Related papers: Packing Concave Molecules in Crystals and Amorphou…
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…
Packing problems, which ask how to arrange a collection of objects in space to meet certain criteria, are important in a great many physical and biological systems, where geometrical arrangements at small scales control behaviour at larger…
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…
Questions surrounding the spatial disposition of particles in various condensed-matter systems continue to pose many theoretical challenges. This paper explores the geometric availability of amorphous many-particle configurations that…
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…
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…
We algorithmically characterize the maximal contact number problem for finite congruent lattice sphere packings in $\mathbb{R}^d$ and show that in $\mathbb{R}^3$ this problem is equivalent to determining the maximal coordination of a…
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…
Mathematical crystal chemistry views crystal structures as the optimal solutions of mathematical optimization problem formalizing inorganic structural chemistry. This paper introduces the minimum and maximum atomic radii depending on the…
Packings of hard polyhedra have been studied for centuries due to their mathematical aesthetic and more recently for their applications in fields such as nanoscience, granular and colloidal matter, and biology. In all these fields, particle…
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…
Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
A rule due to Bravais of wide validity for crystals is that their surfaces correspond to the densest planes of atoms in the bulk of the material. Comparing a theoretical model of i-AlPdMn with experimental results, we find that this…
We revisit the densest binary sphere packings (DBSP) under the periodic boundary conditions and present an updated phase diagram, including newly found 12 putative densest structures over the $x - \alpha$ plane, where $x$ is the relative…
Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure…
We use numerical simulations to study the crystallization of monodisperse systems of hard aspherical particles. We find that particle shape and crystallizability can be easily related to each other when particles are characterized in terms…
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…
The behavior of identical particles interacting through the harmonic-repulsive pair potential has been studied in 3D using molecular dynamics simulations at a number of different densities. We found that at many densities, as the…
Dense packings of hard particles have important applications in many fields, including condensed matter physics, discrete geometry and cell biology. In this paper, we employ a stochastic search implementation of the Torquato-Jiao…