论文标题
具有幂律尺寸分布的密集随机包装：结构因子，质量 - 拉迪乌斯关系和配对分布函数
Dense random packing with a power-law size distribution: the structure factor, mass-radius relation, and pair distribution function
论文作者
论文摘要
我们考虑使用半径的幂律分布对磁盘的致密随机堆积并研究其相关性能。我们研究磁盘中心的相应结构因子，质量 - 拉迪乌斯关系和成对分布函数。精确地解决了一个维度（1D）的密集段的玩具模型。理论上以1D的形式显示，在1D和2D中以数字显示这种包装具有分形特性。发现幂律分布的指数和分形维度重合。得出了任意维度中结构因子的近似关系，可以用作小角度散射中的拟合公式。这些发现对于理解各种系统的微观结构特性，例如超高性能混凝土，高内部相比乳液或生物系统。
We consider dense random packing of disks with a power-law distribution of radii and investigate their correlation properties. We study the corresponding structure factor, mass-radius relation and pair distribution function of the disk centers. A toy model of dense segments in one dimension (1d) is solved exactly. It is shown theoretically in 1d and numerically in 1d and 2d that such packing exhibits fractal properties. It is found that the exponent of the power-law distribution and the fractal dimension coincide. An approximate relation for the structure factor in arbitrary dimension is derived, which can be used as a fitting formula in small-angle scattering. The findings can be useful for understanding microstructural properties of various systems like ultra-high performance concrete, high-internal-phase ratio emulsions or biological systems.
