Summary and Outlook

Abstract

Ferromagnetic materials are widely used as recording media; advanced techniques in designing and analyzing such materials, for example writing heads in magnetic recording, can have an enormous impact on future technologies. Their mathematical theory started with the introduction of the Landau-Lifshitz free energy; a numerical analysis of existing strategies to solve the corresponding minimization problem is presented in part I of this monograph. Dynamics of the magnetization (e.g., switching processes of (averaged) magnetizations) is given by a torque balance, which leads to the (LLG) equation; electromagnetic coupling effects are incorporated in the (MLLG) equation. Part II closes with the numerical analysis for the nematic liquid crystal problem which also imposes a non-convex constraint onto its solution.