Henkes Silke, Chakraborty Bulbul
Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454-9110, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jun;79(6 Pt 1):061301. doi: 10.1103/PhysRevE.79.061301. Epub 2009 Jun 3.
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.
近年来，颗粒材料的物理性质得到了广泛研究。然而，到目前为止，除了唯象的堵塞相图外，还没有一个理论框架能够统一地解释这些观测结果。这项工作聚焦于静态颗粒物质的情况，在此我们构建了一个统计系综，它反映了平衡统计力学。这个基于应力张量守恒性质的系综不同于原始的爱德华兹系综，适用于可变形颗粒的堆积。我们将其与对堆积的场论分析相结合，其中场是由力和力矩平衡条件导出的艾里应力函数。在这个框架中，点J的特征是压力涨落的刚度发散。另外，我们提出了一种堵塞转变的唯象平均场理论，该理论将平均接触数作为一个变量纳入其中。我们在怀亚特等人提出的边缘刚度图景的背景下将这两种方法联系起来。
