Dense packings

Abstract

Dense packings of granular systems are of fundamental importance in the manufacture of hard ceramics and ultra strong concrete. We generalize the reversible parking lot model to describe polydisperse dynamic packings. The key ingredient lies in the size distribution of grains. In the extreme case of perfect filling of spherical beads (density one), one has Apollonian tilings with a powerlaw distribution of sizes. We will present the recent discovery of 3D packings which also have the freedom to rotate (bearings) in three dimensions.