Distinguishing fractional and white noise in one and two dimensions
Abstract
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.
- Publication:
-
Physical Review E
- Pub Date:
- June 2001
- DOI:
- 10.1103/PhysRevE.63.062102
- arXiv:
- arXiv:cond-mat/0007011
- Bibcode:
- 2001PhRvE..63f2102H
- Keywords:
-
- 05.40.Ca;
- 47.55.Mh;
- 47.53.+n;
- Noise;
- Fractals in fluid dynamics;
- Condensed Matter
- E-Print:
- 3 pages RevTeX, 4 Postscript figures