Pattern formation in the models with coupling between order parameter and its gradient

摘要

A possibility of pattern formation in the models of the first order phase transitions with coupling between the order parameter and its gradient is discussed. We use the standard model of phase transitions extended to the higher derivatives of the order parameter that makes possible to describe the formation of various spatial distributions of the order parameter after phase transition. An example of the simple model with coupling between the order parameter and its gradient is considered. The proposed model is analogical to the mechanical nonlinear oscillator with the coordinate-dependent mass or velocity-dependent elastic module. The exact solution of this model is obtained that can be used to predict the order parameter distribution in the case of a spinodal decomposition.