Local and nonlocal anisotropic transport in reversed shear magnetic fields: shearless Cantori and nondiffusive transport.

A study of anisotropic heat transport in reversed shear (nonmonotonic q-profile) magnetic fields is presented. The approach is based on a recently proposed Lagrangian-Green's function method that allows an efficient and accurate integration of the parallel (i.e.

Isotropic model of fractional transport in two-dimensional bounded domains.

A two-dimensional fractional Laplacian operator is derived and used to model nonlocal, nondiffusive transport. This integro-differential operator appears in the long-wavelength, fluid description of quantities undergoing non-Brownian random walks without characteristic length scale. To study bounded domains, a mask function is introduced that modifies the kernel in the fractional Laplacian and removes singularities at the boundary.

Self-consistent dynamics of impurities in magnetically confined plasmas: turbulence intermittency and nondiffusive transport.

Self-consistent turbulent transport of high-concentration impurities in magnetically confined fusion plasmas is studied using a three-dimensional nonlinear fluid global turbulence model which includes ion-temperature gradient and trapped electron mode instabilities. It is shown that the impurity concentration can have a dramatic feedback in the turbulence and, as a result, it can significantly change the transport properties of the plasma. High concentration impurities can trigger strong intermittency that manifests in non-Gaussian heavy tails of the probability density functions of the E × B fluctuations and of the ion-temperature flux fluctuations.

Dynamics and transport in mean-field coupled, many degrees-of-freedom, area-preserving nontwist maps.

Area-preserving nontwist maps, i.e., maps that violate the twist condition, arise in the study of degenerate Hamiltonian systems for which the standard version of the Kolmogorov-Arnold-Moser (KAM) theorem fails to apply.

Local and nonlocal parallel heat transport in general magnetic fields.

A novel approach for the study of parallel transport in magnetized plasmas is presented. The method avoids numerical pollution issues of grid-based formulations and applies to integrable and chaotic magnetic fields with local or nonlocal parallel closures. In weakly chaotic fields, the method gives the fractal structure of the devil's staircase radial temperature profile.

Lagrangian statistics and flow topology in forced two-dimensional turbulence.

A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions.

Universal probability distribution function for bursty transport in plasma turbulence.

Bursty transport phenomena associated with convective motion present universal statistical characteristics among different physical systems. In this Letter, a stochastic univariate model and the associated probability distribution function for the description of bursty transport in plasma turbulence is presented. The proposed stochastic process recovers the universal distribution of density fluctuations observed in plasma edge of several magnetic confinement devices and the remarkable scaling between their skewness S and kurtosis K.

Truncation effects in superdiffusive front propagation with Lévy flights.

A numerical and analytical study of the role of exponentially truncated Lévy flights in the superdiffusive propagation of fronts in reaction-diffusion systems is presented. The study is based on a variation of the Fisher-Kolmogorov equation where the diffusion operator is replaced by a lambda -truncated fractional derivative of order alpha , where 1lambda is the characteristic truncation length scale. For lambda=0 there is no truncation, and fronts exhibit exponential acceleration and algebraically decaying tails.

Fluid limit of the continuous-time random walk with general Lévy jump distribution functions.

The continuous time random walk (CTRW) is a natural generalization of the Brownian random walk that allows the incorporation of waiting time distributions psi(t) and general jump distribution functions eta(x). There are two well-known fluid limits of this model in the uncoupled case. For exponential decaying waiting times and Gaussian jump distribution functions the fluid limit leads to the diffusion equation.

Nondiffusive transport in plasma turbulence: a fractional diffusion approach.

Numerical evidence of nondiffusive transport in three-dimensional, resistive pressure-gradient-driven plasma turbulence is presented. It is shown that the probability density function (pdf) of tracer 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 nonlocality (non-Fickian transport), non-Gaussianity, and nondiffusive scaling.

Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach.

The use of reaction-diffusion models rests on the key assumption that the diffusive process is Gaussian. However, a growing number of studies have pointed out the presence of anomalous diffusion, and there is a need to understand reactive systems in the presence of this type of non-Gaussian diffusion. Here we study front dynamics in reaction-diffusion systems where anomalous diffusion is due to asymmetric Levy flights.

Coherent structures and self-consistent transport in a mean field Hamiltonian model.

A study of coherent structures and self-consistent transport is presented in the context of a Hamiltonian mean field, single wave model. The model describes the weakly nonlinear dynamics of marginally stable plasmas and fluids, and it is related to models of systems with long-range interactions in statistical mechanics. In plasma physics the model applies to the interaction of electron "holes" and electron "clumps," which are depletions and excesses of phase-space electron density with respect to a fixed background.

Lagrangian chaos and Eulerian chaos in shear flow dynamics.

Shear flow dynamics described by the two-dimensional incompressible Navier-Stokes equations is studied for a one-dimensional equilibrium vorticity profile having two minima. These lead to two linear Kelvin-Helmholtz instabilities; the resulting nonlinear waves corresponding to the two minima have different phase velocities. The nonlinear behavior is studied as a function of two parameters, the Reynolds number and a parameter lambda specifying the width of the minima in the vorticity profile.

Self-consistent chaotic transport in fluids and plasmas.

Self-consistent chaotic transport is the transport of a field F by a velocity field v according to an advection-diffusion equation in which there is a dynamical constrain between the two fields, i.e., O(F,v)=0 where O is an integral or differential operator, and the Lagrangian trajectories of fluid particles exhibit sensitive dependence on initial conditions.

Diffusive transport and self-consistent dynamics in coupled maps.

The study of diffusion in Hamiltonian systems has been a problem of interest for a number of years. In this paper we explore the influence of self-consistency on the diffusion properties of systems described by coupled symplectic maps. Self-consistency, i.

Chaotic scattering and self-organization in spheromak sustainment.

Flux core spheromak sustainment by electrostatic helicity injection is studied in resistive MHD. The geometry has magnetized electrodes at the ends held at a potential difference V. For V>V(c) the central current column is kink unstable.

Destabilization of the m = 1 diocotron mode in non-neutral plasmas.

The theory for a Penning-Malmberg trap predicts m = 1 diocotron stability. However, experiments with hollow profiles show robust exponential growth. We propose a new mechanism of destabilization of this mode, involving parallel compression due to end curvature.