| Project/Area Number |
18K13440
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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 | Kanazawa University |
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Principal Investigator |
Pozar Norbert 金沢大学, 数物科学系, 准教授 (00646523)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | generized solutions / crystal growth / mean curvature / annihilation / comparison principle / crystalline curvature / viscosity solutions / many particle limit / free boundary / interacting particles / volume constraint / facet breaking / Hele-Shaw problem / Stefan problem / self-similar solutions |
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| Outline of Final Research Achievements |
Interfaces that separate different moving regions are a feature of many important problems in physics, material science and biology. The mathematical understanding of equations arising in such problems is crucial for developing accurate numerical methods to find a solution on a computer. The interfaces might collide or split, and a proper continuation of solution past such times is mathematically challenging. We contributed to the theory of generalized solutions of a model of crystal growth, showing existence and uniqueness of a new notion of solution of the so called crystalline mean curvature flow with space dependent forcing, which will allow the use of this model in more realistic situation like the growth of snow crystals. We also studied a related problem with a prescribed volume of the crystal. We used similar mathematical tools to study how a large number of dislocations in a material move. Their movement governs how the material will respond to deformations.
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| Academic Significance and Societal Importance of the Research Achievements |
研究した数学問題は、物理学、材料科学、生物学、人口動態などのさまざまな分野の重要なモデルに使われます。得られた理論的結果は、これらの問題の特徴についての理解を深め、コンピューター上で解を求めるための精度が高い数値解法を開発するための重要な基盤となります。これらのモデルを結晶成長、材料の塑性、土壌中の水の流れなどの応用研究に活用していただければ幸いです。
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