Studies of random close packing of spheres have advanced our knowledge about the structure of systems such as liquids, glasses, emulsions, granular media, and amorphous solids. In confined geometries, the structural properties of random-packed systems will change. To understand these changes, we study random close packing in finite-sized confined systems, in both two and three dimensions. Each ...

This paper summarizes recent results about the Hausdorff measure of the image, graph and level sets of Gaussian random fields, the packing dimension and packing measure of the image of fractional Brownian motion, the local times and multiple points of Gaussian random fields. Some open problems are also pointed out.

The packing fraction ρ of a collection of hard spheres in three dimension cannot exceed a maximum of about 0.74. In that limit, the spheres are arranged in a close-packed crystalline lattice (such as the HCP lattice). If, however, a loose collection of hard spheres is compactified, starting from some random initial condition, then the maximum packing fraction ρc that can be achieved by compacti...