Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-29T02:38:05.512Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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