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.

上一个财政年度，在我的研究计划的范围内，通过微观粒子系统的限制通过（由3个部分组成：（a）收敛速率，（b）粒子歼灭和（c）原子模型），我得到了3篇论文，1份被接受，并提交了2篇；所有这些都涉及高度尊敬的同行评审期刊。在一维情况下，第一个发表的论文完成了部分（b）：它为相互作用的粒子系统建立了连续限制，在这种情况下，相反符号的粒子可以互相消灭。它发表在该领域最好的期刊之一中。第二篇已发表的论文适用于我以前的成就，以在（a）中获得近似理论中的更清晰的估计。 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).公认的论文确保了通过动态系统的工具的局部存在和某些奇异的二极管的独特性，该工具为研究粒子碰撞提供了一个新的框架（b）部分。