Coarsening in surface growth models without slope selection

Abstract

We study conserved models of crystal growth in one dimension [${\partial }_{t}z(x,t)=-{\partial }_{x}j(x,t)$] which are linearly unstable and develop a mound structure whose typical size L increases in time ($L=t^n$). If the local slope ($m={\partial }_{x}z$) increases indefinitely, $n$ depends on the exponent $\gamma$ characterizing the large $m$ behaviour of the surface current $j$ ($j=1/|m{|}^{\gamma }$): $n=1/4$ for $1<\gamma <3$ and $n=(1+\gamma )/(1+5\gamma )$ for $\gamma >3$.

7 pages, 2 EPS figures. To be published in J. Phys. A (Letter to the Editor)

References in corpus (3)

• Instabilities in crystal growth by atomic or molecular beams
• Noise-assisted Mound Coarsening in Epitaxial Growth
• An integration scheme for reaction-diffusion models

Cited by in corpus (5)

• Instabilities in crystal growth by atomic or molecular beams
• Four Lectures on the Physics of Crystal Growth
• Asymptotic step profiles from a nonlinear growth equation for vicinal surfaces
• Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations
• Coarsening dynamics in one dimension: The phase diffusion equation and its numerical implementation