2005 Fiscal Year Final Research Report Summary
Mathematical studies for models of superconductivity
| Project/Area Number |
15340037
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ryukoku University |
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Principal Investigator |
MORITA Yoshihisa Ryukoku University, Applied Mathematics and Informatics, Professor, 理工学部, 教授 (10192783)
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| 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)
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| Project Period (FY) |
2003 – 2005
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| Keywords | Superconductivity / Ginzburg-Landau equation / Bifurcation structure / Variational method / Numerical simulation / Pattern dynamics |
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| 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.
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