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Zeros of a complex Ginzburg–Landau order parameter with applications to superconductivity

Published online by Cambridge University Press:  26 September 2008

C. M. Elliott ,
H. Matano  and
Tang Qi
C. M. Elliott
Affiliation:
School of Mathematical and Physical Sciences, University of Sussex, Brighton BN1 9QH, UK
H. Matano
Affiliation:
Department of Mathematical Sciences, University of Tokyo, Hongo, Tokyo 113, Japan
Tang Qi
Affiliation:
School of Mathematical and Physical Sciences, University of Sussex, Brighton BN1 9QH, UK
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Abstract

We consider the minimizers of the Gibbs free energy which couples a complex Ginzburg–Landau order parameter with a magnetic potential. It is established that the set on which the complex order parameter equals zero consists only of isolated points. Some estimates concerning the set on which the absolute value of the order parameter is small are also given. Numerical simulations are presented for the problem without a magnetic potential.

Information

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 5 , Issue 4 , December 1994 , pp. 431 - 448
Copyright
Copyright © Cambridge University Press 1994

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References

[Ba]Ball, J. M. A version of the fundamental theorem for Young measures. Preprint.Google Scholar
[BC]Berger, M. S. & Chen, Y. Y. 1989 Symmetric vortices for the Ginzburg-Landau equations of superconductivity and the nonlinear desingularization phenomenon. J. Funct. Anal. 82, 259–295.Google Scholar
[BK]Brieskorn, E. & Khorrer, H. 1986 Plane Algebraic Curves. Birkhauser Verlag, Boston.Google Scholar
[CHO]Chapman, S. J., Howison, S. D. & Ockendon, J. R. 1990 Macroscopic models for superconductivity. SIAM Rev. 34 (4), 529–560.Google Scholar
[CHMO]Chapman, S. J., Howison, S. D., McLeod, J. B. & Ockendon, J. R. 1991 Normal/superconducting transitions in Ginzburg-Landau theory. Proc. Roy. Soc. Edinburgh, 119A, 117–124.Google Scholar
[Ch]Chen, Y. Y. 1990 Vortices for the Ginzburg-Landau equations — the non-symmetric case in bounded domain. Contemporary Math. 108, 19–32.CrossRefGoogle Scholar
[Cr]Cronström, C. 1980 A simple and complete Lorentz-covariant gauge condition. Phys. Lett. 90B, 267–269.CrossRefGoogle Scholar
[DGP]Du, Q., Gunzburger, M. D. & Peterson, J. S. 1992 Analysis and approximation of the Ginzburg-Landau model of superconductivity. Siam Rev. 34 (1), 54–81.Google Scholar
[Fe]Federen, H. 1968 Geometric Measure Theory. Springer.Google Scholar
[GNN]Gidas, B., Ni, W. M. & Nirenberg, L. 1979 Symmetry and related properties via the maximum principle. Comm. Math. Phys. 68, 209–243.CrossRefGoogle Scholar
[JT]Jaffe, A. & Taube, C. 1990 Vortices and Monopoles. Birkhauser, Boston.Google Scholar
[Mod]Modica, L. 1987 The gradient theory of phase transitions and the minimal interface criterion. Arch. Rat. Mech. Anal. 98, 123–142.Google Scholar
[MGP]Monvel-Berthier, A. B., Georgescu, V. & Purice, R. 1991 A boundary value problem relates to the Ginzburg-Landau Model. Comm. Math. Phys. 142, 1–23.Google Scholar
[Mo]Morrey, C. B. 1966 Multiple Integrals in the Calculus of Variations. Springer-Verlag.Google Scholar
[Na]Nakahara, M. 1990 Geometry, Topology and Physics. Adam Hilger.Google Scholar
[Ne]Neu, J. C. 1990 Vortices in complex scalar fields. Physica D, 42, 385–406.Google Scholar
[St]Sternberg, P. 1988 The effect of a singular perturbation on non-convex variational problems. Arch. Rat. Mech. Anal. 101 (3), 209–260.Google Scholar
[Te]Temam, R. 1979 Navier-Stokes Equations. North-Holland.Google Scholar
[Ya]Yang, Y. 1979 Boundary value problems of the Ginzburg-Landau equations. Proc. Roy. Soc. Edinburgh, 114A, 355–365.Google Scholar