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Ginzburg-Landau model with small pinning domains
1. | Université de Lyon, Université Lyon 1, Institut Camille Jordan CNRS UMR 5208, 43, boulevard du 11 novembre 1918, F-69622 Villeurbanne, France |
2. | Department of Mathematics, The Pennsylvania State University, University Park PA 16802, United States |
References:
[1] |
A. Aftalion, E. Sandier and S. Serfaty, Pinning Phenomena in the Ginzburg-Landau model of superconductivity, J. Math. Pures Appl. (9), 80 (2001), 339-372.
doi: 10.1016/S0021-7824(00)01180-6. |
[2] |
S. Alama and L. Bronsard, Pinning effects and their breakdown for a Ginzburg-Landau model with normal inclusions, J. Math. Phys., 46 (2005), 095102, 39 pp. |
[3] |
N. André, P. Bauman and D. Phillips, Vortex pinning with bounded fields for the Ginzburg-Landau equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, 20 (2003), 705-729. |
[4] |
N. André and I. Shafrir, Asymptotic behavior of minimizers for the Ginzburg-Landau functional with weight. I, II, Arch. Rational Mech. Anal., 142 (1998), 45-73, 75-98.
doi: 10.1007/s002050050083. |
[5] |
H. Aydi and A. Kachmar, Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint. II, Commun. Pure Appl. Anal., 8 (2009), 977-998.
doi: 10.3934/cpaa.2009.8.977. |
[6] |
J. Bardeen and M. Stephen, Theory of the motion of vortices in superconductors, Phys. Rev, 140 (1965), 1197-1207.
doi: 10.1103/PhysRev.140.A1197. |
[7] |
P. Bauman, N. Carlson and D. Phillips, On the zeros of solutions to Ginzburg-Landau type systems, SIAM J. Math. Anal., 24 (1993), 1283-1293.
doi: 10.1137/0524073. |
[8] |
L. Berlyand and P. Mironescu, Ginzburg-Landau minimizers in perforated domains with prescribed degrees, preprint, 2006. Available from: http://math.univ-lyon1.fr/~mironescu/prepublications.htm. |
[9] |
L. Berlyand and P. Mironescu, Two-parameter homogenization for a Ginzburg-Landau problem in a perforated domain, Netw. Heterog. Media, 3 (2008), 461-487.
doi: 10.3934/nhm.2008.3.461. |
[10] |
F. Bethuel, H. Brezis and F. Hélein, Asymptotics for the minimization of a Ginzburg-Landau functional, Calc. Var. Partial Differential Equations, 1 (1993), 123-148. |
[11] |
F. Bethuel, H. Brezis and F. Hélein, "Ginzburg-Landau Vortices," Progress in Nonlinear Differential Equations and their Applications, 13, Birkhäuser Boston, Inc., Boston, MA, 1994. |
[12] |
H. Brezis, Équations de Ginzburg-Landau et singularités, Notes de cours rédigées par Vicentiu Radulescu, 2001. Available from: http://inf.ucv.ro/~radulescu/articles/coursHB.pdf. |
[13] |
H. Brezis, New questions related to the topological degree, in "The Unity of Mathematics," 137-154, Progr. Math., 244, Birkhäuser Boston, Boston, MA, 2006. |
[14] |
M. del Pino and P. Felmer, On the basic concentration estimate for the Ginzburg-Landau equation, Differ Integr Equat., 11 (1998), 771-779. |
[15] |
M. Dos Santos, P. Mironescu and O. Misiats, The Ginzburg-Landau functional with a discontinuous and rapidly oscillating pinning term. Part I: The zero degree case,, Commun. Contemp. Math., ().
|
[16] |
B. A. Glowacki and M. Majoros, Superconducting-magnetic heterostructures: A method of decreasing AC losses and improving critical current density in multifilamentary conductors, J. Phys.: Condens. Matter, 21 (2009), 771-779. |
[17] |
D. Larbalestier, A. Gurevich, M. Feldmann and A. Polyanskii, High-Tc superconducting material for electric power applications, Nature, 414 (2001), 368-377.
