### Abstract

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 language | English (US) |
---|---|

Article number | 051304 |

Journal | Physical Review E |

Volume | 75 |

Issue number | 5 |

DOIs | |

State | Published - May 10 2007 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Physical Review E*,

*75*(5), [051304]. https://doi.org/10.1103/PhysRevE.75.051304

**Underconstrained jammed packings of nonspherical hard particles : Ellipses and ellipsoids.** / Donev, Aleksandar; Connelly, Robert; Stillinger, Frank H.; Torquato, Salvatore.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 75, no. 5, 051304. https://doi.org/10.1103/PhysRevE.75.051304

}

TY - JOUR

T1 - Underconstrained jammed packings of nonspherical hard particles

T2 - Ellipses and ellipsoids

AU - Donev, Aleksandar

AU - Connelly, Robert

AU - Stillinger, Frank H.

AU - Torquato, Salvatore

PY - 2007/5/10

Y1 - 2007/5/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34347270239&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34347270239&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.75.051304

DO - 10.1103/PhysRevE.75.051304

M3 - Article

VL - 75

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 5

M1 - 051304

ER -