Event № 307
Adviser: Prof. Amy Novick-Cohen
Abstract: If we look at most materials under a microscope, we will see a network of grains and grain boundaries as well as holes, cracks, cavities and additional various defects. These features determine the microstructure of the material, whose properties are crucial in determining the various mechanical, electric, magnetic, and optical properties of the material. The microstructure is in turn influenced by the evolution of the exterior surface via the grain boundaries. To describe the evolution we assume that the grain boundaries evolve according to mean curvature motion and the exterior surfaces evolve according to surface diffusion motion. The resultant description for the motion of the grain boundaries, exterior surfaces, quadruple junctions and thermal grooves in thin/thick specimen of triangular geometry containing three grains yields a PDAE system, namely a system of partial differential algebraic equations, which we then solve numerically using an implicit finite difference scheme on staggered grids with a partially parallelized algorithm. Using the program, we identified new physical instabilities numerically. For example, we found that either annihilation of the smallest grain or hole formation at the quadruple junction could occur, depending on the model parameters. A variant algorithm for wetting/dewetting isolated a new grain-hole dewetting instability.