2000 Fiscal Year Annual Research Report

界面現象の複雑性に対する実験解析・数値解析・数学解析の融合的研究

Research Project

Project/Area Number	11440035
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) 河原田秀夫千葉大学, 工学部, 教授 (90010793) 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	ベルーソフ・ザボチンスキー反応 / ヘリカル進行波 / ヴィスコスフィンガリング / 樹枝状形状 / 浸透領域の変化 / 渦の相互作用 / 亀裂伸展
Research Abstract	次のテーマ 1)空間的にスパイラル状に広がっていく光感受性ベルーソフ・ザボチンスキー反応のパターンおよび燃焼合成反応でのヘリカル進行波の出現メカニズム 2)複雑で自己組織的に制御された樹枝状形状が観察される現象として,バクテリアコロニーパターン,自己触媒化学過程での反応パターン,無重力下での燃焼パターン成長の数学的メカニズム 3)粘弾性を示す高分子溶液でのヴィスコスフィンガリングの成長の実験的メカニズム 4)表面張力を考慮した自由境界問題および拡散と吸収のバランスによって生じる浸透域の分離・融合現象 5)完全流体における複数の渦の相互干渉現象 6)破壊力学に現われる亀裂パターンの伸展についての数理モデルを扱い以下の成果が得られた。 1)と2)ではその本質的な部分のモデルは,反応拡散系方程式に統一的に記述された。それによって,複雑なパターンの出現メカニズムおよび樹枝状形状の機構が明らかになった。 3)では,観察されるパターンの成長速度が修正ダルシー則によって記述されることを明らかにした。つまり,シア・シニング挙動を示す非ニュートン流体のヴィスコスフィンガリングの成長に関する基礎方程式が確立できた。 4)では,吸収効果をもった非線形又は半線形拡散方程式で記述されるモデルが得られた。その数値解析から,浸透領域の分離・融合を再現する条件を得た。 5)では渦領域の挙動と渦の相互干渉の両面から調べ,前者では渦領域と渦糸問題の違いを数値的に示し,後者では「複数の台風の挙動モデル」として捉え数学的に解明した。 6)では,亀裂界面の伸展が亀裂長に関する微分方程式に帰着された。それに基づいて数値計算を行い亀裂界面の伸展を再現することができた。

Research Products

(20 results)

All Other

All Publications (20 results)

[Publications] T.Nakaki and K.Tomoeda: "A finite difference schemes for some nonlinear diffusion equations in absorbing medium : support splitting phenomena"Preprint Series in Mathematics, Kyushu University. 2000-18. 1-42 (2001)
[Publications] T.Nakaki and K.Tomoeda: "A finite difference approach to the interface equation for some nonlinear diffusion equation with absorption"To appear in Proc.Japan Acad.Ser.A. 77. 32-37 (2001)
[Publications] K.Tomoeda: "Numerical computations to support splitting phenomena in some diffusion equations"INFORMATION. 3. 331-339 (2000)
[Publications] T.Nakaki and K.Tomoeda: "Numerical waiting time of interfaces in one-dimensional porous medium equations"Free Boundary Problems : Theory and Applications, Mathematical Sciences and Applications. 14. 324-333 (2000)
[Publications] M.Funaki,M.Mimura and T.Tsujikawa: "Travelling front solutions arising in a chemotaxis-growth model"J.Math.Biol.. (to appear).
[Publications] M.Mimura,M.Nagayama and T.Ohta: "Non-Annihilation of travelling pulses in reaction-diffusion systems"J.Methods and Appl.of Analysis. (to appear).
[Publications] M.Rodrigo and M.Mimura: "Exact solutions of reaction-diffusion systems and nonlinear wave equations"Japan J.Indsutrial and Appl.Mathematics. (to appear).
[Publications] D.Hilhorst,M.Ida,M.Mimura and H.Ninomiya: "A competition-diffusion system approximation to the classical two-phase Stefan problem"Japan J.Indsutrial and Appl.Mathematics. (to appear).
[Publications] H.Kawarada,E.Baba and H.Suito: "Effect of spilled oil on Coastal Ecosystems"ECCOMAS2000 CD-ROM Proceedings. (2000)
[Publications] C.Bernardi,V.Girault,F.Hecht,H.Kawarada and O.Pironneau: "A Finite Element Problem issued from Fictitious Domain Techniques"Computational Mechanics. (To appear). (2001)
[Publications] H.Suito and H.Kawarada: "Shape Optimization for an Acoustic Problem"Domain Decomposition Methods in Science and Engineering, Proceedings of 12th International Conference on Domain Decomposition Methods. 419-426 (2001)
[Publications] Tetsuhiko Miyoshi: "Direction and curvature of the cracks in two-dimensional elastic bodies"Japan Journal of Industrial and Applied Mathematics. 12-2. 295-307 (2000)
[Publications] Masami Kawaguchi: "Viscous Fingering in Polymer Solutions"Macromolecular Symposia. 160. 85-90 (2000)
[Publications] Masami Kawaguchi: "Viscous Fingering in Polymeric Systems"Nonlinear Analysis. (to appear).
[Publications] T.Nakaki: "Numerical computation to the advection in the field of some point vortices"数理解析研究所講究録. 1145. 145-152 (2000)
[Publications] T.Nakaki: "The analysis to some point vortex problems using computers"Journal of Nonlinear Analysis, Series A Theory and Methods. (to appear).
[Publications] K.Nakane: "Numerical Computations for Ginzburg-Landau equation with a variable coefficient by using the discrete Morse semiflow"京都大学数理解析研究所講究録. 1145. 153-160 (2000)
[Publications] T.Nagasawa,K.Nakane and S.Omata: "Numerical computations for a hyperbolic Ginzburg-Landau system"Nonlinear Analysis. (to appear).
[Publications] K.Nakane: "Numerical simulation to the behavior of the thin film peeling from the plate"INFORMATION. (to appear).
[Publications] H.Imai,K.Kikuchi,K.Nakane,S.Omata and T.Tachikawa: "A numerical approach to the asymptotic behavior of solutions of a one-dimensional hyperbolic free boundary problem"JJIAM. (to appear).

