Numéro
J. Phys. I France
Volume 5, Numéro 1, January 1995
Page(s) 97 - 109
DOI https://doi.org/10.1051/jp1:1995117
DOI: 10.1051/jp1:1995117
J. Phys. I France 5 (1995) 97-109

Maximum Entropy Analysis of Disordered Droplet Patterns

Clément Sire and Michael Seul

AT&T Bell Laboratories, Murray Hill, NJ 07974, U.S.A.


(Received 6 June 1994, received in final form 12 September 1994, accepted 16 September 1994)

Abstract
A maximum entropy description is developed for disordered planar patterns of droplets and applied to the analysis of such patterns formed in a two-dimensional binary mixture during late-stage coarsening. Global correlations, arising from local "packing" constraints, are shown to produce a virtually symmetric shape of the scaled droplet radius distribution. The examination of geometrical and topological pattern statistics reveals a prominent role of screening at short distance, both of domain area fluctuations, as well as of topological charge.

Résumé
Nous développons un formalisme d'entropie maximale afin de décrire les configurations désordonnées formées au cours de la séparation de phase d'un mélange binaire bidimensionnel. Nous montrons que corrélations provenant des contraintes géométriques locales conduisent à une distribution quasiment gaussienne pour les rayons des bulles de la phase minoritaire. L'examen statistique des propriétés géométriques et topologiques des images expérimentales révèle le rôle majeur joué par l'écrantage à courte distance de la charge topologique, et des fluctuations de la taille des bulles.



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