| 研究課題/領域番号 |
18K13440
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| 研究機関 | 金沢大学 |
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研究代表者 |
POZAR Norbert 金沢大学, 数物科学系, 准教授 (00646523)
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| 研究期間 (年度) |
2018-04-01 – 2022-03-31
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| キーワード | crystalline curvature / viscosity solutions / interacting particles / volume constraint |
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| 研究実績の概要 |
We have finished a paper on the notion of viscosity solutions for the crystalline mean curvature flow (MCF) with a non-uniform driving force. This paves a way for using crystalline mean curvature flow for modelling realistic crystalline evolutions like snowflake growth when the forcing is influenced by variations of external pressure or concentration variations.
I have furthermore joined a work on the application of the above mentioned viscosity solutions with forcing for the problem of the crystalline MCF with a volume constraint, that is, when the evolving crystal keeps the same volume. This is a challenging problem due to the lack of comparison principle even in the usual mean curvature flow case. However, assuming a reflection property resembling starshapeness, we have been able to show existence of solutions of this problem. The paper has been submitted.
Finally, the paper on using viscosity solutions to study continuum limits of particle systems in one dimension interacting with a Newton potential and allowing for annihilation of particles with opposite charges was finished and the paper has been submitted. This work has application to material science as a possible model of dislocation dynamics in metals.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
3: やや遅れている
理由
The COVID-19 pandemic meant restriction of travel and cancellation of many conferences. I was not able to visit my collaborators as I planned which slightly delayed the progress of the project. However, we have been able to mostly progress the work by means of online communication.
I hope that I will be able to make the planned visits in the following fiscal year.
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| 今後の研究の推進方策 |
The final year of this project will be spent on further pursuing the notion of viscosity solutions to other problems in the original proposal, with focus on non-purely crystalline anisotropies and the inverse mean curvature flow. We are also working on a review of the recent results related to crystalline MCF.
We are also continuing our work on the application of viscosity solutions to interacting particle systems with a possibility of handling more general interacting forces.
Another slight variation on the research theme that I am trying to pursue is the study of boundary conditions for the mean curvature flow problem.
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| 次年度使用額が生じた理由 |
Due to COVID-19 travel restrictions, my planned visits of my collaborators and attendance of international conferences have been cancelled in 2020. I hope to make these trips once the travel restrictions are lifted.
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