Dionysian Hard Sphere Packings Are Mechanically Stable at Vanishingly Low Densities.

High strength-to-weight ratio materials can be constructed by either maximizing strength or minimizing weight. Tensegrity structures and aerogels take very different paths to achieving high strength-to-weight ratios but both rely on internal tensile forces. In the absence of tensile forces, removing material eventually destabilizes a structure. Attempts to maximize the strength-to-weight ratio with purely repulsive spheres have proceeded by removing spheres from already stable crystalline structures. This results in a modestly low density and a strength-to-weight ratio much worse than can be achieved with tensile materials. Here, we demonstrate the existence of a packing of hard spheres that has asymptotically zero density and yet maintains finite strength, thus achieving an unbounded strength-to-weight ratio. This construction, which we term Dionysian, is the diametric opposite to the Apollonian sphere packing which completely and stably fills space. We create tools to evaluate the stability and strength of compressive sphere packings. Using these we find that our structures have asymptotically finite bulk and shear moduli and are linearly resistant to every applied deformation, both internal and external. By demonstrating that there is no lower bound on the density of stable structures, this work allows for the construction of arbitrarily lightweight high-strength materials.

Jamming Energy Landscape is Hierarchical and Ultrametric.

The free energy landscape of mean-field marginal glasses is ultrametric. We demonstrate that this feature persists in finite three-dimensional systems that are out of equilibrium by finding sets of minima, which are nearby in configuration space. By calculating the distance between these nearby minima, we produce a small region of the distance metric. This metric exhibits a clear hierarchical structure and shows the signature of an ultrametric space. That such a hierarchy exists for the jamming energy landscape provides direct evidence for the existence of a marginal phase along the zero temperature jamming line.

Flow and fracture in drying nanoparticle suspensions.

Drying aqueous suspensions of monodisperse silica nanoparticles can fracture in remarkable patterns. As the material solidifies, evenly spaced cracks invade from the drying surface, with individual cracks undergoing intermittent motion. We show that the growth of cracks is limited by the advancement of the compaction front, which is governed by a balance of evaporation and flow of fluid at the drying surface. Surprisingly, the macroscopic dynamics of drying show signatures of molecular-scale fluid effects.