On multiply connected mesoscopic superconducting structures
Séminaire de théorie spectrale et géométrie, Tome 15 (1996-1997), pp. 207-220. 
@article{TSG_1996-1997__15__207_0,
     author = {Rubinstein, Jacob and Schatzman, Michelle},
     title = {On multiply connected mesoscopic superconducting structures},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {207--220},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {15},
     year = {1996-1997},
     zbl = {0892.35138},
     language = {en},
     url = {http://www.numdam.org/item/TSG_1996-1997__15__207_0/}
}
TY  - JOUR
AU  - Rubinstein, Jacob
AU  - Schatzman, Michelle
TI  - On multiply connected mesoscopic superconducting structures
JO  - Séminaire de théorie spectrale et géométrie
PY  - 1996-1997
SP  - 207
EP  - 220
VL  - 15
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/item/TSG_1996-1997__15__207_0/
LA  - en
ID  - TSG_1996-1997__15__207_0
ER  - 
%0 Journal Article
%A Rubinstein, Jacob
%A Schatzman, Michelle
%T On multiply connected mesoscopic superconducting structures
%J Séminaire de théorie spectrale et géométrie
%D 1996-1997
%P 207-220
%V 15
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/item/TSG_1996-1997__15__207_0/
%G en
%F TSG_1996-1997__15__207_0
Rubinstein, Jacob; Schatzman, Michelle. On multiply connected mesoscopic superconducting structures. Séminaire de théorie spectrale et géométrie, Tome 15 (1996-1997), pp. 207-220. http://www.numdam.org/item/TSG_1996-1997__15__207_0/

[1] A. A. Abrikosov. - Zh. Eksp. Theor. Fiz., 39 ( 1960).

[2] A. A. Abrikosov. - Zh. Eksp. Theor. Fiz., 41 ( 1961).

[3] A. A. Abrikosov. - "Fundamental theory of Metals", North Holland, 1983.

[4] C. Anné. - "Spectre du laplacien et écrasement d'anses", Ann. Sci. École Norm. Sup., 20 ( 1987), 271-280. | Numdam | MR | Zbl

[5] C. Anné. - "Fonctions propres sur des variétés avec des anses fines, applications à la multiplicité", Comm. Partial Differential Equations, 15 ( 1990), 1617-1630. | MR | Zbl

[6] C. Anné, B. Colbois. - "Opérateur de Hodge-Laplace sur des variétés compactes privées d'un nombre fini de boules", J. Funct. Anal, 115 ( 1993), 190-211. | MR | Zbl

[7] C. Anné, B. Colbois. - "Spectre du laplacien agissant sur les p-formes différentielles et écrasement d'anses", Math. Ann., 303 ( 1995), 545-573. | MR | Zbl

[8] I. Arregui. - P. Destuynder, M. Salaun, "Continuous updating of a shell geometry in a nonlinear analysis and applications to buckling simulations", in "Asymptotic methods for elastic structures", pp. 41-54, Lisbon, 1993. | MR | Zbl

[9] J. Bardeen, L.N. Cooper, J.R. Schrieffer. - "Theory of superconductivity", Phys. Rev., 108 ( 1957), 833. | MR | Zbl

[10] P. Bauman, D. Phillips, Q. Tang. - "Stable nucleation of the Ginzburg-Landau system with an applied magentic field", Arch. Rational Mech. Anal, to appear. | MR | Zbl

[11] J. G. Bednorz, K. A. Müller. - Z Phys., B64 ( 1986), 189.

[12] J. Berger and J. Rubinstein. - "Topology of the order parameter in the Little Parks experiment", Phys. Rev. Lett., 75 ( 1995), 320-322.

[13] J. Berger and J. Rubinstein. - "Bifurcation and phase transitions in nonuniform superconducting rings", SIAM J. Appl. Math., to appear. | MR | Zbl

[14] V. Bruyndoncx, C. Strunk, V. V. Moschalkov, C. Van Haesedonck. - "Y. Bruynseraede, Fluxoid quan-tization effects in superconductingmesoscopic Al multiloop structures", Europhys. Lett., 36 ( 1996), 449-454.

[15] H. J. Carlin and A. B. Giordano. - "Network Theory", Prentice Hall, 1964.

[16] R. Carlson. - "Eigenvalues of domains collapsing to graph", preprint.

