Skip to main content
SpringerLink
Log in

Energy estimate for the type-II superconducting film

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

We study the minimizers of the Ginzburg-Landau model for variable thickness, superconducting, thin films with high κ, placed in an applied magnetic field h ex , when h ex is of the order of the “first critical field”, i.e. of the order of |ln ε|. We obtain the asymptotic estimates of minimal energy and describe the possible locations of the vortices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Tinkham, M.: Intoduction to Superconductivity, 2nd ed., McGraw-Hill, New York, 1994

    Google Scholar 

  2. Chapman, S. J., Du, Q.: A Model for Variable Thickness Superconducting Thin Films. ZAMP., 47, 410–431 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  3. Ding, S., Du, Q.: Critical Magnetic Field and Asymptotic Behavior of Superconducting Thin Films. SIAM J. Math. Anal., 34, 239–256 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ding, S., Du, Q.: On Ginzburg-Landau Vortices of Superconducting Thin Films. Commun. Pure Appl. Anal., 1, 327–343 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  5. Ding, S., Du, Q.: On Ginzburg-Landau Vortices of Superconducting Thin Films. Acta Mathematica Sinica, English Series, 22(2), 469–476 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Lin, F., Du, Q.: Ginzburg-Landau Vortices: Dynamics, Pinning, and Hysteresis. SIAM J. Math. Anal., 28, 1265–1293 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Huang, C., Liu, Z.: Energy Estimate of Type II Variable Thickness Superconducting Thin Films in the Mixed State. Acta Mathematica Sinica, Chinese Series, 149, 763–774 (2006)

    Google Scholar 

  8. Sandier, E., Serfaty, S.: A Rigorous Derivation of a Free-boundary Problem Arising in Superconuctivity. Ann. Sci. École Norm. Sup., 33, 561–592 (2000)

    MATH  MathSciNet  Google Scholar 

  9. Liu, Z., Kim, K.: Estimates of the Energy of Type-II Superconductor. Nonlinear Anal., 4, 51–64 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Aftalion, A., Sandier, E., Serfaty, S.: Pinning Phenomena in the Ginzburg-Landau Model of Superconductivity. J. Math. Pures Appl., 80, 339–372 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  11. Bethuel, F., Brezis, H., Hélein, F.: Ginzburg-Landau Vortices, Birkhäuser, Basel, 1994

    MATH  Google Scholar 

  12. Bethuel, F., Riviére, T.: Vortices for a Variational Problem Related to Superconductivity. Ann. IHP, Anal. non Linéaire, 12, 243–303 (1995)

    MATH  Google Scholar 

  13. Jerrard, R. L.: Lower Bounds for Generalized Ginzburg-Landau Functionals. SIAM J. Math. Anal., 30(4), 721–746 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  14. Sandier, E.: Lower Bounds for the Energy of Unit Vector Fields and Applications. J. Functional Anal., 152, 379–403 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  15. Sandier, E., Serfaty, S.: Global Minimizers for the Ginzburg-Landau Functional Below the First Critical Magnetic Field. Ann. IHP, Anal. non Linéare, 17, 119–145 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  16. Sandier, E., Serfaty, S.: On the Energy of Type-II Superconductors in the Mixed Phase. Revs. Math. Phys., 12, 1219–1259 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  17. Serfaty, S.: Local Minimizer for the Ginzburg-Landau Energy near Critical Magnetic Field: Part I, Comm. Contemp. Math., 1, 213–254 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  18. Serfaty, S.: Local Minimizer for the Ginzburg-Landau Energy near Critical Magnetic Field: Part II. Comm. Contemp. Math., 1, 295–333 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  19. Serfaty, S.: Stable Configurations in Superconductiving: Uniqueness, Multiplicity and Vortex-nucleation. Arch. Rat. Mech. Anal., 149, 329–365 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  20. Murat, F.: L’injection du cône Positif de H −1 dans W −1,q est Compacte Pour Tout q < 2. J. Math. Pures Appl., 60, 309–322 (1981)

    MATH  MathSciNet  Google Scholar 

  21. Du, Q., Gunzburger, M., Peterson, J.: Analysis and Approximation of the Ginzburg-Landau Model of Superconductivity. SIAM Rev., 34, 54–81 (1992)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784, Republic of Korea

    Kwang Ik Kim

  2. Department of Mathematics, Xuzhou Normal University, Xuzhou, 221116, P. R. China

    Zu Han Liu

Authors
  1. Kwang Ik Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zu Han Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kwang Ik Kim.

Additional information

Partially supported by the National Natural Science Foundation of China (No. 10071067, 10471119, 10771181), EYTP

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, K.I., Liu, Z.H. Energy estimate for the type-II superconducting film. Acta. Math. Sin.-English Ser. 24, 75–86 (2008). https://doi.org/10.1007/s10114-007-1014-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-007-1014-9

Keywords

MR(2000) Subject Classification

Search

Navigation