Periodic phase separation: A numerical study via a modified Cahn-Hilliard equation

In this thesis, we investigate a model for periodic phase separation. The model consists primarily of a modified Cahn-Hilliard equation which is simply a gradient flow for a nonlocal energy functional. This functional was introduced to model microphase separation of diblock copolymers. Numerical experiments are performed, both to test certain hypotheses as well as explore the complex energy landscape of the nonlocal functional. The numerical method used is a split-step pseudo-spectral method. We solve the modified Cahn-Hilliard equation in two steps: first we solve the linear part of the equation and the advance the solution according to the nonlinear part. The nonlinear term is treated pseudo-spectrally.