Statistical mechanics framework for static granular matter
Statistical mechanics framework for static granular matter
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DOI：
10.1103/physreve.79.061301
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发表时间：
2009-06-01
影响因子：
2.4
通讯作者：
Chakraborty, Bulbul
中科院分区：
文献类型：
--
作者：
Henkes, Silke;Chakraborty, Bulbul
近年来，颗粒材料的物理性质得到了广泛的研究。然而，到目前为止，除了唯象干扰图之外，还没有一个理论框架可以统一地解释这些观测结果。这项工作的重点是静态颗粒物质的情况下，我们已经构建了一个统计系综，反映平衡统计力学。这个合奏，这是基于应力张量的守恒性质，是不同于原来的爱德华兹合奏，并适用于包装的变形颗粒。我们结合联合收割机，它与一个领域的理论分析的包装，其中的领域是艾里应力函数来自力和扭矩平衡条件。在这个框架中，J点的特征在于压力波动的发散刚度。另外，我们提出了一个唯象的平均场理论的干扰过渡，其中包括平均接触数作为一个变量。我们联系这两种方法的背景下，由怀亚特和其他人提出的边际刚性图片。
The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming diagram. This work focuses on the case of static granular matter, where we have constructed a statistical ensemble which mirrors equilibrium statistical mechanics. This ensemble, which is based on the conservation properties of the stress tensor, is distinct from the original Edwards ensemble and applies to packings of deformable grains. We combine it with a field theoretical analysis of the packings, where the field is the Airy stress function derived from the force and torque balance conditions. In this framework, Point J characterized by a diverging stiffness of the pressure fluctuations. Separately, we present a phenomenological mean-field theory of the jamming transition, which incorporates the mean contact number as a variable. We link both approaches in the context of the marginal rigidity picture proposed by Wyart and others.