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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
35/2002

Coarsening Dynamics for the Convective Cahn-Hilliard Equation

Stephen J. Watson, Felix Otto, Boris Y. Rubinstein and Stephen H. Davis

Abstract

We characterize the coarsening dynamics associated with a convective Cahn-Hilliard equation in one space dimension. First, we derive a sharp-interface theory based on a quasi-static matched asymptotic analysis. Two distinct types of discontinuity (kink and anti-kink) arise due to the presence of convection, and their motions are governed to leading order by a nearest-neighbors interaction dynamical system.

Numerical simulations of the kink/anti-kink dynamics display marked self-similarity in the coarsening process, and reveal a pinching mechanism, identified through a linear stability analysis, as the dominant coarsening event. A self-similar period-doubling pinching ansatz is proposed for the coarsening process, and an analytical coarsening law, valid over all length scales, is derived. Our theoretical predictions are in good agreement with numerical simulations that have been performed both on the sharp-interface model and the original PDE.

Received:
Apr 22, 2002
Published:
Apr 22, 2002

Related publications

inJournal
2003 Repository Open Access
Stephen J. Watson, Felix Otto, Boris Y. Rubinstein and Stephen H. Davis

Coarsening dynamics for the convective Cahn-Hilliard equation

In: Physica / D, 178 (2003) 3-4, pp. 127-148