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2005 Fiscal Year Final Research Report Summary

Mathematical studies for models of superconductivity

Research Project

Project/Area Number 15340037
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionRyukoku University

Principal Investigator

MORITA Yoshihisa  Ryukoku University, Applied Mathematics and Informatics, Professor, 理工学部, 教授 (10192783)

Co-Investigator(Kenkyū-buntansha) YOTSUTANI Shoji  Ryukoku University, Appl.Math.and Informatics, Professor, 理工学部, 教授 (60128361)
NINOMIYA Hirokazu  Ryukoku University, Appl.Math.and Informatics, Associate Professor, 理工学部, 助教授 (90251610)
JIMBO Shuichi  Hokkaido University, Dept.Mathematics, Professor, 大学院・理学研究科, 教授 (80201565)
MACHIDA Masahiko  Japan Atomic Energy Agency, Computational Science Systems Center, Principal Scientist, システム計算科学センター, 主幹 (60360434)
KASAI Hironori  Fukushima University, Faculty of Symbiotic Systems Science, Associate Professor, 共生システム理工学類, 助教授 (20344822)
Project Period (FY) 2003 – 2005
KeywordsSuperconductivity / Ginzburg-Landau equation / Bifurcation structure / Variational method / Numerical simulation / Pattern dynamics
Research Abstract

1.We studied a one-dimensional Ginzburg-Landau equation in a ring, which is a mathematical model in a superconducting wire. When the wire is uniform, we revealed the global bifurcation structure for the two physical parameters and determined which solutions are minimizer of the energy functional. We also studied the configuration of the phase of solutions to the Ginzburg-Landau model in the wire with non-uniform thickness.
2.We studied how the solution structure of a nonlinear equation is affected by the geometry of a domain. This approach would be developed to the Ginzburg-Ladau equation.
3.An asymptotic behavior of the time evolutionary Ginzburg-Landau equations was studied. Some spectral result for the linearized operator of the equations was also obtained
4.A variational method to the transition layer problem in reaction-diffusion equations was developed. This approach would be applied to a model of the superconductivity.
5.Numerical computations for a BEC model and several Ginzburg-Landau models were achieved. We also discovered new pattern-dynamics arising in such nonlinear dissipative systems. In particular we proved the existence of solutions related to dynamics of front waves to reaction-diffusion equations.

  • Research Products

    (38 results)

All 2006 2005 2004 2003

All Journal Article (38 results)

  • [Journal Article] Phase pattern in a Ginzburg-Landau model with a discontinuous coefficient in a ring2006

    • Author(s)
      S.Kosugi
    • Journal Title

      Discrete Contin. Dynam. Systems Vol.14,No.1

      Pages: 149-168

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Phase pattern in a Ginzburg-Landau model with a discontinuous coefficient in a ring2006

    • Author(s)
      S.Kosugi
    • Journal Title

      Discrete Contin.Dynam.Systems Vol.14, No.1

      Pages: 149-168

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Global bifurcation structure of a one-dimensional Ginzburg-Landau model2005

    • Author(s)
      S.Kosugi
    • Journal Title

      J. Math. Physics Vol.46

      Pages: 095111-1-24

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A complete bifurcation diagram of the Ginzburg-Landau equation with periodic boundary conditions2005

    • Author(s)
      S.Kosugi
    • Journal Title

      Comm. Pure Appl. Anal. Vol.4,No.3

      Pages: 665-682

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A variational approach to singular perturbation problems in reaction-diffusion systems2005

    • Author(s)
      S.Ei
    • Journal Title

      Physica D Vol.207,No.3-4

      Pages: 171-219

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations2005

    • Author(s)
      J.-S.Guo
    • Journal Title

      Discrete Contin. Dynam. Systems Vol.12,No.2

      Pages: 193-212

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Existence and global stability of traveling curved fronts in the Allen-Cahn equations2005

    • Author(s)
      H.Ninomiya
    • Journal Title

      J. Differential Equations Vol.213,No.1

      Pages: 204-233

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Structure of a quantized vortex near the BCS-BEC crossover in an atomic Fermi gas2005

    • Author(s)
      M.Machida
    • Journal Title

      Phys. Rev. Lett. Vol.94

      Pages: 140401

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Josephson half-quantized vortices in long square pi junctions around d-dot2005

    • Author(s)
      M.Machida
    • Journal Title

      Physica C Vol.426-431

      Pages: 1566-1571

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Direct numerical simulations for non-equilibrium superconducting dynamics and related neutron detection in MgB22005

    • Author(s)
      M.Machida
    • Journal Title

      Physica C Vol.426-431

      Pages: 169-173

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Vortex dynamics in nano-scaled superconducting complex structures (d-dot)2005

    • Author(s)
      M.Ako
    • Journal Title

      Physica C Vol.426-431

      Pages: 122-126

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Global bifurcation structure of a one-dimensional Ginzburg-Landau model2005

    • Author(s)
      S.Kosugi
    • Journal Title

      J.Math.Physics Vol.46

      Pages: 095111-1-095111-24

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A complete bifurcation diagram of the Ginzburg-Landau equation with periodic boundary conditions2005

    • Author(s)
      S.Kosugi
    • Journal Title

      Comm.Pure Appl.Anal. Vol.4, No.3

      Pages: 665-682

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A variational approach to singular perturbation problems in reaction-diffusion systems2005

