Discrete-to-continuum limits of magnetic forces in dependence on the distance between bodies
Anja Schlömerkemper and Bernd Schmidt
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Submission date: 15. Mar. 2007
published in: Archive for rational mechanics and analysis, 192 (2009) 3, p. 589-611
DOI number (of the published article): 10.1007/s00205-008-0134-4
MSC-Numbers: 82D40, 78A02, 74F15
Keywords and phrases: magnetic forces, lattice-to-continuum theories, multiple scales
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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.