Mathematical studies for bifurcation structures and transient dynamics of model equations in the superconductivity and BEC

• Project/Area Number: 19340026
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Ryukoku University
• Principal Investigator: MORITA Yoshihisa Ryukoku University, 理工学部, 教授 (10192783)
• Co-Investigator(Kenkyū-buntansha): JIMBO Shuichi 北海道大学, 大学院・理学研究科, 教授 (80201565) ; OGAWA Toshiyuki 大阪大学, 大学院・基礎工学研究科, 准教授 (80211811) ; MACHIDA Masahiko 独立行政法人日本原子力研究開発機構, システム計算科学センター, 研究主幹 (60360434) ; MIZUMACHI Tetsu 九州大学, 大学院・数理学研究院, 准教授 (60315827)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥10,270,000 (Direct Cost: ¥7,900,000、Indirect Cost: ¥2,370,000); Fiscal Year 2009: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2008: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2007: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
• Keywords: Ginzburg-Landau方程式 / 渦糸解 / 遷移ダイナミクス / 解の安定性 / 分岐解析 / 超伝導モデル / Gross-Pitaevskii方程式 / パターンダイナミクス / Gross-Pitaevskii方程 / ジョセフソン効果

Research Abstract

We investigate mathematical properties and structures of solutions to the model equations describing the superconductivity and Bose-Einstein condensation, which are typical macroscopic quantum phenomena. We obtained mathematical results on the bifurcation structure and the characteristic dynamics for the model equations such as the Ginzburg-Landau equations and other related equations.

Research Products

• [Journal Article] Phenomenological Theory for ±s-wave Superconducting States of Iron-based Superconductors (2010)
  • Author(s): M. Machida, Y. Nagai, Y. Ohta, N. Nakai, H. Nakamura, N. Hayashi
  • Journal Title: Physica C (掲載確定)
  • Peer Reviewed
• [Journal Article] Quantum Synchronization and Electromagnetic Wave Emission in intrinsic Josephson junctions (2010)
  • Author(s): M. Machida
  • Journal Title: J. Phys. Conf. Ser. (掲載確定)
  • Peer Reviewed
• [Journal Article] Description of the inelastic collision of two solitary waves for the BBM equation (2010)
  • Author(s): Y. Martel, F. Merle, T. Mizumachi
  • Journal Title: Arch. Ration. Mech. Anal. Vol.196 Pages: 517-574
• [Journal Article] Phenomenological Theory for ±s-wave Superconducting States of Iron-based Superconductors (2010)
  • Author(s): M.Machida, Y.Nagai, Y.Ohta, N.Nakai, H.Nakamura, N.Hayashi
  • Journal Title: Physica C (掲載確定)
  • Peer Reviewed
• [Journal Article] Quantum Synchronization and Electromagnetic Wave Emission in intrinsic Josephson junctions (2010)
  • Author(s): M.Machida
  • Journal Title: J.Phys.Conf.Ser. (掲載確定)
  • Peer Reviewed
• [Journal Article] Description of the inelastic collision of two solitary waves for the BBM equation (2010)
  • Author(s): Y.Martel, F.Merle, T.Mizumachi
  • Journal Title: Archive for Rational Mechanics and Analysis 196 Pages: 517-574
  • Peer Reviewed
• [Journal Article] Exponential decay phenomena of the principal eigenvalue of an elliptic operator with a large drift term of gradient type (2009)
  • Author(s): S. Jimbo, M. Kimura, H. Notsu
  • Journal Title: Asymptotic Analysis Vol.65 Pages: 103-123
  • Peer Reviewed
• [Journal Article] Spectra of domains with partial degeneration (2009)
  • Author(s): S. Jimbo, S. Kosugi
  • Journal Title: J. Math. Sci. Vol.16 Pages: 269-414
  • Peer Reviewed
• [Journal Article] An entire solution to the Lotka-Volterra competition-diffusion equations (2009)
  • Author(s): Y. Morita, K. Tachibana
  • Journal Title: SIAM J. Math. Anal. Vol.40 Pages: 2217-2240
  • Peer Reviewed
• [Journal Article] Bifurcation analysis to Swift-Hohenberg equation with Steklov type boundary conditions (2009)
