Pattern Selection in a Phase Field Model for Directional Solidification

TL;DR

This paper investigates wavelength selection in a two-dimensional phase field model for directional solidification, combining numerical minimization of an action with dynamic simulations to identify the most probable stationary state.

Contribution

It introduces a novel approach that integrates action minimization with dynamic simulations to determine wavelength selection in phase field models.

Findings

Identification of the most probable stationary state through action minimization.

Validation of the selected state via dynamic simulations from various initial conditions.

Insight into the wavelength selection mechanism in directional solidification.

Abstract

A symmetric phase field model is used to study wavelength selection in two dimensions. We study the problem in a finite system using a two-pronged approach. First we construct an action and, minimizing this, we obtain the most probable configuration of the system, which we identify with the selected stationary state. The minimization is constrained by the stationary solutions of stochastic evolution equations and is done numerically. Secondly, additional support for this selected state is obtained from straightforward simulations of the dynamics from a variety of initial states.