2001 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)	池田勉龍谷大学, 理工学部, 教授 (50151296) 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, グループリーダー三村昌泰広島大学, 大学院・理学研究科, 教授 (50068128) 川口正美三重大学, 工学部, 助教授 (30093123) 儀我美一北海道大学, 大学院・理学研究科, 教授 (70144110)
Keywords	ベル-ソフ・ザボチンスキ-反応 / 反応拡散 / ヴィスコスフィンガリング / 浸透領域の分離・非分離現象 / 結晶成長 / 非圧縮電気流体 / 等高面法 / 無限制度数値シミュレーション
Research Abstract	本研究のテーマを中心として1)から4)までの成果が得られた。 1.BZ反応では,光刺激を与えたときの応答を検討した。ある閾値下興奮現象を利用して,興奮場で新しいタイプのペースメーカーが構成された。これらは反応拡散系でありその解析として,界面を取り出す手法である「特異極限法」を開発し,競争系における棲み分け界面ダイナミクスの考察に成功した。また燃焼合成反応に現れる燃焼伝播の形態であるヘリカル波の解析が可能となった。 2.高分子溶液のヴィスコスフィンガリングでは,形態変化が現れるせん断速度は溶液が初めて非ニュートン性を示すせん断速度にほぼ等しいことを明らかにし,ダルシー則の粘性項を修正することによって,パターン成長速度の満たす基礎方程式を導出した。また,結晶成長の観点から,特に表面エネルギーの異方性が強く特異であるときには安定な平らな面(ファセット)の出現を数学的に証明し,界面が曲線になる場合には等高面法を確立しその解析に成功した。 3.蒸発過程での浸透領域の変化では,ある強吸収項をもった非線形拡散方程式でモデル化しその数値計算と数学解析から,空間1次元における浸透領域の分離・非分離のための十分条件と界面方程式を得た。一方,海水が砂の中に浸透する過程では,数値シミュレーションによって外力として波動が不可欠であることが明らかにされた。これによって海水を活性化させ生態系を蘇らせるための知見が得られつつある。 4.無限精度数値シミュレーション法では,簡約化された方程式の数値実験の結果,数学的性質を十分明らかにできるという特徴をもっていることがわかった。また有限要素法では,これまで多角形領域を対象にしていたが,これを一般の領域を対象としその一様可解性を得た。泡の上昇と非圧縮電気流体における移動境界問題を扱う準備ができた。

Research Products
(45 results)

All Other

All Publications (45 results)

