1 research outputs found
Maximal Height Scaling of Kinetically Growing Surfaces
The scaling properties of the maximal height of a growing self-affine surface
with a lateral extent are considered. In the late-time regime its value
measured relative to the evolving average height scales like the roughness:
. For large values its distribution obeys
, charaterized by the
exponential-tail exponent . In the early-time regime where the roughness
grows as , we find where either or is the corresponding
exponent of the velocity distribution. These properties are derived from
scaling and extreme-values arguments. They are corroborated by numerical
simulations and supported by exact results for surfaces in 1D with the
asymptotic behavior of a Brownian path.Comment: One reference added. Minor stylistic changes in the abstarct and the
paper. 4 pages, 3 figure