CAREER: Bridging Quantum-Mechanics with Mechanics: Towards Predictive Computations of Materials Behavior

职业：桥接量子力学与力学：材料行为的预测计算

• 批准号: 1053145
• 负责人: Vikram Gavini
• 金额: $ 40万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-02-15 至 2017-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1053145&HistoricalAwards=false
• 关键词: CAREER; Bridging; Quantum; Mechanics; Towards

The objective of this Faculty Early Career Development (CAREER) Program award is to develop a seamless multi-scale computational technique to study crystalline solids with defects by resolving all the relevant length-scales -- from quantum-mechanical interactions at the sub-Angstrom length-scale to the elastic fields on the continuum scale. This will be achieved by (i) developing a real-space finite-element formulation of Kohn-Sham Density Functional Theory (KSDFT) which will scale linearly with the number of electrons; and (ii) developing the quasi-continuum reduction of KSDFT using a hierarchy of adaptive finite-element triangulations which will resolve the quantum-mechanical interactions where necessary (like the core of a defect), while seamlessly coarse-graining away to capture the long-ranged elastic fields. The developed multi-scale scheme will be used to investigate the origins of plasticity in surface dominated structures like nano-pillars. The proposed research will enable quantum-mechanics informed calculations on continuum scales by seamlessly bridging the quantum-mechanical length-scale with the continuum. Importantly, this multi-scale scheme links the material description at any length-scale to their fundamental origin -- the electronic structure. Thus, the developed method is expected to be transferable and predictive. This effort will enable an accurate quantum-mechanical description of defects in materials, and in effect will promote predictive simulations of deformation and failure mechanisms in solids. The educational efforts include developing a core-curriculum for the field of nanoscience, and developing educational modules involving simulations of materials behavior to demonstrate the importance of computations in science and technology to high school students.

这个教师早期职业发展（CAREER）计划奖的目标是开发一种无缝的多尺度计算技术，通过解决所有相关的长度尺度来研究具有缺陷的晶体固体-从亚埃长度尺度的量子力学相互作用到连续尺度上的弹性场。这将通过（i）开发Kohn-Sham密度泛函理论（KSDFT）的实空间有限元公式来实现，该公式将与电子数成线性比例;以及（ii）使用自适应有限元三角剖分的层次来开发KSDFT的准连续约化，这将在必要时解决量子力学相互作用（就像缺陷的核心），同时无缝粗粒化以捕获远程弹性场。开发的多尺度计划将被用来调查的塑性在表面为主的结构，如纳米柱的起源。 拟议的研究将使量子力学通知计算连续尺度无缝桥接量子力学长度尺度与连续。重要的是，这种多尺度方案将任何长度尺度的材料描述与它们的基本来源-电子结构联系起来。因此，开发的方法预计是可转移的和预测的。这一努力将使材料缺陷的精确量子力学描述成为可能，实际上将促进固体变形和失效机制的预测模拟。教育工作包括为纳米科学领域开发核心课程，并开发涉及材料行为模拟的教育模块，以向高中学生展示科学和技术计算的重要性。