Computer simulation of hard-disc packings with spherical boundary conditions

Abstract

Random packings of hard discs are generated on the surface of a sphere by a “successive compression” technique. Since the discs follow the curvature of the sphere their shape is similar to that of watch glasses. The disordering influence of curvature prohibits hexagonal packings. Increasing the number of discs (N) means that the particles shrink compared with the supporting sphere. Accordingly, the effect of curvature decreases. The random dense-packing fraction η_RDP(N) obtained in the compression runs is seen to increase with increasing N. The calculations result in a limiting packing fraction η_RDP(N→∞) between 0.866 and 0.874 with an average contact number between 3 and 4. This may be compared with η= 0.907 and contact number 6 for (Euclidean) hexagonal packing. The possibility of regular disc packings on the surface of a sphere is also considered.