When does coarsening occur in the dynamics of one-dimensional fronts ?

Details When does coarsening occur in the dynamics of one-dimensional fronts ? When does coarsening occur in the dynamics of one-dimensional fronts ?

2003-07-03

arxiv.org/abs/cond-mat/0307072v2

Phys. Rev. Lett. 92, 090601 (2004)

Physics

Condensed Matter

Statistical Mechanics

4 pages. Corrected one mistake in the phase diffusion coefficient, Eq.(11). Accepted for publication in Physical Review Letter

Scientific paper

10.1103/PhysRevLett.92.090601

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 \lambda of 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.

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