Maximal Height Scaling of Kinetically Growing Surfaces

الأصل · EN

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 Lα. For large values its distribution obeys P(h*ₗ) -A(h*ₗ/Lα)ᵃ, charaterized by the exponential-tail exponent a. In the early-time regime where the roughness grows as tβ, we find h*ₗ tβ[L-(β α)t + 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-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.