Pattern formation in magnetic thin films [Elektronische Ressource] : analysis and numerics / Nicolas Condette. Gutachter: Christof Melcher ; Andreas Griewank ; Endre Süli

Pattern Formation in Magnetic Thin Films: Analysisand NumericsDISSERTATIONzur Erlangung des akademischen GradesDr. rer. nat.im Fach Mathematikeingereicht an derMathematisch-Naturwissenschaftlichen Fakultät IIHumboldt-Universität zu BerlinvonHerr Nicolas CondettePräsident der Humboldt-Universität zu Berlin:Prof. Dr. Christoph MarkschiesDekan der Mathematisch-Naturwissenschaftlichen Fakultät II:Prof. Dr. Peter FrenschGutachter:1. Prof. Dr. Christof Melcher2. Prof. Dr. Andreas Griewank3. Prof. Dr. Endre Sülieingereicht am: 22. Februar 2010Tag der mündlichen Prüfung: 05. Oktober 2010To my grandmother.AbstractThis thesis is concerned with the study of a class of variational problems arising inthe context of ferromagnetism. More precisely, it aims at providing a numerical andanalytical background to the study of hard magnetic thin films with perpendicularanisotropy. Magnetic thin films are sheets of materials with thicknesses ofa few micrometers down to a few nanometers used mainly in electronic industry, forexample as magnetic data storage media for computers.Our initial considerations are based on a model of Landau and Lifshitz that asso-ciates the ground states of the magnetization within a three-dimensional body to theminimizers of a nonconvex and nonlocal energy functional, the so-called micromag-netic energy.