[Publications] T.Nakaki, K.Tomoeda: "A finite difference approach to the interface equation for some nonlinear diffusion equation with absorption"Proc. Japan Acad. Ser. A. 77. 32-37 (2001)
[Publications] T.Nakaki, K.Tomoeda: "A finite difference scheme for some nonlinear diffusion equations in absorbing medium : support splitting phenomena"SIAM J. Numer. Anal. (to appear).
[Publications] K.Tomoeda: "Numerical approach to support splitting phenomena in some diffusion equations with strong absorption"Proceedings of the Fifth China-Japan Seminar on Numerica Mathematics. (to appear).
[Publications] M.Rodrigo, M.Mimura: "Exact solutions of reaction-diffusion systems and nonlinear wave equations"Japan J. Indsutrial and Appl. Mathematics. 18. 647-656 (2001)
[Publications] D.Hilhorst, M.Ida, M.Mimura.H.Ninomiya: "A competition-diffusion system approximation to the classical two-phase Stefan problem"Japan J. Indsutrial and Appl. Mathematics. 18. 161-180 (2001)
[Publications] H.Ikeda, M.Mimura, H.Okamoto: "A singular pertrubation problem arising in Oseen's flows Japan J. Indsutrial and Appl. Mathematics"Japan J. Indsutrial and Appl. Mathematics. 18. 393-404 (2001)
[Publications] S.Kawaguchi, M.Mimura, T.Ohya, N.Oikawa, H.Okabe, S.Kai: "Hormone-mediated patterns formation in seeding of plants : a competitive growth dynamics model"J. Phys. Soc. Japan. 70. 3155-3160 (2001)
[Publications] D.Hilhorst, M.Mimura, R.Schaetzle: "Vanishing latent heat limit in a Stefan-like problem arising in Biology"Nonlinear Analysis. (to appear).
[Publications] K.Osaki T.Tsujikawa, A.Yagi, M.kiimura: "Exponential attractor for a chemotaxis growth system of equations"Nonlinear Anal., Series A. (to appear).
[Publications] M.Funaki, M.Mimura, T.Tsujikawa: "Travelling front solutions arising in a chemotaxis growth model"J. Math. Biol.. (to appear).
[Publications] A.Bonami, D.Hilhorst, B.Logak, M.Mimura: "A free boundary problem arising in a chemotaxis model"Free Boundary problems. Theory and Applications (eds. M. Niezgodaka and P. Strzelecki), Longman. (to appear).
[Publications] M.Mimura, M.Nagayama, T.Ohta: "Non-Annihilation of travelling pulses in reaction-diffusion systems"J. Methods and Appl. of Analysis. (to appear).
[Publications] Hideo Kawarada, Hiroshi Suito: "Shape optimization for an acoustic problem"Proceedin of 12th International Conference on Domain Decompo-sitia n Methods. 419-426 (2001)
[Publications] Hideo Kawarada, Kazuyoshi Hiroki, Hiroshi Suito: "Neural network optimization method"Innovative Tools for Scientific Computation in Aeronautical Engineering, (c) CIMNE, Barcelona. 346-350 (2001)
[Publications] Hideo Kawarada, C.Bernardi, V.Girault, F.Hecht, O.Pironneau: "A finite element problem issued from fictitious domain techniques"East-West Journal of Numerical Mathematics. 9(4). 253-316 (2001)
[Publications] M.Tabata: "Uniform solvability of finite element solutions in approximate domains"Japan Journal of Industrial and Applied Mathematics. 18. 567-585 (2001)
[Publications] Y.Mizuyama, M.Tabata: "Lagrangian finite element analysis of the free surface of an incompressible di-electric liquid under an electric field"Theoretical Appliedl Mechanics. 50. 403-410 (2001)
[Publications] M.Tabata, S.Fujima: "Numerical analysis of flow problems by finite element methods"Sugaku Expositions. 14. 155-174 (2001)
[Publications] M.Tabata, A.Suzuki: "Mathematical modeling and numerical simulation of Earth's mantle convection"Mathematical Modeling and Numerical Simulation in Continuum Mechanics of Lecture Notes in Computational Science and Engineering, P. G. Ciarlet I. Babuska and T. Miyoshi, editors, Springer, Berlin. 19. 216-231 (2001)
[Publications] H.Rui, M.Tabata: "A second order characteristic finite element scheme for convection-diffusion problems"Numerische Mathematik. 2002(to appear).
[Publications] 池田勉, 長山雅晴: "燃焼合成反応におけるヘリカル波"応用数理. 11(2). 40-48 (2001)
[Publications] M.Nagayama, T.Ikeda, T.Ishiwata, N.Tamura, M.Ohyanagi: "Three-dimensional numerical simulation of helically propagating combustion waves"J. of Material Synthesis and Processing. 9(3). 153-163 (2001)
