1997 Fiscal Year Annual Research Report

非線形複雑系の3次元数値計算

Research Project

Project/Area Number	07555343
Research Institution	Ryukoku University
Principal Investigator	池田勉龍谷大学, 理工学部, 教授 (50151296)
Co-Investigator(Kenkyū-buntansha)	三村昌泰東京大学, 大学院・数理科学研究科, 教授 (50068128) 友枝謙二大阪工業大学, 工学部, 教授 (60033916) 岡本久京都大学, 数理解析研究所, 教授 (40143359) 今井仁司徳島大学, 工学部共通講座, 教授 (80203298) 高橋大輔龍谷大学, 理工学部, 助教授 (50188025)
Keywords	反応拡散系の並列計算 / バクテリアコロニー / 水の波 / 渦層の巻き上げ / 渦構造の同定 / 管状渦と剪断流 / SOR法の収束率 / 浸透領域
Research Abstract	研究代表者池田は,反応拡散方程式系の並列計算スキームの有限要素法によるコーディングを完成した.これは領域分割法と前処理付き共役勾配法に基づくものである.領域を分割することにより生成される内部界面では整合しない三角形分割も許されるモルタル法のような手法もあるが,我々は分かり易さを前面に押し出す方針を採用した.その結果,三角形分割は内部界面において整合条件を満たさなければならないが,通常の有限要素法と同一の数値計算結果が得られるという特徴を備えている.大腸菌のある種の変異株が,複雑な過程を経て,形成するストライプ・スポット状のパターンの並列計算を行い,並列スキームがほぼ予定通りに機能することを確認した.研究分担者三村は,反応拡散系と界面ダイナミクスの数理解析を分担し,発熱反応拡散系に現れる時空間パターンの特異極限解析と計算機シミュレーション,競争拡散系に現れる棲み分けパターンを捉えるための界面ダイナミクス法の導出,活性抑制因子反応拡散系に現れるパルスダイナミクスの数理解析,バクテリアコロニーの時空間パターンのモデル化とその計算機シミュレーションを行った. 渦と乱流場に関しては,岡本が水の波の数値計算および渦層の巻き上げの数値計算において重要な貢献を行い,木田が渦構造の同定と抽出,管状渦と剪断流の3次元相互作用の2点を中心に詳細な研究を行った.高橋はすべての独立変数と従属変数を離散化する超離散化法の理論を交通流モデルおよびソリトン系に応用することに成功した.今井は自由境界問題の高精度数値解法の開発と応用,ポアソン方程式の差分離散化法およびSOR法の収束率などの研究を,友枝は多孔質媒体を流れる流体によって形成される浸透領域のダイナミクスなどの研究を推進した.

Research Products

(28 results)

All Other

All Publications (28 results)

