American Institute of Mathematical Sciences

Advanced
September  2002, 1(3): 327-340. doi: 10.3934/cpaa.2002.1.327

The global minimizers and vortex solutions to a Ginzburg-Landau model of superconducting films

Shijin Ding 1, and  Qiang Du 2,

1. 

Department of Mathematics, South China Normal University, Guangzhou, Guangdong 510631, China
2. 

Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Received  June 2001 Revised  December 2001 Published  June 2002

In this paper, we discuss the global minimizers of a free energy for the superconducting thin films placed in a magnetic field $h_{e x}$ below the lower critical field $H_{c1}$ or between $H_{c1}$ and the upper critical field $H_{c2}$. For $h_{e x}$ is near but smaller than $H_{c1}$, we prove that the global minimizer having no vortex is unique. For $H_{c1}$<<$h_{e x}$<<$H_{c2}$, we prove that the density of the vortices of the global minimizer is proportional to the applied field.
Keywords: vortices, thin films, Superconductivity, pinning..
Mathematics Subject Classification: 37J55,35Q4.
Citation: Shijin Ding, Qiang Du. The global minimizers and vortex solutions to a Ginzburg-Landau model of superconducting films. Communications on Pure & Applied Analysis, 2002, 1 (3) : 327-340. doi: 10.3934/cpaa.2002.1.327
[1]

Rejeb Hadiji, Ken Shirakawa. Asymptotic analysis for micromagnetics of thin films governed by indefinite material coefficients. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1345-1361. doi: 10.3934/cpaa.2010.9.1345
[2]

Xiao-Ping Wang, Ke Wang, Weinan E. Simulations of 3-D domain wall structures in thin films. Discrete & Continuous Dynamical Systems - B, 2006, 6 (2) : 373-389. doi: 10.3934/dcdsb.2006.6.373
[3]

Laura Sigalotti. Homogenization of pinning conditions on periodic networks. Networks & Heterogeneous Media, 2012, 7 (3) : 543-582. doi: 10.3934/nhm.2012.7.543
[4]

Wafaa Assaad, Ayman Kachmar. The influence of magnetic steps on bulk superconductivity. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 6623-6643. doi: 10.3934/dcds.2016087
[5]

Tai-Chia Lin. Vortices for the nonlinear wave equation. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 391-398. doi: 10.3934/dcds.1999.5.391
[6]

Francesco Maggi, Salvatore Stuvard, Antonello Scardicchio. Soap films with gravity and almost-minimal surfaces. Discrete & Continuous Dynamical Systems - A, 2019, 0 (0) : 1-36. doi: 10.3934/dcds.2019236
[7]

Carolina Mendoza, Jean Bragard, Pier Luigi Ramazza, Javier Martínez-Mardones, Stefano Boccaletti. Pinning control of spatiotemporal chaos in the LCLV device. Mathematical Biosciences & Engineering, 2007, 4 (3) : 523-530. doi: 10.3934/mbe.2007.4.523
[8]

Matteo Novaga, Enrico Valdinoci. Closed curves of prescribed curvature and a pinning effect. Networks & Heterogeneous Media, 2011, 6 (1) : 77-88. doi: 10.3934/nhm.2011.6.77
[9]

Mickaël Dos Santos, Oleksandr Misiats. Ginzburg-Landau model with small pinning domains. Networks & Heterogeneous Media, 2011, 6 (4) : 715-753. doi: 10.3934/nhm.2011.6.715
[10]

Stefanella Boatto. Curvature perturbations and stability of a ring of vortices. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 349-375. doi: 10.3934/dcdsb.2008.10.349
[11]

B. Emamizadeh, F. Bahrami, M. H. Mehrabi. Steiner symmetric vortices attached to seamounts. Communications on Pure & Applied Analysis, 2004, 3 (4) : 663-674. doi: 10.3934/cpaa.2004.3.663
[12]

Hans G. Kaper, Bixiang Wang, Shouhong Wang. Determining nodes for the Ginzburg-Landau equations of superconductivity. Discrete & Continuous Dynamical Systems - A, 1998, 4 (2) : 205-224. doi: 10.3934/dcds.1998.4.205
[13]

Mei-Qin Zhan. Global attractors for phase-lock equations in superconductivity. Discrete & Continuous Dynamical Systems - B, 2002, 2 (2) : 243-256. doi: 10.3934/dcdsb.2002.2.243
[14]

Yilun Shang. Group pinning consensus under fixed and randomly switching topologies with acyclic partition. Networks & Heterogeneous Media, 2014, 9 (3) : 553-573. doi: 10.3934/nhm.2014.9.553
[15]

Frederic Laurent-Polz, James Montaldi, Mark Roberts. Point vortices on the sphere: Stability of symmetric relative equilibria. Journal of Geometric Mechanics, 2011, 3 (4) : 439-486. doi: 10.3934/jgm.2011.3.439
[16]

Takashi Suzuki. Brownian point vortices and dd-model. Discrete & Continuous Dynamical Systems - S, 2014, 7 (1) : 161-176. doi: 10.3934/dcdss.2014.7.161
[17]

A.V. Borisov, A.A. Kilin, I.S. Mamaev. Reduction and chaotic behavior of point vortices on a plane and a sphere. Conference Publications, 2005, 2005 (Special) : 100-109. doi: 10.3934/proc.2005.2005.100
[18]

Joris Vankerschaver, Eva Kanso, Jerrold E. Marsden. The geometry and dynamics of interacting rigid bodies and point vortices. Journal of Geometric Mechanics, 2009, 1 (2) : 223-266. doi: 10.3934/jgm.2009.1.223
[19]

Fanghua Lin, Ping Zhang. On the hydrodynamic limit of Ginzburg-Landau vortices. Discrete & Continuous Dynamical Systems - A, 2000, 6 (1) : 121-142. doi: 10.3934/dcds.2000.6.121
[20]

Taoufik Hmidi, Joan Mateu. Bifurcation of rotating patches from Kirchhoff vortices. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5401-5422. doi: 10.3934/dcds.2016038

2018 Impact Factor: 0.925

Tools

Metrics

  • PDF downloads (4)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences