Improving the Density of Jammed Disordered Packings Using Ellipsoids
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 facecentered cubic lattice has the highest possible packing fraction ϕ = π/<RAD><RCD>18</RCD></RAD> ~ 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 denselyup to ϕ = 0.68 to 0.71 for spheroids with an aspect ratio close to that of M&M's Candiesand 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.
 Publication:

Science
 Pub Date:
 February 2004
 DOI:
 10.1126/science.1093010
 Bibcode:
 2004Sci...303..990D
 Keywords:

 APP PHYSICS