Lèvy flights Superdiffusion: An Introduction

Bernardo Spagnolo, Dubkov, Uchaikin

Risultato della ricerca: Articlepeer review

183 Citazioni (Scopus)

Abstract

After a short excursion from discovery of Brownian motion to the Richardson "law of four thirds" in turbulent diffusion, the article introduces the Lévy flight superdiffusion as a self-similar Lévy process. The condition of self-similarity converts the infinitely divisible characteristic function of the Lévy process into a stable characteristic function of the Lévy motion. The Lévy motion generalizes the Brownian motion on the base of the α-stable distributions theory and fractional order derivatives. The further development of the idea lies on the generalization of the Langevin equation with a non-Gaussian white noise source and the use of functional approach. This leads to the Kolmogorov's equation for arbitrary Markovian processes. As particular case we obtain the fractional Fokker-Planck equation for Lévy flights. Some results concerning stationary probability distributions of Lévy motion in symmetric smooth monostable potentials, and a general expression to calculate the nonlinear relaxation time in barrier crossing problems are derived. Finally we discuss results on the same characteristics and barrier crossing problems with Lévy flights, recently obtained with different approaches.
Lingua originaleEnglish
pagine (da-a)2649-2672
Numero di pagine24
RivistaInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume18 (9)
Stato di pubblicazionePublished - 2008

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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