Solidification fronts with unusual long-time behavior

Precisely at a critical undercooling ${\mathrm{\Delta }}_{\mathit{c}}$, one-dimensional solidification fronts can travel with a velocity v, which scales in time as ${\mathit{t}}^{\mathrm{-}1/3}$. This result, recently found in computer simulations and explained on dimensional grounds, is derived here from the starting equations.