Institut für Theoretische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany.
Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Goettingen, Germany.
Phys Rev Lett. 2015 Apr 17;114(15):158001. doi: 10.1103/PhysRevLett.114.158001. Epub 2015 Apr 14.
In particulate soft matter systems the average number of contacts Z of a particle is an important predictor of the mechanical properties of the system. Using x-ray tomography, we analyze packings of frictional, oblate ellipsoids of various aspect ratios α, prepared at different global volume fractions ϕg. We find that Z is a monotonically increasing function of ϕg for all α. We demonstrate that this functional dependence can be explained by a local analysis where each particle is described by its local volume fraction ϕl computed from a Voronoi tessellation. Z can be expressed as an integral over all values of ϕl: Z(ϕg,α,X)=∫Zl(ϕl,α,X)P(ϕl|ϕg)dϕl. The local contact number function Zl(ϕl,α,X) describes the relevant physics in term of locally defined variables only, including possible higher order terms X. The conditional probability P(ϕl|ϕg) to find a specific value of ϕl given a global packing fraction ϕg is found to be independent of α and X. Our results demonstrate that for frictional particles a local approach is not only a theoretical requirement but also feasible.
在颗粒状软物质系统中，颗粒的平均接触数 Z 是预测系统力学性能的一个重要指标。我们使用 X 射线断层扫描技术，分析了不同纵横比α的摩擦性扁长椭球体在不同总体体积分数ϕg下的堆积情况。我们发现，对于所有的α，Z 都是ϕg 的单调递增函数。我们证明，这种功能依赖性可以通过局部分析来解释，其中每个颗粒都可以通过 Voronoi 镶嵌来计算其局部体积分数ϕl。Z 可以表示为对所有ϕl 值的积分：Z(ϕg,α,X)=∫Zl(ϕl,α,X)P(ϕl|ϕg)dϕl。局部接触数函数 Zl(ϕl,α,X)仅用局部定义的变量来描述相关物理，包括可能的更高阶项 X。给定特定的总体堆积分数ϕg 时，找到特定ϕl 值的条件概率 P(ϕl|ϕg)被发现与α和 X 无关。我们的结果表明，对于摩擦性颗粒，局部方法不仅是理论上的要求，而且也是可行的。
