2003 Fiscal Year Annual Research Report

界面ダイナミクスを再現する数値解析法の開発と実験分野への応用について

Research Project

Project/Area Number	13440038
Research Institution	Osaka Institute of Technology
Principal Investigator	友枝謙二大阪工業大学, 工学部, 教授 (60033916)
Co-Investigator(Kenkyū-buntansha)	川口正美三重大学, 工学部, 教授 (30093123) 山口智彦産業技術総合研究所, ナノテクノロジー研究部門, グループ長三村昌泰広島大学, 大学院・理学研究科, 教授 (50068128) 儀我美一北海道大学, 大学院・理学研究科, 教授 (70144110) 田端正久九州大学, 大学院・数理学研究院, 教授 (30093272)
Keywords	ベル-ソフ・ザボチンスキ-反応 / ヴィスコスフィンガリング / サポートの分裂と再融合 / 反応拡散 / 特異極限法 / ヘリカル進行波 / 適正粘性解 / 渦の相互作用
Research Abstract	以下の項目を扱った 1)BZ反応における閾値下興奮現象に現れる新しい界面パターンの実験解析。 2)界面方程式を導出する特異極限法の開発と界面パターンを形成する進行波の伝播持続メカニズムの解析。 3)高分子溶液中のヴィスコスフィンガリングの実験によるパターンの形態変化の実験解析。 4)蒸発過程での吸収効果の強弱による流体の浸透領域のパターン変化を再現する数値解析法の確立。 5)電気流体及び脳脊髄液流動に現れる移動境界を追跡する有限要素法、領域分割法の確立。 6)完全流体での渦の相互干渉によって引き起こされる界面ダイナミクスに対する数値解析法の確立。 7)1)〜6)の数値計算に必要な領域分割法等を用いた無限精度数値シミュレーション法の効率化。 8)界面ダイナミクスを記述する偏微分方程式の数学解析に有効な粘性解理論と等高面法の確立。結果は次のとおりである。 1)では、m周期の刺激に対してn回の興奮がおこるというn:mの引き込みによる閾値下興奮が確認された。 2)では、パターンの境界の運動を捉える自由境界問題の導出を可能にし、進行波のメカニズムが明らかになった。 3)では、O/Wエマルションでの形態変化はその降伏応力が閾値になっていることが得られた。 4)では、浸透領域の分裂、融合、そして再分裂までを再現する数値・数学解析法が得られた。 5)では、インクジェット・プリンタに現れる移動境界現象の解析と脳脊髄液腔における流動解析法を確立した。 6)では、3つの渦糸についても緩和振動が起こる状況を発見し、その数値解析法を確立した。 7)では、無限精度数値シミュレーションには領域分割法による計算の効率化が極めて有効であることが判明した。 8)では、適正粘性解の導入と等高面法の拡張によって結晶成長のダイナミクスを時間大域的に解く事に成功した。

Research Products
(30 results)

All Other

All Publications (30 results)