[17] S. J. Chapman. - "Nucleation of superconductivity in a decreasing field", Europ. J. Appl. Math., 6 ( 1995), 97-114. | Zbl

[18] P. G. Ciarlet. - "Plates and Junctions in elastic Multi-Structures: an Asymptotic Analysis," Masson, Paris, 1990. | MR | Zbl

[19] P. G. Ciarlet, P. Destuynder. - "A justification of the two-dimensional linear plate model", J. Mécanique, 18 ( 1979), 315-344. | MR | Zbl

[20] P. G. Ciarlet, P. Destuynder. - "AJustification of a nonlinear model in plate theory", Comp. Methods Appl. Mech. Engrg., 17/18 ( 1979), 227-258. | MR | Zbl

[21] P. G. Ciarlet, H. Le Dret, R. Nzengwa. - "Junctions between three-dimensionaJ and two-dimensional linearly elastic structures", J Math. Pures Appl., 68 ( 1989), 261-295. | MR | Zbl

[22] P. G. Ciarlet, V. Lods. - "Asymptotic analysis of linearly elastic shells, I, Justification of membrane shells equations," Arch. Rational Mech. Anal, 136 ( 1996), 119-161. | MR | Zbl

[23] P. G. Ciarlet, V. Lods, B. Miara. - "Asymptotic analysis of linearly elastic shells, II, Justification of flexural shells equations," Arch. Rational Mech. Anal., 136 ( 1996), 163-190. | MR | Zbl

[24] P. G. Ciarlet, V. Lods. - "Asymptotic analysis of linearly elastic shells, III, Justification of Koiter's shells Equations," Arch. Rational. Mech. Anal., 136 ( 1996), 191-200. | MR | Zbl

[25] Y. Colin De Verdière. - "Sur la multiplicité de la première valeur propre non nulle du Laplacien", Comment. Math. Helvetici, 61 ( 1986), 254-270. | MR | Zbl

[26] M. C. Delfour, J.-P. Zolesio. - "Tangential differenrial equations for dynamical thin/shallow shells", J. Differential Equations 128 ( 1996), 125-167. | MR | Zbl

[27] P. Destuynder, M. Salaun. - "Mathematical analysis of thin plate models", Série Mathématiques et Applications, Springer-Verlag, 1996. | MR | Zbl

[28] P.-G. De Gennes. - "Superconductivity of Metals and Alloys", W. A. Benjamin, 1966; Reprinted edition, Addison-Wesley, 1996. | Zbl

[29] V. L. Ginzburg, L. D. Landau. - "On the theory of superconductivity", Zh. Eksp. Theor. Fiz., 20 ( 1950), 1064-1082.

[30] L. P. Gorkov. - "Microscopic derivation of the Ginzburg-Landau equations in the theory of superconductivity", Zh. Eksp. Theor. Fiz., 36 ( 1959) 1918-1923 (inrussian), Soviet Phys.-JETP, 9 ( 1959), 1364-1367. | Zbl

[31] L. P. Gorkov. - Zh.Eksp. Theor. Fiz.37 ( 1959), 833. | MR

[32] L. P. Gorkov. - Zh. Eksp. Theor. Fiz. 37 ( 1959),1407. | MR

[33] H. Kammerungh Onnes. - Leiden Comm., 120b, 122b, 124c ( 1911).

[34] H. Le Dret. - "Convergence of displacements and stresses in linearly elastic slender rods as the thickness goes tozero", Asymptotic Anal. 10( 1995), 367-402. | MR | Zbl

[35] L.-P. Lévy. - "Magnétisme et Supraconductivité", Interéditions et CNRS Éditions, Paris, 1997.

[36] W.A. Little, R.D. Parks. - Phys. Rev. Lett., 9 ( 1962),9.

[37] W.A. Little, R.D. Parks. - Phys. Rev. A, 133 ( 1964), 97.

[38] F. London, H. London. - Z. für Phys., 96 ( 1935), 359. | Zbl

[39] F. London, H. London. - Proc. Roy. Soc.(London) A, 149 ( 1935), 71. | Zbl

[40] F. London. - "Une conception nouvelle de la supraconductivité", Hermann, 1937.

[41] F. London. - "Superfluids", Wiley, 1950. | Zbl

[42] W. Meissner, R. Ochsenfeld. - Naturwisseschaften, 21 ( 1933), 787.

[43] B. Pannetier. - "Superconducting wire networks". In Quantum Coherence in Mesoscopic Systems (ed. B. Kramer) Plenum Press, ( 1991), 457-484.

[44] R.D. Parks. - Science, 146 ( 1964), 1429.

[45] J. Rubinstein and M. Schatzman. - "Asymptotics for thin superconducting rings", J. Math. Pures Appl., to appear. | MR | Zbl

[46] J. Rubinstein and M. Schatzman. - "On some variational problems in multiply connected thin strips", in preparation.

[47] D. Saint-James, P-G. De Gennes. - "Onset of superconductivity in decreasing fields", Phys. Rev. Lett., 9 ( 1962), 266.

[48] L.V. Shubnikov, W.J. De Haas. - Comm. Phys. Lab. Univ. Leiden, 207 ( 1930), 210.

[49] L. V. Shubnikov, W.J. De Haas. - Proc. Acad. Amsterdam. 33 ( 1930), 418.

[50] M. Schatzman. - "On the eigenvalues and eigenvectors of the Laplace operator in a thin set with Neumann boundary conditions", Applicable Analysis, 61 ( 1996), 293-306. | MR | Zbl

[51] M. Tinkham. - "Introduction to Superconductivity", McGraw Hill, 1996.