1993 年度実績報告書

非線形大型計算とその可視化

研究課題

研究課題/領域番号	04554001
研究機関	日本大学
研究代表者	中村正彰日本大学, 理工学部, 助教授 (00017419)
研究分担者	森本浩子明治大学, 理工学部, 教授 (50061974) 名取亮筑波大学, 電子情報系, 教授 (70013745) 渡辺二郎電気通信大学, 電気通信学部, 教授 (90011535) 河原田秀夫千葉大学, 工学部, 教授 (90010793) 藤田宏明治大学, 理工学部, 教授 (80011427)
キーワード	Navier-Stokes eq / 相分離 / 平均曲率 / capillary-gravity wave / Stefan Problem / fuzzy / Benard / free boundary
研究概要	本年度の計画にもとずいてつぎのように研究を実行した. 1.粘性流体に境界での摩擦を考慮したモデルを考案し解析(藤田,河原田).合金の相分離のモデルを解析(中村).磁場のモデルを解析した(河原田). 2.Navier-Stokes方程式の可解性の境界でのflux conditionの関係を示す例をみつけ解析した(森本).表面張力波についての解析(岡本,東海林).流体の方程式における分岐の解析(岡本,東海林,桂田).これらの数値シミュレーションの実行. 3.自由境界をもつ熱対流の解析(花田,今井,名取,河原田).磁場を考慮した熱対流の解析(今井,中村).同時に数値シミュレーションも実行した. 4.界面の解析に関連する平均曲率流の解析と数値シミュレーションの実行(陳). 5.ポテンシャル問題の解決に寄与する代用電荷法を解析した(岡本,桂田). 6.CTスキャンの原理であるラドン変換について解析と数値シミュレーションの実行(渡辺,花田). 7.曲線データの処理について解析した(花田,今井). 8.徳島大学で10大学,5企業からの参加者によって8月10日〜13日に研究集会を開催した(今井,中村). 9.クズネツォフ教授(ロシア科学アカデミー),余偉明助手(電気通信大学),奥田由紀夫(大林組),神保秀一(北大)の諸氏と分担者を講師とする研究会および研究連絡打ち合せを日本大学を会場として開き非線形,可視化の問題について研究討議した. 10.日大,北海道東海大,徳島大にパソコンなどを導入した.

研究成果

(36件)

すべてその他

すべて文献書誌 (36件)

