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

上个财政年度，在我的研究计划范围内，通过微观粒子系统的极限通过来理解可塑性，（由三部分组成：（A）收敛率，（B）粒子湮灭和（C）原子模型），发表论文3篇，被录用1篇，投稿2篇;第一篇发表的论文完成了一维情况下的（B）部分：它为相互作用的粒子系统建立了连续极限，在该系统中，符号相反的粒子可以相互湮灭。它发表在该领域最好的期刊上。第二篇发表的论文应用我以前的成就（A），以获得更尖锐的估计近似理论。其中一篇论文揭示了这篇论文中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（一篇已发表，一篇已接受，两篇已提交），其中两篇建立了包含湮灭和产生的随机相互作用粒子系统的连续极限（流体动力学极限），符合（C）。已被接受的文件，确保局部存在性和唯一性的某些奇异常微分方程的工具，从动力系统，这提供了一个新的框架，研究粒子碰撞部分（B）在高维。

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.