Underconstrained jammed packings of nonspherical hard particles: Ellipses and ellipsoids

Aleksandar Donev, Robert Connelly, Frank H. Stillinger, Salvatore Torquato

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218 Scopus citations


Continuing on recent computational and experimental work on jammed packings of hard ellipsoids we consider jamming in packings of smooth strictly convex nonspherical hard particles. We explain why an 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 (Z̄ =2 df), 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 underconstrained (hypoconstrained, Z̄ <2 df). 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.

Original languageEnglish (US)
Article number051304
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
StatePublished - May 10 2007

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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