Boundary Conditions for Molecular Dynamics Simulations of Solids

分子动力学在原子尺度上对材料进行建模。在计算机模拟中，人们遵循原子的运动，这遵循牛顿第二定律。对于晶体固体，分子动力学提供了晶体和缺陷结构的微观描述，这最终决定了整体材料的性质。它提供了对材质行为方式的更多了解，并且它已成为材质建模和模拟中极其重要的工具。然而，由于计算的复杂性，这样的仿真只能对小系统进行。通常情况下，它聚焦在变形很大的材料缺陷周围，远场中的原子被消除。这样的截断过程产生了人为的边界，其中必须施加边界条件以考虑丢失的原子。例如，边界条件提供了原子在边界上的位置，这将是系统内原子的力计算所需的，因此需要该位置才能进行模拟。简单的方法往往会导致边界处的波浪反射，从而严重影响模拟结果。该项目旨在制定系统的边界条件，以达到以下目的：(A)防止边界上的波浪反射；(B)维持外部负荷；(C)控制系统温度。这些边界条件将大大提高分子动力学模拟的准确性和可靠性，并将有助于研究各种载荷和不同温度条件下材料缺陷的动力学。该项目还涉及这些方法的数值分析方面和应用。这项拟议的研究将使学生接触到物理建模、大规模模拟、数学分析和跨学科研究。

Molecular dynamics models materials at the level of atomic scale. In a computer simulation one follows the motion of the atoms, which obeys Newton's second law. For crystalline solids, molecular dynamics offers a microscopic description of the crystal and defect structure, which is ultimately responsible for the overall material properties. It offers more insight on why the material behaves the way it does, and it has become an extremely important tool in material modeling and simulations. However due to the computational complexity, such a simulation can only be conducted for a small system. Typically it is focused around material defects where the deformation is quite large, and the atoms in the far field are eliminated. Such a truncation procedure creates artificial boundaries, where boundary conditions have to be imposed in order to take into account the missing atoms. The boundary condition provides, for example, the position of the atoms at the boundary, which will be needed in the force calculation for the atoms inside the system, and therefore required to allow the simulation to proceed. Straightforward approaches often lead to wave reflection at the boundary and therefore severely deteriorate the simulation results. This project aims to develop systematic boundary conditions that serve the following purposes: (a) prevent wave reflection at the boundary; (b) maintain the external loading; (c) control the system temperature. These boundary conditions will greatly improve the accuracy and reliability of molecular dynamics simulations and will help to study the dynamics of material defects under various kinds of loading, and in different temperature regimes. The project also involves numerical analysis aspects and applications of these methods. The proposed research will expose the students to physical modeling, large-scale simulations, mathematical analysis, and interdisciplinary research.