Towards Synthesis of Solar Wind and Geomagnetic Scaling Exponents: A Fractional Lévy Motion Model |
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Authors: | Nicholas W Watkins Daniel Credgington Bogdan Hnat Sandra C Chapman Mervyn P Freeman John Greenhough |
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Institution: | (1) British Antarctic Survey, High Cross, Madingley Road, Cambridge, CB3 0ET, U.K.;(2) Space and Astrophysics Group, University of Warwick, Coventry, CV4 7AL, U.K.;(3) Space Research Centre, University of Leicester, Leicester, LE1 7RH, U.K. |
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Abstract: | Mandelbrot introduced the concept of fractals to describe the non-Euclidean shape of many aspects of the natural world. In
the time series context, he proposed the use of fractional Brownian motion (fBm) to model non-negligible temporal persistence,
the ‘Joseph Effect’; and Lévy flights to quantify large discontinuities, the ‘Noah Effect’. In space physics, both effects
are manifested in the intermittency and long-range correlation which are by now well-established features of geomagnetic indices
and their solar wind drivers. In order to capture and quantify the Noah and Joseph effects in one compact model, we propose
the application of the ‘bridging’ fractional Lévy motion (fLm) to space physics. We perform an initial evaluation of some
previous scaling results in this paradigm, and show how fLm can model the previously observed exponents. We suggest some new
directions for the future. |
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Keywords: | auroral indices scaling solar wind turbulence fractional Lévy |
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