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 tetrahedron into a less ideal, physical, tetrahedron and all the way to the sphere. Thus, we also connect the two well-studied problems of sphere ...

Three partial radial distribution functions [RDF's] are calculated by means of relaxed dense-random packing models for a Fe80B20 glass. The model structures reproduce fairly well recently reported experimental partial RDF's derived from x-ray diffraction and neutron diffraction using isotopic substitutional methods. Most significantly, both the model calculated by means of relaxed dense-random ...

The problem of packing a system of particles as densely as possible is foundational in the field of discrete geometry and is a powerful model in the material and biological sciences. As packing problems retreat from the reach of solution by analytic constructions, the importance of an efficient numerical method for conducting de novo (from-scratch) searches for dense packings becomes crucial. I...

The most dense random packings of binary assemblies of hard disks in the plane are considered for the case of disks with a small diRerence in their radii. An expression for the dependence of the packing density on the relative diRerence in disk sizes, disk concentration, and mean value of the gaps is derived. The computer simulation of the random dense packing is carried out using various algor...

Entropy drives the phase behavior of colloids ranging from dense suspensions of hard spheres or rods to dilute suspensions of hard spheres and depletants. Entropic ordering of anisotropic shapes into complex crystals, liquid crystals, and even quasicrystals was demonstrated recently in computer simulations and experiments. The ordering of shapes appears to arise from the emergence of directiona...

We study the length Lk of the shortest permutation containing all patterns of length k. We establish the bounds e−2k2 < Lk ≤ (2/3 + o(1))k2 . We also prove that as k → ∞, there are permutations of length (1/4+o(1))k2 containing almost all patterns of length k.

It has been shown [Balister, 2001] that if n is odd and m1, . . . , mt are integers with mi ≥ 3 and ∑t i=1 mi = |E(Kn)| then Kn can be decomposed as an edge-disjoint union of closed trails of lengths m1, . . . , mt. Here we show that the corresponding result is also true for any sufficiently large and sufficiently dense even graph G.

Human nuclear cataract formation is a multi-factorial disease with contributions to light scattering from many cellular sources that change their scattering properties over decades. The aging process produces aggregation of cytoplasmic crystallin proteins, which alters the protein packing and texture of the cytoplasm. Previous studies of the cytoplasmic texture quantified increases in density f...