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Variational problems on multiply connected thin strips III: Integration of the Ginzburg-Landau equations over graphs
Author(s):
Jacob
Rubinstein;
Michelle
Schatzman
Journal:
Trans. Amer. Math. Soc.
353
(2001),
4173-4187.
MSC (2000):
Primary 82D55, 49S05, 94C15, 34B45
Posted:
May 17, 2001
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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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Additional Information:
Jacob
Rubinstein
Affiliation:
Department of Mathematics, Technion, Haifa 32000, Israel
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
DOI:
10.1090/S0002-9947-01-02804-5
PII:
S 0002-9947(01)02804-5
Keywords:
Graph theory,
differential equations,
Ginzburg-Landau functional,
superconductivity
Received by editor(s):
March 28, 2000
Received by editor(s) in revised form:
August 14, 2000
Posted:
May 17, 2001
Additional Notes:
Supported by Israel Science Foundation, CNRS, and CNRS-MOSA binational agreement
Copyright of article:
Copyright
2001,
American Mathematical Society
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