Having a ball! (ok, but it's more exciting than "Geometrically Exact Treatment of percolation through voids among overlapping spheres")

Fluid flow and charge transport through voids around impenetrable inclusions is relevant in the case of materials comprised of impermeable grains. If the density of the latter is low enough, the void volumes between the grains form a system spanning connected network, allowing for fluid flow on macroscopic scales. On the other hand, higher concentrations of impenetrable inclusions interrupt void volumes and thereby prevent fluid flow through the material. The critical density bounding this transition between navigable void networks and the absence of permeability on macroscipic scales is a percolation transition. Often the absence of a lattice or well defined component volumes hampers an exact geometric treatment. However, in the case of systems comprised of randomly placed interpenetrating spheres, a rigorous geometric treatment is avaliable. Our technique, which scales linearly in the system volume, is also readily generalized to the case of non-monodispersed spheres. After creating a disorder realization, one finds the intersection curves of neighboring spheres, which are circles. Additional neighboring spheres block portions of the circles, dubbed "dark arcs". The latter are tracked as they proliferate and/or fuse together, ultimately yiedling "light" (non-occluded) arcs bounded in points that may be indexed in terms of trios of intersection spheres, except in cases in which the entire circle goes dark, swallowed whole by neighboring inclusions. Subsequently, common intersection points are joined together. Periodic boundary conditions are imposed. A light arc network which spans the cube shaped system volume indicates a navigable void volume network. Otherwise, no route through interstitial volumes exists, and the system is deemed not to percolation. We endeavor to provide preliminary result, and we breifly discuss generalizations to the analysis of systems made up of non-spherical impermeable inclusions.