标题： 二维多分散随机紧密堆积问题的解析解 显示英文标题

标题： Analytical solution for the polydisperse random close packing problem in 2D

摘要： 提供了一种关于多分散硬盘的随机密堆积密度$\phi_\textrm{RCP}$的解析理论，该理论使用了拥挤的平衡模型 [A. Zaccone, Phys. Rev. Lett. 128, 028002 (2022)]，该模型已通过硬球相图中最大随机紧密堆积（MRJ）线的大量数值分析得到验证 [Anzivino 等人, J. Chem. Phys. 158, 044901 (2023)]。该解依赖于硬盘流体的状态方程，并提供了$\phi_\textrm{RCP}$随盘直径分布的标准差与均值之比$s$的函数预测。对于幂律尺寸分布且$s=0.246$的情况，该理论得出$\phi_\textrm{RCP} =0.892$，这与基于蒙特卡洛交换算法的最新数值估计$\phi_\textrm{RCP} =0.905$相比良好 [Ghimenti, Berthier, van Wijland, Phys. Rev. Lett. 133, 028202 (2024)]。 显示英文摘要

摘要： An analytical theory for the random close packing density, $\phi_\textrm{RCP}$, of polydisperse hard disks is provided using an equilibrium model of crowding [A. Zaccone, Phys. Rev. Lett. 128, 028002 (2022)] which has been justified on the basis of extensive numerical analysis of the maximally random jammed (MRJ) line in the phase diagram of hard spheres [Anzivino et al., J. Chem. Phys. 158, 044901 (2023)]. The solution relies on the equations of state for the hard disk fluid and provides predictions for $\phi_\textrm{RCP}$ as a function of the ratio, $s$, of the standard deviation of the distribution of disk diameters to its mean. For a power-law size distribution with $s=0.246$, the theory yields $\phi_\textrm{RCP} =0.892$, which compares well with the most recent numerical estimate $\phi_\textrm{RCP} =0.905$ based on the Monte-Carlo swap algorithms [Ghimenti, Berthier, van Wijland, Phys. Rev. Lett. 133, 028202 (2024)].