Distinguishing fractional and white noise in one and two dimensions.
We discuss the link between uncorrelated noise and the Hurst exponent for one- and two-dimensional interfaces. We show that long range correlations cannot be observed using one-dimensional cuts through two-dimensional self-affine surfaces whose height distributions are characterized by a Hurst exponent H lower than -1/2. In this domain, fractional and white noise are not distinguishable. A method analyzing the correlations in two dimensions is necessary. For H>-1/2, a crossover regime leads to an systematic overestimate of the Hurst exponent.
Hansen
A
A
NORDITA, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark.
Schmittbuhl
J
J
Batrouni
G G
GG