Packing problems have been a source of fascination for millennia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure and bulk properties of condensed phases of matter, including low-temperature states (e.g., molecular and colloidal liquids, crystals, and glasses), multiphase heterogeneous media, granular media, and biological systems. The densest packings are of great interest in pure mathematics, including discrete geometry and number theory. This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable, and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions. In the case of jammed packings, emphasis will be placed on the “geometric-structure” approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and “order” maps. It incorporates extremal jammed states, including the densest packings, maximally random jammed states, and lowest-density jammed structures. Packings of identical spheres, spheres with a size distribution, and nonspherical particles are also surveyed. We close this review by identifying challenges and open questions for future research.

中文翻译：

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观点：通过包装模型基本了解物质的凝聚相

几千年来，包装问题一直是人们着迷的原因，他们的研究产生了涵盖众多学科的丰富文献。硬颗粒堆积模型的研究提供了对物质凝结相结构和体积性质的基本见解，包括低温状态（例如，分子和胶体液体，晶体和玻璃），多相非均质介质，颗粒介质和生物系统。最密集的堆积对纯数学（包括离散几何和数论）非常感兴趣。该观点回顾了有关在各种欧几里得空间尺寸中硬质颗粒堆积的平衡，亚稳态和非平衡堆积的相关理论和计算文献。如果是堵塞的包装，重点将放在“几何结构”方法上，该方法提供了一种强大且统一的方法，可通过干扰类别和“顺序”图来定量表征单个包装。它包含了极端的阻塞状态，包括最密集的堆积，最大程度的随机阻塞状态和最低密度的阻塞结构。还对相同球体，具有尺寸分布的球体和非球形颗粒的堆积进行了调查。通过确定挑战并提出未来研究的问题，我们结束了本评论。还对相同球体，具有尺寸分布的球体和非球形颗粒的堆积进行了调查。通过确定挑战并提出未来研究的问题，我们结束了本评论。还对相同球体，具有尺寸分布的球体和非球形颗粒的堆积进行了调查。通过确定挑战并提出未来研究的问题，我们结束了本评论。