  The study on the relationship between the spheres and voids in packing system
suggests that the edge effect at the interface between the container and the
particles is an important factor lowering the packing ratio. To pack spheres in
a container with high packing ratio, an optimized sphere size and an optimized
sequence of sphere sizes exist for the packing of single-sized and multi-sized
spheres, respectively. We suggest that the concepts of volume and contact
should be clearly defined for the packing problem in specific scale.