[Publications] 丸尾彰: "ある非線形放物型方程式の整合差分近似とその画像修復への応用" 日本応用数理学会論文誌. 7・4. 389-402 (1997)
[Publications] H.Ikeda: "Global structure of travelling pulse solutions in some reaction-diffusion systems" to appear in The Proceedings of International Conference on Asymptotics in Nonliner Diffusion Systems towards the understanding of singularitias in dissipative structurs. (1997)
[Publications] T.Ikeda: "Parallel computation of interfacial dynamics" Gakuto International Series Mathematical Sciences and Applications. 11. (1998)
[Publications] T.Ikeda: "Parallel computation of reaction-diffusion phenemena" to appear in The Proceedings of the Third China-Japan Joint Seminar on Numerical Mathematics.
[Publications] 森下博: "代用電荷法によるポアソン方程式の数値計算" 情報処理学会論文誌. 38. 1483-1491 (1997)
[Publications] Y.Kabeya: "Number of zeros of solutions to singular initial value problems" to appear in Tohoku J.Math.
[Publications] D.Takahashi: "Box and ball system with a carrier and ultradiscrete modified KdV equation" J.Phys.A. 30. 733-739 (1977)
[Publications] Hitoshi IMAI: "Conputations to Free Boundary Problems" 統計数理研究所共同研究リポート. 105. 129-142 (1997)
[Publications] H.Okamoto: "Interfacial progressive water waves:a singularity-theoretic view" Tohoku Math.J. 49. 33-57 (1997)
[Publications] H.Fujita: "Stability analysis of Navier-Stokes flows in annvli" Math.Meth.Appl.Sci. 20. 959-978 (1997)
[Publications] T.Sakajo: "An application of Draghicescu's fast summation method to vortex sheet motion." to appear in J.Phys.Soc.Japan. 67. (1998)
[Publications] H.Okamoto: "Exact solutions of the Navier-Stokes equations via Leray's scheme." Japan J.Indus.Appl.Math. 14. 169-197 (1997)
[Publications] 河原田秀夫: "Variational Inequalities for Navier-Stokes Flows Coupled with Potential Flow through Porous Media:Theory and Numerical Simulation" The proceedings of DDM-8(Beijin). 403-410 (1997)
[Publications] H.Miura: "Identification of tubular vortices in coniplex flows" J.Phys Soc.Japan. 66. 1331-1334 (1997)
[Publications] Kawahara,G: "1998 Wrap,Tilt and Stretch of Vorticity Lines around a Strong Thin Straight Vortex Tube in a Simple Shear Flow" J.Fiuid Mech.
[Publications] Kenji Tomoeda: "The possibility of a support splitting caused by the absorption in some nonlinear diffusion equations" New trends of inverse and ill-posed problems,VSP.
[Publications] T.Nakaki: "On the heteroclinic orbit of the point vortex problem" to appear in the Proceedings of the Second World Congress of Nonlinear Analysts.
[Publications] Naoyuki Ishimura: "Uniqueness for unbounded classical solutions of the MHD equations" Methematical Methods in the Applied Science. 20. 617-623 (1997)
[Publications] M.Mimura: "Singular perturbation problems to a combustion equation in very long cylindrical domains" Studies in Advanced Mathematics. 3. 75-84 (1997)
[Publications] M.Mimura: "Sakamoto:Hopf・bifurcation in a chemical reaction-diffusion system" to appear in Applied Mathematics Letter.
[Publications] T.Ohta: "Collision of propagating pules in a reaction-diffusion system" J.Phys.Soc Japan. 66. 1551-1558 (1997)
[Publications] S.Kawaguchi: "Collision of travelling waves in a reaction-diffusion system with global coupling" to appear in SIAMJ.Appl.Math.
[Publications] M.Mimura: "Non-annihilation dynamics in a sexothermic reaction-diffusion system with mono-stable excitablity" to appear in Journal of CHAOS.
[Publications] Y.Kan-on: "Singular perturbation approach to a 3-component reaction-diffusion system arising in population dynamics" to appear in SIAMJ.Math.Anal.
[Publications] E.N.Dancer: "Spatial segregation limit of a competition-diffusion system" Lecture Notes in Math.Institute,Vniv Leiden.
[Publications] 高橋大輔: "数値計算" 岩波書店, 194 (1996)
[Publications] 藤井宏: "非線型力学" 岩波書店岩波講座「応用数学」, (1995)
[Publications] 岡本久: "関数解析" 岩波書店岩波講座「現代数学の基礎」, (1997)

1997 Fiscal Year Annual Research Report

非線形複雑系の3次元数値計算

Principal Investigator

池田 勉 龍谷大学, 理工学部, 教授 (50151296)

Research Products

[Publications] 丸尾 彰: "ある非線形放物型方程式の整合差分近似とその画像修復への応用" 日本応用数理学会論文誌. 7・4. 389-402 (1997)

[Publications] H.Ikeda: "Global structure of travelling pulse solutions in some reaction-diffusion systems" to appear in The Proceedings of International Conference on Asymptotics in Nonliner Diffusion Systems towards the understanding of singularitias in dissipative structurs. (1997)

[Publications] T.Ikeda: "Parallel computation of interfacial dynamics" Gakuto International Series Mathematical Sciences and Applications. 11. (1998)

[Publications] T.Ikeda: "Parallel computation of reaction-diffusion phenemena" to appear in The Proceedings of the Third China-Japan Joint Seminar on Numerical Mathematics.

[Publications] 森下 博: "代用電荷法によるポアソン方程式の数値計算" 情報処理学会論文誌. 38. 1483-1491 (1997)

[Publications] Y.Kabeya: "Number of zeros of solutions to singular initial value problems" to appear in Tohoku J.Math.

