Title: Statistical mechanics of jammed matter and the nature of fruit packings

Author (Invited): Hernan Makse, City College of New York

Abstract:

The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal. This problem is as much of interest to the mathematician\'s pencil as it is to the granular processing industry all the way to the fruit packing in every corner grocery. There are presently numerous experiments showing that the loosest way to pack spheres gives a density of ~55% (named RLP) while filling all the loose voids results in a maximum density of ~63% (named RCP). While those values seem robustly true, to this date there is no physical interpretation for them. Here we show that random spheres in 3d cannot pack above ~63.4%. The reason for this limit arises from a statistical picture of jammed states in which the RCP can be interpreted as the ground state of the ensemble of jammed matter. The results presented lead to a phase diagram that provides a common view of the hard sphere packing problem and further shedding light on a diverse spectrum of data. Our results suggest an ensemble definition of RLP and RCP, predict their density values, and establish the concomitant equations of state relating observables such as the coordination number, entropy, and volume fraction. The nature of the disorder of the packings is statistically characterized by the entropy, which is shown to be larger in the random loose case than in the random close case. Within a statistical mechanics framework of jammed matter, this result is a natural consequence.