title: Dense periodic packings of tori.
abstract: Dense packings of nonoverlapping bodies in three-dimensional Euclidean space R(3) 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 R(3), 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 [Torquato and Jiao, Phys. Rev. E 86, 011102 (2012)]. 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/sqrt[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.
authors.affiliation: Interdisciplinary Laboratory for Computational Science, Department of Physics, University of Trento, 38123 Trento, Italy.
authors.forename: Ruggero
authors.initials: R
authors.lastname: Gabbrielli
authors.affiliation: Materials Science and Engineering Program, School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, Arizona 85281, USA.
authors.forename: Yang
authors.initials: Y
authors.lastname: Jiao
authors.affiliation: Department of Chemistry, Department of Physics, Program in Applied and Computational Mathematics, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Salvatore
authors.initials: S
authors.lastname: Torquato
mesh_terms: D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D017276:Friction; D008956:Models, Chemical; D053758:Nanoparticles / Q000737:chemistry* / Q000648:ultrastructure*; D010316:Particle Size
chemical_list: D003102:Colloids