Étude de champs critiques en théorie de Ginzburg-Landau

Del Castillo, Pierre

Directeur de thèse : Helffer, Bernard

Membres du jury : Saut, Jean-Claude ; Bolley, Catherine ; Gallay, Thierry ; Helffer, Bernard ; Sandier, Etienne

Thèses d'Orsay, no. 572 (2000) , 172 p.

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@phdthesis{BJHTUP11_2000__0572__P0_0,
     author = {Del Castillo, Pierre},
     title = {\'Etude de champs critiques en th\'eorie de {Ginzburg-Landau}},
     series = {Th\`eses d'Orsay},
     year = {2000},
     publisher = {Universit\'e de Paris-Sud Centre d'Orsay},
     number = {572},
     language = {fr},
     url = {https://www.numdam.org/item/BJHTUP11_2000__0572__P0_0/}
}

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Del Castillo, Pierre. Étude de champs critiques en théorie de Ginzburg-Landau. Thèses d'Orsay, no. 572 (2000), 172 p. https://www.numdam.org/item/BJHTUP11_2000__0572__P0_0/

Bibliographie
Cité par

[1] A. Aftalion et W. C. Troy. On the solutions of the one-dimensional Ginzburg-Landau equations for superconductivity. Physica D 132, No. 1-2, p. 214-232, 1999. | MR | Zbl | DOI

[2] A. Aftalion et W. C. Troy. Uniqueness of solutions of the Ginzburg-Landau system for thin films. Preprint LMENS, 1999. | MR | Zbl

[3] F. Bethuel et T. Rivière. Vortices for a variational problem related to superconductivity. Amn. Inst. Henri Poincaré, Anal, non linéaire 12, No. 3, p. 243-303, 1993. | MR | Zbl | Numdam | DOI

[4] C. Bolley et P. Del Castillo Existence and uniqueness for the half-space Ginzburg-Landau model. A paraître dans Nonlinear Analysis, Theory, Methods and Applications. | MR | Zbl

[5] C. Bolley et B. Helffer. Rigorous results for the Ginzburg-Landau equations associated to a superconducting film in the weak $κ$ limit. Reviews in Mathematical Physics, vol. 8, No. 1, p. 43-83, 1996. | MR | Zbl | DOI

[6] C. Bolley et B. Helffer. Rigorous results on the Ginzburg-Landau models in a film submitted to an exterior magnetic field. Part I. Nonlinear Studies No. 3, p. 1-29, 1996. | MR | Zbl

[7] C. Bolley et B. Helffer. Upper bound for the solution of the Ginzburg-Landau equations in a semi-infinite superconducting field and applications to the superheating field in the large $κ$ regime. European Journal of Applied Mathematics, Vol. 8, p. 347-367, 1997. | MR | Zbl | DOI

[8] C. Bolley et B. Helffer. Proof of the De Gennes formula for the superheating field in the weak $κ$ limit. Annales de l'Institut Henri Poincaré (section analyse non linéaire), Vol. 14, No. 5, p. 597-613, 1997. | MR | Zbl | Numdam | DOI

[9] C. Bolley et B. Helffer. Superheating field in a semi-infinite film in the weak $κ$ limit : numerical results an approximate models. Mathematical modelling and numerical analysis, Vol. 31, No 1, p. 121-165, Novembre 1997. | MR | Zbl | Numdam

[10] C. Bolley, F. Foucher et B. Helffer. Superheating field for the Ginzburg-Landau equations in the case of a large bounded interval. A paraître dans J. Math. Phys. (2000) . | MR | Zbl

[11] S. J. Chapman. Asymptotic analysis of the Ginzburg-Landau model of superconductivity : Reduction to a free boundary model. Lakshmikantham, 5. (ed), World congress of nonlinear analysts'92. Proceedings of the first world congress, Tampa, FL, USA, August 19-26, 1992. | MR | Zbl

[12] S. J. Chapman. Superheating field of type II superconductors. Siam J. Appl. Math., Vol. 55, No 5, p. 1233-1258, 1995. | MR | Zbl | DOI

[13] 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.

