Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed asymptotic matched solutions at order two for the half-space Ginzburg-Landau model, in the weak- limit. These authors deduced a formal expansion for the superheating field in powers of up to order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in Parr’s formula (Parr, 1976). In this paper, we construct asymptotic matched solutions at all orders leading to a complete expansion in powers of for the superheating field.
Mots-clés : superconductivity, Ginzburg-Landau equation, critical field
@article{M2AN_2002__36_6_971_0, author = {Castillo, Pierre Del}, title = {Expansion for the superheating field in a semi-infinite film in the weak-$\kappa $ limit}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {971--993}, publisher = {EDP-Sciences}, volume = {36}, number = {6}, year = {2002}, doi = {10.1051/m2an:2003001}, mrnumber = {1958654}, zbl = {1037.34046}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an:2003001/} }
TY - JOUR AU - Castillo, Pierre Del TI - Expansion for the superheating field in a semi-infinite film in the weak-$\kappa $ limit JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2002 SP - 971 EP - 993 VL - 36 IS - 6 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2003001/ DO - 10.1051/m2an:2003001 LA - en ID - M2AN_2002__36_6_971_0 ER -
%0 Journal Article %A Castillo, Pierre Del %T Expansion for the superheating field in a semi-infinite film in the weak-$\kappa $ limit %J ESAIM: Modélisation mathématique et analyse numérique %D 2002 %P 971-993 %V 36 %N 6 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2003001/ %R 10.1051/m2an:2003001 %G en %F M2AN_2002__36_6_971_0
Castillo, Pierre Del. Expansion for the superheating field in a semi-infinite film in the weak-$\kappa $ limit. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 6, pp. 971-993. doi : 10.1051/m2an:2003001. http://archive.numdam.org/articles/10.1051/m2an:2003001/
[1] Existence and uniqueness for the half-space Ginzburg-Landau model. Nonlinear Anal. 47/1 (2001) 135-146. | Zbl
and ,[2] Rigorous results for the Ginzburg-Landau equations associated to a superconducting film in the weak -limit. Rev. Math. Phys. 8 (1996) 43-83. | Zbl
and ,[3] Rigorous results on the Ginzburg-Landau models in a film submitted to an exterior parallel magnetic field. Part II. Nonlinear Stud. 3 (1996) 1-32. | Zbl
and ,[4] Proof of the De Gennes formula for the superheating field in the weak- limit. Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997) 597-613. | EuDML | Numdam | Zbl
and ,[5] Superheating in a semi-infinite film in the weak- limit: Numerical results and approximate models. ESAIM: M2AN 31 (1997) 121-165. | EuDML | Numdam | Zbl
and ,[6] 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 regime. European J. Appl. Math. 8 (1997) 347-367. | Zbl
and ,[7] Superheating field for the Ginzburg-Landau equations in the case of a large bounded interval. J. Math. Phys. 41 (2000) 7263-7289. | Zbl
, and ,[8] Superheating field of type II superconductors. SIAM J. Appl. Math. 55 (1995) 1233-1258. | Zbl
,[9] Thèse de doctorat. Université Paris-Sud (2000).
,[10] Two terms in the lower bound for the superheating field in a semi-infinite film in the weak- limit. European J. Appl. Math. (2002). | MR | Zbl
,[11] Superconductivity: Selected topics in solid state physics and theoretical Physics, in Proc. of 8th Latin american school of physics. Caracas (1966).
,[12] On the theory of superconductivity. Nuovo Cimento 2 (1955) 1234. | Zbl
,[13] On the destruction and the onset of superconductivity in a magnetic field. Zh. Èksper. Teoret. Fiz. 34 (1958) 113-125; Transl. Soviet Phys. JETP 7 (1958) 78-87. | Zbl
,[14] Dorsey and J. Dolgert, Superheating fields of superconductors: Asymptotic analysis and numerical results. Phys. Rev. B 53 (1996); Erratum. Phys. Rev. B 56 (1997).
[15] Matched asymptotic expansions and singular perturbations. North-Holland, Math. Studies 6 (1973). | MR | Zbl
,[16] On a family of solutions of the second Painlevé equation related to superconductivity. European J. Appl. Math. 9 (1998) 223-243. | Zbl
and ,[17] Superconductive superheating field for finite . Z. Phys. B 25 (1976) 359-361.
,[18] Perturbation Methods in fluid mechanics. Academic Press, Stanford CA (1975). | MR | Zbl
,[19] First and second order phase transitions of moderately small superconductor in a magnetic field. North-Holland (1978).
, and ,[20] Fluid mechanics and singular perturbations. Academic Press (1967). | MR
,Cité par Sources :