Investigating jammed matter from a granocentric point of view

Katherine Newhall, CIMS

Kepler's conjecture that the face-centered-cubic lattice is the densest packing of uniform spheres has long been accepted and recently proven.  However, if marbles are poured into a jar, they do not arrange into this lattice, rather they retain a random state.  Upon agitation the marbles will compact further, settling into a reproducible random close packed state.  The theoretical density of this state and its statistical description remain unknown.  I will present a stochastic model capable of generating the local statistical quantities of experimental random packing of hard spheres.  I will also discuss an application of jammed packing to biological tissue by deriving a 3D version of the empirical Lewis' Law relating the average cell area to the number of cell edges in 2D epithelial tissue.