[Publications] K.Matsuoka, K.Tomoeda: "Numerical computations to pulse splitting phenomena in the thermal waves through an absorbing medium"Journal of Computational and Applied Mathematics. 152/1-2. 319-332 (2003)
[Publications] K.Tomoeda: "The behavior of impulsively initiated thermal waves in an absorbing medium"Dynamics of Continuous, Discrete and Impulsive Systems, Series B : Applications and Alogorithm. 10. 151-164 (2003)
[Publications] K.Tomoeda: "Support splitting phenomena of the solution to the porous media equation with absorption"Progress in Analysis, Proceedings of the 3rd International ISAAC Congress, 20-25 August 2001, Editors : Heinrich G W Begehr, Robert Pertsch Gilbert and Man Wah Wong. 2. 1107-1116 (2003)
[Publications] T.Nakaki, K.Tomoeda: "Numerical approach to the waiting time for the one-dimensional porous medium equation"Quart.Appl.Math.. 61-4. 601-612 (2003)
[Publications] D.Hilhorst, M.Mimura, R.Schaetzle: "Vanishing latent heat limit in a Stefan-like problem arising in Biology"Nonlinear Analysis. 261-285 (2003)
[Publications] E.Feiresl, D.Hilhorst, M.Mimura, R.Weidenfeld: "On a nonlinear diffusion system with resource-consumer interaction"Hiroshima Math.J.. 33. 253-295 (2003)
[Publications] E.C.M.Crooks, E.N.Dancer, D.Hilhorst, M.Mimura, H.Ninomiya: "Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions, to be pressed"Nonlinear Anal.Series B. (2004)
[Publications] M.Kawaguchi: "Viscous Fingering of Silica Suspensions Dispersed in Polymer Fluids"ACS Symposium Series No.869 "Nonlinear Dynamics in Polymeric Systems", Chapter 20. 869. 250-263 (2003)
[Publications] 川口正美: "セルロース誘導体を含む複雑液体のヴィスコスフィンガリング"Cellulose Commun.. 10. 114-118 (2003)
[Publications] M.Kawaguchi, K.Kubota: "Rheo-Optical Properties of Silicone Oil Emulsions in the Presence of Polymer Emulsifers"Langmuir. 20. 1126-1129 (2004)
[Publications] P.Kettunen, P.D.Bourke, H.Hashimoto, T.Amemiya, S.C.Mueller, T.Yamaguchi: "Computational Study of Helix Wave Formation in Active Media"Mathematical and Computer Modelling. (to appear).
[Publications] T.Yamaguchi, N.Suematsu, H.Mahara: "Self - Organization of Hierarchy"ACS Symposium Series 869. 869. 16-27 (2004)
[Publications] H.Suito, H.Kawarada: "Numerical Simulation of Spilled Oil by Fictitious Domain Method"Japan Journal of Industrial and Applied Mathematics. 21-2(to appear). (2004)
[Publications] M.Tabata: "Finite element approximation to infinite Prandtl number Boussinesq equations with temperature dependent coefficients - thermal convection problems in a spherical shell"Future Generation Computer Systems. (to appear).
[Publications] M.Arisawa, Y.Giga: "Anisotropic curvature flow in a thin domain"Indiana Univ.Math.J.. 52. 257-281 (2003)
[Publications] Y.Giga, P.Rybka: "Berg's effect"Adv.Math.Sci.Appl.. 13. 625-637 (2003)
[Publications] Y.-H.R.Tsai, Y.Giga, S.Osher: "A level set approach for computing discontinuous solutions of a class of Hamilton-Jacobi equations"Math.Comp.. 72. 159-181 (2003)
[Publications] T.Takeuchi, H.Imai: "Direct numerical simulations of Cauchy problems for the Lalpace operators"Advances in Mathematical Sciences and Applications. 13. 587-609 (2003)
[Publications] 今井仁司: "応用解析における多倍長計算"数学,日本数学会編集,岩波書店. 55. 316-325 (2003)
[Publications] H.Imai, T.Takeuchi: "Direct simulation of an integral equation of the first kind"Proceedings of International Conference on Inverse Problems - Recent Developments in Theories & Numerics(Eds.Yiu-Chung Hon, Masahiro Yamamoto, Jin Cheng, June-Yub Lee), World Scientific, Singapore. 247-254 (2003)
[Publications] T.Hanada, H.Imai, N.Ishimura, M.A.Nakamura: "Eguchi-Oki-Matsumura equation for phase separation : Numerically guided approach"Proceedings of International Conference on Inverse Problems -Recent Developments in Theories & Numerics(Eds.Yiu-Chung Hon, Masahiro Yamamoto, Jin Cheng, June-Yub Lee), World Scientific, Singapore. 433-442 (2003)
[Publications] T.Nakaki: "Computations on relaxation oscillation of five point vortices"Proceedings of Third International Workshop on Scientific Computing and Applications, Nova Science Publishers Inc., 6 pages. (to appear). 6 (2003)
[Publications] H.Murakawa, T.Nakaki: "A singular limit approach to moving boundary problems and its applications"Theoretical and Applied Mechanics Japan. 52. 255-260 (2003)
[Publications] H.Murakawa, T.Nakaki: "A singular limit method for the Stefan problem"The proceedings of European Conference on Numerical Mathematics and Advanced Applications, Springer-Verlag. (to appear). 6 (2004)
[Publications] K.Nakane, T.Shinohara: "Asymptotic Behavior of Solutions of a Hyperbolic Free Boundary Problem"Dynamics of Continuous, Discrete and Impulsive Systems, Series A : Mathematical Analysis. 10. 289-298 (2003)
[Publications] K.Nakane, T.Shinohara: "The Hyperbolic Free Boundary Problem Arising in Film Peeling Phenomena"Progress in Analysis, Proceedings of the 3rd International ISAAC Congress, 20-25 August 2001, Editors : Heinrich G W Begehr, Robert Pertsch Gilbert and Man Wah Wong. 2. 1087-1096 (2003)
[Publications] K.Nakane, T.Shinohara: "Global solutions to a one-dimensional hyperbolic free boundary problem which arises in peeling phenomena"Journal of Computational and Applied Mathematics. 367-375 (2003)
[Publications] 倉前宏行, 仲町英治: "計算グリッドを用いた結晶均質化並列マルチスケール有限要素解析"日本機械学会第16回計算力学講演会講演論文集. 51-52 (2003)
[Publications] 倉前宏行, 村岡英彦, 仲町英治: "動的負荷分散を考慮した並列マルチスケール有限要素法の開発"日本機械学会関西支部第26回NCP研究会・機械の強度と形態研究懇話会シンポジウム論文集. 41-42 (2003)
[Publications] E.Baba, H.Kawarada, W.Nishijima, M.Okada, H.Suito: "Wavs and Tidal Flat Ecosystems"Springer. 164 (2003)

