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Cross-over in scaling laws: A simple example from micromagnetics

Felix Otto
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Abstract

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.

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Felix Otto. 2003-05-01. Cross-over in scaling laws: A simple example from micromagnetics. https://arxiv.org/abs/math-ph/0305001

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