Numerical Study of the Cahn-Hilliard Equation in Three Dimensions

We present results of the first numerical study of the Cahn-Hilliard equation in three dimensions. We study the asymptotic time dependence of the characteristic domain size $R\left(t\right)\mathrm{}$, as well as the scaling of the pair correlation function and the structure factor. The results indicate that dynamical scaling holds at sufficiently late times and that the data for $R\left(t\right)\mathrm{}$ are consistent with a Lifshitz-Slyozov growth law $R\left(t\right)\mathrm{}\sim t^{\frac{1}{3}}$.