The Cahn-Hilliard-Cook Equation on Curved Surfaces in Three-Dimensional Space

Abstract Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. One model which takes into account additive stochastic noise is the Cahn-Hilliard-Cook (CHC) model. Often, the surface on which phase segregation occurs is not a flat surface. With this motivation, we present a semi-implicit numerical algorithm to solve the fourth order parabolic stochastic partial differential equation on arbitrary curved surfaces. In addition to a description of the numerical method, the effect of Gaussian white noise in the CHC equation is also studied, to draw its significance during the phase segregation process.