VILLAIN-GUILLOT, Simon; JOSSERAND, Christophe

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VILLAIN-GUILLOT, Simon
Centre de physique moléculaire optique et hertzienne [CPMOH]

JOSSERAND, Christophe
Laboratoire de modélisation en mécanique [LMM]

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Ce document a été publié dans

Physical Review E : Statistical, Nonlinear, and Soft Matter Physics. 2002, vol. 66, p. 036308

American Physical Society

Résumé en anglais

We study the growth of a periodic pattern in one dimension for a model of spinodal decomposition, the Cahn-Hilliard equation. We particularly focus on the intermediate region, where the non-linearity cannot be negected anymore, and before the coalescence dominates. The dynamics is captured through the standard technique of a solubility condition performed over a particular family of quasi-static solutions. The main result is that the dynamics along this particular class of solutions can be expressed in terms of a simple ordinary differential equation. The density profile of the stationary regime found at the end of the non-linear growth is also well characterized. Numerical simulations correspond satisfactorily to the analytical results through three different methods and asymptotic dynamics are well recovered, even far from the region where the approximations hold.< Réduire

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Laboratoire Ondes et Matière d'Aquitaine (LOMA) - UMR 5798