| 研究課題/領域番号 |
20K14358
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| 研究種目 |
若手研究
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| 配分区分 | 基金 |
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| 審査区分 |
小区分12040:応用数学および統計数学関連
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| 研究機関 | 金沢大学 |
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研究代表者 |
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| 研究期間 (年度) |
2020-04-01 – 2024-03-31
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| 研究課題ステータス |
交付 (2022年度)
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| 配分額 *注記 |
3,120千円 (直接経費: 2,400千円、間接経費: 720千円)
2023年度: 780千円 (直接経費: 600千円、間接経費: 180千円)
2022年度: 780千円 (直接経費: 600千円、間接経費: 180千円)
2021年度: 780千円 (直接経費: 600千円、間接経費: 180千円)
2020年度: 780千円 (直接経費: 600千円、間接経費: 180千円)
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| キーワード | discrete-to-continuum / interacting particles / dislocations / hydrodynamic limit / continuum limits / particle systems / Particle system |
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| 研究開始時の研究の概要 |
For a century engineers and physicists have tried to understand plastic deformation of metals. Plastic deformation is understood as the group behaviour of many crystallographic defects which move and interact on microscopic length- and time-scales. Due to the complexity of the motion of defects, there is a lot of ambiguity on models for their group behaviour. To work to solving this ambiguity, this research focuses on simplified models for defect dynamics, and aims to derive rigorously the group behaviour of the defects.
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| 研究実績の概要 |
Last fiscal year, within the scope of my research plan on understanding plasticity through the limit passage of microscopic particle systems (which consists of 3 parts: (A) convergence rates, (B) particle annihilation and (C) atomistic models), I got 3 papers published, 1 accepted and 2 submitted; all of which to highly respected peer-reviewed journals.
The first published paper completes part (B) in the one-dimensional case: it establishes the continuum limit for an interacting particle system in which particles of opposite sign can annihilate one another. It got published in one of the best journals in the field. The second published paper applies my previous achievements on (A) to obtain sharper estimates in approximation theory. One of the submitted papers reveals the connection between the particle system of this published paper and a quasi atomistic model (as in (C)).
Concerning the remaining four papers (one published, one accepted and two submitted), two of them establish the continuum limit (hydrodynamic limit) of stochastic interacting particle systems involving both annihilation and creation, which fits to (C). The accepted paper ensures local existence and uniqueness of certain singular ODEs with tools from dynamical systems, which provide a new framework for studying particle collisions in part (B) in higher dimensions.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
Half of the goals in the proposal have been completed in the published papers. These papers have sparked several follow-up problems related to projects (A), (B) and (C) in the proposal. I am currently working on 6 such problems.
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| 今後の研究の推進方策 |
I will continue the 6 problems mentioned in the "Current Status" section, and aim to submit 5 of them as papers to highly respected peer-reviewed journals during FY 2023. These papers will not reach all goals set out in projects (A), (B) and (C) in the proposal, but I believe that they make good progress towards them.
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