Related papers: Symmetry, shape, and order
Packing of spheres is a problem with a long history dating back to Kepler's conjecture in 1611. The highest density is realized in face-centred-cubic (FCC) and hexagonal-close-packed (HCP) arrangements. These are only limiting examples of…
We report an experimental study of the development of orientational order in a crumpled sheet, with a particular focus on the role played by the geometry of confinement. Our experiments are performed on elastomeric sheets immersed in a…
We study the two-dimensional hierarchical rectangle packing problem, motivated by applications in analog integrated circuit layout, facility layout, and logistics. Unlike classical strip or bin packing, the dimensions of the container are…
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…
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…
The aim of the study presented here was the analysis of packings generated according to random sequential adsorption protocol consisting of identical Platonic and Archimedean solids. The computer simulations performed showed, that the…
In the paper, packings built of identical cuboids with a square base created by random sequential adsorption are studied. The result of the study show that the packing of the highest density are obtained for oblate and prolate cuboids of…
The channel size distribution in hard sphere systems, based on the local neighbor correlation of four particle positions, is investigated for all volume fractions up to jamming. For each particle, all three particle combinations of…
The average distance of the equal hard spheres is introduced to evaluate the density of a given arrangement. The absolute smallest value is two radii because the spheres can not be closer to each other than their diameter. The absolute…
Random sequential adsorption (RSA) of various two dimensional objects is studied in order to find a shape which maximizes the saturated packing fraction. This investigation was begun in our previous paper [Cie\'sla et al., Phys. Chem. Chem.…
Packings of regular convex polygons ($n$-gons) that are sufficiently dense have been studied extensively in the context of modeling physical and biological systems as well as discrete and computational geometry. Former results were mainly…
Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to…
Random packings of objects of a particular shape are ubiquitous in science and engineering. However, such jammed matter states have eluded any systematic theoretical treatment due to the strong positional and orientational correlations…
Dense packings of nonoverlapping bodies in three-dimensional Euclidean space are useful models of the structure of a variety of many-particle systems that arise in the physical and biological sciences. Here we investigate the packing…
We study random sequential adsorption (RSA) of a class of solids that can be obtained from a cube by specific cutting of its vertices, in order to find out how the transition from tetrahedral to octahedral symmetry affects the densities of…
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…
Using a Lubachevsky-Stillinger-like growth algorithm combined with biased SWAP Monte Carlo and transient degrees of freedom, we generate ultradense disordered jammed ellipse packings. For all aspect ratios $\alpha$, these packings exhibit…
The steady state packing fraction of a tapped granular bed is studied for different grain shapes via a discrete element method. Grains are monosized regular polygons, from triangles to icosagons. Comparisons with disk packings show that the…
We study random packings of $2\times2$ squares with centers on the square lattice $\mathbb{Z}^{2}$, in which the probability of a packing is proportional to $\lambda$ to the number of squares. We prove that for large $\lambda$, typical…
The packing of hard spheres (HS) of diameter $\sigma$ in a cylinder has been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest packings of HS under this type of confinement,…