| Project/Area Number |
13640095
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Hokkaido University |
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Principal Investigator |
KOBAYASHI Ryo Hokkaido Univ., Research Institute for Electronic Science, Asso.Prof., 電子科学研究所, 助教授 (60153657)
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| Co-Investigator(Kenkyū-buntansha) |
GIGA Yoshikazu Hokkaido Univ., Faculty of Science, Prof., 大学院・理学研究科, 教授 (70144110)
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| Project Period (FY) |
2001 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2003: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2002: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2001: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | phase field mode / gain boundary / polycrystal / recrystallization / singular diffusivity / ascorbic acid / oscillatory crystallization / フェーズフィールドモデル / 振動成長 / 特異極限 |
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| Research Abstract |
(1)Phase field model of polycrystals
We, at first, presented new phase field models, η-θ model and φ-η-θ model, which can handle the polycrystalline structure by introducing an angle variable to the conventional phase field model. Then we constructed φ-θ model by unifying these two models, which enables us to describe the following sequaence of processes : 1.Crystallization after multi nucreation, 2 Formation of grain boundaries, 3.Grain boundary migration and rotation of grains.
The feature of our model is that both of the migration of grain boundaries and the rotation of grains are simultaneously presented, and our model is the only model which can do it. Also, we developed the numenal code of this model and performed the simulations which are corres-ponding various situations.
(2)Singular diffusivity theory
The equation of an angle variable in the above models, which is the most characteristic part of our models is justified mathematically by the theory of singular diffusivity developed by Giga and Kobayashi. We extended the equation of singular difftisivity to the functions which takes the value in the circle. In addition, the numerical scheme for this equation was presented.
(3)Oscillatory crystallization
Various types of patterns are formed when the methanol solution of ascorbic acid crystallize by evaporation according to the conditions such as humidity. Above all, target patterns was intensively studied, which is caused by oscillatory crystallization. We clarified that the interaction between the void whithin the needle crystals and the fluid is responsible for the oscillatory crystallization.
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