doi: 10.1038/35104654. |
[18] |
L. Lassoued and P. Mironescu, Ginzburg-Landau type energy with discontinuous constraint, J. Anal. Math., 77 (1999), 1-26.
doi: 10.1007/BF02791255. |
[19] |
C. Lefter and V. Radulescu, Minimization problems and corresponding renormalized energies, Differential Integral Equations, 9 (1996), 903-917. |
[20] |
C. Lefter and V. Radulescu, On the Ginzburg-Landau energy with weight, Ann. Inst. H. Poincaré Anal. Non Linéaire, 13 (1996), 171-184. |
[21] |
F. Lin and Q. Du, Ginzburg-Landau vortices, dynamics, pinning, and hysteresis, SIAM J. Math. Anal., 28 (1997), 1265-1293.
doi: 10.1137/S0036141096298060. |
[22] |
N. G. Meyers, An L$^p$-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa (3), 17 (1963), 189-206. |
[23] |
P. Mironescu, Explicit bounds for solutions to a Ginzburg-Landau type equation, Rev. Roumaine Math. Pures Appl., 41 (1996), 263-271. |
[24] |
C. Morrey, Jr., "Multiple Integrals in the Calculus of Variations," Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. |
[25] |
P. Newton and G. Chamoun, Vortex lattice theory: A particle interaction perspective, SIAM Rev., 51 (2009), 501-542.
doi: 10.1137/07068597X. |
[26] |
J. Rubinstein, On the equilibrium position of Ginzburg Landau vortices, Z. Angew. Math. Phys., 46 (1995), 739-751.
doi: 10.1007/BF00949077. |
[27] |
E. Sandier and S. Serfaty, "Vortices in the Magnetic Ginzburg-Landau Model,'' Progress in Nonlinear Differential Equations and their Applications, 70, Birkhäuser Boston, Inc., Boston, MA, 2007. |
[28] |
I. Sigal and F. Ting, Pinning of magnetic vortices by an external potential, St. Petersburg Math. J., 16 (2005), 211-236.
doi: 10.1090/S1061-0022-04-00848-9. |
show all references
References:
[1] |
A. Aftalion, E. Sandier and S. Serfaty, Pinning Phenomena in the Ginzburg-Landau model of superconductivity, J. Math. Pures Appl. (9), 80 (2001), 339-372.
doi: 10.1016/S0021-7824(00)01180-6. |
[2] |
S. Alama and L. Bronsard, Pinning effects and their breakdown for a Ginzburg-Landau model with normal inclusions, J. Math. Phys., 46 (2005), 095102, 39 pp. |
[3] |
N. André, P. Bauman and D. Phillips, Vortex pinning with bounded fields for the Ginzburg-Landau equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, 20 (2003), 705-729. |
[4] |
N. André and I. Shafrir, Asymptotic behavior of minimizers for the Ginzburg-Landau functional with weight. I, II, Arch. Rational Mech. Anal., 142 (1998), 45-73, 75-98.
doi: 10.1007/s002050050083. |
[5] |
H. Aydi and A. Kachmar, Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint. II, Commun. Pure Appl. Anal., 8 (2009), 977-998.
doi: 10.3934/cpaa.2009.8.977. |
[6] |
J. Bardeen and M. Stephen, Theory of the motion of vortices in superconductors, Phys. Rev, 140 (1965), 1197-1207.
doi: 10.1103/PhysRev.140.A1197. |
[7] |
P. Bauman, N. Carlson and D. Phillips, On the zeros of solutions to Ginzburg-Landau type systems, SIAM J. Math. Anal., 24 (1993), 1283-1293.
doi: 10.1137/0524073. |
[8] |
L. Berlyand and P. Mironescu, Ginzburg-Landau minimizers in perforated domains with prescribed degrees, preprint, 2006. Available from: http://math.univ-lyon1.fr/~mironescu/prepublications.htm. |
[9] |
L. Berlyand and P. Mironescu, Two-parameter homogenization for a Ginzburg-Landau problem in a perforated domain, Netw. Heterog. Media, 3 (2008), 461-487.
