Non-diffusive transport in plasma turbulence: a fractional diffusion approach
arXiv:physics/0403039 · doi:10.1103/PhysRevLett.94.065003
Abstract
Numerical evidence of non-diffusive transport in three-dimensional, resistive pressure-gradient-driven plasma turbulence is presented. It is shown that the probability density function (pdf) of test particles' radial displacements is strongly non-Gaussian and exhibits algebraic decaying tails. To model these results we propose a macroscopic transport model for the pdf based on the use of fractional derivatives in space and time, that incorporate in a unified way space-time non-locality (non-Fickian transport), non-Gaussianity, and non-diffusive scaling. The fractional diffusion model reproduces the shape, and space-time scaling of the non-Gaussian pdf of turbulent transport calculations. The model also reproduces the observed super-diffusive scaling.
References in corpus (1)
Cited by in corpus (59)
- Matrix approach to discrete fractional calculus II: partial fractional differential equations
- Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation
- A Parabolic Problem with a Fractional-Time Derivative
- Lévy Noise-Induced Stochastic Resonance in a Bistable System
- Stochastic calculus for uncoupled continuous-time random walks
- Fractional kinetics emerging from ergodicity breaking in random media
- Scaling Laws of Passive-Scalar Diffusion in the Interstellar Medium
- Generalized diffusion-wave equation with memory kernel
- Harmonic oscillator under Levy noise: Unexpected properties in the phase space
- Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration
- Fluctuation-driven directed transport in the presence of Levy flights
- Non-diffusive, non-local transport in fluids and plasmas
- Lévy Ratchet in a Weak Noise Limit: Theory and Simulation
- Nondiffusive suprathermal ion transport in simple magnetized toroidal plasmas
- Characterizing Weak Chaos using Time Series of Lyapunov Exponents
- On the kinetic equation of linear fractional stable motion and applications to modeling the scaling of intermittent bursts
- A Fractional Fokker-Planck Model for Anomalous Diffusion
- Lagrangian statistics and flow topology in forced two-dimensional turbulence
- Generalized Central Limit Theorem and Renormalization Group
- On existence and regularity of a terminal value problem for the time fractional diffusion equation
- Numerical method for the time-fractional porous medium equation
- Underdamped stochastic harmonic oscillator
- Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence
- A theory of non-local linear drift wave transport
- Fractional and fractal derivatives modeling of turbulence
- Escape through a time-dependent hole in the doubling map
- Front propagation in reaction-diffusion systems with anomalous diffusion
- Numerical Energy Dissipation for Time-Fractional Phase-Field Equations
- A linear Galerkin numerical method for a quasilinear subdiffusion equation
- Lévy on-off intermittency
- Well-posedness of the stochastic time-fractional diffusion and wave equations and inverse random source problems
- Non-local gyrokinetic model of linear ion-temperature-gradient modes
- Separation of particles leading to decay and unlimited growth of energy in a driven stadium-like billiard
- Numerical study of anomalous diffusion of light in semi-crystalline polymer structures
- Analytic solution to space-fractional Fokker-Planck equations for tempered-stable Lévy distributions with spatially linear, time-dependent drift
- Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations
- Levy-Kolmogorov scaling of turbulence
- Levy ratchets with dichotomic random flashing
- Linear Galerkin-Legendre spectral scheme for a degenerate nonlinear and nonlocal parabolic equation arising in climatology
- Phase transitions in the fractional three-dimensional Navier-Stokes equations
- Noise driven current reversal and stabilisation in the tilted ratchet potential subject to tempered stable Lévy noise
- Second order scheme for self-similar solutions of a time-fractional porous medium equation on the half-line
- Global scaling of the heat transport in fusion plasmas
- Optimal Control of a Diffusive Epidemiological Model Involving the Caputo-Fabrizio Fractional Time-Derivative
- Continuum limit for discrete NLS with memory effect
- Transition from normal to ballistic diffusion in a one-dimensional impact system
- Study of momentum diffusion with the effect of adiabatic focusing
- Excitation of Flow Instabilities due to Nonlinear Scale Invariance
- Sub-diffusive behavior in the Standard Map
- Fully discrete Galerkin scheme for a semilinear subdiffusion equation with nonsmooth data and time-dependent coefficient
- Inverse problems for heat equation and space-time fractional diffusion equation with one measurement
- Anomalous beam diffusion near beam-beam synchro-betatron resonances
- Space-time fractional NLS equation
- Role of long jumps in Lévy noise induced multimodality
- Anomalous fluctuations of renewal-reward processes with heavy-tailed distributions
- Explicit and implicit TVD schemes for conservation laws with Caputo derivatives
- A series representation of the discrete fractional Laplace operator of arbitrary order
- Surface waves enhance particle dispersion
- Identification of an Open-loop Plasma Vertical Position Using Fractional Order Dynamic Neural Network