Underconstrained jammed packings of nonspherical hard particles: Ellipses and ellipsoids

Aleksandar Donev, Robert Connelly, Frank H. Stillinger, and Salvatore Torquato
Phys. Rev. E 75, 051304 – Published 10 May 2007

Abstract

Continuing on recent computational and experimental work on jammed packings of hard ellipsoids [Donev et al., Science 303, 990 (2004)] 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 (Z¯=2df), 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, Z¯<2df). 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.

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  • Received 16 August 2006

DOI:https://doi.org/10.1103/PhysRevE.75.051304

©2007 American Physical Society

Authors & Affiliations

Aleksandar Donev1,2, Robert Connelly3, Frank H. Stillinger4, and Salvatore Torquato1,2,4,5,*

  • 1Program in Applied and Computational Mathematics, Princeton University, Princeton New Jersey 08544, USA
  • 2PRISM, Princeton University, Princeton, New Jersey 08544, USA
  • 3Department of Mathematics, Cornell University, Ithaca, New York 14853, USA
  • 4Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
  • 5Princeton Center for Theoretical Physics, Princeton University, Princeton, New Jersey 08544, USA

  • *Electronic address: torquato@electron.princeton.edu

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Vol. 75, Iss. 5 — May 2007

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