| Project/Area Number |
16340029
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka Institute of Technology |
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Principal Investigator |
TOMOEDA Kenji Osaka Institute of Technology, Faculty of Engineering, Professor (60033916)
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| Co-Investigator(Kenkyū-buntansha) |
MIMURA Masayasu Meiji University, Faculty of Science and Technology, Professor (50068128)
山口 智彦 産業技術総合研究所, ナノテクノロジー研究部門, グループ長 (70358232)
KAWAGUCHI Masami Mie University, Graduate School of Engineering, Professor (30093123)
TABATA Masahisa Kyushu University, Graduate School of Mathematics, Professor (30093272)
GIGA Yoshikazu Tokyo University, Graduate School of Engineering, Professor (70144110)
NAKAKI Tatsuyuki Hiroshima University, Graduate School of Science, Professor (50172284)
今井 仁司 徳島大学, 大学院・ソシオテクノサイエンス研究部, 教授 (80203298)
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| Project Period (FY) |
2004 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥16,030,000 (Direct Cost: ¥15,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2007: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2006: ¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2005: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2004: ¥5,300,000 (Direct Cost: ¥5,300,000)
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| Keywords | free boundary / TCD method / singular limit method / multi-fluid flows / crystal growth / viscous fingering / multi-scale FEM / support splitting phenomena / Hele-Shawセル / リーゼガング現象 / ヘリカル燃焼波 / ギブス・トムソン効果 / 燃焼パルス解 / 二流体問題 / 渦の相互作用 / カーボンナノチューブ / レーリー・ベナール方程式 / 領域分割法 / 等高面法 / 渦の緩和振動 |
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| Research Abstract |
We were concerned with the following numerical methods to the phenomena appearing in the repre-sentative dynamical interfaces :
i) Pattern dynamics in the reaction-diffusion system,
ii) Viscous fingering phenomena in Hele-Shaw Cell,
iii) Dynamical behavior of the region occupied by the water in the process of evaporation.
We obtained several results :
1) The TCD (Threshold Competition Dynamics) method is developed for the numerical computation in reaction-diffusion system, and enables us to realize the dynamical behavior of free boundary in R^n (n=1, 2, 3.). The idea of this method is based on the theory of "Singular limit method".
2) The mathematical model for the crystal growth is considered in the, form of the reaction-diffusion equation with the effect of a convection, and gives us interesting mathematical results.
3) In viscous fingering phenomena, the buoyancy-driven path instabilities of bubble rising in Hele-Shaw Cell are examined. As an interesting phenomenon there appears a wake which is similar to a comet. However, such a wake is not realized in numerical method yet.
4) Multi-scale FEM based on crystallographic homogenization method is developed to predict the dynamics of interfaces in the formability of sheet metal.
5) The repeated support splitting and connecting property in the process of evaporation is investigated, where the the support means the region occupied by the water. The numerical methods for this process are established and the shape of the initial distribution for which such a property appear is explicitly obtained.
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