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

随着材料系统尺寸的减小，其界面原子和体原子的数量之比增加。 因此，界面性质在通常具有非凡物理能力的小系统中可能占主导地位。 例如，如有充分记载的，具有量子点、线或环的高度有序组装的纳米级界面系统表现出具有广泛应用的显著的光电、磁性和机械性质。 一般无效的纳米界面，基本理论的界面散装材料必须检查和返工。该项目开发了一大类复杂界面的计算技术和数学理论，这些复杂界面由纳米级底层异质系统的机械特性所控制，旨在了解这些界面在材料行为中的关键作用。 它结合了新的有限元方法和强大的水平集技术，成为新一代的多尺度模拟程序，并直接适用于主机的纳米材料工艺。 这些过程包括金属和合金的微观结构演变，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，一套经过良好测试的模拟技术，适应学术和工业需求，应该从这项研究中产生。 同时，应建立数学与纳米科学之间的联系，并培养学生进行跨学科研究。

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.