    • Author(s)
      S.Ei
    • Journal Title

      Physica D Vol.207, No.3-4

      Pages: 171-219

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations2005

    • Author(s)
      J.-S.Guo
    • Journal Title

      Discrete Contin.Dynam.Systems Vol.12, No.2

      Pages: 193-212

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Existence and global stability of traveling curved fronts in the Allen-Cahn equations2005

    • Author(s)
      H.Ninomiya
    • Journal Title

      J.Differential Equations Vol.213, No.1

      Pages: 204-233

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Structure of a quantized vortex near the BCS-BEC crossover in an atomic Fermi gas2005

    • Author(s)
      M.Machida
    • Journal Title

      Phys.Rev.Lett. Vol.94

      Pages: 140401

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Stable solutions to the Ginzburg-Landau equation with magnetic effect in a thin domain2004

    • Author(s)
      Y.Morita
    • Journal Title

      Japan J. Indust. Appl. Math. Vol.21,No.2

      Pages: 129-147

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Some entire solutions of the Allen-Cahn equation2004

    • Author(s)
      Y.Fukao
    • Journal Title

      Taiwanese J. Math. Vol.8

      Pages: 15-32

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Bifurcation of a helical wave from a traveling wave2004

    • Author(s)
      T.Ikeda
    • Journal Title

      Japan J. Indust. Appl. Math. Vol.21,No.3

      Pages: 405-424

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Singular perturbation of domains and semilinear elliptic equations III2004

    • Author(s)
      S.Jimbo
    • Journal Title

      Hokkaido Math. J. Vol.33,No.1

      Pages: 11-45

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On a Limiting System in the Lotka-Volterra Competition with Cross-Diffusion2004

    • Author(s)
      Y.Lou
    • Journal Title

      Discrete Contin. Dynam. Systems Vol.10,No.1-2

      Pages: 435-458

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Phase and amplitude fluctuations above Hc2 in type II superconductors2004

    • Author(s)
      M.Machida
    • Journal Title

      Physica C Vol.412-414

      Pages: 333-337

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On an Asymptotic behaviour of Ginzburg-Landau Maxwell equations2004

    • Author(s)
      H.Kasai
    • Journal Title

      Proceedings of The Sth World Multi-Conference on Systemics, Cybernetics and Informatics Vol.15

      Pages: 160-164

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On a resolvent estimate of a system of Laplace operators with perfect wall condition2004

    • Author(s)
      T.Akiyama
    • Journal Title

      FUNKCIALAJ EKVACIOJ Vol.47,No.3

      Pages: 361-394

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Stable solutions to the Ginzburg-Landau equation with magnetic effect in a thin domain2004

    • Author(s)
      Y.Morita
    • Journal Title

      Japan J.Indust.Appl.Math. Vol.21, No.2

      Pages: 129-147

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Some entire solutions of the Allen-Cahn equation2004

    • Author(s)
      Y.Fukao
    • Journal Title

      Taiwanese J.Math. Vol.8

      Pages: 15-32

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Bifurcation of a helical wave from a traveling Wave2004

    • Author(s)
      T.Ikeda
    • Journal Title

      Japan J.Indust.Appl.Math. Vol.21, No.3

      Pages: 405-424

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Singular perturbation of domains and semilinear elliptic equations III2004

    • Author(s)
      S.Jimbo
    • Journal Title

      Hokkaido Math.J. Vol.33, No.1

      Pages: 11-45

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On a Limiting System in the Lotka-Volterra Competition with Cross-Diffusion2004

    • Author(s)
      Y.Lou
    • Journal Title

      Discrete Contin.Dynam.Systems Vol.10, No.1-2

      Pages: 435-458

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On an Asymptotic behaviour of Ginzburg-Landau Maxwell equations2004

    • Author(s)
      H.Kasai
    • Journal Title

      Proceedings of The 8th World Multi-Conference on Systemics, Cybernetics and Informatics Vol.15

      Pages: 160-164

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On a resolvent estimate of a system of Laplace operators with perfect wall condition2004

    • Author(s)
      T.Akiyama
    • Journal Title

      FUNKCIALAJ EKVACIOJ Vol.47, No.3

      Pages: 361-394

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Instability in a geometric parabolic equation on convex domain2003

    • Author(s)
      S.Jimbo
    • Journal Title

      J. Differential Equations Vol.188,No.2

      Pages: 447-460

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Dynamical matching of Josephson vortex lattice with sample edge in layered high-Tc superconductors : Origin of the periodic oscillation of flux flow resistance2003

    • Author(s)
      M.Machida
    • Journal Title

      Phys. Rev. Lett. Vol.90

      Pages: 037001-1-4

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Freidel oscillation in charge profile and position dependent screening around a superconducting vortex core2003

    • Author(s)
      M.Machida
    • Journal Title

      Phys. Rev. Lett. Vol.90

      Pages: 077003-1-4

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Instability in a geometric parabolic equation on convex domain2003

    • Author(s)
      S.Jimbo
    • Journal Title

      J.Differential Equations Vol.188, No.2

      Pages: 447-460

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Dynamical matching of Josephson vortex lattice with sample edge in layered high-Tc superconductors : Origin of the periodic oscillation of flux flow resistance2003

    • Author(s)
      M.Machida
    • Journal Title

      Phys.Rev.Lett. Vol.90

      Pages: 037001-1-037001-4

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Freidel oscillation in charge profile and position dependent screening around a superconducting vortex core2003

    • Author(s)
      M.Machida
    • Journal Title

      Phys.Rev.Lett. Vol.90

      Pages: 077003-1-077003-4

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2007-12-13  

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