| Project/Area Number |
05302013
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ryukoku University |
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Principal Investigator |
IKEDA Tsutomu Ryukoku Univ., Faculty of Science and Technology, Professor, 理工学部, 教授 (50151296)
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| Co-Investigator(Kenkyū-buntansha) |
MIYOSHI Tetsuhiko Yamaguchi Univ., Faculty of Science, Professor, 理学部, 教授 (60040101)
FUJITA Hiroshi Meiji Univ., School of Science and Technology, Professor, 理工学部, 教授 (80011427)
NISHIURA Masayasu Hokkaido Univ., Research Institute for Electronic Sciences, Professor, 電子科学研究所, 教授 (00131277)
TABATA Masahisa Hiroshima Univ., Faculty of Science, Professor, 理学部, 教授 (30093272)
OKAMOTO Hisashi Kyoto Univ., Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (40143359)
森田 善久 龍谷大学, 理学部, 助教授 (10192783)
河原田 秀夫 千葉大学, 工学部, 教授 (90010793)
森 正武 東京大学, 工学部, 教授 (20010936)
西田 孝明 京都大学, 理学部, 教授 (70026110)
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| Project Period (FY) |
1993 – 1995
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| Project Status |
Completed (Fiscal Year 1995)
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| Budget Amount *help |
¥15,400,000 (Direct Cost: ¥15,400,000)
Fiscal Year 1995: ¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 1994: ¥6,100,000 (Direct Cost: ¥6,100,000)
Fiscal Year 1993: ¥5,500,000 (Direct Cost: ¥5,500,000)
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| Keywords | Nonlinear Structures / Scientific Computing / Fluid Dynamics / Free Boundaries / Fracture Phenomena / Singular Points / Bifurcation Structure / Parallel Computation / 理論的解析と科学計算 / 流体系の非線形構造 / 自由境界と界面のダイナミクス / 破壊現象の科学計算 / 微分方程式に現われる特異点 / 分岐構造の追跡 / カオスの応用 / 並列計算のアルゴリズム / 界面ダイナミクスの数理 / 破壊現象の数理 / 微分方程式の特異点 / 力学系の分岐構造 / 自由境界問題 / パターン形成の数理 / 非線形現象と形算科学 / 非線形現象を計算科学 |
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| Research Abstract |
For the purpose of solving the structure of nonlinear phenomena and their dynamics, the present research project has been dealt with the following five major fields : (1) Nonlinear structure in fluid dynamics, (2) Dynamics of free boundaries, (3) Scientific computing of fracture phenomena, (4) Singular points appearing in differential equations, (5) Tracking of bifurcation structure.
Important results are as follows. Air flow computation around an automated guided vehicle (Tabata), Finite element analysis of axisymmetric flow problems (Tabata), Bifurcation of progressive waves of finite depth (Okamoto), Vortex sheet roll-up in the background shear flow (Okamoto) and Flow problems with unilateral boundary conditions (Fujita). Pattern selections for two breathers (Ikeda and Nishiura), Global bifurcation diagram of traveling pulses (Ikeda), Existence and stability of interfacial patterns in higher dimensional spaces (Nishiura), Singular limit systems derived from reaction-diffusion systems
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(Mimura), Numerical computation of generalized curve shortening equations (Tsutsumi) and Free boundaries in porous media (Kawarada) in (2). The arbitrary line method for elasto-plastic problems (Miyoshi) and Improved 4-node quadrilateral plate bending element (Kikuchi) in (3). Blow-up problems of degenerate parabolic equations (Tsutsumi and Matano) in (4). Reaction-diffusion systems and inertial manifolds (Morita) and Navier-Stokes flows down an inclined plate (Nishida) in (5). Other related topics have been also studied, Brain dynamics (Fujii) and Application of chaos theory to social sciences (Yamaguti) for instance.
The present project is characterized by the mathematical analysis in cooperation with numerical computation. The following results have been obtained in the field of the development of numerical methods : An improved conjugate gradient method for large systems of linear equations (Mitsui), Quadrature formulas for Fourier type integrals obtained by variable transformation (Mori), Computer aided proofs for bifurcation problems in equations of fluid dynamics (Nishida) and The domain dependence of convergence rate of a domain decomposition method (Fujita) for instance. Less
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