[Publications] T.Nishida, T.Ikeda, H.Yoshihara: "Pattern formation of heat convection problems"Mathematical Modeling and Numerical Simulation in Continuum Mechanics (eds. I. Babuska, P. G. Ciarlet and T. Miyoshi), Lecture Notes in Computa-tional Sciences and Engineering, Springer. 19. 209-218 (2002)
[Publications] R.Kobayashi, Y.Giga: "On anisotropy and curvature effects for growing crystals"Japan J. Ind. Appl. Math.. 18. 207-230 (2001)
[Publications] Y.Giga, M.Paolini, P.Rybka: "On the motion by singular interfacial energy"Japan J. Ind. Appi. Math.. 18. 231-248 (2001)
[Publications] M.-H.Giga, Y.Giga: "Generalized motion by nonlocal curvature in the plane"Arch. Rational Mech. Anal.. 159. 295-333 (2001)
[Publications] Y.Giga, P.Rybka: "Quasi-static evolution of 3-D cryctals growth from superstaturated vapor"Differential Integral Equations. 15. 1-15 (2002)
[Publications] P.Parmananda, H.Mahara, T.Amemiya, T.Yamaguchi: "Resonance induced pacemakers : A new class of organizing centers for wave propagation in excitable media"Physical Review Letters. 87(23). 238302-238305 (2001)
[Publications] T.Amemiya, T.Yamamoto, T.Ohmori, T.Yamaguchi: "Experimental and model studies of oscillations, photoinduced transitions, and steady states in the Ru(bpy)32+-catalyzed Belousov-Zhabotinsky reaction under different solution comDositions"J. Phys. Chem. A. 106(4). 612-620 (2002)
[Publications] M.Kawaguchi: "Viscous fingering in polymeric systems"Nonhnear Analysis. 47. 907 (2001)
[Publications] M.Kawaguchi, Y.Hibino, T.Kato: "Anisotropy effects of Hele-Shaw cells on viscous fingering instability in dilute polymer solutions"Phys. Rev. E. 64. 0561806 (2001)
[Publications] 石村直之, 今井仁司, 竹内敏己: "自由境界問題の数値解法-数理ファイナンスへの応用-"一橋論義. 126(4). 419-428 (2001)
[Publications] Hitoshi Imai, Toshiki Takeuchi, Shewli Shamim Shanta, Naoyuki Ishimura. Tovohiko Aiki: "Numerical computation of Lyapunov exponents related to attractors in a free boundary problem"Nonlinear Analysis. 47. 3823-3833 (2001)
[Publications] Toshiki Takeuchi, Naoyuki Ishimura, Hitoshi Imai: "A new numerical technique for the option pricing problem of American type World Multiconference on Systemics, Cybernetics and Informatics Proceedings ( Eds., N. Callaos, Y. Hu, M. Rodriguez and Q. Ha ), The International"Institute of Informatics and Systemics. II. 233-236 (2001)
[Publications] T.Nakaki: "The analysis to some point vortex problems using computers"Nonlinear Analysis. 47. 3849-3857 (2001)
[Publications] R.Ikota, M.Mimura, T.Nakaki: "Numerical computation for some competition-diffusion systems on a parallel computer"Proceedins of 12th International Conference on Domain Decompo-sition Methods. 373-379 (2001)
[Publications] T.Nakaki, K.Tomoeda: "Numerical approach to the waiting time for the one-dimensional porous medium equation"Quart. Appl. Math.. (to appear).
[Publications] H.Imai, K.Kikuchi, K.Nakane, S.Omata, T.Tachikawa: "A numerical approach to the asymptotic behavior of solutions of a one-dimensional hyperbolic free boundary problem"Japan J. Indsutrial and Appi. Mathematics. 18(1). 43-58 (2001)
[Publications] K.Nakane: "Global existence of solutions to a one-dimensional free boundary problem of hyperbolic type"Proc. Japan Acad. Ser. A. 77. 103-107 (2001)
[Publications] K.Nakane: "Numerical calculation of singularities for Ginzburg-Landau functionals with a variable coefficient"Nonlinear Analysis. 47. 3803-3811 (2001)
[Publications] C.J.Breward R.C.Darton, P.D.Howell, JAIL Ockendon: "The effect of surfactants on expanding free surfaces"Chem. Eng. Sci.. 56. 2867-2878 (2001)
[Publications] S.Falle, H.Ockendon, J.R.Ockendon: "The Fanno model for turbulent compressible flow"J. Fluid Mech.. (to appear). (2001)
[Publications] H.Ockendon, J.R.Ockendon: "Nonlinearity in fluid resonances"Mecannica. (to appear). (2001)
[Publications] S.D.Howison, J.R.Ockendon: "Kochina and Hele-Shaw in modern mathematics, science and industry"Priklay Math. Mech. (Ed. Yu Gupalo). 532-546 (2001)
[Publications] M.Kawaguchi: ""Viscous fingering instability in polymer solution" in "Recent research developments in polymer science""Transworld, Research Network. 30 (2002)

