Hypoconstrained Jammed Packings of Nonspherical Hard Particles: Ellipses and Ellipsoids

TL;DR

This paper investigates jamming in packings of nonspherical particles like ellipsoids, revealing that such packings can be jammed even when they are hypoconstrained, and develops algorithms to generate and analyze these packings.

Contribution

It introduces first- and second-order jamming conditions for nonspherical particles and demonstrates that hypoconstrained packings can still be jammed, challenging existing isocounting conjectures.

Findings

Nonspherical packings can be jammed despite being hypoconstrained.

Developed an algorithm to generate jammed packings of ellipsoids and ellipses.

Analyzed behavior near the sphere point and for nearly jammed packings.

Abstract

Continuing on recent computational and experimental work on jammed packings of hard ellipsoids [Donev et al., Science, vol. 303, 990-993] we consider jamming in packings of smooth strictly convex nonspherical hard particles. We explain why the isocounting conjecture, which states that for large disordered jammed packings the average contact number per particle is twice the number of degrees of freedom per particle (\bar{Z}=2d_{f}), does not apply to nonspherical particles. We develop first- and second-order conditions for jamming, and demonstrate that packings of nonspherical particles can be jammed even though they are hypoconstrained (\bar{Z}<2d_{f}). We apply an algorithm using these conditions to computer-generated hypoconstrained ellipsoid and ellipse packings and demonstrate that our algorithm does produce jammed packings, even close to the sphere point. We also consider packings that are nearly jammed and draw connections to packings of deformable (but stiff) particles. Finally, we consider the jamming conditions for nearly spherical particles and explain quantitatively the behavior we observe in the vicinity of the sphere point.