doi: 10.3934/nhm.2008.3.461. |
[10] |
F. Bethuel, H. Brezis and F. Hélein, Asymptotics for the minimization of a Ginzburg-Landau functional, Calc. Var. Partial Differential Equations, 1 (1993), 123-148. |
[11] |
F. Bethuel, H. Brezis and F. Hélein, "Ginzburg-Landau Vortices," Progress in Nonlinear Differential Equations and their Applications, 13, Birkhäuser Boston, Inc., Boston, MA, 1994. |
[12] |
H. Brezis, Équations de Ginzburg-Landau et singularités, Notes de cours rédigées par Vicentiu Radulescu, 2001. Available from: http://inf.ucv.ro/~radulescu/articles/coursHB.pdf. |
[13] |
H. Brezis, New questions related to the topological degree, in "The Unity of Mathematics," 137-154, Progr. Math., 244, Birkhäuser Boston, Boston, MA, 2006. |
[14] |
M. del Pino and P. Felmer, On the basic concentration estimate for the Ginzburg-Landau equation, Differ Integr Equat., 11 (1998), 771-779. |
[15] |
M. Dos Santos, P. Mironescu and O. Misiats, The Ginzburg-Landau functional with a discontinuous and rapidly oscillating pinning term. Part I: The zero degree case,, Commun. Contemp. Math., ().
|
[16] |
B. A. Glowacki and M. Majoros, Superconducting-magnetic heterostructures: A method of decreasing AC losses and improving critical current density in multifilamentary conductors, J. Phys.: Condens. Matter, 21 (2009), 771-779. |
[17] |
D. Larbalestier, A. Gurevich, M. Feldmann and A. Polyanskii, High-Tc superconducting material for electric power applications, Nature, 414 (2001), 368-377.
doi: 10.1038/35104654. |
[18] |
L. Lassoued and P. Mironescu, Ginzburg-Landau type energy with discontinuous constraint, J. Anal. Math., 77 (1999), 1-26.
doi: 10.1007/BF02791255. |
[19] |
C. Lefter and V. Radulescu, Minimization problems and corresponding renormalized energies, Differential Integral Equations, 9 (1996), 903-917. |
[20] |
C. Lefter and V. Radulescu, On the Ginzburg-Landau energy with weight, Ann. Inst. H. Poincaré Anal. Non Linéaire, 13 (1996), 171-184. |
[21] |
F. Lin and Q. Du, Ginzburg-Landau vortices, dynamics, pinning, and hysteresis, SIAM J. Math. Anal., 28 (1997), 1265-1293.
doi: 10.1137/S0036141096298060. |
[22] |
N. G. Meyers, An L$^p$-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa (3), 17 (1963), 189-206. |
[23] |
P. Mironescu, Explicit bounds for solutions to a Ginzburg-Landau type equation, Rev. Roumaine Math. Pures Appl., 41 (1996), 263-271. |
[24] |
C. Morrey, Jr., "Multiple Integrals in the Calculus of Variations," Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. |
[25] |
P. Newton and G. Chamoun, Vortex lattice theory: A particle interaction perspective, SIAM Rev., 51 (2009), 501-542.
doi: 10.1137/07068597X. |
[26] |
J. Rubinstein, On the equilibrium position of Ginzburg Landau vortices, Z. Angew. Math. Phys., 46 (1995), 739-751.
doi: 10.1007/BF00949077. |
[27] |
E. Sandier and S. Serfaty, "Vortices in the Magnetic Ginzburg-Landau Model,'' Progress in Nonlinear Differential Equations and their Applications, 70, Birkhäuser Boston, Inc., Boston, MA, 2007. |
[28] |
I. Sigal and F. Ting, Pinning of magnetic vortices by an external potential, St. Petersburg Math. J., 16 (2005), 211-236.
doi: 10.1090/S1061-0022-04-00848-9. |
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