Interface dynamics in directional solidification: A lattice simulation with biased random walkers

Abstract
We devise and implement a technique to study the evolution of the interface for a one-sided model of directional solidification on a lattice with biased random walkers. Results include the appearance of a marginally stable wavelength at the onset of nonlinearity. Also, as the velocity of the interface is increased, there is a morphological transition from flat to cellular, and then to cellular with grooves. Anisotropy in dynamics is not included and the transition from cells to dendrites has not been seen.