Study On The Single-wave Approximation Of Spherical Crystal Phase Field Model

The crystal phase field model is an important model to study the microstructure evolution of crystalline objects.The minimizer of free energy density functional corresponds to the ordered structure.This is a class of variational problems with higher order derivatives,multiple solutions and nonlinearities.It is generally difficult to find its analytical solution.An effective method is to use numerical solution,but there are difficulties in the numerical solution process.The main difficulty is that the initial value of the model,the range of the calculated radius,and the range of physical parameters cannot be determined.In order to solve these problems,we study the single-wave approximation method.This method is an approximation method to study the structural stability.Under certain assumptions,it converts a problem that seeks the minimum value of the free energy density functional to seek the problem of the minima of the function of several variables,and it is able to determine the initial value of the model,the range of the calculated radius.In addition,it can determine the stability region and the range of physical parameters of the ordered structure by qualitatively calculating the phase diagram.This paper takes the spherical Landau-Brazovskii model as an example to study the singlewave approximation method of the spherical crystal phase field model.We verify the validity of the single-wave approximation proposed in this paper by numerically calculating the layered phase and the speckle phase structure on the spherical surface from the initial value selection and the calculation radius selection.