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Modeling and statistical analysis of non-Gaussian random fields with heavy-tailed distributions

Mohsen Ghasemi Nezhadhaghighi1,* and Abbas Nakhlband2

  • 1Department of Physics, Shiraz University, Shiraz 71454, Iran
  • 2Department of Physics, Sharif University of Technology, Tehran 14588-89694, Iran

  • *ghaseminejad@shirazu.ac.ir
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Phys. Rev. E 95, 042114 – Published 7 April, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.042114

Abstract

In this paper, we investigate and develop an alternative approach to the numerical analysis and characterization of random fluctuations with the heavy-tailed probability distribution function (PDF), such as turbulent heat flow and solar flare fluctuations. We identify the heavy-tailed random fluctuations based on the scaling properties of the tail exponent of the PDF, power-law growth of qth order correlation function, and the self-similar properties of the contour lines in two-dimensional random fields. Moreover, this work leads to a substitution for the fractional Edwards-Wilkinson (EW) equation that works in the presence of μ-stable Lévy noise. Our proposed model explains the configuration dynamics of the systems with heavy-tailed correlated random fluctuations. We also present an alternative solution to the fractional EW equation in the presence of μ-stable Lévy noise in the steady state, which is implemented numerically, using the μ-stable fractional Lévy motion. Based on the analysis of the self-similar properties of contour loops, we numerically show that the scaling properties of contour loop ensembles can qualitatively and quantitatively distinguish non-Gaussian random fields from Gaussian random fluctuations.

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Outline

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Phys. Rev. E 95, 042114– Published 7 April, 2017
  • Received 9 November 2016
  • Revised 22 February 2017

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