Discrete-to-continuum limit of magnetic forces
Stefan Müller and Anja Schlömerkemper
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Submission date: 12. May. 2002
published in: Comptes rendus mathematique, 335 (2002) 4, p. 393-398
DOI number (of the published article): 10.1016/S1631-073X(02)02494-9
MSC-Numbers: 82D40, 49J45, 42B20
Keywords and phrases: magnetic forces, atomistic vs. continuum models, hypersingular integrals
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We derive a formula for the forces within a magnetized body, starting from a discrete configuration of magnetic dipoles on a Bravais lattice. The resulting force consists of the usual (nonlocal) volume term and an additional local surface term, whose coefficients involve a singular sum over the lattice. The force thus obtained is different from the usual continuum expression, reflecting the different character of the lattice regularization of the underlying hypersingular integral.