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Internal variables and fine-scale oscillations in micromagnetics

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Abstract

We derive the field energy of micromagnetics by computing the limiting energy of a lattice of dipoles as a typical lattice parameter goes to zero. Different limiting energies are obtained, depending upon whether the dipoles do not oscillate (strong convergence), oscillate on a scale much larger than the scale of the lattice (weak-long) or oscillate on the scale of the lattice (weak-short). The analysis suggests a framework and some methods for the direct derivation of continuum theory from molecular theory.

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Authors and Affiliations

  1. Department of Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 55455, Minneapolis, MN, USA

    R. D. James

  2. Institut für Angewandte Mathematik, Universität Bonn, Beringstr. 4, 53115, Bonn, Germany

    Stefan Müller

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  1. R. D. James
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James, R.D., Müller, S. Internal variables and fine-scale oscillations in micromagnetics. Continuum Mech. Thermodyn 6, 291–336 (1994). https://doi.org/10.1007/BF01140633

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