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Distinguishing fractional and white noise in one and two dimensions

Alex Hansen·Jean Schmittbuhl·George Batrouni
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Abstract

We discuss the link between uncorrelated noise and 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 lower than -1/2. In this domain, fractional and white noise are not distinguishable. A method analysing the correlations in two dimensions is necessary. For Hurst exponents larger than -1/2, a crossover regime leads to a systematic over estimate of the Hurst exponent.

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Alex Hansen, Jean Schmittbuhl, George Batrouni. 2000-07-02. Distinguishing fractional and white noise in one and two dimensions. https://doi.org/10.1103/physreve.63.062102

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