### Abstract

Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction ψ = π/√18 ≈ 0.74. It is also well known that certain random (amorphous) jammed packings have ψ ≈ 0.64. Here, we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely-up to ψ = 0.68 to 0.71 for spheroids with an aspect ratio close to that of M&M's Candies-and even approach ψ ≈ 0.74 for ellipsoids with other aspect ratios. We suggest that the higher density is directly related to the higher number of degrees of freedom per particle and thus the larger number of particle contacts required to mechanically stabilize the packing. We measured the number of contacts per particle Z ≈ 10 for our spheroids, as compared to Z ≈ 6 for spheres. Our results have implications for a broad range of scientific disciplines, including the properties of granular media and ceramics, glass formation, and discrete geometry.

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

Pages (from-to) | 990-993 |

Number of pages | 4 |

Journal | Science |

Volume | 303 |

Issue number | 5660 |

DOIs | |

State | Published - Feb 13 2004 |

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### ASJC Scopus subject areas

- General

### Cite this

*Science*,

*303*(5660), 990-993. https://doi.org/10.1126/science.1093010

**Improving the Density of Jammed Disordered Packings Using Ellipsoids.** / Donev, Aleksandar; Cisse, Ibrahim; Sachs, David; Variano, Evan A.; Stillinger, Frank H.; Connelly, Robert; Torquato, Salvatore; Chaikin, P. M.

Research output: Contribution to journal › Article

*Science*, vol. 303, no. 5660, pp. 990-993. https://doi.org/10.1126/science.1093010

}

TY - JOUR

T1 - Improving the Density of Jammed Disordered Packings Using Ellipsoids

AU - Donev, Aleksandar

AU - Cisse, Ibrahim

AU - Sachs, David

AU - Variano, Evan A.

AU - Stillinger, Frank H.

AU - Connelly, Robert

AU - Torquato, Salvatore

AU - Chaikin, P. M.

PY - 2004/2/13

Y1 - 2004/2/13

N2 - Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction ψ = π/√18 ≈ 0.74. It is also well known that certain random (amorphous) jammed packings have ψ ≈ 0.64. Here, we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely-up to ψ = 0.68 to 0.71 for spheroids with an aspect ratio close to that of M&M's Candies-and even approach ψ ≈ 0.74 for ellipsoids with other aspect ratios. We suggest that the higher density is directly related to the higher number of degrees of freedom per particle and thus the larger number of particle contacts required to mechanically stabilize the packing. We measured the number of contacts per particle Z ≈ 10 for our spheroids, as compared to Z ≈ 6 for spheres. Our results have implications for a broad range of scientific disciplines, including the properties of granular media and ceramics, glass formation, and discrete geometry.

AB - Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction ψ = π/√18 ≈ 0.74. It is also well known that certain random (amorphous) jammed packings have ψ ≈ 0.64. Here, we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely-up to ψ = 0.68 to 0.71 for spheroids with an aspect ratio close to that of M&M's Candies-and even approach ψ ≈ 0.74 for ellipsoids with other aspect ratios. We suggest that the higher density is directly related to the higher number of degrees of freedom per particle and thus the larger number of particle contacts required to mechanically stabilize the packing. We measured the number of contacts per particle Z ≈ 10 for our spheroids, as compared to Z ≈ 6 for spheres. Our results have implications for a broad range of scientific disciplines, including the properties of granular media and ceramics, glass formation, and discrete geometry.

UR - http://www.scopus.com/inward/record.url?scp=1142274207&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1142274207&partnerID=8YFLogxK

U2 - 10.1126/science.1093010

DO - 10.1126/science.1093010

M3 - Article

VL - 303

SP - 990

EP - 993

JO - Science

JF - Science

SN - 0036-8075

IS - 5660

ER -