This project develops algorithms for simulating the motion of grain boundaries in polycrystalline materials. Such materials are very common: Most metals and ceramics belong to this class. Mathematically, the problem is to evolve a network of surfaces in 3D via (weighted) motion by mean curvature. In addition, along curves (free boundaries) known as junctions at which three or more surfaces meet, certain natural boundary conditions (e.g. the Herring angle condition) need to be imposed.
Growth of Nanowires
This project aims to simulate the growth of Si nanowires. The dynamics involves three phases: The solid Si substrate, Si in vapor phase, and a drop of liquid Au catalyst. The differing anisotropies of the surface energies of the various phases is thought to be responsible for behaviors observed in experiments.