2003 Fiscal Year Annual Research Report

界面ダイナミクスを再現する数値解析法の開発と実験分野への応用について

Principal Investigator

友枝 謙二 大阪工業大学, 工学部, 教授 (60033916)

Research Products

[Publications] K.Matsuoka, K.Tomoeda: "Numerical computations to pulse splitting phenomena in the thermal waves through an absorbing medium"Journal of Computational and Applied Mathematics. 152/1-2. 319-332 (2003)

[Publications] K.Tomoeda: "The behavior of impulsively initiated thermal waves in an absorbing medium"Dynamics of Continuous, Discrete and Impulsive Systems, Series B : Applications and Alogorithm. 10. 151-164 (2003)

[Publications] T.Nakaki, K.Tomoeda: "Numerical approach to the waiting time for the one-dimensional porous medium equation"Quart.Appl.Math.. 61-4. 601-612 (2003)

[Publications] D.Hilhorst, M.Mimura, R.Schaetzle: "Vanishing latent heat limit in a Stefan-like problem arising in Biology"Nonlinear Analysis. 261-285 (2003)

[Publications] E.Feiresl, D.Hilhorst, M.Mimura, R.Weidenfeld: "On a nonlinear diffusion system with resource-consumer interaction"Hiroshima Math.J.. 33. 253-295 (2003)

[Publications] E.C.M.Crooks, E.N.Dancer, D.Hilhorst, M.Mimura, H.Ninomiya: "Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions, to be pressed"Nonlinear Anal.Series B. (2004)

[Publications] M.Kawaguchi: "Viscous Fingering of Silica Suspensions Dispersed in Polymer Fluids"ACS Symposium Series No.869 "Nonlinear Dynamics in Polymeric Systems", Chapter 20. 869. 250-263 (2003)

[Publications] 川口正美: "セルロース誘導体を含む複雑液体のヴィスコスフィンガリング"Cellulose Commun.. 10. 114-118 (2003)

[Publications] M.Kawaguchi, K.Kubota: "Rheo-Optical Properties of Silicone Oil Emulsions in the Presence of Polymer Emulsifers"Langmuir. 20. 1126-1129 (2004)

[Publications] P.Kettunen, P.D.Bourke, H.Hashimoto, T.Amemiya, S.C.Mueller, T.Yamaguchi: "Computational Study of Helix Wave Formation in Active Media"Mathematical and Computer Modelling. (to appear).

