Shell structures with "magic numbers" of spheres in a swirled dish

Molecular dynamic simulations of a low number N< or = 54 of spheres in a swirled dish yield solid-like shell structures with stable rings. In contrast to known granular media, solidification occurs only at singular values of N: 7, 8, 12, 14, 19, 21, 30, 37, 40. Otherwise, we obtain intermittent switching of particles between rings -- the average switching time scaling exponentially with a control parameter -- or fluid-like disorder. Stable shell structures can be classified by particular geometrical arrangements (one-centered hexagonal, one-centered "quasicircular," three centered, and four centered).