Mathematics Colloquium: John Lowengrub (UC Irvine)

In applications ranging from energy harvesting to toxin detection, nanocrystalline materials promise to yield revolutionary new technologies. The ability to produce nanomaterials with controlled morphologies remains a difficulty, however. Producing nanomaterials using self-assembly promises to be a low-cost, high-yield approach. However a fundamental understanding of growth instabilities that occur and lead to the natural formation of nanostructures and patterns is still needed. In this talk, we will discuss mathematical models and simulation methods for such problems that account for the influence of strongly anisotropic surface tension forces and elastic stresses that arise during growth of nanocrystalline materials. In the context of epitaxial growth of thin films, we demonstrate the dependence of nanostructure dynamics on the growth conditions, such as the deposition rate and the temperature.