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

纳米尺寸器件的性能可能会受到缺陷（例如裂纹）的形成和传播的极大影响。 考虑到这个过程涉及打破固体晶格中的化学键，量子力学的描述是必要的。 然而，对问题的完全原子化描述是不可行的。 PI建议开发基于分析的数值方法，耦合原子的描述附近的缺陷的位置与粗粒度的描述远离it. Quantum-mechanical效应的密度泛函理论的背景下进行了研究。 这种方法可以有效地消除所考虑的系统的大小的限制，并可以齿轮在新的方向上的纳米尺寸器件的开发。该提案还包括在多尺度建模的特殊课程的开发，并在一个垂直的环境中，涉及本科生，研究生和博士后研究员的本科生研究部分。 此外，该提案还包括与当地高中的外联活动。 通过让学生在如此早期的阶段接触数学，研究人员希望唤醒他们追求数学职业的愿望。

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.