Homogenization of micromagnetics large bodies

Giovanni Pisante

ESAIM: Control, Optimisation and Calculus of Variations (2004)

  • Volume: 10, Issue: 2, page 295-314
  • ISSN: 1292-8119

Abstract

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A homogenization problem related to the micromagnetic energy functional is studied. In particular, the existence of the integral representation for the homogenized limit of a family of energies ℰ ε ( m ) = ∫ Ω φ x , x ε , m ( x ) d x - ∫ Ω h e ( x ) · m ( x ) d x + 1 2 ∫ ℝ 3 | ∇ u ( x ) | 2 d x of a large ferromagnetic body is obtained.

How to cite

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Pisante, Giovanni. "Homogenization of micromagnetics large bodies." ESAIM: Control, Optimisation and Calculus of Variations 10.2 (2004): 295-314. <http://eudml.org/doc/244802>.

@article{Pisante2004,
abstract = {A homogenization problem related to the micromagnetic energy functional is studied. In particular, the existence of the integral representation for the homogenized limit of a family of energies\[\hspace*\{-17.07164pt\}\mathcal \{E\}\_\{\{\varepsilon \}\}(m)=\int \_\{\Omega \} \phi \left(x,\frac\{x\}\{\{\varepsilon \}\},m(x)\right)\,\{\rm d\}x -\int \_\{\Omega \}h\_e(x)\cdot m(x)\,\{\rm d\}x+\frac\{1\}\{2\}\int \_\{\mathbb \{R\}^3\}|\nabla u(x)|^2\,\{\rm d\}x \]of a large ferromagnetic body is obtained.},
author = {Pisante, Giovanni},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {micromagnetics; homogenization; $\Gamma $-convergence; integral representation; homgenized limit},
language = {eng},
number = {2},
pages = {295-314},
publisher = {EDP-Sciences},
title = {Homogenization of micromagnetics large bodies},
url = {http://eudml.org/doc/244802},
volume = {10},
year = {2004},
}

TY - JOUR
AU - Pisante, Giovanni
TI - Homogenization of micromagnetics large bodies
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2004
PB - EDP-Sciences
VL - 10
IS - 2
SP - 295
EP - 314
AB - A homogenization problem related to the micromagnetic energy functional is studied. In particular, the existence of the integral representation for the homogenized limit of a family of energies\[\hspace*{-17.07164pt}\mathcal {E}_{{\varepsilon }}(m)=\int _{\Omega } \phi \left(x,\frac{x}{{\varepsilon }},m(x)\right)\,{\rm d}x -\int _{\Omega }h_e(x)\cdot m(x)\,{\rm d}x+\frac{1}{2}\int _{\mathbb {R}^3}|\nabla u(x)|^2\,{\rm d}x \]of a large ferromagnetic body is obtained.
LA - eng
KW - micromagnetics; homogenization; $\Gamma $-convergence; integral representation; homgenized limit
UR - http://eudml.org/doc/244802
ER -

References

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