Particle Packing Problems

这位研究人员和他的同事研究了各种包装问题。主要研究了以下五个方面：(1)二维和三维形状的非球形颗粒稠密堆积的识别和表征；(2)高欧氏空间中密度最大的球状堆积的研究；(3)不同维的低密度堵塞球状堆积的识别；(4)任意维单位球面上的干扰研究；以及(5)寻求改进的阶度量来刻画填充中的随机程度。这项拟议的研究可能会产生重要的科学进展和结果。这个非常多学科的项目加入了应用数学、统计和凝聚态物理、材料科学、工程学和纯数学社区。统一这些不同的观点和目标是一项具有挑战性的任务，但这一任务总体上为科学界提供了巨大的回报。包装问题，例如密实的固体如何填充空间，自文明诞生以来就一直令人着迷，并由于与物理科学、数学、工程和生物学中出现的一系列问题有关而继续引起科学家的兴趣。虽然最优堆积问题与凝聚态物质的固态密切相关，但无序球状堆积已被用来模拟物质的玻璃态。高维的球形填充在通信理论中具有相关性。病毒将DNA包装在蛋白质容器中的方式是一个包装问题。维度大于3的球体最密集的堆积是什么？在二维和三维空间中，非球形物体最密集的堆积是什么？随机填充能比有序填充更密集地填充空间吗(意味着无序或“玻璃”基态)？包装的“随机性”能以一种准确的方式量化吗？对包装问题的更好理解对新材料的合成、我们有效地设计通信通道以远距离发送数字信号的能力以及新药的设计都有影响，仅举几个例子。

Torquato0804431 The investigator and his colleagues study a variety ofpacking problems. The following five general areas are explored:(1) identification and characterization of dense packings ofnonspherical particles for a wide class shapes in two and threespace dimensions; (2) study of sphere packings of maximal densityin high Euclidean dimensions; (3) identification of low-densityjammed sphere packings in various dimensions; (4) studies ofjamming on the unit sphere in arbitrary dimensions; and (5)pursuit of improved order metrics to characterize the degree ofrandomness in a packing. Important scientific advances andoutcomes are likely to emerge from the proposed research. Thisvery multidisciplinary project joins the applied mathematics,statistical and condensed-matter physics, materials science,engineering, and pure mathematics communities. Unifying thesedifferent perspectives and goals is a challenging task, but onethat offers great rewards to the scientific community in general. Packing problems, such as how densely solid objects fillspace, have fascinated people since the dawn of civilization, andcontinue to intrigue scientists because of their connection to ahost of problems that arise in the physical sciences,mathematics, engineering, and biology. While optimal packingproblems are intimately related to solid states of condensedmatter, disordered sphere packings have been employed to modelthe glassy state of matter. Sphere packings in high dimensionshave relevance in communications theory. The way that virusespackage DNA in protein containers is a packing problem. What arethe densest packings of spheres in dimension greater than three? What are the densest packings of nonspherical objects in two andthree dimensions? Can random packings ever fill space moredensely than ordered packings (implying disordered or "glassy"ground states)? Can "randomness" of a packing be quantified in ameaningful and precise manner? A greater understanding ofpacking problems has implications for the synthesis of novelmaterials, our ability to efficiently design communicationschannels to send digital signals over large distances, and thedesign of new drugs, just to mention a few examples.