Lattice melting in perpetually pulsating equilibria

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 for ever. Despite this pulsation these systems form lattices when the non-pulsational energy is low, and these disintegrate as that energy is increased. The quasi specific heats show the expected halving as the ‘solid’ is gradually replaced by the gas of independent particles. The forms of the lattices are described here for N ⩽ 20 while they become hexagonal close packed for large N. In the larger N limit, a shell structure is formed. Their large N behaviour is analogous to a γ = 5 / 3 polytropic gas with a quasi-gravity such that every element of fluid attracts every other in proportion to their separation. To cite this article: C. Pichon, D. Lynden-Bell, C. R. Physique 7 (2006).