Some observations on the random packing of hard ellipsoids

Recent studies of random packing of ellipsoids show a cusplike increase in the packing density as the aspect ratio deviates from 1 (spheres) followed by a maximum and then a strong density decrease at a higher aspect ratio. We introduce a simple one-dimensional model, the "Paris" parking problem with ellipses randomly oriented along a curb, with many of the same features. Our results suggest that the cusp results from approaching a terminal (jammed) random state, the density increase results from relaxing a parameter constraint (orientation or size of a particle) in the random packing, and the density decrease results from excluded volume effects. We also discuss the isostatic conjecture for strict and local jamming.