[文献書誌] 森本浩子: "Staionary Navier-Stokes equations under the boundary condition with non-vanishing outflow," 京大数理研共同研究集会「超関数と微分方程式」.
[文献書誌] 岡本久: "表面張力波の分類について," 京大数理研共同研究集会「流体中における非線形波動」.
[文献書誌] 東海林まゆみ: "Numerical unfoldings of the bifurcations in Capillary Gravity waves" 日本数学会〓93春期総合分科会.
[文献書誌] 東海林まゆみ: "Secondary and tertiary biturcations of capillary-gravity waves" 阿波ワークショップ〓93,徳島大学.
[文献書誌] 岡本久: "Navier-stokes 方程式に対するKolmogorovnの問題," 日本数学会春期年会応用数学分科会特別講演,. (1993)
[文献書誌] 周偉東-今井仁司-名取亮: "自然対流に対する自由表面の影響について," 日本数学会応用数学分科会講演アブストラクト. 179-180 (1993)
[文献書誌] M. Morimoto,: "Asymptotic behavior of weak solutions of the convection equation," Springer,Lecture Note in Math.1540. 269-276 (1993)
[文献書誌] N. Nakamura,: "Regularity and Analyticity of the Solution of the Magnetic B$' enard Problem," Advances in Mathematical Sciences and Applications,. 2. 117-137 (1993)
[文献書誌] H. Imai-M. Nakamura: "On the bifurcation diagram of the simplified magnetic B$' enard problem," Unstable and Turbulent Motion of Fluid,. 71-78 (1993)
[文献書誌] N. Ishimura-M.Nakamura: "Esitmate on the Hausdorff dimension of the global attractor for the simplified magnetic B$' enard system," Nonlinear mathematical problems in industry II, Mathematical Sciences and Applications. 2. 421-430 (1993)
[文献書誌] H. Imai-M. Nakamura: "Numerical Analysis of the Simplified Magnetic B$' enard Problem," Nonlinear mathematical problems in industry II, Mathematical Sciences and Applications.2. 405-419 (1993)
[文献書誌] 今井仁司-中村正彰: "磁気ベナール対流の簡約化モデルとそのシミュレーション," 日本シミュレーション学会学会誌. 12. 99-106 (1993)
[文献書誌] H. Okamoto-M.Shoji: "Bifurcation diagrams in Kolmogorov's problems of viscous imcompressible fluid on 2-D Tori," Japan J. Indus. Appl. Math.10. 191-218 (1993)
[文献書誌] H. Okamoto-M. Shoji: "Numerical unfoldings of capillary gravity waves," Proceedings of the first China-Japan Seminar on Numerical Mathematics,. 119-132
[文献書誌] H. Okamoto-M. Shoji-M. Katsurada,: "A computer-assisted analysis of the two dimensional Navier-Stokes equations," Springer,Lecture Note in Math.1540. 309-318 (1993)
[文献書誌] H. Okamoto-M.Shoji,: "Secondary and teritary bifurcations of capillary gravity waves," 阿波ワークショップ〓93 報告集.
[文献書誌] S. Kaizu-A. Nishiyama-J. Watanabe,: "Convergence of solutions of nonlinear eigenvlue problems," Advances in Mathematical Scoences and Apllications,. 3. 353-366 (1993)
[文献書誌] 渡辺二郎,: "変分問題における汎関数列の収束について," 阿波ワークショップ〓93 報告集.
[文献書誌] H. Okamoto,: "A uniqueness theorem for the unbounded classical solution of nonstaionary Navier-Stokes equations in R," to appear in J.Math.Anal.Appl.
[文献書誌] H. Okamoto,: "A variational problems arising in the two dimensional Navier-Stokes equations with vanishing viscosity," to appear in Appl. Math Lett.
[文献書誌] H. Okamoto,: "Remarks on the bifurcations of progressive waves of finite depth," to appear in Publ. R.I.M.S.
[文献書誌] 今井仁司: "不適切な問題に対する適用可能な数値解法の検討," 数理解析研究所講究録,京都大学,. 836. 102-112 (1993)
[文献書誌] 中村正彰,: "江口-沖-松村の方程式とそのWell-Posednessについて," 応用数学合同研究集会報告集(1993),. 211-214 (1993)
[文献書誌] 室屋泰三,花田孝郎,渡辺二郎: "ラドン逆変換の近似の収束性について" 応用数学合同研究集会報告集,. 187-190 (1993)
[文献書誌] 檜山澄子-花田孝郎-今井仁司-: "実用的な曲線データ点の間引き法," 日本応用数理学会論文誌,. 3. 85-104 (1993)
[文献書誌] H. Imai-Z. Weidong-H. Kawarada-M. Natori: "NUMERICAL COMPUTATIONS OF FREE BOUNDARY PROBLEMS USING THE SPECTRAL METHOD," Nonlinear Mathematical Problems in Industry I,. 39-47 (1993)
[文献書誌] Z.Weidong-H. Imai-M.Natori: "NUMERICAL STUDY OF CONVECTION WITH A FREE SURFACE BY A SPECTRAL METHOD," in Nonlinear Mathematical Problems in Industry I,. 49-60 (1993)
[文献書誌] N. Ishimura-M. Nakamura: "On the simplified magnetic B$' enard system: Dimension estimate of the attractor," Advances in Mathematical Sciences and Application. 3. (1994)
[文献書誌] H. Imai-H. Kawarada-M.Natori: "An Application of the Fuzzy Theory for an I11-Posed Problem," in Inverse Problems in Engineering Mechanics. 31-38 (1993)
[文献書誌] T. Hanad-H. Imai-H. Kawarada-M.Natori: "NUMERICAL COMPUTATION FOR SOLIDEFICATION PROBLEMS WITH MOVING SURFACE," in Nonlinear Mathematical Problems in Industry I. 17-38 (1993)
[文献書誌] 岡本久: "代用電荷法の電荷点の配置について," 日本応用数理学会年会,.
[文献書誌] 今井仁司-篠原能材: "時間積分におけるスペクトル法の適用可能性について," 日本数学会応用数学分科会講演アブストラクト,. 104-105 (1993)
[文献書誌] 今井仁司-中村正彰: "簡約化磁気ベナール問題の磁場依存性," 日本応用数理学会年会講演予稿集. 71-72 (1993)
[文献書誌] 袴田-石村直之: "Estimating the dimension of the attractor for the complex Lorenz equations," 日本数学会応用数学分科会講演アブストラクト,. 149-152 (1993)
[文献書誌] H. Imai-H. Kawarada-M.Natori: "Adaptive Fuzzy Control for an I11-Posed Problem," in Inverse Problems(S.Kubo,Ed.),Atlanta Technology Publications,. 51-60 (1993)
[文献書誌] 陳薀剛-儀我美一: "動く曲面を追いかけて, 界面ダイナミクスの数理," 日本評論社,

