Improving the density of jammed disordered packings using ellipsoids

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 phi=pi/root18approximate to0.74. It is also well known that certain random (amorphous) jammed packings have phiapproximate to0.64. Here, we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely-up to phi=0.68 to 0.71 for spheroids with an aspect ratio close to that of M&M's Candies-and even approach phiapproximate to0.74 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 Zapproximate to10 for our spheroids, as compared to Zapproximate to6 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.