TY - JOUR
T1 - Dense periodic packings of tori
AU - Gabbrielli, Ruggero
AU - Jiao, Yang
AU - Torquato, Salvatore
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2014/2/24
Y1 - 2014/2/24
N2 - Dense packings of nonoverlapping bodies in three-dimensional Euclidean space R3 are useful models of the structure of a variety of many-particle systems that arise in the physical and biological sciences. Here we investigate the packing behavior of congruent ring tori in R3, which are multiply connected nonconvex bodies of genus 1, as well as horn and spindle tori. Specifically, we analytically construct a family of dense periodic packings of unlinked tori guided by the organizing principles originally devised for simply connected solid bodies [22Torquato and Jiao, Phys. Rev. E 86, 011102 (2012)PLEEE81539- 375510.1103/PhysRevE.86.011102]. We find that the horn tori as well as certain spindle and ring tori can achieve a packing density not only higher than that of spheres (i.e., π/18=0.7404...) but also higher than the densest known ellipsoid packings (i.e., 0.7707...). In addition, we study dense packings of clusters of pair-linked ring tori (i.e., Hopf links), which can possess much higher densities than corresponding packings consisting of unlinked tori.
AB - Dense packings of nonoverlapping bodies in three-dimensional Euclidean space R3 are useful models of the structure of a variety of many-particle systems that arise in the physical and biological sciences. Here we investigate the packing behavior of congruent ring tori in R3, which are multiply connected nonconvex bodies of genus 1, as well as horn and spindle tori. Specifically, we analytically construct a family of dense periodic packings of unlinked tori guided by the organizing principles originally devised for simply connected solid bodies [22Torquato and Jiao, Phys. Rev. E 86, 011102 (2012)PLEEE81539- 375510.1103/PhysRevE.86.011102]. We find that the horn tori as well as certain spindle and ring tori can achieve a packing density not only higher than that of spheres (i.e., π/18=0.7404...) but also higher than the densest known ellipsoid packings (i.e., 0.7707...). In addition, we study dense packings of clusters of pair-linked ring tori (i.e., Hopf links), which can possess much higher densities than corresponding packings consisting of unlinked tori.
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U2 - 10.1103/PhysRevE.89.022133
DO - 10.1103/PhysRevE.89.022133
M3 - Article
C2 - 25353448
AN - SCOPUS:84897769022
VL - 89
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1539-3755
IS - 2
M1 - 022133
ER -