7 research outputs found
Localization of transverse waves in randomly layered media at oblique incidence
We investigate the oblique incidence of transverse waves on a randomly
layered medium in the limit of strong disorder. An approximate method for
calculating the inverse localization length based on the assumptions of zero
energy flux and complete phase stochastization is presented. Two effects not
found at normal incidence have been studied: dependence of the localization
length on the polarization, and decrease of the localization length due to the
internal reflections from layers with small refractive indexes. The inverse
localization length (attenuation rate) for P-polarized radiation is shown to be
always smaller than that of S-waves, which is to say that long enough randomly
layered sample polarizes transmitted radiation. The localization length for
P-polarization depends non-monotonically on the angle of propagation, and under
certain conditions turns to infinity at some angle, which means that typical
(non-resonant) random realizations become transparent at this angle of
incidence (stochastic Brewster effect).Comment: 12 pages, 1 figure, accepted for publication in Physical Review
Lyapunov exponents in 1d disordered system with long-range memory
The Lyapunov exponents for Anderson localization are studied in a one
dimensional disordered system. A random Gaussian potential with the power law
decay of the correlation function is considered. The exponential
growth of the moments of the eigenfunctions and their derivative is obtained.
Positive Lyapunov exponents, which determine the asymptotic growth rate are
found
Generalized Lyapunov Exponent and Transmission Statistics in One-dimensional Gaussian Correlated Potentials
Distribution of the transmission coefficient T of a long system with a
correlated Gaussian disorder is studied analytically and numerically in terms
of the generalized Lyapunov exponent (LE) and the cumulants of lnT. The effect
of the disorder correlations on these quantities is considered in weak,
moderate and strong disorder for different models of correlation. Scaling
relations between the cumulants of lnT are obtained. The cumulants are treated
analytically within the semiclassical approximation in strong disorder, and
numerically for an arbitrary strength of the disorder. A small correlation
scale approximation is developed for calculation of the generalized LE in a
general correlated disorder. An essential effect of the disorder correlations
on the transmission statistics is found. In particular, obtained relations
between the cumulants and between them and the generalized LE show that, beyond
weak disorder, transmission fluctuations and deviation of their distribution
from the log-normal form (in a long but finite system) are greatly enhanced due
to the disorder correlations. Parametric dependence of these effects upon the
correlation scale is presented.Comment: 18 pages, 11 figure
Finite-Correlation-Time Effects in the Kinematic Dynamo Problem
Most of the theoretical results on the kinematic amplification of small-scale
magnetic fluctuations by turbulence have been confined to the model of
white-noise-like advecting turbulent velocity field. In this work, the
statistics of the passive magnetic field in the diffusion-free regime are
considered for the case when the advecting flow is finite-time correlated. A
new method is developed that allows one to systematically construct the
correlation-time expansion for statistical characteristics of the field. The
expansion is valid provided the velocity correlation time is smaller than the
characteristic growth time of the magnetic fluctuations. This expansion is
carried out up to first order in the general case of a d-dimensional
arbitrarily compressible advecting flow. The growth rates for all moments of
the magnetic field are derived. The effect of the first-order corrections is to
reduce these growth rates. It is shown that introducing a finite correlation
time leads to the loss of the small-scale statistical universality, which was
present in the limit of the delta-correlated velocity field. Namely, the shape
of the velocity time-correlation profile and the large-scale spatial structure
of the flow become important. The latter is a new effect, that implies, in
particular, that the approximation of a locally-linear shear flow does not
fully capture the effect of nonvanishing correlation time. Physical
applications of this theory include the small-scale kinematic dynamo in the
interstellar medium and protogalactic plasmas.Comment: revised; revtex, 23 pages, 1 figure; this is the final version of
this paper as published in Physics of Plasma