Anomalous diffusion and Lévy flights in channeling

Greenenko, A.A.; Chechkin, Aleksei V.; Шульга, Н.Ф.

doi:10.1016/j.physleta.2004.02.053

Cited by 33 publications

(25 citation statements)

References 8 publications

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“…In particular, the role of the Lévy noise in the motion of an overdamped particle in a periodic potential has recently attracted great attention [50][51][52]. Moreover, Lévy flights in periodic potentials have been investigated in references [53,54].…”

Section: Introductionmentioning

confidence: 99%

Non-Gaussian noise effects in the dynamics of a short overdamped Josephson junction

2010

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Abstract. The role of thermal and non-Gaussian noise on the dynamics of driven short overdamped Josephson junctions is studied. The mean escape time of the junction is investigated considering Gaussian, Cauchy-Lorentz and Lévy-Smirnov probability distributions of the noise signals. In these conditions we find resonant activation and the first evidence of noise enhanced stability in a metastable system in the presence of Lévy noise. For Cauchy-Lorentz noise source, trapping phenomena and power law dependence on the noise intensity are observed.

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Section: Introductionmentioning

confidence: 99%

Non-Gaussian noise effects in the dynamics of a short overdamped Josephson junction

2010

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“…Using (15) for = ± 1/2 and substituting (9) and (11) into (6) for the case of = 1 and for = 2 substituting (10) and (12) into (6), we have the following discrete system:…”

Section: The Fractional Ce-sementioning

confidence: 99%

“…The standard local diffusion description is linked to Gaussian processes and diffusion differential models are obtained. However, a nonlocal transport flow presents a non-Gaussian particle motion and in this case fractional diffusion models are derived [6][7][8]. One of the most considered proposals for the modeling of the mass flow in media with anomalous diffusion is the fractional advection-dispersion equation (FADE); see, for example, [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation

Jerez

Dzib

2015

Discrete Dynamics in Nature and Society

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We obtain a numerical algorithm by using the space-time conservation element and solution element (CE-SE) method for the fractional advection-dispersion equation. The fractional derivative is defined by the Riemann-Liouville formula. We prove that the CE-SE approximation is conditionally stable under mild requirements. A numerical simulation is performed for the one-dimensional case by considering a benchmark with a discontinuous initial condition in order to compare the results with the analytical solution.

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“…Previous studies revealed that anomalous super-diffusion can be simulated by particles undergoing Lévy motion Greenenko, 2004). The speed variance of particles in super-diffusion is infinite, different from the finite variance for normal diffusion.…”

Section: Introductionmentioning

confidence: 96%

Lattice-Boltzmann Simulation of Two-Dimensional Super-Diffusion

Xia

Zhang

2012

Engineering Applications of Computational Fluid Mechanics

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This study develops a multi-speed numerical approach to simulate the two-dimensional superdiffusion described by the fractional-derivative equation, by extending the standard Lattice-Boltzmann method. To approximate the large displacements of particles due to super-diffusion, the velocity components assigned to each particle need to be refined. This is done by modifying the equilibrium distribution function of Lattice-Boltzmann method. The convergence and accuracy analysis are supplied by Chapman-Enskog expansion. Numerical examples show the applicability of the novel multi-speed model for approximating the anomalous super-diffusion.

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Anomalous diffusion and Lévy flights in channeling

Cited by 33 publications

References 8 publications

Non-Gaussian noise effects in the dynamics of a short overdamped Josephson junction

Non-Gaussian noise effects in the dynamics of a short overdamped Josephson junction

A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation

Lattice-Boltzmann Simulation of Two-Dimensional Super-Diffusion

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