Gabbrielli Ruggero, Jiao Yang, Torquato Salvatore
Interdisciplinary Laboratory for Computational Science, Department of Physics, University of Trento, 38123 Trento, Italy.
Materials Science and Engineering Program, School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, Arizona 85281, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Feb;89(2):022133. doi: 10.1103/PhysRevE.89.022133. Epub 2014 Feb 24.
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.
三维欧几里得空间R(3)中不重叠物体的密集堆积是物理和生物科学中出现的各种多粒子系统结构的有用模型。在这里，我们研究了R(3)中全等环面的堆积行为，环面是具有1亏格的多重连通非凸体，以及喇叭形环面和纺锤形环面。具体来说，我们根据最初为单连通固体设计的组织原则[Torquato和Jiao，《物理评论E》86，011102(2012)]，解析地构造了一族不相连环面的密集周期堆积。我们发现，喇叭形环面以及某些纺锤形环面和环形环面不仅可以实现高于球体的堆积密度(即π/√18 = 0.7404...)，而且高于已知最密集的椭球体堆积(即0.7707...)。此外，我们研究了成对相连环面(即霍普夫链)簇的密集堆积，其密度比由不相连环面组成的相应堆积高得多。
