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.

The manufacture of high resistance concrete or hard ceramics needs extremely dense granular packings. They can only be realised when the size distribution of grains is strongly polydisperse. Typically powerlaw distributions give the best results. We present a simple packing model for polydisperse distributions, namely a generalized reversible parking lot model. We also discuss the perfectly dense limit, namely Apollonian packings in three dimensions and show in particular the existence of space filling bearings rotating without slip and without torsion.