2001 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] T.Nakaki, K.Tomoeda: "A finite difference approach to the interface equation for some nonlinear diffusion equation with absorption"Proc. Japan Acad. Ser. A. 77. 32-37 (2001)

[Publications] T.Nakaki, K.Tomoeda: "A finite difference scheme for some nonlinear diffusion equations in absorbing medium : support splitting phenomena"SIAM J. Numer. Anal. (to appear).

[Publications] K.Tomoeda: "Numerical approach to support splitting phenomena in some diffusion equations with strong absorption"Proceedings of the Fifth China-Japan Seminar on Numerica Mathematics. (to appear).

[Publications] M.Rodrigo, M.Mimura: "Exact solutions of reaction-diffusion systems and nonlinear wave equations"Japan J. Indsutrial and Appl. Mathematics. 18. 647-656 (2001)

[Publications] D.Hilhorst, M.Ida, M.Mimura.H.Ninomiya: "A competition-diffusion system approximation to the classical two-phase Stefan problem"Japan J. Indsutrial and Appl. Mathematics. 18. 161-180 (2001)

[Publications] H.Ikeda, M.Mimura, H.Okamoto: "A singular pertrubation problem arising in Oseen's flows Japan J. Indsutrial and Appl. Mathematics"Japan J. Indsutrial and Appl. Mathematics. 18. 393-404 (2001)

[Publications] S.Kawaguchi, M.Mimura, T.Ohya, N.Oikawa, H.Okabe, S.Kai: "Hormone-mediated patterns formation in seeding of plants : a competitive growth dynamics model"J. Phys. Soc. Japan. 70. 3155-3160 (2001)

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

[Publications] K.Osaki T.Tsujikawa, A.Yagi, M.kiimura: "Exponential attractor for a chemotaxis growth system of equations"Nonlinear Anal., Series A. (to appear).

[Publications] M.Funaki, M.Mimura, T.Tsujikawa: "Travelling front solutions arising in a chemotaxis growth model"J. Math. Biol.. (to appear).

[Publications] A.Bonami, D.Hilhorst, B.Logak, M.Mimura: "A free boundary problem arising in a chemotaxis model"Free Boundary problems. Theory and Applications (eds. M. Niezgodaka and P. Strzelecki), Longman. (to appear).

[Publications] M.Mimura, M.Nagayama, T.Ohta: "Non-Annihilation of travelling pulses in reaction-diffusion systems"J. Methods and Appl. of Analysis. (to appear).

[Publications] Hideo Kawarada, Hiroshi Suito: "Shape optimization for an acoustic problem"Proceedin of 12th International Conference on Domain Decompo-sitia n Methods. 419-426 (2001)

[Publications] Hideo Kawarada, Kazuyoshi Hiroki, Hiroshi Suito: "Neural network optimization method"Innovative Tools for Scientific Computation in Aeronautical Engineering, (c) CIMNE, Barcelona. 346-350 (2001)

[Publications] Hideo Kawarada, C.Bernardi, V.Girault, F.Hecht, O.Pironneau: "A finite element problem issued from fictitious domain techniques"East-West Journal of Numerical Mathematics. 9(4). 253-316 (2001)

[Publications] M.Tabata: "Uniform solvability of finite element solutions in approximate domains"Japan Journal of Industrial and Applied Mathematics. 18. 567-585 (2001)

[Publications] Y.Mizuyama, M.Tabata: "Lagrangian finite element analysis of the free surface of an incompressible di-electric liquid under an electric field"Theoretical Appliedl Mechanics. 50. 403-410 (2001)

[Publications] M.Tabata, S.Fujima: "Numerical analysis of flow problems by finite element methods"Sugaku Expositions. 14. 155-174 (2001)

[Publications] H.Rui, M.Tabata: "A second order characteristic finite element scheme for convection-diffusion problems"Numerische Mathematik. 2002(to appear).

