CAREER: Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations

纳米尺寸器件的性能会受到裂纹等缺陷的形成和扩展的极大影响。考虑到这个过程涉及到打破固体晶格中的化学键，量子力学的描述是必要的。然而，对这个问题的完全原子描述是不可行的。PI建议开发基于分析的数值方法，将缺陷位置附近的原子描述与远离缺陷位置的粗粒度描述结合起来。量子力学效应是在密度泛函理论的背景下研究的。这种方法可以有效地消除所考虑的系统尺寸的限制，并可以将纳米尺寸器件的发展推向新的方向。该提案还包括开发多尺度建模的特殊课程，以及在涉及本科生，研究生和博士后研究员的垂直环境中的本科生研究部分。此外，该提案还包括向当地高中推广。通过让学生在这么早的阶段接触数学，研究者希望唤醒他们追求数学事业的愿望。

The performance of nanometer-sized devices can be greatly affected by the formation and propagation of defects, such as cracks. Given that this process involves breaking the chemical bonds in the solid lattice, a quantum-mechanical description is necessary. However, a fully atomistic description of the problem is not viable. The PI proposes to develop analysis-based numerical methodologies that couple an atomistic description near the location of the defect with a coarse-grained description far from it. Quantum-mechanical effects are studied in the context of Density-Functional Theory. This approach can effectively remove the limitation in the size of the system considered, and could gear the development of nanometer-sized devices in new directions.This proposal also includes the development of special courses in multiscale modeling, and an undergraduate research component in a vertical environment that involves undergraduate students, graduate students, and post-doctoral fellows. In addition, the proposal includes outreach to local high schools. By exposing students to mathematics at such an early stage, the investigator hopes to awaken in them the desire to pursue a career in mathematics.