 
Summary: Understanding complex matter from simple packing models
T. Aste, G. Delaney and T. Di Matteo
Department of Applied Mathematics, The Australian National University, 0200 Canberra,
ACT, Australia.
ABSTRACT
By pouring equal balls into a container one obtains disordered packings with fascinating properties which might
shed light on several elusive properties of complex materials such as amorphous metals or colloids. In any real
experiment with equalsized spheres one cannot reach packing fractions (fraction of volume occupied by the
spheres respect to the total volume, ) below the Random Loose Packing limit (RLP, 0.555) or above the
Random Close Packing limit (RCP, 0.645) unless order is externally induced. What is happening at these
two limits is an open unanswered question. In this paper we address this question by combining statistical
geometry and statistical mechanics methods. Evidences of phase transitions occurring at the RLP and RCP
limits are reported.
PACS: 45.70.n Granular Systems 45.70.Cc Static sandpiles; Granular Compaction 81.05.RmPorous materials;
granular materials
1. INTRODUCTION
Equal sized spheres are the simplest threedimensional geometrical objects. However, despite such simplicity
very little is known about the structures that they form when they pack together. In 1611 Kepler conjectured
that equal spheres cannot be packed denser than the packing fraction = /
