2,196,785 research outputs found
Statistics of the Mesoscopic Field
We find in measurements of microwave transmission through quasi-1D dielectric
samples for both diffusive and localized waves that the field normalized by the
square root of the spatially averaged flux in a given sample configuration is a
Gaussian random process with position, polarization, frequency, and time. As a
result, the probability distribution of the field in the random ensemble is a
mixture of Gaussian functions weighted by the distribution of total
transmission, while its correlation function is a product of correlators of the
Gaussian field and the square root of the total transmission.Comment: RevTex: 5 pages, 2 figures; to be presented at Aspects of Quantum
Chaotic Scattering (Dresden, March 7-12, 2005
Intrinsic Variability and Field Statistics for the Vela Pulsar: 2. Systematics and Single-Component Fits
Individual pulses from pulsars have intensity-phase profiles that differ
widely from pulse to pulse, from the average profile, and from phase to phase
within a pulse. Widely accepted explanations do not exist for this variability
or for the mechanism producing the radiation. The variability corresponds to
the field statistics, particularly the distribution of wave field amplitudes,
which are predicted by theories for wave growth in inhomogeneous media. This
paper shows that the field statistics of the Vela pulsar (PSR B0833-45) are
well-defined and vary as a function of pulse phase, evolving from Gaussian
intensity statistics off-pulse to approximately power-law and then lognormal
distributions near the pulse peak to approximately power-law and eventually
Gaussian statistics off-pulse again. Detailed single-component fits confirm
that the variability corresponds to lognormal statistics near the peak of the
pulse profile and Gaussian intensity statistics off-pulse. The lognormal field
statistics observed are consistent with the prediction of stochastic growth
theory (SGT) for a purely linear system close to marginal stability. The
simplest interpretations are that the pulsar's variability is a direct
manifestation of an SGT state and the emission mechanism is linear (either
direct or indirect), with no evidence for nonlinear mechanisms like
modulational instability and wave collapse which produce power-law field
statistics. Stringent constraints are placed on nonlinear mechanisms: they must
produce lognormal statistics when suitably ensemble-averaged. Field statistics
are thus a powerful, potentially widely applicable tool for understanding
variability and constraining mechanisms and source characteristics of coherent
astrophysical and space emissions.Comment: 11 pages, 12 figures. Accepted by Monthly Notices of the Royal
Astronmical Society in April 200
Quantum statistical measurements of an atom laser beam
We describe a scheme, operating in a manner analogous to a reversed Raman
output coupler, for measuring the phase-sensitive quadrature statistics of an
atom laser beam. This scheme allows for the transferral of the atomic field
statistics to an optical field, for which the quantum statistics may then be
measured using the well-developed technology of optical homodyne measurement.Comment: 4 pages, 2 fugure
Extrema statistics in the dynamics of a non-Gaussian random field
When the equations that govern the dynamics of a random field are nonlinear,
the field can develop with time non-Gaussian statistics even if its initial
condition is Gaussian. Here, we provide a general framework for calculating the
effect of the underlying nonlinear dynamics on the relative densities of maxima
and minima of the field. Using this simple geometrical probe, we can identify
the size of the non-Gaussian contributions in the random field, or
alternatively the magnitude of the nonlinear terms in the underlying equations
of motion. We demonstrate our approach by applying it to an initially Gaussian
field that evolves according to the deterministic KPZ equation, which models
surface growth and shock dynamics.Comment: 9 pages, 3 figure
Pair dispersion in synthetic fully developed turbulence
The Lagrangian statistics of relative dispersion in fully developed
turbulence is numerically investigated. A scaling range spanning many decades
is achieved by generating a synthetic velocity field with prescribed Eulerian
statistical features. When the velocity field obeys Kolmogorov similarity, the
Lagrangian statistics is self similar too, and in agreement with Richardson's
predictions. For an intermittent velocity field the scaling laws for the
Lagrangian statistics are found to depend on Eulerian intermittency in
agreement with a multifractal description. As a consequence of the Kolmogorov
law the Richardson law for the variance of pair separation is not affected by
intermittency corrections. A new analysis method, based on fixed scale averages
instead of usual fixed time statistics, is shown to give much wider scaling
range and should be preferred for the analysis of experimental data.Comment: 9 pages, 9 ps figures, submitted to Physics of Fluid
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