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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

基本信息

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

项目摘要

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.

在上一财年，我的研究计划是通过微观粒子系统的极限通道来理解可塑性(包括三个部分：(A)收敛速率，（B)粒子湮灭，(C)原子模型），我发表了3篇论文，1篇被接受，2篇提交；所有这些都发表在备受尊敬的同行评议期刊上。第一篇发表的论文在一维情况下完成了第(B)部分：它建立了一个相互作用的粒子系统的连续统极限，在这个系统中，相反符号的粒子可以相互湮灭。它被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)上的成就，在近似理论中获得了更清晰的估计。其中一篇提交的论文揭示了这篇发表的论文中的粒子系统与准原子模型之间的联系（如(C)）。其余4篇论文（1篇发表，1篇录用，2篇投稿），其中2篇建立了湮灭和创造两种随机相互作用粒子系统的连续统极限（流体力学极限），符合(C)。本文利用动力系统的工具保证了某些奇异ode的局部存在唯一性，为研究(B)部分的高维粒子碰撞提供了新的框架。