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Archive for Rational Mechanics and Analysis

, Volume 176, Issue 2, pp 227–269 | Cite as

Mathematical Derivation of the Continuum Limit of the Magnetic Force between Two Parts of a Rigid Crystalline Material

  • Anja SchlömerkemperEmail author
Article

Abstract.

The topic of this paper is a mathematically rigorous derivation of the continuum limit of the magnetic force between two parts of a rigid magnetized body. For this we start from a discrete setting of magnetic dipoles fixed to a scaled Bravais lattice, Open image in new window The limit as l→∞ corresponds to the passage to the continuum. The magnetic dipole moments are scaled in such a way that we obtain a finite total magnetic moment per unit volume. Under certain regularity assumptions on the magnetization and the boundaries we derive a force formula in the passage from the discrete setting to the continuum. Compared with a corresponding magnetic-force formula which has been previously discussed in the literature, the limiting force consists of an additional explicit local surface term, which is due to short-range effects and which reflects the lattice approximation of the underlying hypersingular integral.

Keywords

Neural Network Dipole Moment Unit Volume Electromagnetism Magnetic Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Institut für Analysis, Dynamik und ModellierungUniversität StuttgartStuttgartGermany

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