Caging of a d-dimensional sphere and its relevance for the random dense sphere packing - art. no. 021404

We analyze the caging of a hard sphere (i.e.,the complete arrest of all tra nslational motions) by randomly distributed static contact points on the sp here surface for arbitrary dimension d greater than or equal to1, and prove that the average number of uncorrelated contacts required to cage a sphere is (N)(d)=2d+1. Computer simulations, which confirm this analytical result , are also used to model the effect of correlations between contacts that o ccur in real hard-sphere systems. Our analysis predicts an average coordina tion number of 4.79 (+/-0.02) for caged spheres, which agrees surprisingly well with the experimental coordination number for random sphere packings r eported by Mason [Nature 217, 733 (1968)]. This result supports the physica l picture that the coordination number in random dense sphere packings is p rimarily determined by caging effects. It also suggests that it should be p ossible to construct such packings from a local caging rule.