Nous nous proposons de décrire, dans cet article, des travaux récents sur les champs magnétiques critiques liés à certains matériaux supraconducteurs.
@article{RFM_2004__7__17_0, author = {Bolley, Catherine and Helffer, Bernard}, title = {Champs magn\'etiques critiques et hyst\'er\'esis dans les films supraconducteurs}, journal = {Femmes & math}, pages = {17--30}, publisher = {Association femmes et math\'ematiques}, volume = {7}, year = {2004}, language = {fr}, url = {http://www.numdam.org/item/RFM_2004__7__17_0/} }
TY - JOUR AU - Bolley, Catherine AU - Helffer, Bernard TI - Champs magnétiques critiques et hystérésis dans les films supraconducteurs JO - Femmes & math PY - 2004 SP - 17 EP - 30 VL - 7 PB - Association femmes et mathématiques UR - http://www.numdam.org/item/RFM_2004__7__17_0/ LA - fr ID - RFM_2004__7__17_0 ER -
Bolley, Catherine; Helffer, Bernard. Champs magnétiques critiques et hystérésis dans les films supraconducteurs. Femmes & math, Tome 7 (2004), pp. 17-30. http://www.numdam.org/item/RFM_2004__7__17_0/
[AfDa] A. Aftalion, E. N. Dancer, On the symmetry and uniqueness of solutions of the Ginzburg-Landau equations for small domains (2000). Com. Contemp. Math. 3, 1–14 (2001). | MR | Zbl
[AfTr] A. Aftalion, W. C. Troy, On the solutions of the one-dimensional Ginzburg-Landau equations for superconductivity. Physica D 132, 214–232 (1999). | MR | Zbl
[Ag] S. Agmon, Lecture on Exponential Decay of Solutions of Second Order Elliptic Equations. Math. Notes, T. 29, Princeton University Press (1982). | MR | Zbl
[Bo] C. Bolley, Modélisation du champ de retard à la condensation d’un supraconducteur par un problème de bifurcation. Math. Model. Num. Anal., 26 no 2, 235–287 (1992). | Numdam | MR | Zbl
[BoCa] C. Bolley, P. Del Castillo, Existence and uniqueness for the half-space Ginzburg-Landau model. Nonlin. Anal. 47, no 1, 135–146 (2001). | MR | Zbl
[BoFoHe] C. Bolley, F. Foucher, B. Helffer, Superheating field for the Ginzburg-Landau equations in the case of a large bounded interval. J. Math. Phys. 41 no 11, 7263–7289 (2000). | MR | Zbl
[BoHe1] C. Bolley, B. Helffer, An application of semi-classical analysis to the asymptotic study of the supercooling field of a superconducting material. Ann. Inst. Henri Poincaré (Physique Théorique) 58 no 2, 169–233 (1993). | Numdam | MR | Zbl
[BoHe2] C. Bolley, B. Helffer, Rigorous results for the Ginzburg-Landau equations associated to a superconducting film in the weak -limit. Reviews in Math. Physics 8 no 1, 43–83 (1996). | MR | Zbl
[BoHe3] C. Bolley, B. Helffer, Proof of the De Gennes formula for the superheating field in the weak limit. Ann. Inst. Henri Poincaré (Analyse non linéaire) 14 no 5, 597–613 (1997). | Numdam | MR | Zbl
[BoHe4] C. Bolley, B. Helffer, The Ginzburg-Landau equations in a semi-infinite superconducting film in the large limit. Eur. J. Appl. Math. 8, 347–367 (1997). | MR | Zbl
[BoHe5] C. Bolley, B. Helffer, Stability of bifurcating solutions for the Ginzburg-Landau equations. Rev. in Math. Physics 10 no 5, 579–626 (1998). | MR | Zbl
[BoHe6] C. Bolley, B. Helffer : A priori estimates for Ginzburg-Landau solutions. Institut Scientifique de Cargèse (1999). Submitted in Nonlinear PDE’s in Physics, H. Berestycki and Y. Pomeau eds., NATO Science ASI Series. Elsevier Publ. Co., Dordrecht. Rapport de recherche de l’Université de Nantes (2002). | Zbl
[BoHe7] C. Bolley, B. Helffer, Global superheating field for superconductors in a large bounded interval. Physica D 172 no 1–4, 162–189 (2002). | MR | Zbl
[Ca1] P. Del Castillo, Etude de champs critiques en théorie de Ginzburg–Landau, Thèse de Doctorat de l’Université de Paris-Sud, Orsay, 2000.
[Ca2] P. Del Castillo, Two terms in the lower bound for the superheating field in a semi-infinite film in the weak- limit. Europ. J. Appl. Math. 13 no 5, 517–544 (2002). | MR | Zbl
[Ch] S. J. Chapman, Superheating field of type II superconductors. Siam J. Appl. Math. 55 no 5, 1233–1258 (1995). | MR | Zbl
[DBD] A. J. Dolgert, S. J. Di Bartolo, A. T. Dorsey, Superheating fields of superconductors : asymptotic analysis and numerical results. Phys. Rev. B 53 no 9, 5650-5660 (1996). Erratum : Superheating fields of superconductors : asymptotic analysis and numerical results. Phys. Rev. B 56 no 5, 2883 (1997).
[Ge] P. G. de Gennes, Superconductivity, selected topics in solid state physics and theoretical Physics. Proc. of 8-th Latin American School of Physics, Caracas (1966).
[Gi2] V. L. Ginzburg, On the destruction and the onset of superconductivity in a magnetic field, Zh. Eksperim. i Teor. Fiz. 34, 113-125 (1958).Transl. Soviet Physics JETP 7, 78–87 (1958). | Zbl
[GiLa] V. L. Ginzburg, L. D. Landau, On the theory of superconductivity. Zh. Eksperim. i Teor. Fiz. 20, 1064-1082 (1950). English translation Men of Physics, L. D. Landau, D. Ter Haar ed., Pergamon Press, Oxford, 1965.
[JaSaTh] D. Saint James, G. Sarma and E. J. Thomas, Type II Superconductivity. Pergamon Press, Oxford, 1969,.
[Pa] H. Parr, Superconducting superheating field for finite . Z. Physik B 25, 359–361 (1976).