Graduate Student Seminar
Title: Numerical Investigations of Pattern Formation in Binary Systems with Inhibitory Long-range Interaction
Abstract: I investigate pattern formation in a two-phase system on a two-dimensional manifold by numerically computing the minimizers of a Cahn-Hilliard-like model for micro-phase separation of diblock copolymers. The total energy of the system includes a short-range term - a Landau free energy and a long-range term - the Otha-Kawasaki functional. The shortrange term favors large domains with minimum perimeter and the long-range inhibitory term favors small domains. The balance of these terms leads to minimizers with a variety of patterns, including single droplets, droplet assemblies, stripes, wriggled stripes and combinations thereof. I compare the results of our numerical simulations with known analytical results and discuss the stability of the computed solutions and the role of key parameters in pattern formation. I focus on the triaxial ellipsoid for demonstration purposes, but our methods are general and can be applied to higher genus surfaces and surfaces with boundaries.