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

点击翻译按钮获取中文摘要

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.