Test Your Strength: Millikan Library and Lloyd Gong Edition

Yes, really. I am very amused.

Tales from the ArXiv: Superballs!

Here is a intriguing new paper that just got posted on the arXiv preprint server.

Title: Optimal Packings of Superballs

Authors: Yang Jiao, Frank Stillinger, Sal Torquato

Abstract: Dense hard-particle packings are intimately related to the structure of low-temperature phases of matter and are useful models of heterogeneous materials and granular media. Most studies of the densest packings in three dimensions have considered spherical shapes, and it is only more recently that nonspherical shapes (e.g., ellipsoids) have been investigated. Superballs (whose shapes are defined by |x1|^2p + |x2|^2p + |x3|^2p <= 1) provide a versatile family of convex particles (p >= 0.5) with both cubic- and octahedral-like shapes as well as concave particles (0 < p < 0.5) with octahedral-like shapes. In this paper, we provide analytical constructions for the densest known superball packings for all convex and concave cases. The candidate maximally dense packings are certain families of Bravais lattice packings. The maximal packing density as a function of p is nonanalytic at the sphere-point (p = 1) and increases dramatically as p moves away from unity. The packing characteristics determined by the broken rotational symmetry of superballs are similar to but richer than their two-dimensional "superdisk" counterparts, and are distinctly different from that of ellipsoid packings. Our candidate optimal superball packings provide a starting point to quantify the equilibrium phase behavior of superball systems, which should deepen our understanding of the statistical thermodynamics of nonspherical-particle systems.


Comment: But if they want to do something really cool, they'll climb to the top of the tallest building on campus and drop all of the superballs from there. (Not that I got this idea from anything I've seen before or anything...