1D Cahn–Hilliard dynamics: Ostwald ripening and application to modulated phase systems

We use a family of stationary solution of the Cahn–Hilliard dynamics in order to describe the coalescence during a first order phase transition. With this analytical ansatz, we compute the characteristic time for one step of period doubling in Langer's self similar scenario for Ostwald ripening. As an application, the same ansatz is also used to compute the thermodynamically stable period of a 1D modulated phase pattern, described by a Cahn–Hilliard dynamics with long range interaction terms.