THE RANDOM PARKING OF SPHERES ON SPHERES

Given a ''target'' sphere of radius r(1) and ''probe'' spheres of radi us r(2), we consider, as a function of r(2)/r(1), how many probe spher es, on average, can be attached to the target sphere if (1) the attach ment sites are chosen at random, (2) the probe spheres are not permitt ed to overlap, and (3) each attachment is irreversible. We also consid er two separate extremes for selecting new attachment sites: Each prob e sphere is either permitted to diffuse into place from a large distan ce, or the attachment site is chosen completely at random. Diffusion-c ontrolled attachment produces a slightly higher packing density than c ompletely random attachment. (C) 1996 American Institute of Physics.