摩擦族的统计
The statistics of frictional families
摘要：
我们开发了一个理论描述的机械稳定的摩擦填料之间的差异，所需的接触的总数为无摩擦盘的等压填料和摩擦填料，$m=N_c^0-N_c$的接触的数量。鞍阶数$m$表示如果去除摩擦，静态填料将具有的无约束自由度的数量。使用一种新的数值方法，使我们能够枚举磁盘包装为每个$m$，我们表明，在给定的静摩擦系数$μ$，$P_m(μ)$，可以表示为一个幂级数在$μ$的概率，以获得一个填料与鞍阶$m$。使用这种形式的$P_m(μ)$，我们定量地描述了平均接触数对摩擦系数的静态磁盘填料的Cundall-Strack模型直接模拟所有$μ$和$N$。
英文摘要：
We develop a theoretical description for mechanically stable frictional packings in terms of the difference between the total number of contacts required for isostatic packings of frictionless disks and the number of contacts in frictional packings, $m=N_c^0-N_c$. The saddle order $m$ represents the number of unconstrained degrees of freedom that a static packing would possess if friction were removed. Using a novel numerical method that allows us to enumerate disk packings for each $m$, we show that the probability to obtain a packing with saddle order $m$ at a given static friction coefficient $μ$, $P_m(μ)$, can be expressed as a power-series in $μ$. Using this form for $P_m(μ)$, we quantitatively describe the dependence of the average contact number on friction coefficient for static disk packings obtained from direct simulations of the Cundall-Strack model for all $μ$ and $N$.
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