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We present a computer simulation study on the crystal nucleation process in suspensions of hard spheres, fully taking into account the solvent hydrodynamics. If the dynamics of collodial crystallization were purely diffusive, the crystal…

Soft Condensed Matter · Physics 2015-06-12 Marc Radu , Tanja Schilling

We present a method for discovering dense packings of general convex hard particles and apply it to study the dense packing behavior of a one-parameter family of particles with tetrahedral symmetry representing a deformation of the ideal…

Soft Condensed Matter · Physics 2013-01-28 Yoav Kallus , Veit Elser

We present a simple argument to account for crystallization of hard spheres under the action of a gravitational field. The paper attempts to bridge the gap between two communities of scientists, one working on granular materials and the…

Soft Condensed Matter · Physics 2009-10-31 Yan Levin

In experimental systems, colloidal particles are virtually always at least somewhat polydisperse, which can have profound effects on their ability to crystallize. Unfortunately, accurately predicting the effects of polydispersity on phase…

Soft Condensed Matter · Physics 2025-10-09 Antoine Castagnède , Laura Filion , Frank Smallenburg

This is the fifth in a series of papers giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than $\pi/\sqrt{18}\approx 0.74048...$. This is the…

Metric Geometry · Mathematics 2007-05-23 Thomas C. Hales

The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 60's. This problem finds applications…

Soft Condensed Matter · Physics 2014-09-15 Ping Wang , Chaoming Song , Yuliang Jin , Hernan A. Makse

In the study of crystal nucleation via computer simulations, hard spheres are arguably the most extensively explored model system. Nonetheless, even in this simple model system, the complex thermodynamics of crystal nuclei can sometimes…

Soft Condensed Matter · Physics 2025-02-19 Marjolein de Jager , Carlos Vega , Pablo Montero de Hijes , Frank Smallenburg , Laura Filion

The rich variety of densest columnar structures of identical hard spheres inside a cylinder can surprisingly be constructed from a simple and computationally fast sequential deposition of cylinder-touching spheres, if the cylinder-to-sphere…

Mathematical Physics · Physics 2015-05-30 Ho-Kei Chan

We develop a simple analytical theory that relates dense sphere packings in a cylinder to corresponding disk packings on its surface. It applies for ratios R=D/d (where d and D are the diameters of the hard spheres and the bounding…

Soft Condensed Matter · Physics 2015-05-20 Adil Mughal , Ho Kei Chan , Denis Weaire

We simulate the dynamics of polydisperse hard spheres at high packing fractions, $\phi$, with an experimentally-realistic particle size distribution (PSD) and other commonly-used PSDs such as gaussian or top hat. We find that the mode of…

Soft Condensed Matter · Physics 2013-10-21 Emanuela Zaccarelli , Siobhan M. Liddle , Wilson C. K. Poon

This review paper is devoted to the problems of sphere packings in 4 dimensions. The main goal is to find reasonable approaches for solutions to problems related to densest sphere packings in 4-dimensional Euclidean space. We consider two…

Metric Geometry · Mathematics 2018-06-26 Oleg R. Musin

We analyze the phase diagram of a model of hard spheres of chemical radius one, which is defined over a generalized Bethe lattice containing short loops. We find a liquid, two different crystalline, a glassy and an unusual crystalline…

Statistical Mechanics · Physics 2009-11-11 Hendrik Hansen-Goos , Martin Weigt

We present the first study of disordered jammed hard-sphere packings in four-, five- and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the…

Statistical Mechanics · Physics 2009-11-11 M. Skoge , A. Donev , F. H. Stillinger , S. Torquato

We perform a rigorous study of the identical sphere packing problem in $\mathbb{Z}^3$ and of phase transitions in the corresponding hard-core model. The sphere diameter $D>0$ and the fugacity $u\gg 1$ are the varying parameters of the…

Mathematical Physics · Physics 2023-04-17 A. Mazel , I. Stuhl , Y. Suhov

We study the motion of a rigid sphere falling in a two-layer stratified fluid under the action of gravity in the potential flow regime. Experiments at a moderate Reynolds number of approximately 20 to 450 indicate that a sphere with the…

A fresh approach to the data from experiments with hard sphere colloids yields seminal insights into the glass transition. The precise determination of the fraction of particles caged by their neighbours is unprecedented and provides…

Soft Condensed Matter · Physics 2021-10-01 W. van Megen , H. J. Schöpe

The interplay between densification and positional ordering during the process of crystal nucleation is a greatly investigated topic. Even for the simplest colloidal model -- hard spheres -- there has been much debate regarding the…

Soft Condensed Matter · Physics 2025-02-19 Marjolein de Jager , Nena Slaats , Laura Filion

We investigate the early part of the crystal nucleation process in the hard sphere fluid using data produced by computer simulation. We find that hexagonal order manifests continuously in the overcompressed liquid, beginning approximately…

Soft Condensed Matter · Physics 2016-06-29 Joshua T. Berryman , Muhammad Anwar , Sven Dorosz , Tanja Schilling

We study theoretically and numerically the microscopic cause of the mechanical stability of hard sphere glasses near their maximum packing. We show that, after coarse-graining over time, the hard sphere interaction can be described by an…

Soft Condensed Matter · Physics 2007-05-23 Carolina Brito , Matthieu Wyart

We numerically study structural properties of mechanically stable packings of hard spheres (HS), in a wide range of packing fractions $0.53 \le \phi \le 0.72$. Detailed structural information is obtained from the analysis of orientational…

Soft Condensed Matter · Physics 2014-07-30 Boris A. Klumov , Yuliang Jin , Hernan A. Makse