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 $γ$ characterizing the large $m$ behaviour of the surface current $j$ ($j = 1/|m|^γ$): $n=1/4$ for $1< γ<3$ and $n=(1+γ)/(1+5γ)$ for $γ>3$.