1993 年度 実績報告書

非線形大型計算とその可視化

研究代表者

中村 正彰 日本大学, 理工学部, 助教授 (00017419)

研究成果

[文献書誌] 森本浩子: "Staionary Navier-Stokes equations under the boundary condition with non-vanishing outflow," 京大数理研共同研究集会「超関数と微分方程式」.

[文献書誌] 岡本久: "表面張力波の分類について," 京大数理研共同研究集会「流体中における非線形波動」.

[文献書誌] 東海林まゆみ: "Numerical unfoldings of the bifurcations in Capillary Gravity waves" 日本数学会〓93春期総合分科会.

[文献書誌] 東海林まゆみ: "Secondary and tertiary biturcations of capillary-gravity waves" 阿波ワークショップ〓93,徳島大学.

[文献書誌] 岡本久: "Navier-stokes 方程式に対するKolmogorovnの問題," 日本数学会春期年会応用数学分科会特別講演,. (1993)

[文献書誌] 周偉東-今井仁司-名取亮: "自然対流に対する自由表面の影響について," 日本数学会応用数学分科会講演アブストラクト. 179-180 (1993)

[文献書誌] M. Morimoto,: "Asymptotic behavior of weak solutions of the convection equation," Springer,Lecture Note in Math.1540. 269-276 (1993)

[文献書誌] N. Nakamura,: "Regularity and Analyticity of the Solution of the Magnetic B$' enard Problem," Advances in Mathematical Sciences and Applications,. 2. 117-137 (1993)

[文献書誌] H. Imai-M. Nakamura: "On the bifurcation diagram of the simplified magnetic B$' enard problem," Unstable and Turbulent Motion of Fluid,. 71-78 (1993)

[文献書誌] N. Ishimura-M.Nakamura: "Esitmate on the Hausdorff dimension of the global attractor for the simplified magnetic B$' enard system," Nonlinear mathematical problems in industry II, Mathematical Sciences and Applications. 2. 421-430 (1993)

[文献書誌] H. Imai-M. Nakamura: "Numerical Analysis of the Simplified Magnetic B$' enard Problem," Nonlinear mathematical problems in industry II, Mathematical Sciences and Applications.2. 405-419 (1993)

[文献書誌] 今井仁司-中村正彰: "磁気ベナール対流の簡約化モデルとそのシミュレーション," 日本シミュレーション学会学会誌. 12. 99-106 (1993)

[文献書誌] H. Okamoto-M.Shoji: "Bifurcation diagrams in Kolmogorov's problems of viscous imcompressible fluid on 2-D Tori," Japan J. Indus. Appl. Math.10. 191-218 (1993)

[文献書誌] H. Okamoto-M. Shoji: "Numerical unfoldings of capillary gravity waves," Proceedings of the first China-Japan Seminar on Numerical Mathematics,. 119-132

[文献書誌] H. Okamoto-M. Shoji-M. Katsurada,: "A computer-assisted analysis of the two dimensional Navier-Stokes equations," Springer,Lecture Note in Math.1540. 309-318 (1993)

[文献書誌] H. Okamoto-M.Shoji,: "Secondary and teritary bifurcations of capillary gravity waves," 阿波ワークショップ〓93 報告集.