[Publications] D.Takahashi: "Box and ball system with a carrier and ultradiscrete modified KdV equation" J.Phys.A. 30. 733-739 (1977)

[Publications] Hitoshi IMAI: "Conputations to Free Boundary Problems" 統計数理研究所共同研究リポート. 105. 129-142 (1997)

[Publications] H.Okamoto: "Interfacial progressive water waves:a singularity-theoretic view" Tohoku Math.J. 49. 33-57 (1997)

[Publications] H.Fujita: "Stability analysis of Navier-Stokes flows in annvli" Math.Meth.Appl.Sci. 20. 959-978 (1997)

[Publications] T.Sakajo: "An application of Draghicescu's fast summation method to vortex sheet motion." to appear in J.Phys.Soc.Japan. 67. (1998)

[Publications] H.Okamoto: "Exact solutions of the Navier-Stokes equations via Leray's scheme." Japan J.Indus.Appl.Math. 14. 169-197 (1997)

[Publications] 河原田 秀夫: "Variational Inequalities for Navier-Stokes Flows Coupled with Potential Flow through Porous Media:Theory and Numerical Simulation" The proceedings of DDM-8(Beijin). 403-410 (1997)

[Publications] H.Miura: "Identification of tubular vortices in coniplex flows" J.Phys Soc.Japan. 66. 1331-1334 (1997)

[Publications] Kawahara,G: "1998 Wrap,Tilt and Stretch of Vorticity Lines around a Strong Thin Straight Vortex Tube in a Simple Shear Flow" J.Fiuid Mech.

[Publications] Kenji Tomoeda: "The possibility of a support splitting caused by the absorption in some nonlinear diffusion equations" New trends of inverse and ill-posed problems,VSP.

[Publications] T.Nakaki: "On the heteroclinic orbit of the point vortex problem" to appear in the Proceedings of the Second World Congress of Nonlinear Analysts.

[Publications] Naoyuki Ishimura: "Uniqueness for unbounded classical solutions of the MHD equations" Methematical Methods in the Applied Science. 20. 617-623 (1997)

[Publications] M.Mimura: "Singular perturbation problems to a combustion equation in very long cylindrical domains" Studies in Advanced Mathematics. 3. 75-84 (1997)

[Publications] M.Mimura: "Sakamoto:Hopf・bifurcation in a chemical reaction-diffusion system" to appear in Applied Mathematics Letter.

[Publications] T.Ohta: "Collision of propagating pules in a reaction-diffusion system" J.Phys.Soc Japan. 66. 1551-1558 (1997)

[Publications] S.Kawaguchi: "Collision of travelling waves in a reaction-diffusion system with global coupling" to appear in SIAMJ.Appl.Math.

[Publications] M.Mimura: "Non-annihilation dynamics in a sexothermic reaction-diffusion system with mono-stable excitablity" to appear in Journal of CHAOS.

[Publications] Y.Kan-on: "Singular perturbation approach to a 3-component reaction-diffusion system arising in population dynamics" to appear in SIAMJ.Math.Anal.

[Publications] E.N.Dancer: "Spatial segregation limit of a competition-diffusion system" Lecture Notes in Math.Institute,Vniv Leiden.

[Publications] 高橋 大輔: "数値計算" 岩波書店, 194 (1996)

[Publications] 藤井 宏: "非線型力学" 岩波書店 岩波講座「応用数学」, (1995)

[Publications] 岡本 久: "関数解析" 岩波書店 岩波講座「現代数学の基礎」, (1997)

池田勉龍谷大学, 理工学部, 教授 (50151296)

[Publications] 丸尾彰: "ある非線形放物型方程式の整合差分近似とその画像修復への応用" 日本応用数理学会論文誌. 7・4. 389-402 (1997)

[Publications] 森下博: "代用電荷法によるポアソン方程式の数値計算" 情報処理学会論文誌. 38. 1483-1491 (1997)

[Publications] 河原田秀夫: "Variational Inequalities for Navier-Stokes Flows Coupled with Potential Flow through Porous Media:Theory and Numerical Simulation" The proceedings of DDM-8(Beijin). 403-410 (1997)

[Publications] 高橋大輔: "数値計算" 岩波書店, 194 (1996)

[Publications] 藤井宏: "非線型力学" 岩波書店岩波講座「応用数学」, (1995)

[Publications] 岡本久: "関数解析" 岩波書店岩波講座「現代数学の基礎」, (1997)