[Publications] 池田勉, 長山雅晴: "燃焼合成反応におけるヘリカル波"応用数理. 11(2). 40-48 (2001)

[Publications] M.Nagayama, T.Ikeda, T.Ishiwata, N.Tamura, M.Ohyanagi: "Three-dimensional numerical simulation of helically propagating combustion waves"J. of Material Synthesis and Processing. 9(3). 153-163 (2001)

[Publications] R.Kobayashi, Y.Giga: "On anisotropy and curvature effects for growing crystals"Japan J. Ind. Appl. Math.. 18. 207-230 (2001)

[Publications] Y.Giga, M.Paolini, P.Rybka: "On the motion by singular interfacial energy"Japan J. Ind. Appi. Math.. 18. 231-248 (2001)

[Publications] M.-H.Giga, Y.Giga: "Generalized motion by nonlocal curvature in the plane"Arch. Rational Mech. Anal.. 159. 295-333 (2001)

[Publications] Y.Giga, P.Rybka: "Quasi-static evolution of 3-D cryctals growth from superstaturated vapor"Differential Integral Equations. 15. 1-15 (2002)

[Publications] P.Parmananda, H.Mahara, T.Amemiya, T.Yamaguchi: "Resonance induced pacemakers : A new class of organizing centers for wave propagation in excitable media"Physical Review Letters. 87(23). 238302-238305 (2001)

[Publications] T.Amemiya, T.Yamamoto, T.Ohmori, T.Yamaguchi: "Experimental and model studies of oscillations, photoinduced transitions, and steady states in the Ru(bpy)32+-catalyzed Belousov-Zhabotinsky reaction under different solution comDositions"J. Phys. Chem. A. 106(4). 612-620 (2002)

[Publications] M.Kawaguchi: "Viscous fingering in polymeric systems"Nonhnear Analysis. 47. 907 (2001)

[Publications] M.Kawaguchi, Y.Hibino, T.Kato: "Anisotropy effects of Hele-Shaw cells on viscous fingering instability in dilute polymer solutions"Phys. Rev. E. 64. 0561806 (2001)

[Publications] 石村直之, 今井仁司, 竹内敏己: "自由境界問題の数値解法-数理ファイナンスへの応用-"一橋論義. 126(4). 419-428 (2001)

[Publications] Hitoshi Imai, Toshiki Takeuchi, Shewli Shamim Shanta, Naoyuki Ishimura. Tovohiko Aiki: "Numerical computation of Lyapunov exponents related to attractors in a free boundary problem"Nonlinear Analysis. 47. 3823-3833 (2001)

[Publications] T.Nakaki: "The analysis to some point vortex problems using computers"Nonlinear Analysis. 47. 3849-3857 (2001)

[Publications] R.Ikota, M.Mimura, T.Nakaki: "Numerical computation for some competition-diffusion systems on a parallel computer"Proceedins of 12th International Conference on Domain Decompo-sition Methods. 373-379 (2001)

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

[Publications] H.Imai, K.Kikuchi, K.Nakane, S.Omata, T.Tachikawa: "A numerical approach to the asymptotic behavior of solutions of a one-dimensional hyperbolic free boundary problem"Japan J. Indsutrial and Appi. Mathematics. 18(1). 43-58 (2001)

[Publications] K.Nakane: "Global existence of solutions to a one-dimensional free boundary problem of hyperbolic type"Proc. Japan Acad. Ser. A. 77. 103-107 (2001)

[Publications] K.Nakane: "Numerical calculation of singularities for Ginzburg-Landau functionals with a variable coefficient"Nonlinear Analysis. 47. 3803-3811 (2001)

[Publications] C.J.Breward R.C.Darton, P.D.Howell, JAIL Ockendon: "The effect of surfactants on expanding free surfaces"Chem. Eng. Sci.. 56. 2867-2878 (2001)

[Publications] S.Falle, H.Ockendon, J.R.Ockendon: "The Fanno model for turbulent compressible flow"J. Fluid Mech.. (to appear). (2001)

[Publications] H.Ockendon, J.R.Ockendon: "Nonlinearity in fluid resonances"Mecannica. (to appear). (2001)

[Publications] S.D.Howison, J.R.Ockendon: "Kochina and Hele-Shaw in modern mathematics, science and industry"Priklay Math. Mech. (Ed. Yu Gupalo). 532-546 (2001)

[Publications] M.Kawaguchi: ""Viscous fingering instability in polymer solution" in "Recent research developments in polymer science""Transworld, Research Network. 30 (2002)

友枝謙二大阪工業大学, 工学部, 教授 (60033916)