Graduate Analysis Seminar
Jack Arbunich
UIC
Multiscale Expansion in Periodic Structures
Abstract: Building off some of the ideas last week, we shall explore an alternative method in multiscale analysis on periodic structures via a formal two scale asymptotic expansion. We will motivate this by considering a model for an electron moving in a periodic potential created by atoms in a crystal lattice. If we search for high frequency solutions, where the wavelength is comparable to the period of the lattice, then two natural length scales arise, a microscopic and macroscopic length scale. Starting from a microscopic description of a problem, we convert to a semiclassical scaling in time and space, and seek an approximate macroscopic description through multiscale expansion. Our aim will be to highlight the formal expansion and to show the framework for the stability result which verifies indeed that our approximation has an agreeable degree of accuracy. Along the way we will definitely encounter the Bloch-Floquet eigenvalue problem and possibly some snacks which for now is left to the whim of the speaker.
Monday March 14, 2016 at 2:00 PM in SEO 612