Lattice melting in perpetually pulsating equilibria

Christophe Pichon; Donald Lynden-Bell

doi:10.1016/j.crhy.2006.03.007

Lattice melting in perpetually pulsating equilibria
[Fusion de réseaux en équilibre d'oscillations perpétuelles]

Christophe Pichon ¹ ; Donald Lynden-Bell ²

¹ Institut d'astrophysique de Paris, UMR 7595 UPMC, 98 bis, boulevard d'Arago, 75014 Paris, France
² Institute of Astronomy and Clare College, Madingley Road, Cambridge CB3 0HA, UK

Comptes Rendus. Physique, Statistical mechanics of non-extensive systems, Volume 7 (2006) no. 3-4, pp. 373-382.

Résumé
Abstract

Les systèmes dont l'énergie potentielle est constituée d'une composante en $r^{−2}$ et d'une composante en $r^{2}$ ne presentent pas de relaxation violente vers l'équilibre du viriel mais vont osciller fortement indéfiniment. En dépit de ces pulsations, de tels systèmes forment un réseau quand l'énergie non oscillatoire reste faible, et se désintegrent si elle augmente. Leurs quasi chaleur spécifique est divisée par deux quand le gaz de particules indépendantes remplace la phase solide. La forme du crystal est décrite ici pour $N ⩽ 20$ . Dans la limite des grands N le réseau se stratifie en coquilles suivant un motif hexagonal compact.

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.

Publié le : 2006-04-01

DOI : 10.1016/j.crhy.2006.03.007

Keywords: Gravitation, Statistical mechanics, Phase transition
Mots-clés : Gravitation, Mécanique statistique, Transition de phase

Affiliations des auteurs :

Christophe Pichon ¹ ; Donald Lynden-Bell ²

¹ Institut d'astrophysique de Paris, UMR 7595 UPMC, 98 bis, boulevard d'Arago, 75014 Paris, France
² Institute of Astronomy and Clare College, Madingley Road, Cambridge CB3 0HA, UK

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     title = {Lattice melting in perpetually pulsating equilibria},
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     pages = {373--382},
     publisher = {Elsevier},
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     number = {3-4},
     year = {2006},
     doi = {10.1016/j.crhy.2006.03.007},
     language = {en},
}

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Christophe Pichon; Donald Lynden-Bell. Lattice melting in perpetually pulsating equilibria. Comptes Rendus. Physique, Statistical mechanics of non-extensive systems, Volume 7 (2006) no. 3-4, pp. 373-382. doi : 10.1016/j.crhy.2006.03.007. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2006.03.007/

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