1999 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 Category	Grant-in-Aid for Scientific Research (B)
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)	河原田秀夫千葉大学, 工学部, 教授 (90010793) 川口正美三重大学, 工学部, 助教授 (30093123) 三村昌泰広島大学, 理学部, 教授 (50068128) 儀我美一北海道大学, 大学院・理学研究科, 教授 (70144110) 池田勉龍谷大学, 理工学部, 教授 (50151296)
Keywords	ベルーソフ・ザボチンスキー反応 / ヴィスコスフィンガリング / 樹枝状形状 / ギンツブルグ・ランダウ方程式 / 渦の相互作用 / ヘリカル進行波 / クリスタライン・アルゴリズム / 反応拡散
Research Abstract	次のテーマを扱った。 1)空間的にスパイラル状に広がっていくエイジングの効果を取り入れた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。 2)複雑で自己組織的に制御された美しい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および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。 3)表面張力を考慮した非定常非圧縮性流体の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。 4)油濁による地下海水循環領域の変動および流体に発生した複数の渦の相互干渉。 5)超伝導現象を表すギンツブルグ・ランダウ型方程式での自由境界問題。 6)曲率の効果が非局所的であるような界面運動での特異性の出現。その結果,次の成果が得られた。 1),2)についてはそれらの背後にある本質的な部分を取り出すことから,複雑なスパイラルおよび樹枝状形状の機構解明とヘリカル進行波の出現メカニズムを反応拡散系モデルを通じて,実験家との共同研究のもとに明らかにした。 3)については数値解析法の確立,特に数値解の収束,誤差評価が得られた。 4)については自然現象に良く一致した数値計算法が構成された。渦の相互干渉については数学的証明が得られた。 5)については時間差分型汎関数という考えを導入して数値計算が可能になった。 6)については曲率の効果が局所的であるような問題の極限とみなすことによって等高面の方法が適用できることを示した。その結果、数値計算法のひとつであるクリスタライン・アルゴリズムの収束性が示された。

Research Products
(30 results)

All Other

All Publications (30 results)

