Anomalous Diffusion by the Fractional Fokker-Planck Equation and Lévy Stable Processes

• The work presented here is a review of current developments in modelling anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives and Langevin dynamics where L´evy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degree of fractionality of the stable L´evy distribution as solutions to the Fokker-Planck equation and is compared to results from Langevin simulations. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics.

Ämnesord

NATURVETENSKAP  -- Fysik -- Annan fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Other Physics Topics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

NATURVETENSKAP  -- Fysik -- Fusion, plasma och rymdfysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Fusion, Plasma and Space Physics (hsv//eng)

Nyckelord

Fractional Fokker-Plank Equation.

Tsallis entropy

Non-local theory

L´evy noise

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