| Project/Area Number |
63840001
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| Research Category |
Grant-in-Aid for Developmental Scientific Research
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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 | HIROSHIMA UNIVERSITY |
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Principal Investigator |
MIMURA Masayasu Hiroshima University, Faculty of Science, Professor, 理学部, 教授 (50068128)
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| Co-Investigator(Kenkyū-buntansha) |
KOBAYASHI Ryo Ryukoku Univ. Fac. of Sci. & Tech., Lecturer, 理工学部, 講師 (60153657)
ITOH Masayuki Tokushima Univ. Fac. of Integral Sci., Associate Prof., 総合科学部, 助教授 (70136034)
HAYASHI Takaya National Inst. of Fusion Sci., Associate Professor, 助教授 (60156445)
NISHIDA Takaaki Kyoto Univ. Fac. of Sci., Professor, 理学部, 教授 (70026110)
FUJIKOSHI Yasunori Hiroshima Univ. Fac. of Sci., Professor, 理学部, 教授 (40033849)
俣野 博 東京大学, 理学部, 助教授 (40126165)
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| Project Period (FY) |
1988 – 1989
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| Project Status |
Completed (Fiscal Year 1989)
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| Budget Amount *help |
¥9,600,000 (Direct Cost: ¥9,600,000)
Fiscal Year 1989: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1988: ¥8,000,000 (Direct Cost: ¥8,000,000)
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| Keywords | Numerical simulations of reaction-diffusion equations / Visualization of numerical simulations / Numerical study of Interfacial patterns / 数値シミュレーションの動画化処理 / 界面パターンの数値計算 |
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| Research Abstract |
In 1988, we developed visualization system of numerical simulations which connected with mini-super computer under local network systems in the department of Mathematics at Hiroshima University. By using this system, our first study is to visualize spatio-temporal patterns dynamics in combustions, by numerically solving two mathematical models of reaction-diffusion type. The first example is to demonstrate the propagation of combustion waves in one dimension. We can observe that there occurs a bifurcation phenomenon in the wave velocity. That is, when we change the difference of the temperatures at the both side X = <plus-minus>*, the wave which propagates with constant velocity becomes unstable through Hopf-bifurcation and there appears a new wave which propagates with periodic velocity. This phenomenon can be also observed in real experiments. Another example is the pattern formation of cellular flame in a 2 dimensional annular domain. We find that radially symmetric flame patterns become unstable and then there appear cellular flame patterns through static bifurcatio
In 1989, we are interested in visualizing the phenomena of phase separation and coarsening process in binary alloy from a theoretical view point. We numerically solved several reaction-diffusion equation models which has been proposed so far to understand these phenomena. The results show so complex and beautiful patterns which has not been expected until now.
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