Capillary-Wave Description of Rapid Directional Solidification
  A recently introduced capillary-wave description of binary-alloy solidification is generalized to include the procedure of directional solidification. For a class of model systems a universal dispersion relation of the unstable eigenmodes of a planar steady-state solidification front is derived, which readjusts previously known stability considerations. We, moreover, establish a differential equation for oscillatory motions of a planar interface that offers a limit-cycle scenario for the formation of solute bands, and, taking into account the Mullins-Sekerka instability, of banded structures. 
Alexander L. Korzhenevskii, Richard Bausch, Rudi Schmitz
cond-mat.mes-hall cond-mat.mtrl-sci cond-mat.other cond-mat.stat-mech