Derivation of Lower Critical Magnetic Field for Anisotropic Ginzburg-Landau Model in Superconductivity
In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field Hc1 which is the first critical value of hex corresponding to the first phase transition in which...
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| Published in | Acta mathematica Sinica. English series Vol. 27; no. 5; pp. 953 - 982 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
01.05.2011
Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 1439-8516 1439-7617 |
| DOI | 10.1007/s10114-011-8206-z |
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| Abstract | In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field Hc1 which is the first critical value of hex corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers of the anisotropic superconducting thin film with a large parameter k, and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers. |
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| AbstractList | In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field Hc1 which is the first critical value of hex corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers of the anisotropic superconducting thin film with a large parameter k, and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers. In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field $ H_{C_1 } $HC1which is the first critical value of h ex corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers of the anisotropic superconducting thin film with a large parameter Delta *k, and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers. In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field H C 1 which is the first critical value of h ^sub ex^ corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers of the anisotropic superconducting thin film with a large parameter κ, and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers.[PUBLICATION ABSTRACT] In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field which is the first critical value of h ex corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers of the anisotropic superconducting thin film with a large parameter κ , and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers. |
| ArticleNumber | 953 |
| Author | Yan Lei KOU Shi Jin DING |
| AuthorAffiliation | Department of Mathematics, South China Normal University, Guangzhou 510631, P. R. China |
| Author_xml | – sequence: 1 givenname: Yan Lei surname: Kou fullname: Kou, Yan Lei email: kouyanlei@tom.com organization: Department of Mathematics, South China Normal University – sequence: 2 givenname: Shi Jin surname: Ding fullname: Ding, Shi Jin organization: Department of Mathematics, South China Normal University |
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| Cites_doi | 10.1007/978-1-4612-0287-5 10.3934/cpaa.2002.1.327 10.1142/S0129055X00000411 10.1142/S0219199799000109 10.1007/s002050050083 10.1137/S0036141096303086 10.1137/S0036141096298060 10.1016/S0294-1449(99)00106-7 10.1137/S0036141000378619 10.1016/S0294-1449(16)30157-3 10.1142/S0219199799000134 10.1007/s10114-005-0550-4 10.1007/BF01191614 10.1137/1034003 10.1017/S0956792500001716 10.1007/BF00916647 10.1016/S0021-7824(00)01180-6 |
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| References_xml | – reference: SandierE.SerfatyS.Global minimizers for the Ginzburg-Landau functional below the first critical magnetic fieldAnn. Inst. H. Poincare Anal. Non Lineaire20001711914510.1016/S0294-1449(99)00106-70947.490041743433 – reference: BethuelF.RiviereT.Vortices for a variational problem related to supercinductivityAnn. Inst. H. Poincare Anal. Non Lineaire1995122433030842.351191340265 – reference: BethuelF.BrezisH.HeleinF.Ginzburg-Landau Vortices1994BostonBirkhäuser0802.35142 – reference: DingS.LiuZ.YuW.A variational problem related to the Ginzburg-Landau model of superconductivity with normal impurity inclusionsSIAM J. Math. Anal.199829486810.1137/S00361410963030860913.350401617174 – reference: DuQ.GunzburgerM.PetersonJ.Analysis and approximation of the Ginzburg-Landau model of superconductivitySIAM Rev.199234548110.1137/10340030787.650911156289 – reference: DingS.LiuZ.YuW.Pinning of vortices for the Ginzburg-Landau functional with variable coefficientAppl. Math JCU, Ser. B199712177880874.350151446546 – reference: LinF. H.DuQ.Ginzburg-Landau vortices: Dynamics, pinning and hysteresisSIAM