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

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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.