Geometric structure of magnetic walls

Myriam Lecumberry[1]

  • [1] Université de Nantes Laboratoire de Mathématiques Jean Leray UFR Sciences et Techniques 2 rue de la Houssinière 44322 Nantes Cedex 3

Journées Équations aux dérivées partielles (2005)

  • page 1-11
  • ISSN: 0752-0360

Abstract

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After a short introduction on micromagnetism, we will focus on a scalar micromagnetic model. The problem, which is hyperbolic, can be viewed as a problem of Hamilton-Jacobi, and, similarly to conservation laws, it admits a kinetic formulation. We will use both points of view, together with tools from geometric measure theory, to prove the rectifiability of the singular set of micromagnetic configurations.

How to cite

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Lecumberry, Myriam. "Geometric structure of magnetic walls." Journées Équations aux dérivées partielles (2005): 1-11. <http://eudml.org/doc/10608>.

@article{Lecumberry2005,
abstract = {After a short introduction on micromagnetism, we will focus on a scalar micromagnetic model. The problem, which is hyperbolic, can be viewed as a problem of Hamilton-Jacobi, and, similarly to conservation laws, it admits a kinetic formulation. We will use both points of view, together with tools from geometric measure theory, to prove the rectifiability of the singular set of micromagnetic configurations.},
affiliation = {Université de Nantes Laboratoire de Mathématiques Jean Leray UFR Sciences et Techniques 2 rue de la Houssinière 44322 Nantes Cedex 3},
author = {Lecumberry, Myriam},
journal = {Journées Équations aux dérivées partielles},
keywords = {micromagnetism; Hamilton-Jacobi problem; rectifiability; silicon-iron crystal},
language = {eng},
month = {6},
pages = {1-11},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Geometric structure of magnetic walls},
url = {http://eudml.org/doc/10608},
year = {2005},
}

TY - JOUR
AU - Lecumberry, Myriam
TI - Geometric structure of magnetic walls
JO - Journées Équations aux dérivées partielles
DA - 2005/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 11
AB - After a short introduction on micromagnetism, we will focus on a scalar micromagnetic model. The problem, which is hyperbolic, can be viewed as a problem of Hamilton-Jacobi, and, similarly to conservation laws, it admits a kinetic formulation. We will use both points of view, together with tools from geometric measure theory, to prove the rectifiability of the singular set of micromagnetic configurations.
LA - eng
KW - micromagnetism; Hamilton-Jacobi problem; rectifiability; silicon-iron crystal
UR - http://eudml.org/doc/10608
ER -

References

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  3. L. Ambrosio, B. Kirchheim, M. Lecumberry and T. Rivière, On the rectifiability of defect measures arising in micromagnetic domains, Nonlinear problems in mathematical physics and related topics, II, 29-60, Int. Math. Ser. (N.Y.), 2. KluwerPlenum, New York, (2002). Zbl1055.49008MR1971988
  4. L. Ambrosio, M. Lecumberry and T. Riviere, A viscosity property of minimizing micromagnetic configurations, Comm. Pure Appl. Math.56 (2003), no 6, 681-688. Zbl1121.35309MR1959737
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  7. C. De Lellis and T. Rivière, Concentration estimates for entropy measures, to appear in J. Math. Pures et Appl.. 
  8. A. Hubert and A. Schäfer, Magnetic domains: the analysis of magnetic microstructures, Springer, Berlin-New York, (1998). 
  9. M. Lecumberry and T. Rivière, The rectifiability of shock waves for the solutions of genuinely non-linear scalar conservation laws in 1+1 D., Preprint (2002). 
  10. T. Rivière, Parois et vortex en micromagnétisme, Journées “Equations aux dérivées partielles” (Forges-les-Eaux, 2002), Exp. no XIV. MR1968210
  11. T. Rivière and S. Serfaty, Limiting Domain Wall Energy for a Problem Related to Micromagnetics, Comm. Pure Appl. Math., 54, (2001), 294-338. Zbl1031.35142MR1809740
  12. T. Rivière and S. Serfaty, Compactness, kinetic formulation and entropies for a problem related to micromagnetics, Comm. Partial Differential Equations28 (2003), no 1-2, 249-269. Zbl1094.35125MR1974456
  13. D. Serre, Systèmes de lois de conservation I, Diderot, (1996). Zbl0930.35002MR1459988

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