  • Author(s): T. Ogawa, T. Okuda
  • Journal Title: Vol.25 Pages: 273-297
  • Peer Reviewed
• [Journal Article] Asymptotic stability of lattice solitons in the energy space (2009)
  • Author(s): T. Mizumachi
  • Journal Title: Comm. Math. Phys. Vol.288 Pages: 125-144
  • Peer Reviewed
• [Journal Article] Exponential decay phenomena of the principal eigenvalue of an elliptic operator with a large drift term of gradient type (2009)
  • Author(s): S.Jimbo, M.Kimura, H.Notsu
  • Journal Title: Asymptotic Analysis 65 Pages: 103-123
  • Peer Reviewed
• [Journal Article] Spectra of domains with partial degeneration (2009)
  • Author(s): S.Jimbo, S.Kosugi
  • Journal Title: J.Mathematical Sciences, the University of Tokyo 16 Pages: 269-414
  • Peer Reviewed
• [Journal Article] Bifurcation analysis to Swift-Hohenberg equation with Steklov type boundary conditions (2009)
  • Author(s): T.Ogawa, T.Okuda
  • Journal Title: Discrete and Continuous Dynamical Systems-A 25 Pages: 273-297
  • Peer Reviewed
• [Journal Article] Bifurcation analysis to Swift-Hohenberg equation with Steklov type boundary conditions (2009)
  • Author(s): T. Ogawa, T. Okuda
  • Journal Title: Discrete and Contin. Dynam. Systems (掲載確定)
  • Peer Reviewed
• [Journal Article] Asymptotic stability of lattice solitons in the energy space (2009)
  • Author(s): T. Mizumachi
  • Journal Title: Comm. Math. Phys. 288 Pages: 125-144
  • Peer Reviewed
• [Journal Article] Monostable-type traveling waves of bistable reaction-diffusion equations in the multi-dimensional space (2008)
  • Author(s): Y. Morita, H. Ninomiya
  • Journal Title: Bull. Inst. Math. Acad. Sin. (N.S. ) Vol.3 Pages: 567-584
  • Peer Reviewed
• [Journal Article] Bifurcation of vortex solutions to a Ginzburg-Landau equation in an annulus (2008)
  • Author(s): Y. Morita
  • Journal Title: Centre de Recherches Mathematiques Vol.44 Pages: 187-200
• [Journal Article] Bifurcation analysis for a Ginzburg-Landau equation (2008)
  • Author(s): Y. Morita
  • Journal Title: 数理解析研究所講究録 Vol.1591 Pages: 119-124
• [Journal Article] Ginzburg-Landau equations and solution structure (2008)
  • Author(s): S. Jimbo, Y. Morita
  • Journal Title: Sugaku Expositions Vol.21 Pages: 117-131
  • Peer Reviewed
• [Journal Article] Stripe Formation in Repulsive 4-leg Hubbard Ladder: Directly-extended DMRG Studies (2008)
  • Author(s): M. Machida, S. Yamada, M. Okumura, Y. Ohhasi, H. Matsumoto
  • Journal Title: Physica C Vol.468 Pages: 1141-1141
  • Peer Reviewed
• [Journal Article] Numerical Simulation for Non-equlibrium Superconducting Dynamics and the Transition Edge: Simulation for MgB2 Neutron Detector (2008)
  • Author(s): M. Machida, T. Kano, T. Koyama, M. Kato, T. Ishida
  • Journal Title: J. Low Temp. Phys. Vol.151 Pages: 58-63
  • Peer Reviewed
• [Journal Article] Synchronization Effects in Intrinsic Josephson Junctions by Non-equilibrium Heating (2008)
  • Author(s): M. Machida, T. Koyama, H. Matsumoto
  • Journal Title: J. Phy. Conf. Vol.129 Pages: 12027-12027
  • Peer Reviewed
• [Journal Article] Quantum Effects on Capacity-coupled Intrinsic Josephson Junctions (2008)
  • Author(s): M. Machida, S. Yamada, T. Kano, M. Okumura, T. Imamura, T. Koyama
  • Journal Title: J. Phys. Chem. Solids Vol.69 Pages: 3221-3221
  • Peer Reviewed
• [Journal Article] Asymptotic stability of Toda lattice solutions (2008)
  • Author(s): T. Mizumachi, R.L. Pego
  • Journal Title: Nonlinearity Vol.21 Pages: 2061-2071
  • Peer Reviewed
• [Journal Article] Asymptotic stability of small solitons to 1D NLS with potential (2008)
  • Author(s): T. Mizumachi
