1D Cahn-Hilliard equation for modulated phase systems. (English) Zbl 1192.82056
Summary: 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.
MSC:
82C27 | Dynamic critical phenomena in statistical mechanics |
82C26 | Dynamic and nonequilibrium phase transitions (general) in statistical mechanics |
82C35 | Irreversible thermodynamics, including Onsager-Machlup theory |