423 research outputs found
On how a joint interaction of two innocent partners (smooth advection & linear damping) produces a strong intermittency
Forced advection of passive scalar by a smooth -dimensional incompressible
velocity in the presence of a linear damping is studied. Acting separately
advection and dumping do not lead to an essential intermittency of the steady
scalar statistics, while being mixed together produce a very strong
non-Gaussianity in the convective range: -th (positive) moment of the
absolute value of scalar difference,
is proportional to , , where measures the rate of the damping in the units
of the stretching rate. Probability density function (PDF) of the scalar
difference is also found.Comment: 4 pages, RevTex, Submitted to Phys. Fluid
Diffusion of optical pulses in dispersion-shifted randomly birefringent optical fibers
An effect of polarization-mode dispersion, nonlinearity and random variation
of dispersion along an optical fiber on a pulse propagation in a randomly
birefringent dispersion-shifted optical fiber with zero average dispersion is
studied. An averaged pulse width is shown analytically to diffuse with
propagation distance for arbitrary strong pulse amplitude. It is found that
optical fiber nonlinearity can not change qualitatively a diffusion of pulse
width but can only modify a diffusion law which means that a root mean square
pulse width grows at least as a linear function of the propagation distance.Comment: 11 pages, submitted to Optics Communication
Approximating the Permanent with Fractional Belief Propagation
We discuss schemes for exact and approximate computations of permanents, and
compare them with each other. Specifically, we analyze the Belief Propagation
(BP) approach and its Fractional Belief Propagation (FBP) generalization for
computing the permanent of a non-negative matrix. Known bounds and conjectures
are verified in experiments, and some new theoretical relations, bounds and
conjectures are proposed. The Fractional Free Energy (FFE) functional is
parameterized by a scalar parameter , where
corresponds to the BP limit and corresponds to the exclusion
principle (but ignoring perfect matching constraints) Mean-Field (MF) limit.
FFE shows monotonicity and continuity with respect to . For every
non-negative matrix, we define its special value to be the
for which the minimum of the -parameterized FFE functional is
equal to the permanent of the matrix, where the lower and upper bounds of the
-interval corresponds to respective bounds for the permanent. Our
experimental analysis suggests that the distribution of varies for
different ensembles but always lies within the interval.
Moreover, for all ensembles considered the behavior of is highly
distinctive, offering an emprirical practical guidance for estimating
permanents of non-negative matrices via the FFE approach.Comment: 42 pages, 14 figure
Non-universality of the scaling exponents of a passive scalar convected by a random flow
We consider passive scalar convected by multi-scale random velocity field
with short yet finite temporal correlations. Taking Kraichnan's limit of a
white Gaussian velocity as a zero approximation we develop perturbation theory
with respect to a small correlation time and small non-Gaussianity of the
velocity. We derive the renormalization (due to temporal correlations and
non-Gaussianity) of the operator of turbulent diffusion. That allows us to
calculate the respective corrections to the anomalous scaling exponents of the
scalar field and show that they continuously depend on velocity correlation
time and the degree of non-Gaussianity. The scalar exponents are thus non
universal as was predicted by Shraiman and Siggia on a phenomenological ground
(CRAS {\bf 321}, 279, 1995).Comment: 4 pages, RevTex 3.0, Submitted to Phys.Rev.Let
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