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Nucleation of superconductivity in decreasing fields. I

Published online by Cambridge University Press:  26 September 2008

S. J. Chapman
S. J. Chapman
Affiliation:
Mathematical Institute, 24–29 St. Giles', Oxford OX1 3LB, UK
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Abstract

The bifurcation from a normally conducting to a superconducting state as an external magnetic field is lowered is examined using the Ginzburg-Landau theory. The results for three specific examples are reviewed, extended and unified in the framework of a systematic perturbation theory introduced in [1].

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 5 , Issue 4 , December 1994 , pp. 449 - 468
Copyright
Copyright © Cambridge University Press 1994

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References

[1]Millman, M. H. & Keller, J. B. 1969 Perturbation theory of nonlinear boundary-value problems. J. Math. Phys. 10 (2), 342.Google Scholar
[2]Chapman, S. J. 1994 Asymptotic analysis of the Ginzburg-Landau model of superconductivity: reduction to a free boundary model. Q.A.M. (to appear).Google Scholar
[3]Essmann, U. & TräUble, H. 1967 The direct observation of individual flux lines in type II superconductors. Phys. Lett. A24, 526.CrossRefGoogle Scholar
[4]Chapman, S. J., Howison, S. D. & Ockendon, J. R. 1992 Macroscopic models of superconductivity. SIAM Review, 34 (4), 529–560.Google Scholar
[5]Ginzburg, V. L. & Landau, L. D. 1950 On the theory of superconductivity. J.E.T.P. 20, 1064.Google Scholar
[6]Gor'Kov, L. P. & Éliashberg, G. M. 1968 Generalisation of the Ginzburg-Landau equations for non-stationary problems in the case of alloys with paramagnetic impurities. Soviet Phys. J.E.T.P. 27, 328.Google Scholar
[7]Abrikosov, A. A. 1957 On the magnetic properties of superconductors of the second group. Soviet Phys. J.E.T.P. 5 (6), 1174.Google Scholar
[8]Kleiner, W. H., Roth, L. M. & Autler, S. H. 1964 Bulk solution of Ginzburg-Landau equations for Type II superconductors: Upper critical field region. Phys. Rev. 133 (5A), 1226.Google Scholar
[9]Odeh, F. 1967 Existence and bifurcation theorems for the Ginzburg-Landau equations. J. Math. Phys. 8 (12), 2351.CrossRefGoogle Scholar
[10]Saint-James, D. & De Gennes, P. G. 1963 Onset of superconductivity in decreasing fields. Phys. Lett. 7 (5), 306.CrossRefGoogle Scholar
[11]Chapman, S. J. 1994 Nucleation of superconductivity in decreasing fields II. Euro. J. Appl. Math. 5 (4).Google Scholar
[12]De Gennes, P. G. 1966 Superconductivity of Metals and Alloys. Benjamin, New York.Google Scholar
[13]Moroz, I. M. 1990 On quasi-holomorphic differential equations. Phys. Lett. A 143, 43–46.CrossRefGoogle Scholar
[14]Berger, M. S. 1983 Creation and breaking of self-duality symmetry-a modern aspect of calculus of variations. Cont. Math. 17, 379–394.CrossRefGoogle Scholar
[15]Du, Q., Gunzburger, M. D. & Peterson, S. 1992 Analysis and approximation of the Ginzburg-Landau model of superconductivity. SIAM Review, 34 (1), 54–81.CrossRefGoogle Scholar
[16]Taubes, C. H. 1980 Arbitrary N-vortex solutions to the first order Ginzburg-Landau equations. Comm. Math. Phys. 72, 277–292.CrossRefGoogle Scholar
[17]Chapman, S. J. 1991 Thesis, Oxford University.Google Scholar