Systems whose potential energies consists of pieces that scale as $r^{-2}$ together with pieces that scale as $r^2$, show no violent relaxation to Virial equilibrium but may pulsate at considerable amplitude forever. Despite this pulsation these systems form lattices when the nonpulsational “energy” is low, and these disintegrate as that energy is increased. The “specific heats” show the expected halving as the “solid” is gradually replaced by the “fluid” of independent particles. The forms of the lattices are described here for $N⩽18$ and they become hexagonal close packed for large $N$. In the larger $N$ limit, a shell structure is formed. Their large $N$ behavior is analogous to a $\gamma =5∕3$ polytropic fluid with a quasigravity such that every element of fluid attracts every other in proportion to their separation. For such a fluid, we study the “rotating pulsating equilibria” and their relaxation back to uniform but pulsating rotation. We also compare the rotating pulsating fluid to its discrete counterpart, and study the rate at which the rotating crystal redistributes angular momentum and mixes as a function of extra heat content.

• Received 13 September 2006

DOI:https://doi.org/10.1103/PhysRevE.75.011125