When does coarsening occur in the dynamics of one-dimensional fronts ?
Abstract
Description
Dynamics of a one-dimensional growing front with an unstable straight profile are analyzed. We argue that a coarsening process occurs if and only if the period λof the steady state solution is an increasing function of its amplitude A. This statement is rigorously proved for two important classes of conserved and nonconserved models by investigating the phase diffusion equation of the steady pattern. We further provide clear numerical evidences for the growth equation of a stepped crystal surface.
4 pages. Corrected one mistake in the phase diffusion coefficient, Eq.(11). Accepted for publication in Physical Review Letters
4 pages. Corrected one mistake in the phase diffusion coefficient, Eq.(11). Accepted for publication in Physical Review Letters