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Discrete-to-Continuum Limit of Magnetic Forces: Dependence on the Distance Between Bodies

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Abstract

We investigate force formulae for two rigid magnetic bodies in dependence on their mutual distance. These formulae are derived as continuum limits of atomistic dipole–dipole interactions. For bodies that are far apart in terms of the typical lattice spacing we recover a classical formula for magnetic forces. For bodies whose distance is comparable to the atomistic lattice spacing, however, we discover a new term that explicitly depends on the distance, measured in atomic units, and the underlying crystal lattice structure. This new term links the classical force formula and a limiting force formula obtained earlier in the case of two bodies being in contact on the atomistic scale.

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Acknowledgments

The largest part of this work was performed while Bernd Schmidt was affiliated with the Max Planck Institute for Mathematics in the Sciences, Leipzig. Anja Schlömerkemper was partly supported by the RTN network MRTN-CT2004-50522.

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This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Inselstraße 22-26, 04103, Leipzig, Germany

    Anja Schlömerkemper

  2. Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, 85747, Garching, Germany

    Bernd Schmidt

Authors
  1. Anja Schlömerkemper
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  2. Bernd Schmidt
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Correspondence to Anja Schlömerkemper.

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Communicated by A. Mielke

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Schlömerkemper, A., Schmidt, B. Discrete-to-Continuum Limit of Magnetic Forces: Dependence on the Distance Between Bodies. Arch Rational Mech Anal 192, 589–611 (2009). https://doi.org/10.1007/s00205-008-0134-4

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  • DOI: https://doi.org/10.1007/s00205-008-0134-4

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