Small Surface Energy , Coarse - Graining , and Selection of MicrostructureRobert
نویسندگان
چکیده
We discuss some static and dynamic problems involving a competition between \bulk" and \surface" energy. In each case the bulk energy prefers microstructure, and the surface energy is a singular perturbation. It is natural to treat the surface energy density as a small parameter. In our static examples { involving branching of twins and magnetic domains { this leads to scaling laws for the energy and the length scale of microstructure. In our dynamic example { involving the fracture of a ferroouid thin lm by an applied magnetic eld { it provides a novel approach to coarse-graining.
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