ABSTRACT
To capture nucleation and interface fluctuations in solidification, phase field equations must introduce stochastic noise into each dynamical equation in order to emulate fast atomic-scale fluctuations that are washed out when one considers dynamical equations driven from a mean-field level free energy. When starting directly with phase field models as mesoscale theories in their own right, thermal fluctuations must be added as stochastic noise in the equations of motion, effectively making them Langevin type equations. The noise associated with the chemical potential creates fluctuations of appropriate strength on long wavelengths and is critical to promote proper side-branching in dendritic growth, but it has a small effect on short wavelengths.