  • Journal Title: J. Math. Vol.48 Pages: 471-498
  • Peer Reviewed
• [Journal Article] On asymptotic stability in energy space of ground states for nonlinear Schrodinger equations (2008)
  • Author(s): T. Mizumachi, S. Cuccagna
  • Journal Title: Comm. Math. Phys. Vol.284 Pages: 51-71
  • Peer Reviewed
• [Journal Article] Selection principle for various nodes of spatially non-uniform electrochemical oscillations (2008)
  • Author(s): S. Fukushima, S. Nakahashi, Y. Nakato, T. Ogawa
  • Journal Title: J. Chem. Phys. Vo128 Pages: 14714-14714
  • Peer Reviewed
• [Journal Article] Bifurcation of vortex solutions to a Ginzburg-Landau equation in an annulus (2008)
  • Author(s): Y. Morita
  • Journal Title: Centre de Recherches Mathematiques, CRM Proceedings and Lecture Notes 44 Pages: 187-200
• [Journal Article] Bifurcation analysis for a Ginzburg-Landau equation (2008)
  • Author(s): Y. Morita
  • Journal Title: 数理解析研究所講究録 1591 Pages: 119-124
• [Journal Article] Ginzburg-Landau equations and solution structure (2008)
  • Author(s): S. Jimbo, Y. Morita
  • Journal Title: Sugaku Expositions 21 Pages: 117-131
  • Peer Reviewed
• [Journal Article] Stripe Formation in Repulsive 4-leg Hubbard Ladder : Directly-extended DMRG Studies (2008)
  • Author(s): M. Machida, S. Yamada, M. Okumura, Y. Ohashi, H. Matsumoto
  • Journal Title: Physica C 468 Pages: 1141-1141
  • Peer Reviewed
• [Journal Article] Quantum Synchronization Effects in Intrinsic Josephson Junctions (2008)
  • Author(s): M. Machida, T. Kano, S. Yamada, M. Okumura, T. Imamura, T. Koyama
  • Journal Title: Physica C 468 Pages: 689-689
  • Peer Reviewed
• [Journal Article] Numerical Simulation for Non-equilibrium Superconducting Dynamics at the Transition Edge : Simulation for MgB2 Neutron Detector (2008)
  • Author(s): M. Machida, T. Kano, T. Koyama, M. Kato, T. Ishida
  • Journal Title: Journal of Low Temp. Phys. 151 Pages: 58-63
  • Peer Reviewed
• [Journal Article] Synchronization Effects in Intrinsic Josephson Junctions by Non-equilibrium Heating (2008)
  • Author(s): M. Machida, T. Koyama, H. Matsumoto
  • Journal Title: J. Phys., Conf. 129 Pages: 12027-12027
  • Peer Reviewed
• [Journal Article] Quantum Effects on Capacitively-coupled Intrinsic Josephson Junctions (2008)
  • Author(s): M. Machida, S. Yamada, T. Kano, M. Okumura, T. Imamura, T. Koyaraa
  • Journal Title: J. Phys. Chem. Solids 69 Pages: 3221-3221
  • Peer Reviewed
• [Journal Article] Asymptotic stability of Toda lattice solitons (2008)
  • Author(s): T. Mizumachi, R. L. Pego
  • Journal Title: Nonlinearity 21 Pages: 2061-2071
  • Peer Reviewed
• [Journal Article] Asymptotic stability of small solitons to 1D NLS with potential (2008)
  • Author(s): T. Mizumachi
  • Journal Title: Journal Math. Kyoto University 48 Pages: 471-498
  • Peer Reviewed
• [Journal Article] On asymptotic stability in energy space of ground states for Nonlinear Schrodinger equations (2008)
  • Author(s): T. Mizumachi, S. Cuccagna
  • Journal Title: Comm. Math. Phys. 284 Pages: 51-71
  • Peer Reviewed
• [Journal Article] Selection principle for valious modes of spatially non-uniform electrochemical oscillations (2008)
  • Author(s): S.Fukushima, S.Nakanishi, Y.Nakato and T.Ogawa
  • Journal Title: J.Chemical Physics Vol.128,No.1 Pages: 14714-14714
  • Peer Reviewed
• [Journal Article] Existence of periodic traveling wave solutions for the Ostrovsky equation (2008)
  • Author(s): N.Ishimura and T.Mizumachi
  • Journal Title: Mathematical Methods in the Applied Sciences (to be published)
  • NAID: 120006933445
  • Peer Reviewed
