Sphere Packings, I

Density Doubling, Double-circulants, and New Sphere Packings

New nonlattice sphere packings in dimensions 20, 22, and 44–47 that are denser than the best previously known sphere packings were recently discovered. We extend these results, showing that the density of many sphere packings in dimensions just below a power of 2 can be doubled using orthogonal binary codes. This produces new dense sphere packings in Rn for n = 25, 26, . . . , 31 and 55, 56, . ...

Deriving Finite Sphere Packings

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 deriving all packings of n spheres in R3 satisfying minimal rigidity constraints (≥ 3 contacts per sphere and ≥ 3n− 6 total contacts). We derive such packing...

Sphere Packings Iv

Disks vs. Spheres: Contrasting Properties of Random Packings

Collections of random packings of rigid disks and spheres have been generated by computer using a previously described concurrent algorithm. Particles begin as infinitesimal moving points, grow in size at a uniform rate, undergo energynonconserving collisions, and eventually jam up. Periodic boundary conditions apply, and various numbers of particles have been considered (N~<2000 for disks, N~<...

Average Kissing Numbers for Non-congruent Sphere Packings