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2020 年度 実施状況報告書

Understanding plasticity of metals through proving discrete-to-continuum limits of interacting particle systems

研究課題

研究課題/領域番号 20K14358
研究機関金沢大学

研究代表者

VANMEURS PATRICK  金沢大学, 数物科学系, 助教 (20815378)

研究期間 (年度) 2020-04-01 – 2024-03-31
キーワードcontinuum limits / particle systems
研究実績の概要

Last fiscal year, within the scope of my research plan, I got 4 papers published and 1 submitted; all to highly respected peer-reviewed journals.
The first published paper establishes for a class of particle systems the first ever convergence rate. The second published paper provides a new atomistic validation for models used in plasticity. The submitted paper establishes the continuum limit for an interacting particle system in which particles of opposite sign can annihilate one another. These three papers worked out as planned in projects (A), (B) and (C) of the proposal.
The two other published papers establish a variational framework for disclinations and a continuum limit for a multiple-species particle system. Both fit to the theme of the proposed research.

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

Several of the goals in the proposal have been met in the already published and submitted papers. The results in these papers reveal that the more ambitious parts of the proposal may be hard to tackle, but that there are several interesting subtle problems to understand before facing the ambitious goals. Currently, I'm working on figuring out these more subtle problems.

今後の研究の推進方策

Instead of facing immediately the ambitious parts of the proposal, I continue with working on the interesting questions that arose from the first part of the proposal which has been solved. I expect that the results of these studies will be helpful when facing the ambitious parts of the proposal at a later stage.

次年度使用額が生じた理由

It depends on the corona situation how much of the budget I can use for travelling. Since many events will be held online, I will prepare a proper setup for such events.

  • 研究成果

    (8件)

すべて 2021 2020 その他

すべて 国際共同研究 (2件) 雑誌論文 (4件) (うち国際共著 4件、 査読あり 4件) 学会発表 (1件) (うち招待講演 1件) 備考 (1件)

  • [国際共同研究] Eindhoven University of Technology(オランダ)

    • 国名
      オランダ
    • 外国機関名
      Eindhoven University of Technology
  • [国際共同研究] University of Warwick(英国)

    • 国名
      英国
    • 外国機関名
      University of Warwick
  • [雑誌論文] Discrete-to-continuum limits of planar disclinations2021

    • 著者名/発表者名
      Cesana Pierluigi、van Meurs Patrick
    • 雑誌名

      ESAIM: Control, Optimisation and Calculus of Variations

      巻: 27 ページ: 23~23

    • DOI

      10.1051/cocv/2021025

    • 査読あり / 国際共著
  • [雑誌論文] Quantitative Estimate of the Continuum Approximations of Interacting Particle Systems in One Dimension2021

    • 著者名/発表者名
      Kimura Masato、van Meurs Patrick
    • 雑誌名

      SIAM Journal on Mathematical Analysis

      巻: 53 ページ: 681~709

    • DOI

      10.1137/20M1322054

    • 査読あり / 国際共著
  • [雑誌論文] The continuum limit of interacting dislocations on multiple slip systems2020

    • 著者名/発表者名
      van Meurs Patrick
    • 雑誌名

      ESAIM: Control, Optimisation and Calculus of Variations

      巻: 26 ページ: 102~102

    • DOI

      10.1051/cocv/2020038

    • 査読あり / 国際共著
  • [雑誌論文] Atomistic origins of continuum dislocation dynamics2020

    • 著者名/発表者名
      Hudson Thomas、van Meurs Patrick、Peletier Mark
    • 雑誌名

      Mathematical Models and Methods in Applied Sciences

      巻: 30 ページ: 2557~2618

    • DOI

      10.1142/S0218202520500505

    • 査読あり / 国際共著
  • [学会発表] Quantification of the difference between discrete and continuum descriptions of arrays of dislocations2021

    • 著者名/発表者名
      van Meurs Patrick
    • 学会等名
      Cardiff School of Mathematics Seminar
    • 招待講演
  • [備考] Homepage

    • URL

      https://sites.google.com/site/pjpvmeurs/

URL: 

公開日: 2021-12-27  

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