A review of domain coarsening using phase field models

March 16, 2007

Here is a review of Cahn-Hilliard and Allen-Cahn models with specific reference to coarsening studies:

Author: Bray, A.J.

Source: Advances In Physics, Volume 43, Number 3, May/June 1994, pp. 357-459 (103)

Abstract:

The theory of phase-ordering dynamics, that is the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase, is reviewed, with the emphasis on recent developments. Interest will focus on the scaling regime that develops at long times after the quench. How can one determine the growth laws that describe the time dependence of characteristic length scales, and what can be said about the form of the associated scaling functions? Particular attention will be paid to systems described by more complicated order parameters than the simple scalars usually considered, for example vector and tensor fields. The latter are needed, for example, to describe phase ordering in nematic liquid crystals, on which there have been a number of recent experiments. The study of topological defects (domain walls, vortices, strings and monopoles) provides a unifying framework for discussing coarsening in these different systems

The review collects all the important results pertaining to the mathematical aspects of the problem and describes them in a very lucid fashion, making it a very pleasant read indeed.

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