Fractional Levy motion as an Alternative Model for Apparent Multiaffinity in Solar Wind Time Series

Details Fractional Levy motion as an Alternative Model for Apparent Multiaffinity in Solar Wind Time Series Fractional Levy motion as an Alternative Model for Apparent Multiaffinity in Solar Wind Time Series

Dec 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006agufmsh13a0392c&link_type=abstract

American Geophysical Union, Fall Meeting 2006, abstract #SH13A-0392

Mathematics

Logic

3235 Persistence, Memory, Correlations, Clustering (3265, 7857), 4475 Scaling: Spatial And Temporal (1872, 3270, 4277), 7833 Mathematical And Numerical Techniques (0500, 3200), 7863 Turbulence (4490)

Scientific paper

One widely used technique in the testing of multifractal theories of turbulence has been the the multiaffinity plot of ζ(q) versus q, where ζ is the exponent of the q^{th} order structure function, provided that has already been found to be a power law. However, it is not obvious that the most economical description of all derived solar wind quantities, for example the Poynting flux or the ɛ function, must also be a multifractal. We have elsewhere argued that it is also instructive to capture the "stylised facts" of the scaling behaviour of auroral indices and solar wind quantities in simpler phenomenological models. To make this idea more concrete we here consider the use of fractional Lévy motion as a model for solar wind time series. fLm has only three parameters, the Lévy exponent μ, the persistence exponent β and the selfsimilarity exponent H which depends additively on the other two. By making the fLm hypothesis we explore how experimentally measured quantities, in particular the growth of variance, the scaling of the first return probability, and the multiaffinity plot depend on the fLm model's parameters. Comparison of these predictions with data is then used to assess the usefulness of fLm as an alternative model for solar wind time series.

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