Coarsening versus pattern formation

Alexander A. Nepomnyashchy

doi:10.1016/j.crhy.2015.03.004

Coarsening versus pattern formation
[Coarsening contre formation de motifs]

Alexander A. Nepomnyashchy ¹

¹ Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel

Comptes Rendus. Physique, Coarsening dynamics / Dynamique de coarsening, Volume 16 (2015) no. 3, pp. 267-279.

Résumé
Abstract

Il est connu que des systèmes physiques similaires peuvent révéler deux comportements assez similaires, le coarsening, qui crée un état uniforme ou une structure à grande échelle, ou la formation de motifs ordonnés ou désordonnés, qui ne sont jamais homogénéisés. Nous présentons une description du coarsening utilisant deux modèles basiques simples, l'équation d'Allen–Cahn et celle de Cahn–Hilliard, et discutons les facteurs qui peuvent ralentir et arrêter le processus de coarsening. On trouve parmi ceux-ci l'ancrage de parois de domaines sur des inhomogénéités, les queues oscillatoires de parois de domaines, ainsi que d'autres. Le coarsening de domaines de motifs est aussi discuté.

It is known that similar physical systems can reveal two quite different ways of behavior, either coarsening, which creates a uniform state or a large-scale structure, or formation of ordered or disordered patterns, which are never homogenized. We present a description of coarsening using simple basic models, the Allen–Cahn equation and the Cahn–Hilliard equation, and discuss the factors that may slow down and arrest the process of coarsening. Among them are pinning of domain walls on inhomogeneities, oscillatory tails of domain walls, nonlocal interactions, and others. Coarsening of pattern domains is also discussed.

Publié le : 2015-03-31

DOI : 10.1016/j.crhy.2015.03.004

Keywords: Coarsening, Pattern formation, Domain walls
Mots-clés : Coarsening, Formation de motifs, Parois de domaines

Affiliations des auteurs :

Alexander A. Nepomnyashchy ¹

¹ Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel

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Alexander A. Nepomnyashchy. Coarsening versus pattern formation. Comptes Rendus. Physique, Coarsening dynamics / Dynamique de coarsening, Volume 16 (2015) no. 3, pp. 267-279. doi : 10.1016/j.crhy.2015.03.004. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2015.03.004/

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