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

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

[16] V. L. Ginzburg et L. D. Landau. "On the theory of superconductivity". Zh. Eksperim. i teor. Fiz. 20 1950, p. 1064-1082 English translation in Men of Physics : L. D. Landau, I, Ed. by D. Ter Harr, Pergamon oxford, 1965, p. 138-167., 1965.

[17] The Orsay Group. Quantum Fluids. ed. D. F. Brewer, p. 26, Amsterdam, North Holland, 1966.

[18] D.S. Mclachlan, H.J. Fink et B. Rothberg-Bibby. First and second order phase transitions of moderately small superconductor in a magnetic field. North-Holland, 1978.

[19] T. Dorsey, J. Dolgert et Di Bartolo. Superheating fields of superconductors : Asymptotic analysis and numerical results. Physical Review B, vol. 53, No 9, 1996. Erratum : Vol. 56, No. 5, 1997.

[20] M. K. Kwong. On the one-dimensional Ginzburg-Landau BVPs. Diff. Int. Equations 8, p. 1395-1405, 1995. | MR | Zbl

[21] H. Parr. Superconductive superheating field for finite $κ$ . Z. Physik B 25, p. 359-361, 1976. | DOI

[22] S. Alama, L. Bronsard et T. Giorgi. Uniqueness of symmetric vortex solutions in the Ginzburg-Landau model of superconductivity. J. Funct. Anal. 167, No. 2, p. 399-424, 1999 | MR | Zbl | DOI

[23] E. Sandier et S. Serfaty. Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field. Annales de l'Institut Henri Poincare, Analyse non linéaire | MR | Zbl | Numdam

[24] S. Serfaty. Stable configurations in superconductivity : uniqueness, multiplicity, and vortex-nucleation. Archive for Rational Mechanics and Analysis 149, No. 4, p. 329-365, 1999 | MR | Zbl | DOI

[25] S. Serfaty. Local minimizers for the Ginzburg-Landau energy near critical magnetic field : Part I. Commun. Contemp. Math. 1, No. 2, p. 213-254, 1999 | MR | Zbl

[26] S. Serfaty. Local minimizers for the Ginzburg-Landau energy near critical magnetic field : Part II. Archive for rational mechanics and analysis, November 1998. | Zbl

[27] M. Struwe. Variational methods. Springer, Berlin, 1990. | MR | Zbl | DOI

[28] M. Van Dyke. Perturbation methods in fluid mechanics. Academic Press, Stanford CA, 1975. | MR | Zbl

[1] A. Aftalion et W. C. Troy. On the solutions of the one-dimensionnal Ginzburg-Landau equations for superconductivity. Physica D 132, No. 1-2, p. 214-232, 1999. | MR | Zbl | DOI

[2] C. Bolley et P. Del Castillo Existence and uniqueness for the half-space Ginzburg-Landau model. A paraître dans Nonlinear Analysis, Theory, Methods and Applications. | MR | Zbl

[3] C. Bolley., F. Foucher et B. Helffer Superheating field for the Ginzburg-Landau equations in the case of a large bounded interval. A paraître dans J. Math. Phys. (2000). | MR | Zbl

[4] C. Bolley et B. Helffer. Rigorous results for the Ginzburg-Landau equations associated to a superconducting film in the weak $κ$ limit. Reviews in Mathematical Physics, Vol. 8, No. 1, p. 43-83, 1996. | MR | Zbl | DOI

[5] C. Bolley et B. Helffer. Upper bound for the solution of the Ginzburg-Landau equations in a semi-infinite superconducting field and applications to the superheating field in the large $κ$ regime. European Journal of Applied Mathematics, Vol. 8, p. 347-367, 1997. | MR | Zbl | DOI

