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Related papers: Densest ternary sphere packings

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We present the densest known packing of regular tetrahedra with density phi = 4000/4671 = 0.856347... Like the recently discovered packings of Kallus et al. [arXiv:0910.5226] and Torquato-Jiao [arXiv:0912.4210], our packing is crystalline…

Statistical Mechanics · Physics 2010-07-27 Elizabeth R. Chen , Michael Engel , Sharon C. Glotzer

High strength-to-weight ratio materials can be constructed by either maximizing strength or minimizing weight. Tensegrity structures and aerogels take very different paths to achieving high strength-to-weight ratios but both rely on…

Soft Condensed Matter · Physics 2021-09-06 R. C. Dennis , E. I. Corwin

We consider circle packings in the plane with circles of sizes $1$, $r\simeq 0.834$ and $s\simeq 0.651$. These sizes are algebraic numbers which allow a compact packing, that is, a packing in which each hole is formed by three mutually…

Computational Geometry · Computer Science 2019-12-06 Thomas Fernique

Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest, as they are related to important…

Disordered Systems and Neural Networks · Physics 2015-03-13 Giorgio Parisi , Francesco Zamponi

Large-scale computational surveys are increasingly used to map the landscape of stable crystalline materials. We report a high-throughput energy screening of inorganic crystals that enumerates binary and ternary compositions up to a…

Materials Science · Physics 2026-01-30 Abhijith S Parackal , Florian Trybel , Felix Andreas Faber , Rickard Armiento

This work investigates dense packings of congruent hard infinitesimally--thin circular arcs in the two-dimensional Euclidean space. It focuses on those denotable as major whose subtended angle $\theta \in \left ( \pi, 2\pi \right ]$.…

Soft Condensed Matter · Physics 2020-10-28 Juan Pedro Ramírez González , Giorgio Cinacchi

A systematic search for multicomponent crystal structures is carried out for five different ternary systems of nuclei in a polarizable background of electrons, representative of accreted neutron star crusts and some white dwarfs. Candidate…

High Energy Astrophysical Phenomena · Physics 2016-03-09 T. A. Engstrom , N. C. Yoder , V. H. Crespi

Motivated by breakthroughs in the synthesis of faceted nano- and colloidal particles, as well as theoretical and computational studies of their packings, we investigate a family of truncated triangular bipyramids. We report dense periodic…

Statistical Mechanics · Physics 2013-08-16 Amir Haji-Akbari , Elizabeth R. Chen , Michael Engel , Sharon C Glotzer

Advancements in the synthesis of faceted nanoparticles and colloids have spurred interest in the phase behavior of polyhedral shapes. Regular tetrahedra have attracted particular attention because they prefer local symmetries that are…

Soft Condensed Matter · Physics 2011-11-24 Amir Haji-Akbari , Michael Engel , Sharon C. Glotzer

The emergence of deep learning has brought the long-standing goal of comprehensively understanding and exploring crystalline materials closer to reality. Yet, universal exploration across all elements remains hindered by the combinatorial…

Materials Science · Physics 2025-11-18 Fengyu Xie , Ruoyu Wang , Taoyuze Lv , Yuxiang Gao , Hongyu Wu , Zhicheng Zhong

The densest packings of N unit squares in a torus are studied using analytical methods as well as simulated annealing. A rich array of dense packing solutions are found: density-one packings when N is the sum of two square integers; a…

Statistical Mechanics · Physics 2012-03-20 Don Blair , Christian D. Santangelo , Jon Machta

Packings of regular convex polygons ($n$-gons) that are sufficiently dense have been studied extensively in the context of modeling physical and biological systems as well as discrete and computational geometry. Former results were mainly…

Metric Geometry · Mathematics 2022-11-22 Miloslav Torda , John Y. Goulermas , Vitaliy Kurlin , Graeme M. Day

During the past 20 years, the idea that non-spherical planetary nebulae (PN) may need a binary or planetary interaction to be shaped was discussed by various authors. It is now generally agreed that the varied morphologies of PN cannot be…

Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains…

Artificial Intelligence · Computer Science 2025-12-09 Rasul Tutunov , Alexandre Maraval , Antoine Grosnit , Xihan Li , Jun Wang , Haitham Bou-Ammar

The recent discovery of planets orbiting main sequence binaries will provide crucial constraints for theories of binary and planet formation. The formation pathway for these planets is complicated by uncertainties in the formation mechanism…

Earth and Planetary Astrophysics · Physics 2015-06-17 Kaitlin M. Kratter , Andrew Shannon

Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static…

Disordered Systems and Neural Networks · Physics 2011-10-28 Patrick Charbonneau , Atsushi Ikeda , Giorgio Parisi , Francesco Zamponi

Previously we reported on the stable (i.e. minimal enthalpy) structures of soft monodisperse spheres in a long cylindrical channel. Here, we present further simulations, which significantly extend the original phase diagram up to D/d =…

Soft Condensed Matter · Physics 2018-10-10 Adil Mughal , Jens Winkelmann , Denis Weaire , Stefan Hutzler

We construct the densest known two-dimensional packings of superdisks in the plane whose shapes are defined by |x^(2p) + y^(2p)| <= 1, which contains both convex-shaped particles (p > 0.5, with the circular-disk case p = 1) and…

Soft Condensed Matter · Physics 2009-11-13 Y. Jiao , F. H. Stillinger , S. Torquato

Structural organization and correlations are studied in very large packings of equally sized acrylic spheres, reconstructed in three-dimensions by means of X-ray computed tomography. A novel technique, devised to analyze correlations among…

Soft Condensed Matter · Physics 2007-09-19 Tomaso Aste

We explore the use of the nested sampling technique to sample the configuration space of non-spherical hard particles. We employ the technique on the hard dumbbell system consisting of two hard spheres connected by a rigid bond, and…

Soft Condensed Matter · Physics 2025-12-18 Omar-Farouk Adesida , David Quigley , Livia B. Partay