Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Another approach to the thin-film $ \Gamma$-limit of the micromagnetic free energy in the regime of small samples


Author: Carolin Kreisbeck
Journal: Quart. Appl. Math. 71 (2013), 201-213
MSC (2010): Primary 49J45, 35E99, 35Q61, 74F15, 74K35
DOI: https://doi.org/10.1090/S0033-569X-2012-01323-5
Published electronically: August 28, 2012
MathSciNet review: 3087419
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Abstract | References | Similar Articles | Additional Information

Abstract: The asymptotic behavior of the micromagnetic free energy governing a ferromagnetic film is studied as its thickness gets smaller and smaller compared to its cross section. Here the static Maxwell equations are treated as a Murat's constant-rank PDE constraint on the energy functional. In contrast to previous work, this approach allows us to keep track of the induced magnetic field without solving the magnetostatic equations. In particular, the mathematical results of Gioia and James [Proc. R. Soc. Lond. A 453 (1997), pp. 213-223] regarding convergence of minimizers are recovered by giving a characterization of the corresponding $ \Gamma $-limit.


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Additional Information

Carolin Kreisbeck
Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Address at time of publication: Departamento de Matemática and Centro de Matemática e Aplicaçoẽs, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal
Email: carolink@andrew.cmu.edu

DOI: https://doi.org/10.1090/S0033-569X-2012-01323-5
Received by editor(s): May 12, 2011
Published electronically: August 28, 2012
Additional Notes: The author is grateful to Irene Fonseca for pointing her to this topic, for valuable conversations on the subject and for reading carefully a first draft of the manuscript. Also, the author thanks Filip Rindler, who contributed with useful ideas on closely related issues. This research was carried out during a one-year stay at Carnegie Mellon University funded by the Fundação para a Ciência e a Tecnologia (FCT) through the ICTI CMU–Portugal program and UTA-CMU/MAT/0005/2009.
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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