Atomistic and Continuum Models of Solids

E0708026 研究人员继续从第一性原理出发，发展结晶固体的系统数学理论，重点是理解原子/电子结构模型和连续模型之间的联系。 他和他的合作者研究电子结构模型的连续极限，例如Kohn-Sham密度泛函理论中的模型。 他们还研究结合Kohn-Sham密度泛函理论和连续模型的数值算法。 特别是，他们研究这些算法的准确性和findstrategies实现统一的准确性。 这些问题对于理解电子结构模型并使其成为材料科学的强大而实用的工具至关重要。该工程为固体连续力学提供了微观基础。 从更广泛的角度来看，该项目作为一个例子，需要做的工作，以建立多尺度，多物理建模的基础。 现在人们普遍认识到，在科学学科的广泛范围内，下一个重大进展将来自多尺度，多物理建模，将量子力学模型与经典或连续力学模型相结合。 然而，由于缺乏坚实的基础，目前多尺度、多物理场模拟的许多活动在性质上都是临时性的。 这种做法违背了多尺度、多物理场建模的初衷。 这个项目旨在为晶体固体的情况建立必要的基础。 此外，对纳米技术和基于第一性原理的材料设计的兴趣要求更好地理解固体的机械性质和它们的电子结构之间的联系。 在连续介质理论中经常使用的传统概念将不得不被修改，以便考虑电子结构水平上的影响。 建立这样的联系是拟议项目的一个主要重点。

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.