Maximal height scaling of kinetically growing surfaces.
The scaling properties of the maximal height of a growing self-affine surface with a lateral extent L are considered. In the late-time regime its value measured relative to the evolving average height scales like the roughness: h*(L) approximately L alpha. For large values its distribution obeys logP(h*(L)) approximately (-)A(h*(L)/L(alpha))(a). In the early-time regime where the roughness grows as t(beta), we find h*(L) approximately t(beta)[lnL-(beta/alpha)lnt+C](1/b), where either b = a or b is the corresponding exponent of the velocity distribution. These properties are derived from scaling and extreme-value arguments. They are corroborated by numerical simulations and supported by exact results for surfaces in 1D with the asymptotic behavior of a Brownian path.
Raychaudhuri
S
S
Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA.
Cranston
M
M
Przybyla
C
C
Shapir
Y
Y
D001419:Bacteria / Q000254:growth & development; D003460:Crystallization; D007700:Kinetics; D008962:Models, Theoretical; D013499:Surface Properties