Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Variational problems on multiply connected thin strips III: Integration of the Ginzburg-Landau equations over graphs
HTML articles powered by AMS MathViewer

by Jacob Rubinstein and Michelle Schatzman PDF
Trans. Amer. Math. Soc. 353 (2001), 4173-4187 Request permission

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.
References
  • H.J. Carlin and A.B. Giordano. Network Theory. Prentice Hall, 1964.
  • Takayuki Furuta, Parametric operator function via Furuta inequality, Sci. Math. 1 (1998), no. 1, 1–5. MR 1688425
  • W.A. Little and R.D. Parks. Observation of quantum periodicity in the transition temperature of a superconducting cylinder. Phys. Rev. Lett., 9:9–12, 1962.
  • V.V. Moshchalkov, L.Gielen, and Y.Bruynseraede. Effect of sample topology on the critical fields of mesoscopic superconductors. Nature, 373(6512):319, 1995.
  • B.Pannetier. Superconducting wire networks. In B.Kramer, editor, Quantum Coherence in Mesoscopic Systems, pages 457–484. Plenum Press, 1991.
  • J.Rubinstein and M.Schatzman. Variational problems on multiply connected thin strips IV: Zero sets for the Ginzburg-Landau linearized equations. in preparation.
  • J.Rubinstein and M.Schatzman. Variational problems on multiply connected thin strips II: convergence of the Ginzburg - Landau functional. Technical Report 294, UMR 5585 CNRS Equipe d’Analyse Numérique, April 1999.
Similar Articles
Additional Information
  • Jacob Rubinstein
  • Affiliation: Department of Mathematics, Technion, Haifa 32000, Israel
  • MR Author ID: 204416
  • Email: koby@leeor.technion.ac.il
  • Michelle Schatzman
  • Affiliation: UMR 5585 CNRS MAPLY, Laboratoire de Mathématiques Appliquées de Lyon, Université Claude Bernard – Lyon 1, 69622 Villeurbanne Cedex, France
  • Email: schatz@maply.univ-lyon1.fr
  • 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