Superheating in a semi-infinite film in the weak $\kappa$ limit : numerical results and approximate models

Bolley, Catherine; Helffer, Bernard

ESAIM: Modélisation mathématique et analyse numérique, Tome 31 (1997) no. 1, pp. 121-165.

[1] J. Blot, 1987, Relation entre les grandeurs supraconductrices caractéristiques de l'aluminium massif et les champs de transition de films en fonction de leur épaisseur. Thesis, Rennes 1.

[2] C. Bolley, 1992, Modélisation du champ de retard à la condensation d'un supraconducteur par un problème de bifurcation, M2AN, 26, n° 2, pp. 235-287. | Numdam | MR | Zbl

[3] C. Bolley, 1993, Remarks on critical fields of a superconducting film. International conférence on mathematics of superconductivity, Seattle, (25-29 July).

[4] C. Bolley, 1995, Numerical study of the superheating field for the Ginzburg-Landau equations in the half-space model. Preprint École Centrale de Nantes.

[5] C. Bolley, B. Helffer, 1996, Rigorous results on the Ginzburg-Landau modelsm a film submitted to an extenor parallel magnetic field. Part II - Nonlinear Studies, 3, n° 2, pp 1-32. | MR | Zbl

[6] C. Bolley, B. Helffer, 1993, Sur les asymptotiques des champs critiques pourl' équation de Ginzburg-Landau, Séminaire équations aux dérivées partielles de l'École Polytechnique, expose n° IV (novembre). | Numdam | Zbl

[7]C. Bolley, B. Helffer, 1994, On the asymptotics of the critical field for the Ginzburg-Landau equation, Progress in Partial Differential Equations the Metz Surveys 3. Ed. M. Chipot, J. Saint Jean Paulin, I. Shafrir, Pitman Research Notes in Math, Series 314. | MR | Zbl

[8] C. Bolley, B. Helffer, Rigorous results for the Ginzburg-Landau equations associated to a superconductmg film in the weak k limit, in Reviews in Math. Physics, Vol 8, n° 1, pp 43-83. | MR | Zbl

[9] C. Bolley, B. Helffer, 1994, Superheating in a film in the weak K limit : numerical results and approxmiate model, Preprint de l'École Centrale de Nantes.

[10] C. Bolley, B. Helffer, 1995, Proof of the De Gennes formula for the superheating field in the weak k limit, to appear in Ann. Institut Henri Poincaré Anal. non lin. | Numdam | MR | Zbl

[11] A. R. Champneys, P. G. Hjorth, 1992, Symplectic integration of separatrix crossing orbits, Mat. report n° 1992-25, Math. Institute, Denmark.

[12] S.J. Chapman, 1993, Nucleation of superconductivity in decreasing fields, Preprint. | Zbl

[13] S. J. Chapman, S. D. Howison, J. B. Mcleod and J.R. Ockendon, 1991, Normal-superconducting transitions in Ginzburg-Landau theory, Proc. Roy. Soc. Edin, 119A,pp 117-124. | MR | Zbl

[14] S. J. Chapman, S D Howison, J.R. Ockendon, 1992, Macroscopic models for superconductivity, SIAM review, 34, n° 4, pp. 529-560. | MR | Zbl

[15] M. Crouzeix, 1975, Sur l'approximation des équations différentielles opérationnelles linéaires par des méthodes de Runge-Kutta, Thesis, Rennes.

[16] M. Crouzeix, A. L. Mlgnot, 1984, Analyse numérique des équations différentielles, Masson. | MR | Zbl

[17] H. J. Fink, D. S. Mclachlan, B. Rothberg-Bibby, 1978, First and second order phase transitions of moderately small superconductors in a magnetic field. Chap. 6 in Progress in Low temperature Physics, Vol. VIIB, North-Holland.

[18] V. P. Galaiko, 1968, Superheating critical field for superconductors of the first kind, Soviet Physics JETP, 27, n° 1, July.

[19] P. G. De Gennes, 1966, Superconductivity : selected topics in solid state physics and theoretical Physics, Proc. of 8th Latin american school of physics, Caracas.

[20] V. L. Ginzburg, 1955, On the theory of superconductivity, Nuovo Cimento 2, p 1234. | Zbl

[21] V. L. Glnzburg, 1958, On the destruction and the onset of superconductivity in a magnetic field, Soviet Physics JETP 7, 78. | Zbl

[22] V. L. Ginzburg, L. D. Landau, 1950, On the theory of superconductivity, Zh. Eksperim. i teor. Fiz., 20, pp 1064-1082 English translation Men of Physics : L. D. Landau, I, Ed. by D. Ter Haar, Pergamon Oxford, pp. 138-167 (1965).

[23] J. Guckenheimer, P. Holmes, 1983, Nonlinear oscillations, dynamical systems and bifurcations of vector fields, Springer Verlag. | MR | Zbl

[24] D. Saint James, G. Sarma and E. J. Thomas, 1969, Type II Superconductivity, Pergamon Press.

[25] J. Matricon, D. Saint James, 1967, Superheating fields in superconductors. Physics Letters, 24A, n° 5, pp. 241-242.

[26] The Orsay group, 1966, in Quantum fluids (éd. D. F. Brewer), p. 26, Amsterdam,North Holland.

[27] H. Parr, 1976, Superconductive superheating field for finite K, Z. Physik B25,pp. 359-361.

[28] H. Parr and J. Feder, 1973, Superconductivity in ß-Phase gallium, Physical review B, 7, n° 1.

[29] Y. Pellan, 1987, Étude de la stabilité de la transition supraconductrice de films divisés d'Indium sous champ magnétique parallèle et perpendiculaire. Thesis, Rennes 1.

[30] S. Wang, Y. Yang, 1992, Symmetric superconducting states in thin films, SIAM J. Appl. Math., 52, p. 614. | MR | Zbl