Ginzburg-Landau vortices: Dynamics, pinning, and hysteresis

SIAM Journal on Mathematical Analysis

Volumn 28, Issue 6, 1997, Pages 1265-1293

  Lin, Fang Hua ^a   Du, Qiang ^b,c  

^a NEW YORK UNIVERSITY   (United States)

^b IOWA STATE UNIVERSITY   (United States)

^c HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Ginzburg Landau equations; Hysteresis; Long time behavior; Superconductivity; Vortex pinning; Vortex solution

Indexed keywords

EID: 0031512221     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141096298060     Document Type: Article

References (28)

1. N. ANDRE AND I. SHAFRIR, Asymptotic Behavior of Minimizers for the Ginzburg-Landau Functional with Weights, I and II, preprint.
2. H. BERESTYCKI, A. BONNET, AND S. CHAPMAN, A semi-elliptic system arising in the theory of type-II superconductivity, Comm. Appl. Nonlinear Anal., 1 (1994), pp. 1-21.
3. F. BETHUEL, H. BREZIS, AND F. HELEIN, Ginzburg-Landau Vortices, Birkhäuser Boston, Cambridge, MA, 1994.
4. P. BAUMAN, D. PHILLIPS, AND Q. TANG, Stable Nucleation for the Ginzburg-Landau System with an Applied Magnetic Field, preprint.
5. F. BETHUEL AND T. RIVIERE, Vortices for a Variational Problem Related to Superconductivity, preprint.
6. S. CHAPMAN, Q. DU, AND M. GUNZBURGER, A variable thickness model for superconducting thin films, Z. Angew. Math. Phys., 47 (1995), pp. 410-431.
7. Z. CHEN, K. H. HOFFMANN, AND L. S. JIANG, On the Lawrence-Doniach model for layered superconductors, European J. Appl. Math, to appear.
8. Z. CHEN, C. M. ELLIOT, AND Q. TANG, Justification of a Two-Dimensional Evolutionary Ginzburg Landau Superconductivity Model, preprint.
9. S. DING AND Z. LIU, Pinning of Vortices for a Variational Problem Related to the Superconducting Thin Film having Variable Thickness, preprint.
10. P. DE GENNES, Superconductivity of Metals and Alloys, Addison-Wesley Publishing Company, Reading, MA.
11. Q. DU, Global existence and uniqueness of solutions of the time-dependent Ginzburg-Landau model for superconductivity, Appl. Anal., 53 (1994), pp. 1-17.
12. Q. DU AND M. D. GUNZBURGER, A model for super-conducting thin films having variable thickness. Phys. D, 69 (1993), pp. 215-231.
13. Q. DU, M. D. GUNZBURGER, AND J. PETERSON, Analysis and approximation of Ginzburg-Landau models for superconductivity, SIAM Rev., 34 (1992), pp. 54-81.
14. Q. DU, M. D. GUNZBURGER, AND J. PETERSON, Computational simulations of type-II superconductivity including pinning mechanisms, Phys Rev. B. (3), (1995), pp. 16194-16203.
15. W. E, Dynamics of vortices in Ginzburg-Landau theories and applications to superconductivity, Phys. D, 77 (1994), pp. 383-404.
16. W. E, Dynamics of vortex liquid in Ginzburg-Landau theories, with applications to superconductivity. Phys. Rev. B. 50, (1994), pp. 1126-1135.
17. L. GORKOV AND G. ELIASHBERG, Generalization of the Ginzburg-Landau equations for nonstationary problems in the case of alloys with paramagnetic impurities, Soviet Phys. JETP, 27 (1968), pp. 328-334.
18. C. LEFTER AND V. D. RADULESCU, On the Ginzburg-Landau energy with weight, C. R. Acad. Sci. Paris, to appear.
19. C. LIN AND F. H. LIN, Minimax solutions of Ginzburg-Landau equations, Select Math. (N.S.), 3 (1991), pp. 99-113.
20. F. H. LIN, Solutions of Ginzburg-Landau equations and critical points of the renormalized energy, Ann. Inst. H. Poincaré Anal. Non Linéaire, 12 (1995), pp. 599-622.
21. F. H. LIN, Some dynamic properties of Ginzburg-Landau vortices, Comm. Pure Appl. Math., 49 (1996), pp. 323-364.
22. F. H. LIN, Mixed vortex and anti-vortex solutions of Ginzburg-Landau equations, Arch. Rational Mech. Anal., 133 (1995), pp. 103-127.
23. J. NEU, Vortices in complex scalar fields, Phys. D, 43 (1990), pp. 385-406.
24. L. PISMAN AND J. D. RODRIGUEZ, Mobilities of singularities in dissipative Ginzburg-Landau equations, Phys. Rev. A, 42 (1990), pp. 2471-2474.
25. J. RUBINSTEIN AND P. STERNBERG, On the Slow Motion of Vortices in the Ginzburg-Landau Heat Flow, preprint.
26. L. SIMON, Lectures on geometric measure theory, Austral. Nat. Univ. CMA (1983).
27. L. SIMON, Asymptotics for a class of non-linear evolution equations with applications to geometric problems, Ann. of Math, 118 (1983), pp. 525-572.
28. Q. TANG AND S. WANG, Time dependent Ginzburg Landau equations of superconductivity, Physica D, 88 (1995), pp. 139-166.