2007/12/04 by Yang Jiao, Y. Jiao, Frank H. Stillinger +3 · 92 citations
Chemistry · Materials Science · Mathematics · Physics and Astronomy · #Bravais lattice #Chemistry #Combinatorics #Condensed matter physics #Crystal structure #Crystallography #Geometry #Hexagonal lattice #Lattice (music) #Material Dynamics and Properties #Mathematics #Mechanics #Physics #Point (geometry) #Regular polygon #Rotational symmetry #Sphere packing #Supramolecular Self-Assembly in Materials #Symmetry (geometry) #Theoretical and Computational Physics #cond-mat.soft
paper · pdf · doi:10.1103/physrevlett.100.245504
published in Physical Review Letters 100(24), 245504 (American Physical Society) · 15 pages, 8 figures
arxiv created 2007/12/04 · openalex publication_date 2008/06/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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<or=1 and thus contain a large family of both convex (p>or=0.5) and concave (0<p<0.5) 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.