Preprint 40/2002

Discrete-to-continuum limit of magnetic forces

Stefan Müller and Anja Schlömerkemper

Contact the author: Please use for correspondence this email.
Submission date: 12. May. 2002
Pages: 13
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
PACS-Numbers: 75.80.+q
Keywords and phrases: magnetic forces, atomistic vs. continuum models, hypersingular integrals
Download full preprint: PDF (172 kB), PS ziped (178 kB)

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.

18.10.2019, 02:11