1D Cahn–Hilliard equation for modulated phase systems
Résumé
Formation of modulated phase patterns can be modelized by a modified Cahn–Hilliard equation which includes a non-local term preventing the formation of macroscopic domains. Using stationary solutions of the original Cahn–Hilliard equation as analytical ansatzs, we compute the thermodynamically stable period of a 1D modulated phase pattern. We find that the period scales like the power −1/3 of the strength of the long-range interaction.