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

上一财年，在我的通过微观粒子系统的极限通过理解可塑性的研究计划(由3部分组成：(A)收敛速度，(B)粒子湮没和(C)原子模型)的范围内，我发表了3篇论文，1篇被接受，2篇提交给备受尊敬的同行评议的期刊。第一篇发表的论文完成了一维情况下的(B)部分：它建立了相互作用的粒子系统的连续极限，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在(A)上的成果，在逼近理论中得到了更精确的估计。其中一篇论文揭示了这篇论文的粒子系统与准原子模型(如(C))之间的联系，结合其余四篇论文(一篇发表，一篇接受，两篇提交)，其中两篇建立了同时涉及湮灭和创造的随机相互作用粒子系统的连续统极限(流体动力学极限)，这与(C)相吻合。本文利用动力系统的工具，证明了某些奇异常微分方程组的局部存在唯一性，为高维研究(B)中的粒子碰撞提供了新的框架。

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.