2000 Fiscal Year Annual Research Report

界面現象の複雑性に対する実験解析・数値解析・数学解析の融合的研究

Principal Investigator

友枝 謙二 大阪工業大学, 工学部, 教授 (60033916)

Research Products

[Publications] T.Nakaki and K.Tomoeda: "A finite difference schemes for some nonlinear diffusion equations in absorbing medium : support splitting phenomena"Preprint Series in Mathematics, Kyushu University. 2000-18. 1-42 (2001)

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

[Publications] K.Tomoeda: "Numerical computations to support splitting phenomena in some diffusion equations"INFORMATION. 3. 331-339 (2000)

[Publications] T.Nakaki and K.Tomoeda: "Numerical waiting time of interfaces in one-dimensional porous medium equations"Free Boundary Problems : Theory and Applications, Mathematical Sciences and Applications. 14. 324-333 (2000)

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

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

[Publications] M.Rodrigo and M.Mimura: "Exact solutions of reaction-diffusion systems and nonlinear wave equations"Japan J.Indsutrial and Appl.Mathematics. (to appear).

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

[Publications] H.Kawarada,E.Baba and H.Suito: "Effect of spilled oil on Coastal Ecosystems"ECCOMAS2000 CD-ROM Proceedings. (2000)

[Publications] C.Bernardi,V.Girault,F.Hecht,H.Kawarada and O.Pironneau: "A Finite Element Problem issued from Fictitious Domain Techniques"Computational Mechanics. (To appear). (2001)

[Publications] H.Suito and H.Kawarada: "Shape Optimization for an Acoustic Problem"Domain Decomposition Methods in Science and Engineering, Proceedings of 12th International Conference on Domain Decomposition Methods. 419-426 (2001)

[Publications] Tetsuhiko Miyoshi: "Direction and curvature of the cracks in two-dimensional elastic bodies"Japan Journal of Industrial and Applied Mathematics. 12-2. 295-307 (2000)

[Publications] Masami Kawaguchi: "Viscous Fingering in Polymer Solutions"Macromolecular Symposia. 160. 85-90 (2000)

[Publications] Masami Kawaguchi: "Viscous Fingering in Polymeric Systems"Nonlinear Analysis. (to appear).

[Publications] T.Nakaki: "Numerical computation to the advection in the field of some point vortices"数理解析研究所講究録. 1145. 145-152 (2000)

[Publications] T.Nakaki: "The analysis to some point vortex problems using computers"Journal of Nonlinear Analysis, Series A Theory and Methods. (to appear).

[Publications] K.Nakane: "Numerical Computations for Ginzburg-Landau equation with a variable coefficient by using the discrete Morse semiflow"京都大学数理解析研究所講究録. 1145. 153-160 (2000)

[Publications] T.Nagasawa,K.Nakane and S.Omata: "Numerical computations for a hyperbolic Ginzburg-Landau system"Nonlinear Analysis. (to appear).

[Publications] K.Nakane: "Numerical simulation to the behavior of the thin film peeling from the plate"INFORMATION. (to appear).

[Publications] H.Imai,K.Kikuchi,K.Nakane,S.Omata and T.Tachikawa: "A numerical approach to the asymptotic behavior of solutions of a one-dimensional hyperbolic free boundary problem"JJIAM. (to appear).

友枝謙二大阪工業大学, 工学部, 教授 (60033916)