• [Journal Article] Stationary solutions to the one-dimensional Cahn-Hilliard equation: Proof by the complete elliptic integrals (2007)
  • Author(s): S. Kosugi, Y. Morita, S. Yotsutani
  • Journal Title: Discrete Contin. Dynam. Systems Vol.19 Pages: 609-629
  • Peer Reviewed
• [Journal Article] Bifurcation of vortex and boundary-vortex solutions in a Ginzburg-Landau model (2007)
  • Author(s): C.-N. Chen, Y. Morita
  • Journal Title: Nonlinearity Vol20 Pages: 943-964
  • Peer Reviewed
• [Journal Article] Strong paring and microscopic inhomogeneity of lattice fermion systems (2007)
  • Author(s): S. Yamada, M. Machda, Y. Ohashi, H. Matsumoto
  • Journal Title: Physica C Vol.463-465 Pages: 103-106
  • Peer Reviewed
• [Journal Article] Theory for collective macroscopic tunneling in high-Tc intrinsic Josephson junction (2007)
  • Author(s): M. Machida, T. Koyama
  • Journal Title: Physica C Vol.463-465 Pages: 84-88
  • Peer Reviewed
• [Journal Article] Collective macroscopic tunneling in intrinsic Josephson junction (2007)
  • Author(s): M. Machida, T. Koyama
  • Journal Title: Physica C Vol.460-462 Pages: 289-292
  • Peer Reviewed
• [Journal Article] Asymptotic stability of small solitons for 2D Nonlinear Schrodinger equation with potential (2007)
  • Author(s): T. Mizumachi
  • Journal Title: J. Math. Vol.47 Pages: 599-620
  • Peer Reviewed
• [Journal Article] Instability of vortex solitons for 2D focusing NLS (2007)
  • Author(s): T. Mizumachi
  • Journal Title: Adv. Differential Equations Vol.12 Pages: 241-264
  • Peer Reviewed
• [Journal Article] Stationary solutions to the one-dimensional Cahn-Hilliard equation:Proof by the complete elliptic integrals (2007)
  • Author(s): S.Kosugi, Y.Morita and S.Yotsutani
  • Journal Title: Discrete Contin.Dynam.Systems Vol.19,No.4 Pages: 609-629
  • Peer Reviewed
• [Journal Article] Bifurcation of vortex and boundary-vortex solutions in a Ginzburg-Landau model (2007)
  • Author(s): C.-N.Chen and Y.Morita
  • Journal Title: Nonlinearity Vol.20,Issue 4 Pages: 943-964
  • Peer Reviewed
• [Journal Article] 反応拡散方程式の進行波と全域解 (2007)
  • Author(s): 二宮 広和、森田 善久
  • Journal Title: 数学 59巻、3号 Pages: 40-58
  • Peer Reviewed
• [Journal Article] Strong pairing and microscopic inhomogeneity of lattice fermion systems (2007)
  • Author(s): S.Yamada, M.Machida, Y.Ohashi, and H.Matsumoto
  • Journal Title: Physica C 463-465 Pages: 103-106
  • Peer Reviewed
• [Journal Article] Theory for collective macroscopic tunneling in high-Tc intrinsic Josephson junction (2007)
  • Author(s): M.Machida, T.Koyama
  • Journal Title: Physica C 463-465 Pages: 84-88
  • Peer Reviewed
• [Journal Article] Collective macroscopic tunneling in intrinsic Josephson junction (2007)
  • Author(s): M.Machida, T.Koyama, M.Machida, T.Koyama, M.Kato and T.Ishida
  • Journal Title: Physica C 460-462 Pages: 289-292
  • Peer Reviewed
• [Journal Article] Asymptotic stability of small solitons for 2D Nonlinear Schrodinger equations with potential (2007)
  • Author(s): T.Mizumachi
  • Journal Title: Journal of Mathematics of Kyoto University Vol.47,No.3 Pages: 599-620
  • Peer Reviewed
• [Journal Article] Instability of vortex solitons for 2D focusing NLS (2007)
  • Author(s): T.Mizumachi
  • Journal Title: Advances in Differential Equations Vol.12,No3 Pages: 241-264
  • Peer Reviewed
• [Journal Article] Vortex Core Structure in Strongly-Correlated Superfluidity
  • Author(s): S.Yamada, M.Okumura, M.Machida, Y.Ohashi and H.Matsumoto
  • Journal Title: Physica C (to be published)
  • Peer Reviewed
• [Journal Article] Josephson effect between conventional and Rashba superconductors
