2003/05/01 by Felix Otto
Physics and Astronomy · Mathematics · #math-ph #math.MP
published as Proceedings of the ICM, Beijing 2002, vol. 3, 829--838
arxiv created 2003/05/01 · arxiv updated 2009/11/30
Scaling laws for characteristic length scales (in time or in the model parameters) are both experimentally robust and accessible for rigorous analysis. In multiscale situations cross--overs between different scaling laws are observed. We give a simple example from micromagnetics. In soft ferromagnetic films, the geometric character of a wall separating two magnetic domains depends on the film thickness. We identify this transition from a Néel wall to an Asymmetric Bloch wall by rigorously establishing a cross--over in the specific wall energy.