Stephan Zschiegner

Multifractal detrended fluctuation analysis of nonstationary time series

We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based multifractal formalism, and prove that both approaches are equivalent for stationary signals with compact support. By analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series. By comparing the multifractal DFA results for original series with those for shuffled series we can distinguish multifractality due to long-range correlations from multifractality due to a broad probability density function. We also compare our results with the wavelet transform modulus maxima method, and show that the results are equivalent.

Multifractality of river runoff and precipitation: comparison of fluctuation analysis and wavelet methods

We study the multifractal temporal scaling properties of river discharge and precipitation records. We compare the results for the multifractal detrended fluctuation analysis method with the results for the wavelet-transform modulus maxima technique and obtain agreement within the error margins. In contrast to previous studies, we find non-universal behaviour: on long time scales, above a crossover time scale of several weeks, the runoff records are described by fluctuation exponents varying from river to river in a wide range. Similar variations are observed for the precipitation records which exhibit weaker, but still significant multifractality. For all runoff records the type of multifractality is consistent with a modified version of the binomial multifractal model, while several precipitation records seem to require different models.

Lambert Diffusion in Porous Media in the Knudsen Regime

We study molecular diffusion in nanopores with different types of roughness under the exclusion of mutual molecular collisions, i.e., in the so-called Knudsen regime. We show that the diffusion problem can be mapped onto Levy walks and discuss the roughness dependence of the diffusion coefficients D(s) and D(t) of self- and transport diffusion, respectively. While diffusion is normal in d=3, diffusion is anomalous in d=2 with D(s) approximately ln t and D(t) approximately ln L, where t and L are time and system size, respectively. Both diffusion coefficients decrease significantly when the roughness is enhanced, in remarkable disagreement with earlier findings.