Model of surface structure formation by stabilized spinodal decomposition

A one-dimensional model of stabilized spinodal decomposition is proposed and investigated. In the model, a curvature field couples adiabatically to the order parameter field of standard nonlinear Cahn-Hilliard theory for spinodal decomposition on a membrane. A simple geometric interpretation of the specific coupling is given. Alternatively the theory can also be described by an additional nonlocal self coupling introduced into the usual Cahn-Hilliard theory. An exact stationary solution is found. It predicts a sinusoidal decomposition profile and a global curvature of the initially flat membrane which also develops long wavelength ripples. Stability of this solution against small fluctuations is investigated and conditions for stability are derived. The case of maximal effective coupling is studied in detail and the geometrical surface profile is evaluated analytically.