Ostojic Srdjan, Somfai Ellák, Nienhuis Bernard
Institute for Theoretical Physics, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands.
Nature. 2006 Feb 16;439(7078):828-30. doi: 10.1038/nature04549.
Force networks form the skeleton of static granular matter. They are the key factor that determines mechanical properties such as stability, elasticity and sound transmission, which are important for civil engineering and industrial processing. Previous studies have focused on investigations of the global structure of external forces (the boundary condition) and on the probability distribution of individual contact forces. So far, however, precise knowledge of the disordered spatial structure of the force network has remained elusive. Here we report that molecular dynamics simulations of realistic granular packings reveal scale invariance of clusters of particles interacting by means of relatively strong forces. Despite visual variation, force networks for various values of the confining pressure and other parameters have identical scaling exponents and scaling function, thereby determining a universality class. Unexpectedly, the flat ensemble of force configurations (a simple generalization of equilibrium statistical mechanics) belongs to this universality class, whereas some widely studied simplified models do not. This implies that the elasticity of the grains and their geometrical disorder do not affect the universal mechanical properties.
力网络构成了静态颗粒物质的骨架。它们是决定诸如稳定性、弹性和声音传播等力学性能的关键因素，而这些性能对土木工程和工业加工至关重要。以往的研究主要集中在外力的全局结构（边界条件）的研究以及单个接触力的概率分布上。然而，到目前为止，力网络无序空间结构的精确知识仍然难以捉摸。在此我们报告，对实际颗粒堆积的分子动力学模拟揭示了通过相对较强的力相互作用的粒子簇的尺度不变性。尽管外观有所不同，但对于各种围压值和其他参数的力网络具有相同的标度指数和标度函数，从而确定了一个普适类。出乎意料的是，力构型的平坦系综（平衡统计力学的一种简单推广）属于这个普适类，而一些广泛研究的简化模型则不属于。这意味着颗粒的弹性及其几何无序并不影响普遍的力学性能。
