P. M. Chaikin^*,1,2, Aleksandar Donev^2,3, Weining Man^4,5, Frank H. Stillinger⁶, and Salvatore Torquato^2,3,6,7

^* To whom correspondence should be addressed. Tel.: (212) 998- 7694. E-mail: chaikin@nyu.edu.
¹ Department of Physics and Center for Soft Condensed Matter Research, New York University, New York, New York 10003
² Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544
³ Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544
⁴ Department of Physics, Princeton University, Princeton, New Jersey 08544
⁵ Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544
⁶ Department of Chemistry, Princeton University, Princeton, New Jersey 08544
⁷ Princeton Center for Theoretical Physics, Princeton University, Princeton, New Jersey 08544

Received for review January 9, 2006
Revised manuscript received April 8, 2006
Accepted April 11, 2006

Ind. Eng. Chem. Res., 45 (21), 6960 -6965, 2006

Abstract

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.