We consider a family of hard core objects moving as independent BrownianView original: http://arxiv.org/abs/0912.5398
motions confined to a vessel by reflection. These are subject to gravitational
forces modeled by drifts. The stationary distribution for the process has many
interesting implications, including an illustration of the Archimedes'
principle. The analysis rests on constructing reflecting Brownian motion with
drift in a general open connected domain and studying its stationary
distribution. In dimension two we utilize known results about sphere packing.