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

通过证明相互作用粒子系统的离散到连续极限来了解金属的可塑性

• 批准号: 20K14358
• 负责人: VANMEURS PATRICK
• 金额: $ 2万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Early-Career Scientists
• 财政年份: 2020
• 资助国家: 日本
• 起止时间: 2020-04-01 至 2024-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-20K14358/
• 关键词: discrete-to-continuum; interacting particles; dislocations; hydrodynamic limit; continuum limits; particle systems; Particle system

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.

上一财年，在我通过微观粒子系统的极限通道理解可塑性的研究计划范围内（由三部分组成：（A）收敛速度，（B）粒子湮灭和（C）原子模型），我得到了发表论文3篇，录用1篇，投稿2篇；第一篇发表的论文在一维情况下完成了 (B) 部分：它建立了相互作用粒子系统的连续统极限，在该系统中，相反符号的粒子可以相互湮灭。它发表在该领域最好的期刊之一上。第二篇发表的论文应用了我之前在（A）方面的成果，以获得近似理论中更清晰的估计。其中一篇提交的论文揭示了该发表论文的粒子系统与准原子模型之间的联系（如（C））。关于其余四篇论文（一篇发表，一篇接受，两篇提交），其中两篇建立了涉及湮灭和创造的随机相互作用粒子系统的连续介质极限（流体动力学极限），符合（C）。被接受的论文利用动力系统的工具确保了某些奇异常微分方程的局部存在性和唯一性，这为研究更高维度的（B）部分中的粒子碰撞提供了一个新的框架。

项目成果

Uniqueness of Local, Analytic Solutions to Singular ODEs

奇异常微分方程局部解析解的唯一性

• DOI: 10.1007/s10440-022-00517-7
• 发表时间: 2022
• 影响因子: 1.6
• 作者: de Jong Thomas Geert;van Meurs Patrick
• 通讯作者: van Meurs Patrick

Convergence rates of interacting particle systems in the many particle limit

多粒子极限下相互作用粒子系统的收敛率

• 发表时间: 2021
• 作者: van Meurs Patrick

The continuum limit of interacting dislocations on multiple slip systems

多滑移系统上相互作用位错的连续极限

• DOI: 10.1051/cocv/2020038
• 发表时间: 2020
• 作者: van Meurs Patrick

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Expansions for the linear-elastic contribution to the self-interaction force of dislocation curves

位错曲线自相互作用力的线弹性贡献的展开式

• DOI: 10.1017/s0956792521000322
• 发表时间: 2021
• 影响因子: 1.9
• 作者: van Meurs P