Collaborative Research: Hybrid Finite Element Level-Set Methods for Stress-Driven Interface Dynamics

随着材料体系尺寸的减小，其界面原子与体原子的比例增大。因此，在通常具有非凡物理能力的小系统中，界面性质可能成为主导。例如，众所周知，具有高度有序的量子点、线或环组装的纳米界面系统具有显著的光电、磁和机械性能，具有广泛的应用。一般情况下，纳米尺度的界面是无效的，因此必须对块体材料界面的基本理论进行检查和修改。该项目开发了一大类复杂界面的计算技术和数学理论，这些界面受纳米尺度下非均质体系的力学性质控制，旨在了解这些界面在材料行为中的关键作用。它将新颖的有限元方法和强大的Level-Set技术结合到新一代多尺度模拟程序中，并直接应用于许多纳米级材料过程。这些过程包括金属和合金中微结构的演变，外延薄膜中应变岛的聚集，以及应力固体中的一般形态不稳定性。在严格的数学理论的支持下，这项研究应该会产生一套经过充分测试的、适应学术和工业需求的模拟技术。同时，应该建立数学和纳米科学之间的联系，并对学生进行这种跨学科研究的培训。

As the size of a material system decreases, the ratio of the amount of its interfacial and bulk atoms increases. Consequently, interfacial properties can become dominant in small systems that often possess extraordinary physical powers. As is well documented, for instance, nanoscale interfacial systems with highly ordered assemblies of quantum dots, wires, or rings exhibit remarkable optoelectronic, magnetic, and mechanical properties that have a wide range of applications. Generally invalid for nanoscale interfaces, fundamental theories for interfaces of bulk materials must be examined and reworked. This project develops computational techniques and mathematical theories for a large class of complex interfaces governed by the mechanical properties of underlying heterogeneous systems at nanoscale, aiming at the understanding of the crucial role of such interfaces in material behavior. It combines the novel finite-element methodology and the powerful level-set technique into a new generation multiscale simulation program, and applies directly to a host of nanoscale material processes. Such processes include microstructural evolution in metals and alloys, aggregation of strained islands in epitaxial thin films, and general morphological instability in stressed solids. Powered by rigorous mathematical theories, a set of well tested simulation technologies that are adapted to academic and industrial needs should result from this research. Meanwhile, connections between mathematics and nanoscience should be established, and students will be trained in this interdisciplinary research.