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The microstructure of coagulated colloidal particles, for which the inter-particle potential is described by the DLVO theory, is strongly influenced by the particles' surface potential. Depending on its value, the resulting microstructures…

Soft Condensed Matter · Physics 2009-11-09 Iwan Schenker , Frank T. Filser , Tomaso Aste , Hans J. Herrmann , Ludwig J. Gauckler

Maximally random jammed (MRJ) particle packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The prediction of the MRJ packing density phi, among other packing…

Soft Condensed Matter · Physics 2016-05-24 Jianxiang Tian , Y. Xu , Y. Jiao , S. Torquato

Sphere packing problems have a rich history in both mathematics and physics; yet, relatively few analytical analyses of sphere packings exist, and answers to seemingly simple questions are unknown. Here, we present an analytical method for…

Soft Condensed Matter · Physics 2013-10-17 Natalie Arkus , Vinothan N. Manoharan , Michael P. Brenner

We provide a perfect sampling algorithm for the hard-sphere model on subsets of $\mathbb{R}^d$ with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate sampling…

Data Structures and Algorithms · Computer Science 2024-08-22 Konrad Anand , Andreas Göbel , Marcus Pappik , Will Perkins

This is the sixth 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

Discovering relationships between materials' microstructures and mechanical properties is a key goal of materials science. Here, we outline a strategy exploiting Bayesian optimization to efficiently search the multidimensional space of…

Materials Science · Physics 2022-12-08 Mika Sarvilahti , Lasse Laurson

We study jammed configurations of hard spheres as a function of compression speed using an event-driven molecular dynamics algorithm. We find that during the compression, the pressure follows closely the metastable liquid branch until the…

Soft Condensed Matter · Physics 2016-05-19 Michiel Hermes , Marjolein Dijkstra

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

Metric Geometry · Mathematics 2007-05-23 Boris D. Lubachevsky , Ronald Graham

We study the problem of discrete geometric packing. Here, given weighted regions (say in the plane) and points (with capacities), one has to pick a maximum weight subset of the regions such that no point is covered more than its capacity.…

Computational Geometry · Computer Science 2011-12-01 Alina Ene , Sariel Har-Peled , Benjamin Raichel

We study the ballistic adsorption of a polydisperse mixture of spheres onto a line. Within a mean-field approximation, the problem can be analytically solved by means of a kinetic equation for the gap distribution. In the mean-field…

Soft Condensed Matter · Physics 2009-10-31 Romualdo Pastor-Satorras

We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…

Statistical Mechanics · Physics 2008-10-17 Chih-Yuan Tseng , Ariel Caticha

Many experimental studies of protein deposition on solid surfaces involve alternating adsorption/desorption steps. In this paper, we investigate the effect of a desorption step (separating two adsorption steps) on the kinetics, the…

Statistical Mechanics · Physics 2009-10-31 Paul R. Van Tassel , Pascal Viot , Gilles Tarjus , Jeremy J. Ramsden , Julian Talbot

Granular materials segregate spontaneously due to differences in particle size, shape, density and flow behaviour. In this paper we experimentally investigate density-difference-driven segregation for a range of density ratios and a range…

Soft Condensed Matter · Physics 2021-05-05 Monica Tirapelle , Andrea Santomaso , Patrick Richard , Riccardo Artoni

In [3], algorithms to compute the density of the distance to a random variable uniformly distributed in (a) a ball, (b) a disk, (c) a line segment, or (d) a polygone were introduced. For case (d), the algorithm, based on Green's theorem,…

Computational Geometry · Computer Science 2019-06-06 Vincent Guigues

Unlike atoms, colloidal particles are not identical, but can only be synthesised within a finite size tolerance. Colloids are therefore polydisperse, i.e. mixtures of infinitely many components with sizes drawn from a continuous…

Soft Condensed Matter · Physics 2009-11-07 R. M. L. Evans , C. B. Holmes

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

Predicting theoretically the highest density, which a disordered packing of discs can achieve, has been a long-standing unresolved problem. Such predictions are hindered by two difficulties - the dependence of the density on the packing…

Soft Condensed Matter · Physics 2026-05-26 Raphael Blumenfeld

We have recently devised organizing principles to obtain maximally dense packings of the Platonic and Archimedean solids, and certain smoothly-shaped convex nonspherical particles [Torquato and Jiao, Phys. Rev. E 81, 041310 (2010)]. Here we…

Statistical Mechanics · Physics 2012-07-26 Salvatore Torquato , Yang Jiao

In this paper we study the combined effects of size and shape of small solid state particles on the absorption, emission and scattering characteristics. We use the statistical approach to calculate these optical properties. In this approach…

Astrophysics · Physics 2009-11-10 M. Min , J. W. Hovenier , A. de Koter

We have formulated the problem of generating periodic dense paritcle packings as an optimization problem called the Adaptive Shrinking Cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E {\bf 80}, 041104 (2009)]. Because the…

Statistical Mechanics · Physics 2010-12-15 Sal Torquato , Yang Jiao