Pattern formation due to 1 : 2 resonance

• Project/Area Number: 21540387
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Tottori University
• Principal Investigator: FUJIMURA Kaoru 鳥取大学, 大学院・工学研究科, 教授 (70294337)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 流体物理 / パターン形成 / 定常モード間共鳴 / 弱非線形理論

Research Abstract

Spatio-temporal pattern formation due to resonant mode interaction between steady modes having wavenumbers in the ratio 1 : 2 was investigated on a hexagonal lattice Six-dimensional amplitude equations were derived on the weakly nonlinear basis and were analyzed of the bifurcation of their solutions. Based on amplitude equations derived from modified Swift-Hohenben equation and those derived from governing equations for thermal convections, bifurcation characteristic of steady solutions were clarified. Details of unsteady solutions including heteroclinic cycles were investigated. It was found that heteroclinic orbit in two-dimensional invariant subspace was destabilize(when non-self-adjointness of the operators involved in the linearized PDEs is getting significant.

Research Products

• [Journal Article] 1:2 Resonance and Pattern Formation in Thermal Convections (2011)
  • Author(s): Kaoru Fujimura
  • Journal Title: Bulletin of the American Physical Society Volume: 56 Pages: 85-85
• [Journal Article] 液柱マランゴニ対流の安定性 (2011)
  • Author(s): 藤村薫
  • Journal Title: 日本流体力学会年会2011講演論文集 Volume: (CD-ROM)
• [Journal Article] Range of Validity of Weakly Nonlinear Theory in the Rayleigh–Bénard Problem (2009)
  • Author(s): S. C. Generalis and K. Fujimura
  • Journal Title: Journal of the Physical Society of Japan Volume: 78 Issue: 8 Pages: 084401-084401
  • DOI: 10.1143/jpsj.78.084401
  • NAID: 130005437827
  • ISSN: 0031-9015, 1347-4073
  • Peer Reviewed
• [Journal Article] Range of Validity of Weakly Nonlinear Theory in Rayleigh-Benard Problem (2009)
  • Author(s): S.C.Generalis, K.Fujimura
  • Journal Title: Journal of The Physical Society of Japan 78
  • NAID: 40016692845
  • Peer Reviewed
• [Presentation] マランゴニ対流の安定性 (2012)
  • Author(s): 藤村薫
  • Organizer: オフパイル研究会
  • Place of Presentation: 東京大学原子炉「弥生」(茨城県那珂郡東海村)
  • Year and Date: 2012-03-26
• [Presentation] 1:2 resonance and pattern formation in thermal convections (2011)
  • Author(s): Kaoru Fujimura
  • Organizer: 64th American Physical Society-Division of Fluid Dynamics Meeting
  • Place of Presentation: アメリカ合衆国メリーランド州ボルティモア市
  • Year and Date: 2011-11-20
• [Presentation] 熱対流における1 : 2共鳴とヘテロクリニックサイクル (2011)
  • Author(s): 藤村薫
  • Organizer: 日本物理学会秋季大会
  • Place of Presentation: 富山大学
  • Year and Date: 2011-09-23
• [Presentation] 熱対流における1:2共鳴とヘテロクジニックサイクル (2011)
  • Author(s): 藤村薫
  • Organizer: 日本物理学会2011秋季大会
  • Place of Presentation: 富山大学
  • Year and Date: 2011-09-23
• [Presentation] 液柱Marangoni対流の安定性 (2011)
  • Author(s): 藤村薫
  • Organizer: 日本流体力学会年会2011
  • Place of Presentation: 首都大学東京南大沢キャンパス
  • Year and Date: 2011-09-07
• [Presentation] 液柱マランゴニ対流の安定性 (2011)
  • Author(s): 藤村薫
  • Organizer: 日本流体力学会年会2011
  • Place of Presentation: 首都大学東京南大沢キャンパス
  • Year and Date: 2011-09-07
• [Presentation] 液柱のMarangoni対流に対する弱非線形安定性 (2011)
  • Author(s): 藤村薫
  • Organizer: 第60回理論応用力学講演会
  • Place of Presentation: 東京工業大学大岡山キャンパス
  • Year and Date: 2011-03-10
• [Presentation] 液柱Marangoni対流の弱非線形安定性 (2011)
  • Author(s): 藤村薫
  • Organizer: 第60回理論応用力学講演会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2011-03-10
• [Presentation] 1 : 2 resonance and pattern formation in thermal convections (2011)
  • Author(s): K. Fujimura
  • Organizer: 64th Annual Meeting of the APS Division of Fluid Dynamics
  • Place of Presentation: メリーランド州ボルティモア市
• [Presentation] 1 : 2共鳴によるパターン形成 (2010)
  • Author(s): 藤村薫
  • Organizer: 流体数学セミナー
  • Place of Presentation: 早稲田大学
  • Year and Date: 2010-10-08
• [Presentation] 1:2共鳴によるパターン形成 (2010)
  • Author(s): 藤村薫
  • Organizer: 流体数学セミナー
  • Place of Presentation: 早稲田大学
  • Year and Date: 2010-10-08
• [Presentation] 水平加振した浅い水の内部に見られる流れの構造の分類 (2009)
  • Author(s): 尾崎史明, 大信田丈志, 加藤由紀, 藤村薫
  • Organizer: 日本流体力学会2009年会
  • Place of Presentation: 東洋大学(東京都文京区)
  • Year and Date: 2009-09-03
• [Remarks]
  • URL: http://www.damp.tottori-u.ac.jp/%7Elab4/kaoru/cv_j.html