在α-x平面中，小球体与大球体半径比α和小球体相对浓度x的致密二元球体填充历来非常难以确定。先前的研究已经导致预测这些填充物由几种已知的“合金”相组成，包括例如AlB 2（六方Ω）、HgBr 2和AuTe 2结构，并且导致XYn结构由紧密填充的大球与间隙中的小球（数量比为n比1）组成，例如，n = 1的NaCl填充。然而，利用Torquato-Jiao球填充算法的实现[S. Torquato和Y. Jiao，Phys.Rev.E82，061302（2010）]中，我们已经发现，更多的结构出现在致密填充中。例如，以前所有已知的致密结构都是由小到大的球体组成的，其数量比为1：1、2：1，最近还有3：1，而我们已经发现了数量比为7：3和5：2的致密结构。在最近的工作[A。B.霍普金斯，Y. Jiao，F. H. Stillinger和S. Torquato，Phys. Rev. Lett. 107，125501（2011）]，我们总结了这些发现。在这项工作中，我们提出了已知的最密集的填料的结构，并提供有关其特性的细节。我们的研究结果表明，一个广泛的阵列的不同的dennious机械稳定的结构组成的只有两种类型的组件可以形成没有任何考虑的吸引力或各向异性的相互作用。此外，我们已经确定的新结构可能对应于某些二元原子和分子系统的当前未识别的稳定相，特别是在高温和高压下。
英文摘要：
The densest binary sphere packings in the alpha-x plane of small to large sphere radius ratio alpha and small sphere relative concentration x have historically been very difficult to determine. Previous research had led to the prediction that these packings were composed of a few known "alloy" phases including, for example, the AlB2 (hexagonal omega), HgBr2, and AuTe2 structures, and to XYn structures composed of close-packed large spheres with small spheres (in a number ratio of n to 1) in the interstices, e.g., the NaCl packing for n = 1. However, utilizing an implementation of the Torquato-Jiao sphere-packing algorithm [S. Torquato and Y. Jiao, Phys. Rev. E 82, 061302 (2010)], we have discovered that many more structures appear in the densest packings. For example, while all previously known densest structures were composed of spheres in small to large number ratios of one to one, two to one, and very recently three to one, we have identified densest structures with number ratios of seven to three and five to two. In a recent work [A. B. Hopkins, Y. Jiao, F. H. Stillinger, and S. Torquato, Phys. Rev. Lett. 107, 125501 (2011)], we summarized these findings. In this work, we present the structures of the densest-known packings and provide details about their characteristics. Our findings demonstrate that a broad array of different densest mechanically stable structures consisting of only two types of components can form without any consideration of attractive or anisotropic interactions. In addition, the novel structures that we have identified may correspond to currently unidentified stable phases of certain binary atomic and molecular systems, particularly at high temperatures and pressures.
Packings of regular convex polygons ($n$-gons) that are sufficiently dense have been studied extensively in the context of modeling physical and biological systems as well as discrete and computational geometry. Former results were mainly regarding densest lattice or double-lattice configurations. Here we consider all two-dimensional crystallographic symmetry groups (plane groups) by restricting the configuration space of the general packing problem of congruent copies of a compact subset of the two-dimensional Euclidean space to particular isomorphism classes of the discrete group of isometri…
尽可能密集地填充粒子系统的问题是离散几何领域的基础，也是材料和生物科学中的一个强大模型。随着填充问题从解析构造的解决方案范围内撤退，进行\textit{de novo}（从头开始）搜索密集填充的有效数值方法的重要性变得至关重要。在本文中，我们使用\textit{divide and concur}框架，发展了一个通用的搜索法的周期约束问题的解决方案，我们把它应用到发现密集周期包装。该方法的一个重要特点是将晶胞参数与组态空间定义中的其他填充变量相结合。我们提出的方法导致了[arXiv：0910.5226]中报道的最密集的已知四面体堆积的改进。在这里，我们使用的方法来重现dennies已知的晶格球包装和最知名的晶格接吻安排分别在14和11维（第一个这样的数字证据，他们的最优性，在这些方面）。对于非球形粒子，我们报告了一个新的密度为$ϕ=128/219\approx0.5845$的规则四维单形的稠密堆积，并具有与已知的四面体堆积类似的结构。
Based on results from the physics and mathematics literature which suggest a series of clearly defined conjectures, we formulate three simple scenarios for the fate of hard sphere crystallization in high dimension: (A) crystallization is impeded and the glass phase constitutes the densest packing, (B) crystallization from the liquid is possible, but takes place much beyond the dynamical glass transition and is thus dynamically implausible, or (C) crystallization is possible and takes place before (or just after) dynamical arrest, thus making it plausibly accessible from the liquid state. In or…
The notion of random close packings of a bulk static collection of ball bearings or sand grains was introduced in the 1960's by G.D. Scott and J.D. Bernal. There have been numerous attempts to understand the packings. We give a short argument, based on recent experiments and simulations, which explains the packings in purely geometric terms.
The sphere packing problem is an old puzzle. We consider packings with m spheres in the unit cell (m-periodic packings). For the case m = 1 (lattice packings), Voronoi proved there are finitely many inequivalent local optima and presented an algorithm to enumerate them, and this computation has been implemented in up to d = 8 dimensions. We generalize Voronoi's method to m > 1 and present a procedure to enumerate all locally optimal 2-periodic sphere packings in any dimension, provided there are finitely many. We implement this computation in d = 3, 4, and 5 and show that no 2-periodic packing…
