标题： 包装协议对密集多分散堆积中分形指数的影响 显示英文标题

标题： Influence of packing protocol on fractal exponents in dense polydisperse packings

摘要： 我们研究了由密集且随机堆积的圆盘组成的系统，这些圆盘遵循半径的幂律分布，该分布是通过使用不同的协议生成的：具有零边界条件和周期性边界条件的Delaunay三角剖分（DT）以及具有周期性边界条件的恒压协议。 对于各种大小比值的分布，定义为最大半径与最小半径的比值，数值上得到了质量-半径关系和结构因子的幂律指数。 结果表明，大小比值是一个重要的控制参数，负责系统分形特性的一致性：比值越大，有限尺寸效应越不明显，指数之间的吻合度越好。 对于DT协议，即使在中等大小比值下，质量-半径关系、结构因子和幂律分布的指数也是一致的。 相比之下，对于恒压协议，在中等（约300）和大（约1500）的大小比值下，这三个指数都被发现是不同的，这可能表明圆盘的空间分布是偏向的而非随机的。 然而，随着大小比值的增加，指数有趋同的趋势，这表明在无限大小比值的极限下，所有指数都会相等。 显示英文摘要

摘要： We study fractal properties of a system of densely and randomly packed disks, obeying a power-law distribution of radii, which is generated by using various protocols: Delaunay triangulation (DT) with both zero and periodic boundary conditions and the constant pressure protocol with periodic boundary conditions. The power-law exponents of the mass-radius relation and structure factor are obtained numerically for various values of the size ratio of the distribution, defined as the largest-to-smallest radius ratio. It is shown that the size ratio is an important control parameter responsible for the consistency of the fractal properties of the system: the greater the ratio, the less the finite size effects are pronounced and the better the agreement between the exponents. For the DT protocol, the exponents of the mass-radius relation, structure factor, and power-law distribution coincide even at moderate values of the size ratio. By contrast, for the constant-pressure protocol, all three exponents are found to be different for both moderate (around 300) and large (around 1500) size ratios, which might indicate a biased rather than random spatial distribution of the disks. Nevertheless, there is a tendency for the exponents to converge as the size ratio increases, suggesting that all the exponents become equal in the limit of infinite size ratio.