Three-Dimensional Apollonian Packing as a Model for Dense Granular Systems

An iterative procedure according to which new spheres are inserted between existing ones is realized for computer simulation of dense granular systems. The method is based on the rigorous geometrical Voronoi-Delaunay approach generalized for pore volume analysis inside an ensemble of polydisperse hard spheres [N. N. Medvedev, Dokl. Akad. Nauk 337, 767 (1994)] [Dokl. Phys. Chem. 337, 157 (1994)]]. Models with packing fraction $\eta \sim 0.9$ are constructed. The particle size distribution and fractal nature of the packings are investigated. The fractal dimension $D=2.45\mathrm{}$ is obtained.