We study the structure of numerically simulated hard sphere packings at different densities by investigating local tetrahedral configurations of the spheres. Clusters of tetrahedra adjacent by faces present relatively dense aggregates of spheres atypical for crystals. The number of spheres participating in such polytetrahedral configurations increases with densification of the packing, and at t...

We present the densest known packing of regular tetrahedra with density φ = 4000 4671 = 0.856347 . . . . Like the recently discovered packings of Kallus et al. and Torquato–Jiao, our packing is crystalline with a unit cell of four tetrahedra forming two triangular dipyramids (dimer clusters). We show that our packing has maximal density within a three-parameter family of dimer packings. Numeric...

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...

In this paper we generalize the classical theorem of Thue about the optimal circular disc packing in the plane. We are given a family of circular discs, not necessarily of equal radii, with the property that the inflation of every disc by a factor of 2 around its center does not contain any center of another disc in the family (notice that this implies that the family of discs is a packing). We...

We study packing densities for set partitions, which is a generalization of packing words. We use results from the literature about packing densities for permutations and words to provide packing densities for set partitions. These results give us most of the packing densities for partitions of the set {1, 2, 3}. In the final section we determine the packing density of the set partition {{1, 3}...

The packing density of the regular cross-polytope in Euclidean n-space is unknown except in dimensions 2 and 4 where it is 1. The only non-trivial upper bound is due to Gravel, Elser, and Kallus [9] who proved that for n = 3 the packing density of the regular octahedron is at most 1 − 1.4 . . .× 10. In this paper, we prove upper bounds for the packing density of the n-dimensional regular cross-...