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Zeitschrift für angewandte Mathematik und Physik

, Volume 66, Issue 6, pp 3519–3534 | Cite as

Ferromagnetic of nanowires of infinite length and infinite thin films

  • Khaled Chacouche
  • Rejeb HadijiEmail author
Article

Abstract

The aim of the work described in this paper is to determine, via an asymptotic analysis, the limiting form of the free energy governing in the first case 3D ferromagnetic nanowires of infinite length in the limit and in the second case 3D thin films which become infinite when their thickness is vanished. A 1D limit problem on the nanowires and a 2D limit problem on the thin films are obtained.

Mathematics Subject Classification

78A25 49S05 78M35 

Keywords

Micromagnetics Variational problem Thin film Nanowire 

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References

  1. 1.
    Attouch, H., Buttazzo, G., Michaille, G.: Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization, vol. 17. SIAM (2014)Google Scholar
  2. 2.
    Brown W.F.: Micromagnetics, Interscience Tracts on Physics and Astronomy, no 18. Wiley, New York (1963)Google Scholar
  3. 3.
    Carbou G.: Thin layers in micromagnetism. M 3AS: Math. Models Methods Appl. Sci. 11(9), 1529–1546 (2001)Google Scholar
  4. 4.
    Carbou G., Labbé S.: Stabilization of walls for nano-wires of finite length. ESAIM J. Appl. Math. 18(1), 1–21 (2012)zbMATHGoogle Scholar
  5. 5.
    Ciarlet P.G., Destuynder P.: A justification of the two-dimensional linear plate model. J. Mech. 18(2), 315–344 (1979)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Faulkner C.C., Allwood D.A., Cooke M.D., Xiong G., Atkinson D., Cowburn R.P.: Controlled switching of ferromagnetic wire junctions by domain wall injection. IEEE Trans. Magn. 39(5), 2860–2862 (2003)CrossRefGoogle Scholar
  7. 7.
    Courilleau P., Dumont S., Hadiji R.: Regularity of minimizing maps with values in S 2 and some numerical simulations. Adv. Math. Sci. Appl. 10(2), 711–733 (2000)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Gioia G., James R.D.: Micromagnetics of very thin film. Proc. R. Soc. Lond. A 453, 213–223 (1997)CrossRefGoogle Scholar
  9. 9.
    Hadiji R., Shirakawa K.: Asymptotic analysis for micromagnetics of thin films governed by indefinite material coefficients. Commun. Pure Appl. Anal. 9(5), 1345–1361 (2010)zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Hadiji, R., Shirakawa, K.: 3D–2D asymptotic observation for minimization problems associated with degenerative energy-coefficients. Discrete and Continuous Dynamical Systems, Series A, vol. 2011, pp. 624–633. American Institute of Mathematical Sciences (AIMS) (2011)Google Scholar
  11. 11.
    Hadiji R., Zhou F.: Regularity of \({\int_\Omega \mid \nabla u \mid^2 + \lambda \int_\Omega \mid u - f \mid^2}\) and some gap phenomenon. Potential Anal. 1(4), 385–400 (1992)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Gaudiello A., Hadiji R.: Ferromagnetic thin multi-structures. J. Differ. Equ. 257, 1591–1622 (2014)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Gaudiello A., Hadiji R.: Junction of ferromagnetic thin films. Calc. Var. Partial Differ. Equ. 39(3), 593–619 (2010)zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Gaudiello A., Hadiji R.: Asymptotic analysis, in a thin multidomain, of minimizing maps with values in S 2. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26(1), 59–80 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Gaudiello A., Hadiji R.: Junction of one-dimensional minimization problems involving S 2 valued maps. Adv. Differ. Equ. 13(9-10), 935–958 (2008)zbMATHMathSciNetGoogle Scholar
  16. 16.
    Gaudiello A., Hamdache K.: The polarization in a ferroelectric thin film: local and non local limit problems. ESAIM COCV 19, 657–667 (2013)zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    James R.D., Kinderlehrer D.: Frustration in ferromagnetic materials. Contin. Mech. Thermodyn. 2(3), 215–239 (1990)MathSciNetCrossRefGoogle Scholar
  18. 18.
    SKOMSKI R.: Nanomagnetics. J. Phys. Condens. Matter. 15, R841–R896 (2003)CrossRefGoogle Scholar
  19. 19.
    Sanchez D.: Behaviour of the Landau–Lifschitz equation in a ferromagnetic wire. Math. Methods Appl. Sci. 32(2), 167–205 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    Visintin A.: On Landau–Lifshitz’ equations for ferromagnetism. Jpn. J. Appl. Math. 2(1), 69–84 (1985)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.LAMA, Laboratoire d’Analyse et de Mathématiques Appliquées UMR 8050 UPECUniversité Paris-EstCréteilFrance
  2. 2.DIEI, Università degli Studi di Cassino e del Lazio MeridionaleCassinoItaly

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