English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We present results of the numerical simulations and the scalingcharacteristics of one-dimensional random fluctuations with heavy tailedprobability distribution functions. Assuming that the distribution function ofthe random fluctuations obeys L\'evy statistics with a power-law scalingexponent, we investigate the fractional diffusion equation in the presence of$\mu$-stable L\'evy noise. e study the scaling properties of the global widthand two point correlation functions, we then compare the analytical andnumerical results for the growth exponent $\beta$ and the roughness exponent$\alpha$. We also investigate the fractional Fokker-Planck equation forheavy-tailed random fluctuations. We show that the fractional diffusionprocesses in the presence of $\mu$-stable L\'evy noise display special scalingproperties in the probability distribution function (PDF). Finally, we studynumerically the scaling properties of the heavy-tailed random fluctuations byusing the diffusion entropy analysis. This method is based on the evaluation ofthe Shannon entropy of the PDF generated by the random fluctuations, ratherthan on the measurement of the global width of the process. We apply thediffusion entropy analysis to extract the growth exponent $\beta$ and toconfirm the validity of our numerical analysis. The proposed fractionallangevin equation can be used for modeling, analysis and characterization ofexperimental data, such as solar flare fluctuations, turbulent heat flow andetc.

Scaling characteristics of fractional diffusion processes in the presence of power-law distributed random noise