The Symmetry and Order of Densest Packings of Space

空间最密堆积的对称性和有序性

• 批准号: 0700120
• 负责人: Charles Radin
• 金额: $ 16.67万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-15 至 2011-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0700120&HistoricalAwards=false
• 关键词: Symmetry; Order; Densest; Packings; Space

The PI has recently obtained new results on qualitative features of packings : proof of an abrupt change (phase transition) between low and high density packings of a certain deformed disk in the plane, and the experimental discovery of a phase transition in packings of sand (that is, with anisotropy produced by gravity) as density is varied.These results give a uniform approach to understanding certain qualitative features of the geometry of packings, linking research areas in unexpected and fruitful ways, and using a variety of mathematical techniques unusual in the traditional approaches to such studies.

PI最近获得了关于填料质量特性的新结果：突变的证据在平面内某一变形圆盘的低密度和高密度填料之间的相变，以及砂填料中相变的实验发现（即，重力产生的各向异性）这些结果给出了一个统一的方法来理解某些定性特征的几何填料，连接研究领域的意想不到的和富有成效的方式，并使用了在传统研究方法中不常见的各种数学技术。