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.
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Received 16 October 2001 / Received in final form 15 March 2002 Published online 2 October 2002
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ID="a"e-mail: josseran@lmm.jussieu.fr
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ID="b"UMR CNRS 7607
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Villain-Guillot, S., Josserand, C. Non-linear dynamics of spinodal decomposition. Eur. Phys. J. B 29, 305–309 (2002). https://doi.org/10.1140/epjb/e2002-00306-7
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DOI: https://doi.org/10.1140/epjb/e2002-00306-7