Abstract:We analyze the one-dimensional Ginzburg-Landau functional of superconductivity on a planar graph. In the Euler-Lagrange equations, the equation for the phase can be integrated, provided that the order parameter does not vanish at the vertices; in this case, the minimization of the Ginzburg-Landau functional is equivalent to the minimization of another functional, whose unknowns are a real-valued function on the graph and a finite set of integers.
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- Jacob Rubinstein
- Affiliation: Department of Mathematics, Technion, Haifa 32000, Israel
- MR Author ID: 204416
- Email: email@example.com
- Michelle Schatzman
- Affiliation: UMR 5585 CNRS MAPLY, Laboratoire de Mathématiques Appliquées de Lyon, Université Claude Bernard – Lyon 1, 69622 Villeurbanne Cedex, France
- Email: firstname.lastname@example.org
- Received by editor(s): March 28, 2000
- Received by editor(s) in revised form: August 14, 2000
- Published electronically: May 17, 2001
- Additional Notes: Supported by Israel Science Foundation, CNRS, and CNRS-MOSA binational agreement
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 4173-4187
- MSC (2000): Primary 82D55, 49S05, 94C15, 34B45
- DOI: https://doi.org/10.1090/S0002-9947-01-02804-5
- MathSciNet review: 1837226