Coarsening in surface growth models without slope selection

Details Coarsening in surface growth models without slope selection Coarsening in surface growth models without slope selection

2000-01-24

arxiv.org/abs/cond-mat/0001337v1

J. Phys. A: Math. Gen. 33, L77-L82 (2000)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/0305-4470/33/8/102

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 $\gamma>3$.

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