2017 Fiscal Year Final Research Report
Mathematical analysis of contact angle dynamics
| 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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| Keywords | 界面ネットワーク運動 / 数値解析 / レベルセット法 |
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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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| Free Research Field |
応用数学
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