Tighe Brian P, van Eerd Adrianne R T, Vlugt Thijs J H
Instituut-Lorentz, Universiteit Leiden, Leiden, The Netherlands.
Phys Rev Lett. 2008 Jun 13;100(23):238001. doi: 10.1103/PhysRevLett.100.238001. Epub 2008 Jun 12.
A long-standing issue in the area of granular media is the tail of the force distribution, in particular, whether this is exponential, Gaussian, or even some other form. Here we resolve the issue for the case of the force network ensemble in two dimensions. We demonstrate that conservation of the total area of a reciprocal tiling, a direct consequence of local force balance, is crucial for predicting the local stress distribution. Maximizing entropy while conserving the tiling area and total pressure leads to a distribution of local pressures with a generically Gaussian tail that is in excellent agreement with numerics, both with and without friction and for two different contact networks.
颗粒介质领域长期存在的一个问题是力分布的尾部，特别是其是否为指数分布、高斯分布，甚至是其他某种形式。在此，我们解决了二维力网络系综情况下的这一问题。我们证明，互反平铺总面积的守恒是预测局部应力分布的关键，而这是局部力平衡的直接结果。在保持平铺面积和总压力的同时最大化熵，会导致局部压力分布具有一般为高斯分布的尾部，这与有无摩擦情况下以及两种不同接触网络的数值结果都非常吻合。