[Publications] K.Tomoeda: "Numerical computations to support splitting phenomena in some diffusion equations"to appear in Information. 3. 9 (2000)
[Publications] T.Nakaki and K.Tomoeda: "Numerical approach to the waiting time for the one-dimesional porous medium equation"Preprint Series in Mathematics,Kyushu University. 1999-14. 1-14 (1999)
[Publications] S.Kawaguchi and M.Mimura: "Collision of travelling waves in a reaction-diffusion system with global coupling effect"SIAM J.Appl.Math.. 59. 920-941 (1999)
[Publications] E.N.Dancer,D.Hilhorst,M.Mimura and L.A.Peletier: "Spatial segregation limit of a competition-diffusion system,"European J.Appl.Math.. 10. 97-115 (1999)
[Publications] S.-I. Ei,R.Ikota and M.Mimura: "Segregating partition problem in competition-diffusion systems"Interfaces and Free Boundaries. 1. 57-80 (1999)
[Publications] M.Rodrigo and M.Mimura: "Exact solutions of a competition-diffusion system"to appear n Hiroshima Math.J..
[Publications] M.Funaki,M.Mimura and T.Tsujikawa: "Travelling front solutions arising in a chemotaxis-growth model"to appear in J.Math.Biol..
[Publications] Masami Kawaguchi,Kohkichi Shimomoto,Atsushi Shibata,and Tadaya Kato: "Effect of anisotropy on viscous fingering patterns of polymer solutions in linear Hele-Shaw cells"Chaos. 9-2. 323-328 (1999)
[Publications] 川口正美,牧野恭子,加藤忠哉: "高分子溶液のヴィスコスフィンガリング"化学工学論文集. 25巻4号. 516-519 (1999)
[Publications] 川口正美: "高分子系のヴィスコスフィンガリング"高分子論文集. 56巻10号. 597-608 (1999)
[Publications] H.Mahara,T.Yamaguchi,Y.Amagishi: "A numerical study of the decomposition of chemical waves in a closed system"Chem.Phys.Lett.,in press..
[Publications] Kettunen,T.Amemiya,T.Ohmori,T.Yamaguchi: "Spontaneous spiral formation in two-dimensional oscillatory media"Phys.Rev.E. 60(2). 1512-1515 (1999)
[Publications] 山口智彦: "ベローソフ・ジャボチンスキー反応"化学. 55(2). 55-57 (2000)
[Publications] H.Kawarada and H.Suito: "Hybridized Fuzzy and GAs Distributed Optimization Method"EUROGEN99,Jyvaskyla,Finland,May 1999.. (1999)
[Publications] H.Kawarada and H.Suito: "Influence of Spilled Oil to bring about on Coastal Ecosystem"Differential Equations and their Applications,An International Symposium dedicated to J.L.Lions on the occasion of his 70th birthday,University of Houston,October 1999.. (1999)
[Publications] H.Kawarada and H.Suito: "Optimal Shape of Pine for Sound Absorption in Water"Domain Decomposition Methods in Science and Engineering,Proceedings of 11th International Conference on Domain Decomposition Methods,Domain Decomposition Press,Bergen.. 270-281 (1999)
[Publications] K.Itakura and M.Tabata: "An error analysis of streaklines as curves"Japan Journal of Industrial and Applied Mathematics. 16. 1-23 (1999)
[Publications] A.Suzuki,M.Tabata,and S.Honda: "Numerical solution of an unsteady earth's mantle convection problem by a stabilized finite element method"Theoretical and Applied Mechanics. 48. 371-378 (1999)
[Publications] M.Tabata and D.Tagami: "A finite element analysis of a linearized problem of the Navier-Stokes equations with aurface tension"to appear in SIAM Journal on Numerical Analysis.
[Publications] T.Nakaki: "Behavior of point vortices in a plane and existence of heteroclinic orbits"Dynam.Contin.Discrete Impuls.Systems. 5. 159-169 (1999)
[Publications] H.Ikeda and T.Ikeda: "Bifurcation phenomena from standing pulse solutions of bistable reaction-diffusion systems"to appear in Journal of Dynamics and Differential Equations.
[Publications] T.Ikeda and H.Ikeda: "Hopf bifurcation of traveling pulses in some bistable reaction-diffusion systems"to appear in Methods and Applications of Analysis.
[Publications] M.Mimura,M.Nagayama,H.Ikeda and T.Ikeda: "Dynamics of travelling breathers arising in reaction-diffusion systems-ODE mod-elling approach-"to appear in Hiroshima Mathematical Journal.
[Publications] M.-H.Giga and Y.Giga: "Stability for evolving graphs by nonlocal weighted curvature"Comm.in Partial Differential Equations. 24. 109-184 (1999)
[Publications] Y.Giga,M.Ohnuma and M.-H.Sato: "On strong maximum principle and large time behaviour of generalized mean cuvature flow witn the Neumann boundary condition"J.Differential Equations. 154. 107-131 (1999)
[Publications] R.Kobayashi and Y.Giga: "Equations with singular diffusivity"J.Stat.Phys.. 95. 1187-1220 (1999)
[Publications] T.Nagasawa,K.Nakane and S.Omata: "Numerical computations for a hyperbolic Ginzburg-Landau system"to appear in Nonlinear Analysis.
[Publications] K.Nakane: "Numerical simulation to the behavior of the thin film peeling from the plate"to appear in Information. 3. -9 (2000)
[Publications] 川口正美: "高分子の界面・コロイド科学"コロナ社. 199 (1999)
[Publications] 儀我美一・儀我美保: "非線形偏微分方程式-解の漸近挙動と自己相似解"共立出版. 300 (1999)

1999 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] K.Tomoeda: "Numerical computations to support splitting phenomena in some diffusion equations"to appear in Information. 3. 9 (2000)

[Publications] T.Nakaki and K.Tomoeda: "Numerical approach to the waiting time for the one-dimesional porous medium equation"Preprint Series in Mathematics,Kyushu University. 1999-14. 1-14 (1999)

[Publications] S.Kawaguchi and M.Mimura: "Collision of travelling waves in a reaction-diffusion system with global coupling effect"SIAM J.Appl.Math.. 59. 920-941 (1999)

[Publications] E.N.Dancer,D.Hilhorst,M.Mimura and L.A.Peletier: "Spatial segregation limit of a competition-diffusion system,"European J.Appl.Math.. 10. 97-115 (1999)

[Publications] S.-I. Ei,R.Ikota and M.Mimura: "Segregating partition problem in competition-diffusion systems"Interfaces and Free Boundaries. 1. 57-80 (1999)

[Publications] M.Rodrigo and M.Mimura: "Exact solutions of a competition-diffusion system"to appear n Hiroshima Math.J..

