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Related papers: Enumerating rigid sphere packings

200 papers

In this paper, we recall various features of non equilibrium granular systems. Clusters with specific properties are found depending on the packing density, going from loose (a granular gas) to sintered (though brittle) polycrystalline…

Materials Science · Physics 2009-09-29 M. Ausloos , R. Lambiotte , K. Trojan , Z. Koza , M. Pekala

We analyze the general problem of determining optimally dense packings, in a Euclidean or hyperbolic space, of congruent copies of some fixed finite set of bodies. We are strongly guided by examples of aperiodic tilings in Euclidean space…

Metric Geometry · Mathematics 2018-07-11 Lewis Bowen , Charles Holton , Charles Radin , Lorenzo Sadun

We systematically investigate the self-assembly of anisotropic cone-shaped particles decorated by ring-like attractive patches. We demonstrate that the self-assembled clusters, which arise due to the conical particle's anisotropic shape…

Materials Science · Physics 2007-05-23 Ting Chen , Zhenli Zhang , Sharon C. Glotzer

In this paper we consider the problem of packing a fixed number of identical circles inside the unit circle container, where the packing is complicated by the presence of fixed size circular prohibited areas. Here the objective is to…

Optimization and Control · Mathematics 2018-11-05 C. O. Lopez , J. E. Beasley

Dense hard-particle packings are intimately related to the structure of low-temperature phases of matter and are useful models of heterogeneous materials and granular media. Most studies of the densest packings in three dimensions have…

Soft Condensed Matter · Physics 2015-05-13 Yang Jiao , Frank Stillinger , Sal Torquato

Spatially ordered systems confined to surfaces such as spheres exhibit interesting topological structures because of curvature induced frustration in orientational as well as translational order. The study of these structures is important…

Soft Condensed Matter · Physics 2022-06-24 Dharanish Rajendra , Jaydeep Mandal , Yashodhan Hatwalne , Prabal K. Maiti

By virtue of their high galaxy space densities and their large spatial separations, clusters are efficient and accurate tracers of the large-scale density and velocity fields. Substantial progress has been made over the past decade in the…

Astrophysics · Physics 2007-05-23 Marc Postman

The most successful cosmological models to date envision structure formation as a hierarchical process in which gravity is constantly drawing lumps of matter together to form increasingly larger structures. Clusters of galaxies currently…

Astrophysics · Physics 2008-11-26 G. Mark Voit

Using computed x-ray tomography we determine the three dimensional (3d) structure of binary hard sphere mixtures as a function of composition and size ratio of the particles, q. Using a recently introduced four-point correlation function we…

Soft Condensed Matter · Physics 2023-02-15 Houfei Yuan , Zhen Zhang , Walter Kob , Yujie Wang

We show through rigorous calculations that dielectric microspheres can be organized by an incident electromagnetic plane wave into stable cluster configurations, which we call photonic molecules. The long-range optical binding force arises…

Mesoscale and Nanoscale Physics · Physics 2009-11-11 Jack Ng , Zhifang Lin , C. T. Chan , Ping Sheng

We present a new numerical scheme to study systems of non-convex, irregular, and punctured particles in an efficient manner. We employ this method to analyze regular packings of odd-shaped bodies, not only from a nanoparticle but also both…

Soft Condensed Matter · Physics 2015-05-28 Joost de Graaf , René van Roij , Marjolein Dijkstra

The densest binary sphere packings in the alpha-x plane of small to large sphere radius ratio alpha and small sphere relative concentration x have historically been very difficult to determine. Previous research had led to the prediction…

Statistical Mechanics · Physics 2015-06-03 Adam B. Hopkins , Frank H. Stillinger , Salvatore Torquato

This note initiates an investigation of packing links into a region of Euclidean space to achieve a maximal density subject to geometric constraints. The upper bounds obtained apply only to the class of homotopically essential links and…

Geometric Topology · Mathematics 2024-01-31 Michael H. Freedman

Clustering provides a common means of identifying structure in complex data, and there is renewed interest in clustering as a tool for the analysis of large data sets in many fields. A natural question is how many clusters are appropriate…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Susanne Still , William Bialek

Using X-ray tomography, we experimentally investigate the structural evolution of packings composed of 3D-printed hexapod particles, each formed by three mutually orthogonal spherocylinders, during tap-induced compaction. We identify two…

Disks of low-mass bodies on high-eccentricity orbits in near-Keplerian potentials can be dynamically unstable to buckling out of the plane. In this letter, we present $N$-body simulations of the long-term behavior of such a system, finding…

Earth and Planetary Astrophysics · Physics 2020-06-03 Alexander Zderic , Angela Collier , Maria Tiongco , Ann-Marie Madigan

We prove that the space of circle packings consistent with a given triangulation on a surface of genus at least two is projectively rigid, so that a packing on a complex projective surface is not deformable within that complex projective…

Geometric Topology · Mathematics 2023-07-19 Francesco Bonsante , Michael Wolf

A rigidity theory is developed for bar-joint frameworks in $\mathbb{R}^{d+1}$ whose vertices are constrained to lie on concentric $d$-spheres with independently variable radii. In particular, combinatorial characterisations are established…

Metric Geometry · Mathematics 2017-02-14 Anthony Nixon , Bernd Schulze , Shin-ichi Tanigawa , Walter Whiteley

This paper presents a novel geometrical approach to investigate the convexity of a density-based cluster. Our approach is grid-based and we are about to calibrate the value space of the cluster. However, the cluster objects are coming from…

Computational Geometry · Computer Science 2020-09-25 Sayyed-Ahmad Naghavi-Nozad

We propose a new class of space-filling designs called rotated sphere packing designs for computer experiments. The approach starts from the asymptotically optimal positioning of identical balls that covers the unit cube. Properly scaled,…

Methodology · Statistics 2016-08-15 Xu He