A review of domain coarsening using phase field models

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.

In Nature this week

The latest issue of Nature is a Linnaeus special issue:

Linnaeus himself sought a universal classification of all creation, animal, vegetable and mineral. His categorizations were not uniformly valuable, but his systematic spirit, his stress on the concept of species, and the formal but adaptable conventions of nomenclature he introduced have endured. Nature is glad to celebrate his legacy in this special issue.

John Whitfield writes about the need for geneticists and evolutionary biologists to work together in updating the tree of life; Emma Marris writes on the legacy of Linnaeus and conservation; Brendan Borrel asks if amateur naturalists are bad for science; Henry Nicholls writes about Linnaeus, the anatomist and pet keeper:

Not many people would respond to the death of a pet by dissecting it. But Carl Linnaeus was an exceptional man.

H C J Godfray Jr., asks about the relationship of taxonomy to the rest of biology; in the process, he has some interesting observation to make:

Linnaeus would have been a ‘techie’, exploiting the Internet and other modern means of coordinating data.

In a similar vein, Sandra Knapp et al argue for purely web based taxonomies; in a bit of interesting science history, Staffan Mueller-Wille lets us in on a secret known only to botanists:

Carl Linnaeus’s use of erotic language to describe plants ultimately helped him to recruit a global network of specimen collectors.

So, there is not much of materials science for me to write about this week; but, a biological break is nice too — Have fun!