A Caltech Library Service

Improving the Density of Jammed Disordered Packings Using Ellipsoids

Donev, Aleksander and Cissé, Ibrahim and Sachs, David and Variano, Evan A. and Stillinger, Frank H. and Connelly, Robert and Torquato, Salvatore and Chaikin, P. M. (2004) Improving the Density of Jammed Disordered Packings Using Ellipsoids. Science, 303 (5660). pp. 990-993. ISSN 0036-8075. doi:10.1126/science.1093010.

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item:


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 φ = π/√18 ≈ 0.74. It is also well known that certain random (amorphous) jammed packings have φ ≈ 0.64. Here, we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely—up to φ = 0.68 to 0.71 for spheroids with an aspect ratio close to that of M&M's Candies—and even approach φ ≈ 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.

Item Type:Article
Related URLs:
URLURL TypeDescription
Cissé, Ibrahim0000-0002-8764-1809
Variano, Evan A.0000-0001-5102-238X
Stillinger, Frank H.0000-0002-1225-8186
Connelly, Robert0000-0003-3757-8124
Torquato, Salvatore0000-0003-4614-335X
Chaikin, P. M.0000-0001-9864-0089
Additional Information:© 2004 American Association for the Advancement of Science. Received for publication October 27, 2003. Accepted for publication December 9, 2003. Supported by American Chemical Society PRF grant 36967-AC9 (S.T., A.D., F.H.S.), NASA grant NAG3-1762 (P.M.C.), and NSF grants DMR-0213706 (S.T., P.M.C., A.D., F.H.S.), DMS-0312067 (S.T., A.D., F.H.S.), and DMS-0209595 (R.C.).
Funding AgencyGrant Number
American Chemical Society Petroleum Research Fund36967-AC9
Issue or Number:5660
Record Number:CaltechAUTHORS:20201112-143949250
Persistent URL:
Official Citation:Improving the Density of Jammed Disordered Packings Using Ellipsoids BY ALEKSANDAR DONEV, IBRAHIM CISSE, DAVID SACHS, EVAN A. VARIANO, FRANK H. STILLINGER, ROBERT CONNELLY, SALVATORE TORQUATO, P. M. CHAIKIN Science 13 Feb 2004: Vol. 303, Issue 5660, pp. 990-993 DOI: 10.1126/science.1093010
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106657
Deposited By: George Porter
Deposited On:16 Nov 2020 17:43
Last Modified:16 Nov 2021 18:55

Repository Staff Only: item control page