Atomistic and Continuum Models of Solids

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E0708026 The investigator continues work on developing a systematicmathematical theory of crystalline solids starting from firstprinciples, with emphasis on understanding the connection betweenatomistic/electronic structure models and continuum models. Heand his collaborators study the continuum limit of electronicstructure models such as models in Kohn-Sham density functionaltheory. They also study numerical algorithms that combineKohn-Sham density functional theory and continuum models. Inparticular, they study the accuracy of these algorithms and findstrategies for achieving uniform accuracy. These issues arecritical for understanding the electronic structure models andmaking them powerful and practical tools for material science. The project helps to provide the microscopic foundation of thecontinuum mechanics of solids. From a broader perspective, the project serves as an exampleof the kind of work that needs to be done in order to establishthe foundation for multi-scale, multi-physics modeling. It isnow generally recognized across a wide spectrum of scientificdisciplines that the next major advances will come frommulti-scale, multi-physics modeling that integrates models fromquantum mechanics with models from classical or continuummechanics. However, due to the lack of a solid foundation, muchof the current activities in multi-scale, multi-physics modelingare ad hoc in nature. Such a practice defeats the originalpurpose of multi-scale, multi-physics modeling. This project isaimed at establishing the necessary foundation for the case ofcrystalline solids. In addition, interest in nanotechnology andfirst-principle-based material design demands a much betterunderstanding of the connection between the mechanical propertiesof solids and their electronic structure. Traditional conceptsthat are often used in continuum theory will have to be modifiedin order to take into account the effects at the electronicstructure level. Establishing such a connection is a major focusof the proposed project.