On multiply connected mesoscopic superconducting structures
Jacob Rubinstein; Michelle Schatzman
Séminaire de théorie spectrale et géométrie (1996-1997)
- Volume: 15, page 207-220
- ISSN: 1624-5458
Access Full Article
topHow to cite
topRubinstein, Jacob, and Schatzman, Michelle. "On multiply connected mesoscopic superconducting structures." Séminaire de théorie spectrale et géométrie 15 (1996-1997): 207-220. <http://eudml.org/doc/114410>.
@article{Rubinstein1996-1997,
author = {Rubinstein, Jacob, Schatzman, Michelle},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {Ginzburg-Landau theory; multiconnected mesoscopic superconductors; Ginzburg-Landau functional; subsequence of minimizers; limit problem},
language = {eng},
pages = {207-220},
publisher = {Institut Fourier},
title = {On multiply connected mesoscopic superconducting structures},
url = {http://eudml.org/doc/114410},
volume = {15},
year = {1996-1997},
}
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
PB - Institut Fourier
VL - 15
SP - 207
EP - 220
LA - eng
KW - Ginzburg-Landau theory; multiconnected mesoscopic superconductors; Ginzburg-Landau functional; subsequence of minimizers; limit problem
UR - http://eudml.org/doc/114410
ER -
References
top- [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. Zbl0634.58035MR911759
- [5] C. ANNÉ. - "Fonctions propres sur des variétés avec des anses fines, applications à la multiplicité", Comm. Partial Differential Equations, 15 ( 1990), 1617-1630. Zbl0723.35052MR1079605
- [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. Zbl0791.58018MR1228148
- [7] C. ANNÉ, B. COLBOIS. - "Spectre du laplacien agissant sur les p-formes différentielles et écrasement d'anses", Math. Ann., 303 ( 1995), 545-573. Zbl0909.58054MR1355003
- [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. Zbl0828.73043MR1333201
- [9] J. BARDEEN, L.N. COOPER, J.R. SCHRIEFFER. - "Theory of superconductivity", Phys. Rev., 108 ( 1957), 833. Zbl0090.45401MR95694
- [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. Zbl0922.35157MR1629119
- [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. Zbl0911.35041MR1610025
- [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. Zbl0843.35120
- [18] P. G. CIARLET. - "Plates and Junctions in elastic Multi-Structures: an Asymptotic Analysis," Masson, Paris, 1990. Zbl0706.73046MR1071376
- [19] P. G. CIARLET, P. DESTUYNDER. - "A justification of the two-dimensional linear plate model", J. Mécanique, 18 ( 1979), 315-344. Zbl0415.73072MR533827
- [20] P. G. CIARLET, P. DESTUYNDER. - "AJustification of a nonlinear model in plate theory", Comp. Methods Appl. Mech. Engrg., 17/18 ( 1979), 227-258. Zbl0405.73050MR533827
- [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. Zbl0661.73013MR1025905
- [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. Zbl0887.73038MR1423005
- [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. Zbl0887.73039MR1423006
- [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. Zbl0887.73040MR1423007
- [25] Y. COLIN DE VERDIÈRE. - "Sur la multiplicité de la première valeur propre non nulle du Laplacien", Comment. Math. Helvetici, 61 ( 1986), 254-270. Zbl0607.53028MR856089
- [26] M. C. DELFOUR, J.-P. ZOLESIO. - "Tangential differenrial equations for dynamical thin/shallow shells", J. Differential Equations 128 ( 1996), 125-167. Zbl0852.73035MR1392399
- [27] P. DESTUYNDER, M. SALAUN. - "Mathematical analysis of thin plate models", Série Mathématiques et Applications, Springer-Verlag, 1996. Zbl0860.73001MR1422248
- [28] P.-G. DE GENNES. - "Superconductivity of Metals and Alloys", W. A. Benjamin, 1966; Reprinted edition, Addison-Wesley, 1996. Zbl0138.22801
- [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. Zbl0088.45602
- [31] L. P. GORKOV. - Zh.Eksp. Theor. Fiz.37 ( 1959), 833. MR114617
- [32] L. P. GORKOV. - Zh. Eksp. Theor. Fiz. 37 ( 1959),1407. MR114614
- [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. Zbl0846.73025MR1338254
- [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. Zbl0012.32902
- [39] F. LONDON, H. LONDON. - Proc. Roy. Soc.(London) A, 149 ( 1935), 71. Zbl0011.42803
- [40] F. LONDON. - "Une conception nouvelle de la supraconductivité", Hermann, 1937.
- [41] F. LONDON. - "Superfluids", Wiley, 1950. Zbl0058.23405
- [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. Zbl0904.35071MR1646800
- [46] J. RUBINSTEIN and M. SCHATZMAN. - "On some variational problems in multiply connected thin strips", in preparation. Zbl0997.49003
- [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. Zbl0865.35098MR1618236
- [51] M. TINKHAM. - "Introduction to Superconductivity", McGraw Hill, 1996.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.