Atomistic and Continuum Models of Solids

Princeton University, Princeton NJ

Investigators

Abstract

E 0708026 The investigator continues work on developing a systematic mathematical theory of crystalline solids starting from first principles, with emphasis on understanding the connection between atomistic/electronic structure models and continuum models. He and his collaborators study the continuum limit of electronic structure models such as models in Kohn-Sham density functional theory. They also study numerical algorithms that combine Kohn-Sham density functional theory and continuum models. In particular, they study the accuracy of these algorithms and find strategies for achieving uniform accuracy. These issues are critical for understanding the electronic structure models and making them powerful and practical tools for material science. The project helps to provide the microscopic foundation of the continuum mechanics of solids. From a broader perspective, the project serves as an example of the kind of work that needs to be done in order to establish the foundation for multi-scale, multi-physics modeling. It is now generally recognized across a wide spectrum of scientific disciplines that the next major advances will come from multi-scale, multi-physics modeling that integrates models from quantum mechanics with models from classical or continuum mechanics. However, due to the lack of a solid foundation, much of the current activities in multi-scale, multi-physics modeling are ad hoc in nature. Such a practice defeats the original purpose of multi-scale, multi-physics modeling. This project is aimed at establishing the necessary foundation for the case of crystalline solids. In addition, interest in nanotechnology and first-principle-based material design demands a much better understanding of the connection between the mechanical properties of solids and their electronic structure. Traditional concepts that are often used in continuum theory will have to be modified in order to take into account the effects at the electronic structure level. Establishing such a connection is a major focus of the proposed project.