Magnetic microstructures - a paradigm of multiscale problems
Antonio DeSimone, Robert V. Kohn, Stefan Müller, and Felix Otto
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Submission date: 13. Dec. 1999
published in: ICIAM 99 : proceedings of the Fourth International Congress on Industrial and Applied Mathematics, Edinburgh / J. M. Ball ... (eds.)
Oxford : Oxford University Press, 2000. - P. 175 - 190
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Ferromagnetic materials display a complex microstructure of domains, walls, Bloch lines and singular points on scales ranging from 100 m down to a few nm. Understanding the formation and overall effects of these structures is crucial for key technological applications. At the same time the rich source of experimental data and the simple mathematical formulation makes the analysis of magnetic microstructure an excellent model problem to develop new mathematical tools for the understanding of multiscale problems, which are ubiquitous in science.
In this paper we describe some basic mathematical problems and report on recent analytical progress in three areas: rigorous scaling laws, branching and dimensionally reduced theories for thin films.