Development of mathematical analysis for interface motions of crystals
| Project/Area Number |
15H03632
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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 |
Mathematical analysis
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| Research Institution | Shibaura Institute of Technology |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
矢崎 成俊 明治大学, 理工学部, 専任教授 (00323874)
木村 正人 金沢大学, 数物科学系, 教授 (70263358)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥16,640,000 (Direct Cost: ¥12,800,000、Indirect Cost: ¥3,840,000)
Fiscal Year 2018: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2016: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
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| Keywords | 界面ダイナミクス / 結晶界面 / 自由境界問題 / 漸近挙動 / 特異点 / 曲率 / 数値解析 / 形状解析 / 移動境界問題 / 数値計算 / 界面の挙動 / 非線形現象 / 曲率流方程式 / 構造保存数値計算法 / 非線型現象 / 解の挙動 / 界面運動の数理解析 / 数値計算法 |
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| Outline of Final Research Achievements |
We consider the evolution problems of interfaces. Here, "interface" means that
separates more than two different states, such as surface of crystal. In this research project, we mainly discuss curvature dependent motions and obtain the following results: (1) Deformation process of (negative) crystals under the area preserving property. (2) Propose the mathematical model of growing spiral-shaped steps on the crystal surface and show the unique solvability and rotational behavior. (3) Extension of the framework of crystalline motion and discuss edge splitting phenomena. (4) Properties of singularities on the interface mathematically and numerically. (5) Propose structure-preserving numerical methods for area-preserving crystalline motion.
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| Academic Significance and Societal Importance of the Research Achievements |
現実に起こる様々な現象を観測する際見ているのは、時間無限大ではなく有限時間での挙動である。よって、界面運動に限らず現象の数理的理解において時間発展途中の挙動の解析は重要である。本研究では特に解の形状変化に着目し、時間発展途中で起こりうる解図形の凸性の変化や多角形曲線の辺の数の変化に焦点を当てこれらを明らかにした。また、高精度あるいは構造保存型の数値計算法を開発することで数値シミュレーションの信頼性を向上させた。
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Report
(5 results)
Research Products
(89 results)
