论文标题
在“ $ d = 2 $和$ d = 3 $中的随机关闭包装的显式分析解决方案上，回复Morse和Charbonneau”
Reply to Morse and Charbonneau on "Explicit analytical solution for random close packing in $d=2$ and $d=3$"
论文作者
论文摘要
Morse和Charbonneau的评论表明，我们最近针对随机关闭包装（RCP）问题的分析解决方案与尺寸的包装数据非常吻合$ d <6 $，但以$ d \ geq6 $的方式偏离了数据。在此答复中，我们使用与$ e_ {8} $ lie组相关的结果说，没有基于联系数字和边际稳定性的RCP解决方案将在大空间尺寸中捕获RCP $ d \ geq 8 $，其中已经存在$ d = 8 $的最近邻居之间的大间隙。事实仍然是[A. Zaccone，物理。莱特牧师。 128，028002（2022）]目前是基于统计参数的RCP问题的唯一简单分析解决方案，该解决方案在$ d = 2,3,4,5 $中捕获了大量基础物理。
A Comment by Morse and Charbonneau shows that our recent analytical solution to the random close packing (RCP) problem is in good agreement with packings data in dimensions $d<6$ but deviates from the data for $d\geq6$. In this Reply we argue, using results related to the $E_{8}$ Lie group, that no RCP solution based on contact numbers and marginal stability is expected to capture RCP in large space dimensions $d \geq 8$ where a large gap exists between nearest neighbours already at $d=8$. The fact remains that the result in [A. Zaccone, Phys. Rev. Lett. 128, 028002 (2022)] is currently the only simple analytical solution to the RCP problem based on statistical arguments, which captures a good deal of the underlying physics in $d=2,3,4,5$.
