The Ginzburg-Landau Equation Solved by the Finite Element Method

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearch

Abstract

Around 1950 V.L. Ginzburg and L.D. Landau proposed a phenomenological theory for phase transitions1. The theory is based on a phenomenological Schrödinger equation with a φ-4 potential and a kinetic term involving the momentum operator. One of the more successful applications of the theory is to superconductivity and in particular to superconductors placed in a magnetic field. Superconductors expel magnetic fields from the inside bulk by setting up screening currents in the surface (type I superconductors). However, some supercon-ductors allow for magnetic field penetration through quantized current vortices when the magnetic field exceeds a threshold value. These superconductors are called type II supercon-ductors. In this article we solve numerically the time dependent Ginzburg-Landau equation coupled to a magnetic field for type II superconductors of complex geometry, where the finite element method is particularly suited.
Original languageEnglish
Title of host publicationProceedings of the Comsol Conference
EditorsLars Gregersen
Number of pages150
Place of PublicationCopenhagen, Denmark
PublisherCOMSOL Inc.
Publication date2006
Pages75-78
ISBN (Print)87-989426-1-1
Publication statusPublished - 2006
EventNordic Comsol Conference - Kgs. Lyngby, Denmark
Duration: 1 Jan 2006 → …

Conference

ConferenceNordic Comsol Conference
CityKgs. Lyngby, Denmark
Period01/01/2006 → …

Keywords

  • nonlinear dynamics
  • phase transition
  • Ginzburg-Landau model
  • Superconductivity

Cite this

Alstrøm, T. S., Sørensen, M. P., Pedersen, N. F., & Madsen, S. (2006). The Ginzburg-Landau Equation Solved by the Finite Element Method. In L. Gregersen (Ed.), Proceedings of the Comsol Conference (pp. 75-78). Copenhagen, Denmark: COMSOL Inc..
Alstrøm, Tommy Sonne ; Sørensen, Mads Peter ; Pedersen, Niels Falsig ; Madsen, Søren. / The Ginzburg-Landau Equation Solved by the Finite Element Method. Proceedings of the Comsol Conference. editor / Lars Gregersen. Copenhagen, Denmark : COMSOL Inc., 2006. pp. 75-78
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abstract = "Around 1950 V.L. Ginzburg and L.D. Landau proposed a phenomenological theory for phase transitions1. The theory is based on a phenomenological Schr{\"o}dinger equation with a φ-4 potential and a kinetic term involving the momentum operator. One of the more successful applications of the theory is to superconductivity and in particular to superconductors placed in a magnetic field. Superconductors expel magnetic fields from the inside bulk by setting up screening currents in the surface (type I superconductors). However, some supercon-ductors allow for magnetic field penetration through quantized current vortices when the magnetic field exceeds a threshold value. These superconductors are called type II supercon-ductors. In this article we solve numerically the time dependent Ginzburg-Landau equation coupled to a magnetic field for type II superconductors of complex geometry, where the finite element method is particularly suited.",
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Alstrøm, TS, Sørensen, MP, Pedersen, NF & Madsen, S 2006, The Ginzburg-Landau Equation Solved by the Finite Element Method. in L Gregersen (ed.), Proceedings of the Comsol Conference. COMSOL Inc., Copenhagen, Denmark, pp. 75-78, Nordic Comsol Conference, Kgs. Lyngby, Denmark, 01/01/2006.

The Ginzburg-Landau Equation Solved by the Finite Element Method. / Alstrøm, Tommy Sonne; Sørensen, Mads Peter; Pedersen, Niels Falsig; Madsen, Søren.

Proceedings of the Comsol Conference. ed. / Lars Gregersen. Copenhagen, Denmark : COMSOL Inc., 2006. p. 75-78.

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearch

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Alstrøm TS, Sørensen MP, Pedersen NF, Madsen S. The Ginzburg-Landau Equation Solved by the Finite Element Method. In Gregersen L, editor, Proceedings of the Comsol Conference. Copenhagen, Denmark: COMSOL Inc. 2006. p. 75-78