we test this using a herewith developed free cell analytical model. We conclude that, in principle, the microstructural characteristics are governed mainly by the packing procedure, while the effects of intergranular friction and initial states are details that can be scaled away. However, mechanical stability constraints suppress slightly the occurrence of small quadron volumes in cells of order, and the magnitude of this effect does depend on friction. We quantify in detail this dependence and the deviation it causes from an exact collapse for these cells. (vi) We argue that our results support strongly the view that ensemble granular statistical mechanics does not satisfy the uniform measure assumption of conventional statistical mechanics. Results (i)–(iv) have been reported in the aforementioned reference, and they are reviewed and elaborated on here.
超静定结构：超静定结构理论简介
影响因子：
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作者：
J. Matheson
通讯作者：
J. Matheson