1,146 research outputs found
L\'evy flights on a comb and the plasma staircase
We formulate the problem of confined L\'evy flight on a comb. The comb
represents a sawtooth-like potential field , with the asymmetric teeth
favoring net transport in a preferred direction. The shape effect is modeled as
a power-law dependence within the sawtooth period,
followed by an abrupt drop-off to zero, after which the initial power-law
dependence is reset. It is found that the L\'evy flights will be confined in
the sense of generalized central limit theorem if (i) the spacing between the
teeth is sufficiently broad, and (ii) , where is the fractal
dimension of the flights. In particular, for the Cauchy flights (),
. The study is motivated by recent observations of
localization-delocalization of transport avalanches in banded flows in the Tore
Supra tokamak and is intended to devise a theory basis to explain the observed
phenomenology.Comment: 13 pages; 3 figures; accepted for publication in Physical Review
Fusion, collapse, and stationary bound states of incoherently coupled waves in bulk cubic media
We study the interaction between two localized waves that propagate in a bulk (two transverse dimensions) Kerr medium, while being incoherently coupled through cross-phase modulation. The different types of stationary solitary wave solutions are found and their stability is discussed. The results of numerical simulations suggest that the solitary waves are unstable. We derive sufficient conditions for when the wave function is bound to collapse or spread out, and we develop a theory to describe the regions of different dynamical behavior. For localized waves with the same center we confirm these sufficient conditions numerically and show that only when the equations and the initial conditions are symmetric are they also close to being necessary conditions. Using Gaussian initial conditions we predict and confirm numerically the power-dependent characteristic initial separations that divide the phase space into collapsing and diffracting solutions, and further divide each of these regions into subregions of coupled (fusion) and uncoupled dynamics. Finally we illustrate how, close to the threshold of collapse, the waves can cross several times before eventually collapsing or diffracting
Impurity transport in plasma edge turbulence
The turbulent transport of minority species/impurities is investigated in 2D
drift-wave turbulence as well as in 3D toroidal drift-Alfven edge turbulence.
The full effects of perpendicular and -- in 3D -- parallel advection are kept
for the impurity species. Anomalous pinch effects are recovered and explained
in terms of Turbulent EquiPartition (TEP)Comment: 12th International Congress on Plasma Physics, 25-29 October 2004,
Nice (France
Stretched exponential relaxation and ac universality in disordered dielectrics
This paper is concerned with the connection between the properties of
dielectric relaxation and ac (alternating-current) conduction in disordered
dielectrics. The discussion is divided between the classical linear-response
theory and a self-consistent dynamical modeling. The key issues are, stretched
exponential character of dielectric relaxation, power-law power spectral
density, and anomalous dependence of ac conduction coefficient on frequency. We
propose a self-consistent model of dielectric relaxation, in which the
relaxations are described by a stretched exponential decay function.
Mathematically, our study refers to the expanding area of fractional calculus
and we propose a systematic derivation of the fractional relaxation and
fractional diffusion equations from the property of ac universality.Comment: 8 pages, 2 figure
Generic features of modulational instability in nonlocal Kerr media
The modulational instability (MI) of plane waves in nonlocal Kerr media is
studied for a general, localized, response function. It is shown that there
always exists a finite number of well-separated MI gain bands, with each of
them characterised by a unique maximal growth rate. This is a general property
and is demonstrated here for the Gaussian, exponential, and rectangular
response functions. In case of a focusing nonlinearity it is shown that
although the nonlocality tends to suppress MI, it can never remove it
completely, irrespectively of the particular shape of the response function.
For a defocusing nonlinearity the stability properties depend sensitively on
the profile of the response function. It is shown that plane waves are always
stable for response functions with a positive-definite spectrum, such as
Gaussians and exponentials. On the other hand, response functions whose spectra
change sign (e.g., rectangular) will lead to MI in the high wavenumber regime,
provided the typical length scale of the response function exceeds a certain
threshold. Finally, we address the case of generalized multi-component response
functions consisting of a weighted sum of N response functions with known
properties.Comment: 9 pages, 5 figure
Numerical Simulations of Intermittent Transport in Scrape-Off Layer Plasmas
Two-dimensional fluid simulations of interchange turbulence for geometry and
parameters relevant for the scrape-off layer of confined plasmas are presented.
We observe bursty ejection of particles and heat from the bulk plasma in the
form of blobs. These structures propagate far into the scrape-off layer where
they are lost due to transport along open magnetic field lines. From
single-point recordings it is shown that the blobs have asymmetric conditional
wave forms and lead to positively skewed and flat probability distribution
functions. The radial propagation velocity may reach one tenth of the sound
speed. These results are in excellent agreement with recent experimental
measurements.Comment: 8 pages, 7 figure
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