[6] C. Bolley et B. Helffer. Rigorous results on the Ginzburg-Landau models in a film submitted to an exterior magnetic field. Part I. Nonlinear Studies No. 3, p. 1-29, 1996. | MR | Zbl

[7] C. Bolley et B. Helffer. Rigorous results on the Ginzburg-Landau models in a film submitted to an exterior parallel magnetic field. Part II. Nonlinear Studies, Vol. 3, No. 1, p. 43-83, 1996. | Zbl

[8] C. Bolley et B. Helffer. Superheating field in a semi-infinite film in the weak $κ$ limit : numerical results and approximate models. Mathematical modelling and numerical analysis, Vol. 31, No. 1, p. 121 à 165, Novembre 1997. | MR | Zbl | Numdam | DOI

[9] C. Bolley et B. Helffer. A priori estimates for Ginzburg-Landau solutions. Contribution pour Cargèse, 1999. A paraître dans NATO Science Series. | Zbl

[10] M.K. Kwong. On the one-dimensional Ginzburg-Landau BVPs. Diff. Int. Equations 8, p. 1395-1405, 1995. | MR | Zbl

[1] C. Bolley et B. Helffer. Rigorous results for the Ginzburg-Landau equations associated to a superconducting film in the weak $κ$ limit. Reviews Mathematical Physics, Vol. 8, No.1, p. 43-83, 1996. | MR | Zbl | DOI

[2] C. Bolley et B. Helffer. Rigorous results on the Ginzburg-Landau models in a film submitted to an exterior magnetic field. Part I. Nonlinear Studies No. 3, p. 1-29, 1996. | MR | Zbl

[3] C. Bolley et B. Helffer. Proof of the De Gennes formula for the superheating field in the weak $κ$ limit. Annales de l'Institut Henri Poincaré (section analyse non linéaire), Vol. 14, No. 5, p. 597-613, 1997. | MR | Zbl | Numdam | DOI

[4] B. Helffer et Fred B. Weissler. On a family of solutions of the second painlevé equation related to superconductivity. European Journal of Applied Mathematics, Vol. 9, No. 3, p. 223-243, 1998. | MR | Zbl | DOI

[6] C. Bolley et B. Helffer. A priori estimates for Ginzburg-Landau solutions. Contribution pour Cargèse, 1999. A paraître dans NATO Science Series. | Zbl

[7] S. J. Chapman. Asymptotic analysis of the Ginzburg-Landau model of superconductivity : Reduction to a free boundary model. Lakshmikantham, 5. (ed), World congress of nonlinear analysts'92. Proceedings of the first world congress, Tampa, FL, USA, August 19-26, 1992. | MR | Zbl

[8] S. J. Chapman. Superheating field of type ii superconductors. Siam J. Appl. Math., vol. 55, No. 5, p. 1233-1258, 1995. | MR | Zbl | DOI

[9] 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.

[10] The Orsay Group. Quantum Fluids. ed. D. F. Brewer, p. 26, Amsterdam, North Holland, 1966.

[11] B. Rothberg-Bibby, H. J. Fink et D. S. Mclachlan. First and second order phase transitions of moderately small superconductor in a magnetic field. North-Holland, 1978.

[12] T. Dorsey, J. Dolgert et Di Bartolo. Superheating fields of superconductors : Asymptotic analysis and numerical results. Physical Review B, vol. 53, No. 9, 1996.

[13] T. Dorsey, J. Dolgert et Di Bartolo. Erratum : Superheating fields of superconductors: Asymptotic analysis and numerical results. Physical Review B, vol. 56, No. 5, 1997.

