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Non-linear dynamics of spinodal decomposition

  • S. Villain-Guillot
  • C. Josserand

Abstract:

We develop a new technique describing the non linear growth of interfaces. We apply this analytical approach to the one dimensional Cahn-Hilliard equation. The dynamics is captured through a solvability 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 are compared in a satisfactory way with the analytical results through three different fitting methods and asymptotic dynamics are well recovered, even far from the region where the approximations hold.

PACS. 05.45.Yv Solitons – 47.20.Ky Nonlinearity – 47.54.+r Pattern selection; pattern formation 

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Copyright information

© EDP Sciences, Springer-Verlag 2002

Authors and Affiliations

  • S. Villain-Guillot
    • 1
  • C. Josserand
    • 2
  1. 1.Centre de Physique Moléculaire Optique et Hertzienne, Université Bordeaux I, 33406 Talence Cedex, FranceFR
  2. 2.Laboratoire de Modélisation en Mécanique, Université Pierre et Marie Curie, 8 rue du Capitaine Scott, 75015 Paris, FranceFR

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