Singularities in thin magnetic films

Baffetti, Marco (2021) Singularities in thin magnetic films. PhD thesis, University of Nottingham.

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Abstract

We study a particular regime for thin rectangular micromagnetic films. Following an idea of Ignat and Kurzke we reduce the full three-dimensional non-local vector-valued model to a two-dimensional local scalar model and study some of the properties of the latter. We then recover some results for the full model. As part of our study we study a particular PDE in a quadrant, for which we prove uniqueness and regularity results. The general structure follows the ideas of Ignat and Kurzke who studied more regular domains but we need to make some crucial modifications to deal with the presence of corners. We study boundary vortices and we prove rigorously that the so-called S state in a rectangle is minimizing in the aforementioned regime.

In the last chapter we study a different problem about critical points of a family of scalar functionals related to micromagnetics. We extend a previously known result about minimizers: we show that critical points of the energy for which the penalty terms is bounded have single jumps.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Kurzke, Matthias
Keywords: Micromagnetics, Partial differential equations, Thin films, Vortices
Subjects: Q Science > QA Mathematics > QA299 Analysis
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 66962
Depositing User: Baffetti, Marco
Date Deposited: 08 Dec 2021 04:40
Last Modified: 08 Dec 2021 04:40
URI: http://eprints.nottingham.ac.uk/id/eprint/66962

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