[14] H. Parr. Superconductive superheating field for finite $κ$ . Z. physik B25, p. 359-361, 1976. | DOI

[15] M. Van Dyke. Perturbation Methods in fluid mechanics. Academic Press, Stanford CA, 1975. | MR | Zbl

[1] C. Bolley et B. Helffer. Rigorous results for the Ginzburg-Landau equations associated to a superconducting film in the weak $κ$ limit. Reviews in Mathematical Physics, Vol. 8, No. 1, p. 43-83, 1996. | MR | Zbl | DOI

[2] C. Bolley et B. Helffer. Rigorous results on the Ginzburg-Landau models in a film submitted to an exterior magnetic field. Part I. Nonlinear Studies No. 3, p. 1-29, 1996. | MR | Zbl

[3] C. Bolley et B. Helffer. Rigorous results on the Ginzburg-Landau models in a film submitted to a exterior parallel magnetic field. Part II. Nonlinear Studies, Vol. 3, No. 1, p. 43-83, 1996. | Zbl

[4] C. Bolley et B. Helffer. Superheating field in a semi-infinite film in the weak $κ$ limit : numerical results an approximate models. Mathematical modelling and numerical analysis, Vol. 31, No. 1, p. 121-165, Novembre 1997. | MR | Zbl | Numdam | DOI

[5] C. Bolley, F. Foucher et B. Helffer. Superheating field for the Ginzburg-Landau equations in the case of a large bounded interval. A paraître dans J. Math. Phys. (2000) . | MR | Zbl

[6] C. Bolley et B. Helffer. Superheating in a semi-infinite film in the weak $κ$ limit : numerical results and approximate models Mathematical modelling and numerical analysis, Vol. 31, No. 1, p. 121-165, 1997. | MR | Zbl | Numdam | DOI

[7] S. Alama, L. Bronsard et T. Giorgi. Uniqueness of symmetric vortex solutions in the Ginzburg-Landau model of superconductivity. J. Funct. Anal. 167, No. 2, p. 399-424, 1999 | MR | Zbl | DOI

[8] M. Struwe. Variational methods. Springer, Berlin, 1990. | MR | Zbl | DOI

[2] C. Bolley et B. Helffer. Rigorous results on the Ginzburg-Landau models in a film submitted to an exterior magnetic field. Part I. Nonlinear Studies No. 3, p. 1-29, 1996. | MR | Zbl

[3] C. Bolley et B. Helffer. Rigorous results on the Ginzburg-Landau models in a film submitted to an exterior parallel magnetic field. Part II. Nonlinear Studies, Vol. 3, No. 1, p. 43-83, 1996. | Zbl

[4] C. Bolley et B. Helffer. Proof of the De Gennes formula for the superheating field in the weak $κ$ limit. Annales de l'Institut Henri Poincaré (section analyse non linéaire), Vol. 14, No. 5, p. 597-613, 1997. | MR | Zbl | DOI | Numdam

[5] C. Bolley et B. Helffer. A priori estimates for Ginzburg-Landau solutions. Contribution pour Cargèse, 1999. | Zbl

[6] C. Bolley et B. Helffer. Superheating field in a semi-infinite film in the weak $κ$ limit : numerical results and approximate models. Mathematical modelling and numerical analysis, Vol. 31, No. 1, p. 121-165, Novembre 1997. | MR | Zbl | DOI | Numdam

[7] V.L. Ginzburg et L.D. Landau. "On the theory of superconductivity". Zh. Eksperim. i teor. Fiz. 20 1950, p. 1064-1082 English translation in Men of Physics : L. D. Landau, I, Ed. by D. Ter Harr, Pergamon Oxford, 1965, p. 138-167, 1965.

[8] Di Bartolo, T. Dorsey et J. Dolgert. Superheating fields of superconductors: Asymptotic analysis and numerical results. Physical Review B, Vol. 53, No. 9, 1996.

[9] H. Parr. Superconductive superheating field for finite $κ$ . Z. Physik B25, p. 359-361, 1976. | DOI

[10] M. Van Dyke. Perturbation Methods in fluid mechanics. Academic Press, Stanford CA, 1975. | MR | Zbl