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Optimal Packings of Superdisks and the Role of Symmetry

作     者:Y. Jiao F. H. Stillinger S. Torquato 

作者机构:Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08540 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA 

出 版 物:《Physical Review Letters》 (Phys Rev Lett)

年 卷 期:2008年第100卷第24期

页      面:245504-245504页

核心收录:

学科分类:07[理学] 0702[理学-物理学] 

基  金:National Science Foundation  NSF  (0312067) 

主  题:Condensed matter physics 

摘      要:Almost all studies of the densest particle packings consider convex particles. Here, we provide exact constructions for the densest known two-dimensional packings of superdisks whose shapes are defined by |x1|2p+|x2|2p≤1 and thus contain a large family of both convex (p≥0.5) and concave (0p0.5) particles. Our candidate maximal packing arrangements are achieved by certain families of Bravais lattice packings, and the maximal density is nonanalytic at the “circular-disk point (p=1) and increases dramatically as p moves away from unity. Moreover, we show that the broken rotational symmetry of superdisks influences the packing characteristics in a nontrivial way.

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