[Publications] T.Yamaguchi, N.Suematsu, H.Mahara: "Self - Organization of Hierarchy"ACS Symposium Series 869. 869. 16-27 (2004)

[Publications] H.Suito, H.Kawarada: "Numerical Simulation of Spilled Oil by Fictitious Domain Method"Japan Journal of Industrial and Applied Mathematics. 21-2(to appear). (2004)

[Publications] M.Tabata: "Finite element approximation to infinite Prandtl number Boussinesq equations with temperature dependent coefficients - thermal convection problems in a spherical shell"Future Generation Computer Systems. (to appear).

[Publications] M.Arisawa, Y.Giga: "Anisotropic curvature flow in a thin domain"Indiana Univ.Math.J.. 52. 257-281 (2003)

[Publications] Y.Giga, P.Rybka: "Berg's effect"Adv.Math.Sci.Appl.. 13. 625-637 (2003)

[Publications] Y.-H.R.Tsai, Y.Giga, S.Osher: "A level set approach for computing discontinuous solutions of a class of Hamilton-Jacobi equations"Math.Comp.. 72. 159-181 (2003)

[Publications] T.Takeuchi, H.Imai: "Direct numerical simulations of Cauchy problems for the Lalpace operators"Advances in Mathematical Sciences and Applications. 13. 587-609 (2003)

[Publications] 今井 仁司: "応用解析における多倍長計算"数学,日本数学会編集,岩波書店. 55. 316-325 (2003)

[Publications] T.Nakaki: "Computations on relaxation oscillation of five point vortices"Proceedings of Third International Workshop on Scientific Computing and Applications, Nova Science Publishers Inc., 6 pages. (to appear). 6 (2003)

[Publications] H.Murakawa, T.Nakaki: "A singular limit approach to moving boundary problems and its applications"Theoretical and Applied Mechanics Japan. 52. 255-260 (2003)

[Publications] H.Murakawa, T.Nakaki: "A singular limit method for the Stefan problem"The proceedings of European Conference on Numerical Mathematics and Advanced Applications, Springer-Verlag. (to appear). 6 (2004)

[Publications] K.Nakane, T.Shinohara: "Asymptotic Behavior of Solutions of a Hyperbolic Free Boundary Problem"Dynamics of Continuous, Discrete and Impulsive Systems, Series A : Mathematical Analysis. 10. 289-298 (2003)

[Publications] K.Nakane, T.Shinohara: "The Hyperbolic Free Boundary Problem Arising in Film Peeling Phenomena"Progress in Analysis, Proceedings of the 3rd International ISAAC Congress, 20-25 August 2001, Editors : Heinrich G W Begehr, Robert Pertsch Gilbert and Man Wah Wong. 2. 1087-1096 (2003)

[Publications] K.Nakane, T.Shinohara: "Global solutions to a one-dimensional hyperbolic free boundary problem which arises in peeling phenomena"Journal of Computational and Applied Mathematics. 367-375 (2003)

[Publications] 倉前宏行, 仲町英治: "計算グリッドを用いた結晶均質化並列マルチスケール有限要素解析"日本機械学会第16回計算力学講演会講演論文集. 51-52 (2003)

[Publications] 倉前宏行, 村岡英彦, 仲町英治: "動的負荷分散を考慮した並列マルチスケール有限要素法の開発"日本機械学会関西支部第26回NCP研究会・機械の強度と形態研究懇話会シンポジウム論文集. 41-42 (2003)

[Publications] E.Baba, H.Kawarada, W.Nishijima, M.Okada, H.Suito: "Wavs and Tidal Flat Ecosystems"Springer. 164 (2003)

友枝謙二大阪工業大学, 工学部, 教授 (60033916)

[Publications] 今井仁司: "応用解析における多倍長計算"数学,日本数学会編集,岩波書店. 55. 316-325 (2003)