[文献書誌] S. Kaizu-A. Nishiyama-J. Watanabe,: "Convergence of solutions of nonlinear eigenvlue problems," Advances in Mathematical Scoences and Apllications,. 3. 353-366 (1993)

[文献書誌] 渡辺二郎,: "変分問題における汎関数列の収束について," 阿波ワークショップ〓93 報告集.

[文献書誌] H. Okamoto,: "A uniqueness theorem for the unbounded classical solution of nonstaionary Navier-Stokes equations in R," to appear in J.Math.Anal.Appl.

[文献書誌] H. Okamoto,: "A variational problems arising in the two dimensional Navier-Stokes equations with vanishing viscosity," to appear in Appl. Math Lett.

[文献書誌] H. Okamoto,: "Remarks on the bifurcations of progressive waves of finite depth," to appear in Publ. R.I.M.S.

[文献書誌] 今井仁司: "不適切な問題に対する適用可能な数値解法の検討," 数理解析研究所講究録,京都大学,. 836. 102-112 (1993)

[文献書誌] 中村正彰,: "江口-沖-松村の方程式とそのWell-Posednessについて," 応用数学合同研究集会報告集(1993),. 211-214 (1993)

[文献書誌] 室屋泰三,花田孝郎,渡辺二郎: "ラドン逆変換の近似の収束性について" 応用数学合同研究集会報告集,. 187-190 (1993)

[文献書誌] 檜山澄子-花田孝郎-今井仁司-: "実用的な曲線データ点の間引き法," 日本応用数理学会論文誌,. 3. 85-104 (1993)

[文献書誌] H. Imai-Z. Weidong-H. Kawarada-M. Natori: "NUMERICAL COMPUTATIONS OF FREE BOUNDARY PROBLEMS USING THE SPECTRAL METHOD," Nonlinear Mathematical Problems in Industry I,. 39-47 (1993)

[文献書誌] Z.Weidong-H. Imai-M.Natori: "NUMERICAL STUDY OF CONVECTION WITH A FREE SURFACE BY A SPECTRAL METHOD," in Nonlinear Mathematical Problems in Industry I,. 49-60 (1993)

[文献書誌] N. Ishimura-M. Nakamura: "On the simplified magnetic B$' enard system: Dimension estimate of the attractor," Advances in Mathematical Sciences and Application. 3. (1994)

[文献書誌] H. Imai-H. Kawarada-M.Natori: "An Application of the Fuzzy Theory for an I11-Posed Problem," in Inverse Problems in Engineering Mechanics. 31-38 (1993)

[文献書誌] T. Hanad-H. Imai-H. Kawarada-M.Natori: "NUMERICAL COMPUTATION FOR SOLIDEFICATION PROBLEMS WITH MOVING SURFACE," in Nonlinear Mathematical Problems in Industry I. 17-38 (1993)

[文献書誌] 岡本久: "代用電荷法の電荷点の配置について," 日本応用数理学会年会,.

[文献書誌] 今井仁司-篠原能材: "時間積分におけるスペクトル法の適用可能性について," 日本数学会応用数学分科会講演アブストラクト,. 104-105 (1993)

[文献書誌] 今井仁司-中村正彰: "簡約化磁気ベナール問題の磁場依存性," 日本応用数理学会年会講演予稿集. 71-72 (1993)

[文献書誌] 袴田-石村直之: "Estimating the dimension of the attractor for the complex Lorenz equations," 日本数学会応用数学分科会講演アブストラクト,. 149-152 (1993)

[文献書誌] H. Imai-H. Kawarada-M.Natori: "Adaptive Fuzzy Control for an I11-Posed Problem," in Inverse Problems(S.Kubo,Ed.),Atlanta Technology Publications,. 51-60 (1993)

[文献書誌] 陳 薀剛-儀我美一: "動く曲面を追いかけて, 界面ダイナミクスの数理," 日本評論社,

1993 年度実績報告書

中村正彰日本大学, 理工学部, 助教授 (00017419)

[文献書誌] 陳薀剛-儀我美一: "動く曲面を追いかけて, 界面ダイナミクスの数理," 日本評論社,