Singularities in thin magnetic films

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...

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Main Author: Baffetti, Marco
Format: Thesis (University of Nottingham only)
Language:English
Published: 2021
Subjects:
Online Access:https://eprints.nottingham.ac.uk/66962/
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author Baffetti, Marco
author_facet Baffetti, Marco
author_sort Baffetti, Marco
building Nottingham Research Data Repository
collection Online Access
description 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.
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spelling nottingham-669622021-12-08T04:40:31Z https://eprints.nottingham.ac.uk/66962/ Singularities in thin magnetic films Baffetti, Marco 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. 2021-12-08 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/66962/1/Singularities%20in%20thin%20magnetic%20films.pdf Baffetti, Marco (2021) Singularities in thin magnetic films. PhD thesis, University of Nottingham. Micromagnetics Partial differential equations Thin films Vortices
spellingShingle Micromagnetics
Partial differential equations
Thin films
Vortices
Baffetti, Marco
Singularities in thin magnetic films
title Singularities in thin magnetic films
title_full Singularities in thin magnetic films
title_fullStr Singularities in thin magnetic films
title_full_unstemmed Singularities in thin magnetic films
title_short Singularities in thin magnetic films
title_sort singularities in thin magnetic films
topic Micromagnetics
Partial differential equations
Thin films
Vortices
url https://eprints.nottingham.ac.uk/66962/