| Project/Area Number |
26870224
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
Mathematical analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 界面ネットワーク運動 / 数値解析 / レベルセット法 / 界面運動 / 双曲型問題 / 位相変化 / 双曲型平均曲率流 / 多相問題 / ヒステレシスのモデリング / マルチスケール有限要素法 / 連成モデル / 非対称な接合点 / BMOアルゴリズム / 符号付距離関数 / 自由境界問題 / ペナルティ法 |
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| Outline of Final Research Achievements |
With the purpose of mathematical understanding of evolutionary free boundary problems, represented by the wetting phenomenon, and development of a wide range of applications following this theoretical understanding, in this research I established the basis of analysis methods for moving interfacial networks. In particular, I proposed approximation methods forming the ground for numerical solution of interfacial network motion due to energy gradient descent and oscillatory energy-preserving motion, provided their mathematical justification and, based on these, developed algorithms for simulations of network evolutions including singularities and constraints, which are topics recently receiving attention in the research community. These results facilitate higher-level simulations in tissue morphogenesis research, development of new materials, etc.
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