Stochastic phase-field simulations of symmetric alloy solidification
  We study initial transient stages in directional solidification by means of a non-variational phase field model with fluctuations. This model applies for the symmetric solidification of dilute binary solutions and does not invoke fluctuation-dissipation theorem to account for the fluctuation statistics. We devote our attention to the transient regime during which concentration gradients are building up and fluctuations act to destabilize the interface. To this end, we calculate both the temporally dependent growth rate of each mode and the power spectrum of the interface evolving under the effect of fluctuations. Quantitative agreement is found when comparing the phase-field simulations with theoretical predictions. 
R. Ben\'itez and L. Ram\'irez-Piscina