Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T15:48:30.217Z Has data issue: false hasContentIssue false
  • English
  • Français

The polarization in a ferroelectric thin film: local andnonlocal limit problems

Published online by Cambridge University Press:  28 March 2013

Antonio Gaudiello  and
Kamel Hamdache
Antonio Gaudiello
Affiliation:
DIEI, Università degli Studi di Cassino e del Lazio meridionale, via G. Di Biasio 43, 03043 Cassino (FR), Italia. gaudiell@unina.it
Kamel Hamdache
Affiliation:
Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau, France; kamel.hamdache@polytechnique.edu
Get access

Abstract

In this paper, starting from classical non-convex and nonlocal3D-variational model of the electric polarization in a ferroelectricmaterial, via an asymptotic process we obtain a rigorous2D-variational model for a thin film. Depending on the initial boundaryconditions, the limit problem can be either nonlocal or local.

Keywords

Electric polarizationthin filmnonlocal problems
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 3 , July 2013 , pp. 657 - 667
Copyright
© EDP Sciences, SMAI, 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alouges, F. and Labbé, S., Convergence of a ferromagnetic film model. C. R. Math. Acad. Sci. Paris 344 (2007) 77–82. Google Scholar
Ammari, H., Halpern, L. and Hamdache, K., Asymptotic behavior of thin ferromagnetic films. Asymptot. Anal. 24 (2000) 277–294. Google Scholar
Carbou, G., Thin Layers in Micromagnetism. Math. Model. Methods Appl. Sci. 11 (2001) 1529–1546. Google Scholar
P. Chandra and P.B. Littlewood, A Landau primer for ferroelectrics, The Physics of ferroelectrics: A modern perspective, edited by K. Rabe, C.H. Ahn and J.-M. Triscone. Topics Appl. Phys. 105 (2007) 69–116.
Ciarlet, P.G. and Destuynder, P., A Justification of the two-dimensional linear plate model. J. Méca. 18 (1979) 315–344. Google Scholar
Costabel, M., Dauge, M. and Nicaise, S., Singularities of Maxwell interface problems. ESAIM: M2AN 33 (1999) 627–649. Google Scholar
De Giorgi, E. and Franzoni, T., Su un tipo di convergenza variazionale. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58 (1975) 842–850. Google Scholar
Desimone, A., Kohn, R.V., Muller, S. and Otto, F., A reduced theory for thin-film micromagnetics. Commun. Pure Appl. Math. 55 (2002) 1408–1460. Google Scholar
Gaudiello, A. and Hadiji, R., Junction of ferromagnetic thin films. Calc. Var. Partial Differ. Equ. 39 (2010) 593–619. Google Scholar
Gioia, G. and James, R.D., Micromagnetism of very thin films. Proc. of R. London A 453 (1997) 213–223. Google Scholar
Kohn, R.V. and Slastikov, V.V., Another thin-film limit of micromagnetics. Arch. Ration. Mech. Anal. 178 (2005) 227–245. Google Scholar
R.C. Smith, Smart material systems. model development, in Front. Appl. Math. Vol. 32. SIAM (2005).
Su, Y. and Landis, C.M., Continuum thermodynamics of ferroelectric domain evolution: theory, finite element implementation, and application to domain wall pinning. J. Mech. Phys. Solids 55 (2007) 280–305. Google Scholar
Zhang, W. and Bhattacharya, K., A computational model of ferroelectric domains. Part I. Model formulation and domain switching. Acta Mater. 53 (2005) 185–198. Google Scholar