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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Discrete-to-continuum limit of magnetic forces
Stefan Müller and Anja SchlömerkemperAbstract
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.
- Received:
- 12.05.02
- Published:
- 12.05.02
- MSC Codes:
- 82D40, 49J45, 42B20
- PACS:
- 75.80.+q
- Keywords:
- magnetic forces, atomistic vs. continuum models, hypersingular integrals