English
Related papers

Related papers: Enumerating rigid sphere packings

200 papers

The packing problem of long thin filaments that are injected into confined spaces is of fundamental interest for physicists and biologists alike. How linear threads pack and coil is well known only for the ideal case of rigid containers,…

Soft Condensed Matter · Physics 2015-12-11 Roman Vetter , Falk K. Wittel , Hans J. Herrmann

Packings of identical objects have fascinated both scientists and laymen alike for centuries, in particular the sphere packings and the packings of identical regular tetrahedra. Mathematicians have tried for centuries to determine the…

Metric Geometry · Mathematics 2014-10-07 Chuanming Zong

Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…

Machine Learning · Statistics 2017-01-02 Andreas Henelius , Kai Puolamäki , Henrik Boström , Panagiotis Papapetrou

The most efficient way to pack equally sized spheres isotropically in 3D is known as the random close packed state, which provides a starting point for many approximations in physics and engineering. However, the particle size distribution…

Soft Condensed Matter · Physics 2010-01-05 Robert S. Farr , Robert D. Groot

This paper deals with the problem of circle packing, in which the largest radii circle is to be fit in a confined space filled with arbitrary circles of different radii and centers. A circle packing problem is one of a variety of cutting…

Optimization and Control · Mathematics 2024-03-19 Pulkit Mundra , Veni Goyal , Kusum Deep

Granular packings of non-convex or elongated particles can form free-standing structures like walls or arches. For some particle shapes, such as staples, the rigidity arises from interlocking of pairs of particles, but the origins of…

Soft Condensed Matter · Physics 2020-07-06 Yuchen Zhao , Jonathan Barés , Joshua E. S. Socolar

Connecting the collective behavior of disordered systems with local structure on the particle scale is an important challenge, for example in granular and glassy systems. Compounding complexity, in many scientific and industrial…

Soft Condensed Matter · Physics 2016-11-21 Fabian M. Schaller , Robert F. B. Weigel , Sebastian C. Kapfer

A homothetic packing of squares is any set of various-size squares with the same orientation where no two squares have overlapping interiors. If all $n$ squares have the same size then we can have up to roughly $4n$ contacts by arranging…

Combinatorics · Mathematics 2023-10-26 Sean Dewar

We use computational experiments to find the rectangles of minimum perimeter into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. In many of the packings…

Metric Geometry · Mathematics 2009-04-03 Boris D. Lubachevsky , Ronald L. Graham

We investigate the clustering morphology of a swarm of freely rising deformable bubbles. A three-dimensional Vorono\"i analysis enables us to quantitatively distinguish between two typical clustering configurations: preferential clustering…

The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained for selected values of N up to N = 1054. In the predecessor to this paper…

Statistical Mechanics · Physics 2013-05-29 Adam B. Hopkins , Frank H. Stillinger , Salvatore Torquato

We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $. A multiple packing is a set…

Metric Geometry · Mathematics 2022-11-10 Yihan Zhang , Shashank Vatedka

Elastic properties and internal states of isotropic sphere packings are studied by numerical simulations. Several numerical protocols to assemble dense configurations are compared. One, which imitates experiments with lubricated contacts,…

Materials Science · Physics 2009-01-16 Ivana Agnolin , Jean-Noël Roux

We have previously explored cylindrical packings of disks and their relation to sphere packings. Here we extend the analytical treatment of disk packings, analysing the rules for phyllotactic indices of related structures and the variation…

Soft Condensed Matter · Physics 2015-06-18 Adil Mughal , Denis Weaire

The topological structure resulting from the network of contacts between grains (\emph{contact network}) is studied for large samples of monosized spheres with densities (fraction of volume occupied by the spheres) ranging from 0.59 to…

Disordered Systems and Neural Networks · Physics 2007-09-21 T. Aste , M. Saadatfar , T. J. Senden

Although jammed packings of soft spheres exist in potential energy landscapes with a vast number of minima, when subjected to cyclic shear they may revisit the same configurations repeatedly. Simple hysteretic spin models, in which particle…

Soft Condensed Matter · Physics 2025-04-04 Chloe W. Lindeman , Sidney R. Nagel

This review describes the diversity of jammed configurations attainable by frictionless convex nonoverlapping (hard) particles in Euclidean spaces and for that purpose it stresses individual-packing geometric analysis. A fundamental feature…

Statistical Mechanics · Physics 2015-05-19 Salvatore Torquato , Frank H. Stillinger

Random packings of stiff rods are self-supporting mechanical structures stabilized by long range interactions induced by contacts. To understand the geometrical and topological complexity of the packings, we first deploy X-ray computerized…

Soft Condensed Matter · Physics 2024-09-24 Yeonsu Jung , Thomas Plumb-Reyes , Hao-Yu Greg Lin , L. Mahadevan

Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they…

Soft Condensed Matter · Physics 2018-05-09 Rose Cersonsky , Greg van Anders , Paul M. Dodd , Sharon C. Glotzer

We study, via the replica method of disordered systems, the packing problem of hard-spheres with a square-well attractive potential when the space dimensionality, d, becomes infinitely large. The phase diagram of the system exhibits…

Disordered Systems and Neural Networks · Physics 2013-12-17 Mauro Sellitto , Francesco Zamponi