We determine by a scaling calculation the limiting form of the free energy governing a ferromagnetic film of vanishing thickness. Our theory generalizes Stoner and Wohlfarth's results for flat ellipsoids to arbitrary-shaped very thin films.

The classical experiments on turbulent friction in rough pipes were performed by Nikuradse in the 1930s. Seventy years later, they continue to defy theory. Here we model Nikuradse's experiments using the phenomenological theory of Kolmogórov, a theory that is widely thought to be applicable only to highly idealized flows. Our results include both the empirical scalings of Blasius and Strickler and are otherwise in minute qualitative agreement with the experiments; they suggest that the phenomenological theory may be relevant to other flows of practical interest; and they unveil the existence of close ties between two milestones of experimental and theoretical turbulence.

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SUMMARYA new finite element formulation aimed at the solution of problems involving strain localization is presented. The proposed formulation incorporates displacement interpolated embedded localization lines. Results are shown to converge to an 'exact solution' when the mesh is refined and also to be quite insensitive to mesh distortions.