Numerical simulations of superconducting rings using a Ginzburg-Landau model

dc.contributor.author Calhoun-Lopez, Marcus
dc.contributor.department Mathematics
dc.date 2020-11-22T06:41:26.000
dc.date.accessioned 2021-02-26T09:03:30Z
dc.date.available 2021-02-26T09:03:30Z
dc.date.copyright Mon Jan 01 00:00:00 UTC 2001
dc.date.issued 2001-01-01
dc.description.abstract <p>In this thesis, we will present numerical simulations of type-II superconducting rings using the time dependent Ginzburg-Landau model of superconductivity. In a type-II superconductor, discrete normal regions form called vortices. Our main objective is to better understand the behavior of these vortices as we change the inner radius of the ring and the magnetic field we apply to the ring. In chapter 1, we present some history of superconductivity. We also present some current and future applications of superconductivity to real world applications. In chapter 2, we present the time dependent Ginzburg-Landau model of superconductivity. In chapter 3, we present a weak formulation of the time dependent Ginzburg-Landau equations on an annulus domain. The weak form is the problem we will approximate to obtain our simulations. To dicretize the problem, we use a Galerkin finite element method in space and the backward Euler method in time. The finite dimensional approximation of the weak solution is presented in Chapter 4. Finally, we will report the numerical results of our experiments in chapter 5. Our numerical simulation will yield a complex order parameter [Psi symbol] = [Single bond symbol Psi symbol single bond symbol]e[Superscript iØ]. [Single bond symbol Psi symbol single bond symbol]2 is the density of superconducting charge carriers. By generating contour plots of [Single bond symbol Psi symbol single bond symbol]2 and vector plots of Ø, we will be able to determine the behavior of the vortices as we vary the applied magnetic field and inner radius of the ring. The motion of a vortex induces resistance in a superconductor, so understanding and controlling vortex behavior is important in the construction of devices that use superconductors.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/rtd/21103/
dc.identifier.articleid 22102
dc.identifier.contextkey 20252206
dc.identifier.doi https://doi.org/10.31274/rtd-20201118-67
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/21103
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/98470
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/rtd/21103/Calhoun_Lopez_ISU_2001_C355.pdf|||Fri Jan 14 22:34:54 UTC 2022
dc.subject.keywords Mathematics
dc.subject.keywords Applied mathematics
dc.title Numerical simulations of superconducting rings using a Ginzburg-Landau model
dc.type article
dc.type.genre thesis
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
thesis.degree.discipline Applied Mathematics
thesis.degree.level thesis
thesis.degree.name Master of Science
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