2021 Fiscal Year Final Research Report
Mathematical analysis about misorientations and triple junctions effects on evolution of grain boundaries
| Project/Area Number |
18K13446
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 12020:Mathematical analysis-related
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| Research Institution | Nihon University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Keywords | 結晶成長 / 曲率流方程式 / 幾何学的変分問題 / Fokker-Planck方程式 / 結晶方位差 / 三重点 |
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| Outline of Final Research Achievements |
I studied mathematical modeling related to grain boundary motion and its mathematical analysis. In particular, to understand the interaction between misorientations and triple junctions, I derived a new mathematical model of grain boundary motion. And I studied its well-posedness and long-time asymptotic behavior. Next, I considered nonlinear Fokker-Planck equations involving spatial inhomogeneous free energy to treat critical events. As a result, new mathematical models containing the interaction between the misorientations and the triple junctions and mathematical analysis, such as well-posedness and long-time asymptotic behavior for the models, were obtained.
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| Free Research Field |
非線形解析学
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| Academic Significance and Societal Importance of the Research Achievements |
結晶粒界の運動における臨界現象の理解は特異性の解析の困難さにより，未解明な点が多い．本研究では，この困難さを克服するために，臨界現象による相互作用をホワイトノイズによって表した．このモデリングは，結晶粒界における臨界現象の解明のみならず，様々な特異性の解析に新たな手法を与えるものと考えられる．また，この解析によって得られた新しい公式は結晶粒界の運動の理解を助けるとともに，結晶粒界エネルギーの性質を導くことの助けになると考えられる．
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