J. Math. Anal.1997281265129310.1137/S00361410962980600888.350541474214 – reference: DuQ.Quantized Vortices in Superfliuds — A Mathematical and Computational Study, Dynamics in Model of Coarsening, Coagulation, Condensation and Quantization2007SingaporeWorld Scientific Press – reference: DingS.Renormalized energy with vortices pinning effectsJournal of Partial Differential Equation2000133413600977.35045 – reference: DingS.LiuZ.Pinning of vortices for a variational problem related to the superconducting thin films having variable thicknessJournal of Partial Differential Equation1997101741920887.350221460687 – reference: AndreN.ShafrirI.Asmptotic behavior of minimizers for the Ginzburg-Landau functional with weightArchive for Rational Mechanics and Analysis1998142457310.1007/s0020500500830905.490051629123 – reference: ChapmanS.DuQ.GunzburgerM. A.Ginzburg-Landau type model of superconducting/normal junctions including Josephson junctionsEuropean Journal of Applied Mathematics199569711410.1017/S09567925000017160843.351201331493 – reference: DingS.LiuZ.Asmptotic behavior for minimizers of an anisotropic Ginzburg-Landau functionalDifferential and Integral Equations20001312272540986.351031811957 – reference: BeaulieuA.HadijiR.On a class of Ginzburg-Landau equations with weightPan American Mathematical Journal1995541330843.490031361617 – reference: SerfatyS.Local minimizer for the Ginzburg-Landau energy near critical magnetic field: Part IICommun. Contemp. Math.1999129533310.1142/S02191997990001340964.490051707887 – reference: DingS.DuQ.The global minimizers and vortex solutions to a Ginzburg-Landau model of superconducting thin filmsComm. Pure Appl. Anal.20021332734010.3934/cpaa.2002.1.3271011.370391903001 – reference: DingS.DuQ.Critical magnetic field and asymptotic behavior of superconducting thin filmsSIAM J. Math. Anal.200234123925610.1137/S00361410003786191055.351241950834 – reference: DingS.DuQ.On Ginzburg-Landau vortices of superconducting thin filmsActa Mathematica Sinica, English Series200622246947610.1007/s10114-005-0550-4050638902214368 – reference: SandierE.SerfatyS.On the energy of type-II superconductors in the mixed phaseRev. Math. Phys.2000121219125710.1142/S0129055X000004110964.490061794239 – reference: BethuelF.BrezisH.HeleinF.Asymptotics for the minimization of a Ginzburg-Landau functionalCalculus of Variations and Partial Differential Equations19931212314810.1007/BF011916140834.350141261720 – reference: TinkhamM.Introduction to Superconductivity19942nd ed.New YorkMcGraw-Hill – reference: AftalionA.SandierE.SerfatyS.Pinning phenomena in the Ginzburg-Landau model of superconductivityJ. Math. Pures Appl.200180933937210.1016/S0021-7824(00)01180-61027.351231826348 – reference: ChapmanS.DuQ.GunzburgerM.A model for variable thickness superconducting thin filmZ. Angew Math. Phys.19964724330310.1007/BF009166471394916 – reference: SerfatyS.Local minimizer for the Ginzburg-Landau energy near critical magnetic field: Part ICommun. Contemp. Math.1999121325410.1142/S02191997990001090944.490071696100 – volume-title: Ginzburg-Landau Vortices year: 1994 ident: 8206_CR3 doi: 10.1007/978-1-4612-0287-5 – volume: 12 start-page: 77 issue: 1 year: 1997 ident: 8206_CR6 publication-title: Appl. Math JCU, Ser. B – volume: 13 start-page: 341 year: 2000 ident: 8206_CR10 publication-title: Journal of Partial Differential Equation – volume: 1 start-page: 327 issue: 3 year: 2002 ident: 8206_CR9 publication-title: Comm. Pure Appl. Anal. doi: 10.3934/cpaa.2002.1.327 – volume-title: Quantized Vortices in Superfliuds — A Mathematical and Computational Study, Dynamics in Model of Coarsening, Coagulation, Condensation and Quantization year: 2007 ident: 8206_CR1 – volume: 12 start-page: 1219 year: 2000 ident: 8206_CR12 publication-title: Rev. Math. 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| Snippet | In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the... |
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| SubjectTerms | Anisotropy Asymptotic properties Boundary conditions Coordinate transformations Energy Fluid flow Landau Magnetic fields Mathematical models Mathematics Mathematics and Statistics Phase transitions Studies Superconductivity Thin films Vortices 临界磁场 十六进制 各向异性参数 旋涡结构 渐近行为 超导模型 超导薄膜 |
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| Title | Derivation of Lower Critical Magnetic Field for Anisotropic Ginzburg-Landau Model in Superconductivity |
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