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

[Publications] Masami Kawaguchi,Kohkichi Shimomoto,Atsushi Shibata,and Tadaya Kato: "Effect of anisotropy on viscous fingering patterns of polymer solutions in linear Hele-Shaw cells"Chaos. 9-2. 323-328 (1999)

[Publications] 川口正美,牧野恭子,加藤忠哉: "高分子溶液のヴィスコスフィンガリング"化学工学論文集. 25巻4号. 516-519 (1999)

[Publications] 川口正美: "高分子系のヴィスコスフィンガリング"高分子論文集. 56巻10号. 597-608 (1999)

[Publications] H.Mahara,T.Yamaguchi,Y.Amagishi: "A numerical study of the decomposition of chemical waves in a closed system"Chem.Phys.Lett.,in press..

[Publications] Kettunen,T.Amemiya,T.Ohmori,T.Yamaguchi: "Spontaneous spiral formation in two-dimensional oscillatory media"Phys.Rev.E. 60(2). 1512-1515 (1999)

[Publications] 山口智彦: "ベローソフ・ジャボチンスキー反応"化学. 55(2). 55-57 (2000)

[Publications] H.Kawarada and H.Suito: "Hybridized Fuzzy and GAs Distributed Optimization Method"EUROGEN99,Jyvaskyla,Finland,May 1999.. (1999)

[Publications] H.Kawarada and H.Suito: "Influence of Spilled Oil to bring about on Coastal Ecosystem"Differential Equations and their Applications,An International Symposium dedicated to J.L.Lions on the occasion of his 70th birthday,University of Houston,October 1999.. (1999)

[Publications] H.Kawarada and H.Suito: "Optimal Shape of Pine for Sound Absorption in Water"Domain Decomposition Methods in Science and Engineering,Proceedings of 11th International Conference on Domain Decomposition Methods,Domain Decomposition Press,Bergen.. 270-281 (1999)

[Publications] K.Itakura and M.Tabata: "An error analysis of streaklines as curves"Japan Journal of Industrial and Applied Mathematics. 16. 1-23 (1999)

[Publications] A.Suzuki,M.Tabata,and S.Honda: "Numerical solution of an unsteady earth's mantle convection problem by a stabilized finite element method"Theoretical and Applied Mechanics. 48. 371-378 (1999)

[Publications] M.Tabata and D.Tagami: "A finite element analysis of a linearized problem of the Navier-Stokes equations with aurface tension"to appear in SIAM Journal on Numerical Analysis.

[Publications] T.Nakaki: "Behavior of point vortices in a plane and existence of heteroclinic orbits"Dynam.Contin.Discrete Impuls.Systems. 5. 159-169 (1999)

[Publications] H.Ikeda and T.Ikeda: "Bifurcation phenomena from standing pulse solutions of bistable reaction-diffusion systems"to appear in Journal of Dynamics and Differential Equations.

[Publications] T.Ikeda and H.Ikeda: "Hopf bifurcation of traveling pulses in some bistable reaction-diffusion systems"to appear in Methods and Applications of Analysis.

[Publications] M.Mimura,M.Nagayama,H.Ikeda and T.Ikeda: "Dynamics of travelling breathers arising in reaction-diffusion systems-ODE mod-elling approach-"to appear in Hiroshima Mathematical Journal.

[Publications] M.-H.Giga and Y.Giga: "Stability for evolving graphs by nonlocal weighted curvature"Comm.in Partial Differential Equations. 24. 109-184 (1999)

[Publications] Y.Giga,M.Ohnuma and M.-H.Sato: "On strong maximum principle and large time behaviour of generalized mean cuvature flow witn the Neumann boundary condition"J.Differential Equations. 154. 107-131 (1999)

[Publications] R.Kobayashi and Y.Giga: "Equations with singular diffusivity"J.Stat.Phys.. 95. 1187-1220 (1999)

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

[Publications] K.Nakane: "Numerical simulation to the behavior of the thin film peeling from the plate"to appear in Information. 3. -9 (2000)

[Publications] 川口正美: "高分子の界面・コロイド科学"コロナ社. 199 (1999)

[Publications] 儀我美一・儀我美保: "非線形偏微分方程式-解の漸近挙動と自己相似解"共立出版. 300 (1999)

友枝謙二大阪工業大学, 工学部, 教授 (60033916)