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Superheating in a semi-infinite film in the weak \(k\) limit: Numerical results and approximate models. (English) Zbl 0868.65087
The purpose of this paper is to analyse numerically the different results concerning the superheating field for Ginzburg-Landau equations in the case when the size of the film is larger in comparison with the inverse of the characteristic constant of the material. A number of numerical experiments are also demonstrated for theoretical foundation.

MSC:
65Z05 Applications to the sciences
35Q72 Other PDE from mechanics (MSC2000)
80A20 Heat and mass transfer, heat flow (MSC2010)
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[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] [2] C. BOLLEY, 1992, Modélisation du champ de retard à la condensation d’un supraconducteur par un problème de bifurcation, M2AN, 26, n^\circ 2, pp. 235-287. Zbl0741.35085 MR1153002 · Zbl 0741.35085 · eudml:193663
[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^\circ 2, pp 1-32. Zbl0869.34016 MR1396033 · Zbl 0869.34016
[6] [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^\circ IV (novembre). Zbl0877.35120 · Zbl 0877.35120 · eudml:112092
[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. Zbl0836.35019 MR1300899 · Zbl 0836.35019
[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^\circ 1, pp 43-83. Zbl0864.35097 MR1372515 · Zbl 0864.35097 · doi:10.1142/S0129055X96000032
[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. · Zbl 0868.65087
[10] [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. Zbl0889.34010 MR1637965 · Zbl 0889.34010 · doi:10.1016/S0294-1449(97)80127-8 · numdam:AIHPC_1997__14_5_597_0 · eudml:78422
[11] A. R. CHAMPNEYS, P. G. HJORTH, 1992, Symplectic integration of separatrix crossing orbits, Mat. report n^\circ 1992-25, Math. Institute, Denmark.
[12] S.J. CHAPMAN, 1993, Nucleation of superconductivity in decreasing fields, Preprint. Zbl0820.35124 · Zbl 0820.35124
[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. Zbl0732.34003 MR1130600 · Zbl 0732.34003 · doi:10.1017/S0308210500028353
[14] S. J. CHAPMAN, S D HOWISON, J.R. OCKENDON, 1992, Macroscopic models for superconductivity, SIAM review, 34, n^\circ 4, pp. 529-560. Zbl0769.73068 MR1193011 · Zbl 0769.73068 · doi:10.1137/1034114
[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. Zbl0635.65079 MR762089 · Zbl 0635.65079
[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^\circ 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. · Zbl 0138.22801
[20] V. L. GINZBURG, 1955, On the theory of superconductivity, Nuovo Cimento 2, p 1234. Zbl0067.23504 · Zbl 0067.23504 · doi:10.1007/BF02731579
[21] V. L. GlNZBURG, 1958, On the destruction and the onset of superconductivity in a magnetic field, Soviet Physics JETP 7, 78. Zbl0099.44703 · Zbl 0099.44703
[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. Zbl0515.34001 MR709768 · Zbl 0515.34001
[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^\circ 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^\circ 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. Zbl0758.35075 MR1163796 · Zbl 0758.35075 · doi:10.1137/0152034
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