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

缺陷的形成和扩展会极大地影响纳米器件的性能，如裂纹。考虑到这个过程涉及到打破固体晶格中的化学键，量子力学描述是必要的。然而，对问题进行完全原子化的描述是不可行的。PI建议开发基于分析的数值方法，将靠近缺陷位置的原子描述与远离缺陷位置的粗粒度描述结合在一起。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规模的限制，并可以推动纳米器件朝着新的方向发展。该建议还包括开发多尺度建模的专门课程，以及在涉及本科生、研究生和博士后的垂直环境中建立本科生研究部分。此外，该提案还包括对当地高中的宣传。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.