  • Author(s): N.Hayashi, C. Iniotakis, M.Machida and M.Sigrist
  • Journal Title: Physica C (to be published)
  • Peer Reviewed
• [Journal Article] Josephson effect between conventional and non-centrosymmetric superconductors
  • Author(s): N.Hayashi, C. Iniotakis, M.Machida and M.Sigrist
  • Journal Title: J.Phys.Chem.Solids (to be published)
  • Peer Reviewed
• [Journal Article] Ginzburg-Landau Simulation for a Vortex around a Columnar Defect in a Superconducting Film
  • Author(s): N.Nakai, N.Hayashi and M.Machida
  • Journal Title: J.Phys.Chem.Solids (to be published)
  • Peer Reviewed
• [Journal Article] Direct Numerical Simulations for Non-equilibrium Superconducting Dynamics at the Transition Edge:Simulation for MgB2 Neutron Detectors
  • Author(s): M.Machida, T.Koyama, M.Kato and T.Ishida
  • Journal Title: J.Low.Temp.Phys. (to be published)
  • Peer Reviewed
• [Presentation] Traveling waves of a reaction-diffusion equation in the higher-dimensional space (2009)
  • Author(s): Y. Morita
  • Organizer: Equadiff 12
  • Place of Presentation: Masaryk University, Brno, Czech Republic
  • Year and Date: 2009-07-22
• [Presentation] A mass-conserved reaction-diffusion system (2009)
  • Author(s): Y. Morita
  • Organizer: The 2nd International Conference on Reaction-Diffusion Systems and Viscosity Solutions
  • Place of Presentation: Providence University, Taichung, Taiwan
  • Year and Date: 2009-07-15
• [Presentation] A mass-conserved reaction-diffusion system (2009)
  • Author(s): Y.Morita
  • Organizer: The 2nd International Conference on Reaction-Diffusion Systems and Viscosity Solutions
  • Place of Presentation: Providence University Taichung, Taiwan
  • Year and Date: 2009-07-15
• [Presentation] Asymptotic stability of lattice solitons (2008)
  • Author(s): T. Mizumachi
  • Organizer: Rykoku Workshop, Recent Progress on Pattern Formation and Dynamics in Mathematical Sciences
  • Place of Presentation: Seta campus, Ryukoku University
  • Year and Date: 2008-06-13
• [Presentation] Bifurcation analysis for a Ginzburg-Landau model (2008)
  • Author(s): Y. Morita
  • Organizer: Workshop of Nonlinear Partial Differential Equations Related to Physical Models
  • Place of Presentation: Taida Institute of Mathem atical Science, National T aiwan University
  • Year and Date: 2008-05-31
• [Presentation] Spatio-temporal Oscillations by Wave Bifurcation (2007)
  • Author(s): T.Ogawa
  • Organizer: International Symposium on Nonlinear Theory and its Applications
  • Place of Presentation: Vancouver,Canada
  • Year and Date: 2007-09-18
• [Presentation] Bifuracation analysis for Ginzburg-Landau model (2007)
  • Author(s): Y.Morita
  • Organizer: Equadiff 07
  • Place of Presentation: Vienna University of Technology
• [Presentation] Bifurcation of vortex solutions in a Ginzburg-Landau model for small kappa (2007)
  • Author(s): Y.Morita
  • Organizer: International Conference on Mathematical Theory of Superconductivity and Liquid Crystals
  • Place of Presentation: East China Normal University
• [Presentation] Ginzburg-Landau Equation in Thin Domains (2007)
  • Author(s): S.Jimbo
  • Organizer: International Conference on Mathematical Theory of Superconductivity and Liquid Crystals
  • Place of Presentation: East China Normal University
• [Book] ギンツブルク-ランダウ方程式と安定性解析 (2009)
  • Author(s): 神保秀一, 森田善久著
  • Total Pages: 310
  • Publisher: 岩波書店
• [Book] ギンツブルクーランダウ方程式と安定性解析 (2009)
  • Author(s): 神保秀一, 森田善久
  • Total Pages: 310
  • Publisher: 岩波書店
• [Remarks]
  • URL: http://www.math.ryukoku.ac.jp/~morita/index.html