Random packing of disks in two dimensions

Abstract

The geometry of a random dense packing of disks of equal size obtained by compacting a random sequential adsorption configuration is discussed. The configuration is shown to be without any long-ranged order, and no local configurations of ordered domains were found. The fraction of area covered by disks is \ensuremath{\theta}=0.772\ifmmode\pm\else\textpm\fi{}0.002, and the number of contacts per disk are 3.02\ifmmode\pm\else\textpm\fi{}0.03. It is argued that this random packing is a stable configuration close to the random loose-packed limit in two dimensions. The packing fraction of the compacted packing is close to a prediction we make of \ensuremath{\theta}=0.78 for a random loose-packed configuration. Several statistical distributions calculated from the limiting geometry is studied. Both the area and circumference distributions of the Voronoi-Dirichlet polygons could be fitted to \ensuremath{\Gamma} distribution functions.