通过堆积模型对物质凝聚相的基本认识
Basic Understanding of Condensed Phases of Matter via Packing Models
摘要：
包装问题一直是一个来源的魅力千年和他们的研究产生了丰富的文献，跨越众多学科。对硬颗粒堆积模型的研究提供了对物质凝聚相的结构和本体性质的基本见解，包括低温状态（例如，分子和胶体液体、晶体和玻璃）、多相非均匀介质、颗粒介质和生物系统。离散填充在纯数学中有着重要的意义，包括离散几何和数论。这一观点回顾了有关的理论和计算文献的平衡，亚稳态和非平衡硬粒子包装在各种欧几里德空间维度的包装。在堵塞填料的情况下，重点将放在“几何结构”的方法，它提供了一个强大的和统一的手段，定量表征个别填料通过堵塞类别和“秩序”地图。它包括极端堵塞状态，包括密集包装，最大随机堵塞状态，和最低密度堵塞结构。同样的球，球的尺寸分布，和非球形颗粒的填料也进行了调查。我们通过确定未来研究的挑战和开放问题来结束这篇综述。
英文摘要：
Packing problems have been a source of fascination for millenia 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.
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