Quasi-universality in the packing of uniform spheres under gravity

A hypothesis that packing fraction alone can be used to characterize the structure of a sphere packing, known as the quasi-universality in the literature, is tested. The analysis, conducted in terms of coordination number, radial distribution function, and structural properties from the Voronoi/Delaunay tessellation, is based on the packing results generated under different conditions, covering a wide packing fraction range. The results show strong similarities in these properties for a given packing fraction, indicating that although not generally valid, the quasi-universality approximately holds for the packing of spheres formed when the gravity is the driving force. The usefulness of this finding is also demonstrated through representative examples.