608,584 research outputs found

### 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

### Computation of canonical correlation and best predictable aspect of future for time series

The canonical correlation between the (infinite) past and future of a stationary time series is shown to be the limit of the canonical correlation between the (infinite) past and (finite) future, and computation of the latter is reduced to a (generalized) eigenvalue problem involving (finite) matrices. This provides a convenient and essentially, finite-dimensional algorithm for computing canonical correlations and components of a time series. An upper bound is conjectured for the largest canonical correlation

### Real Time Correlation Functions at Finite Temperature and their Classical Limit

In order to investigate the reliability of the classical approximation for
non-perturbative real time correlation functions at finite temperature we study
the two-point correlator for the anharmonic oscillator. For moderately large
times the classical limit gives a good approximation of the quantum result but
after some time $t_*$ the classical approximation breaks down even at high
temperature.Comment: 6 pages, Talk given at the E"otv"os Conference in Science: Strong and
Electroweak Matter, Eger, Hungary, 21-25 May 199

### Classical Real Time Correlation Functions And Quantum Corrections at Finite Temperature

We consider quantum corrections to classical real time correlation functions
at finite temperature. We derive a semi-classical expansion in powers of
$\hbar$ with coefficients including all orders in the coupling constant. We
give explicit expressions up to order $\hbar^2$. We restrict ourselves to a
scalar theory. This method, if extended to gauge theories, might be used to
compute quantum corrections to the high temperature baryon number violation
rate in the Standard Model.Comment: 21 pages (revtex

### Spectral analysis of finite-time correlation matrices near equilibrium phase transitions

We study spectral densities for systems on lattices, which, at a phase
transition display, power-law spatial correlations. Constructing the spatial
correlation matrix we prove that its eigenvalue density shows a power law that
can be derived from the spatial correlations. In practice time series are short
in the sense that they are either not stationary over long time intervals or
not available over long time intervals. Also we usually do not have time series
for all variables available. We shall make numerical simulations on a
two-dimensional Ising model with the usual Metropolis algorithm as time
evolution. Using all spins on a grid with periodic boundary conditions we find
a power law, that is, for large grids, compatible with the analytic result. We
still find a power law even if we choose a fairly small subset of grid points
at random. The exponents of the power laws will be smaller under such
circumstances. For very short time series leading to singular correlation
matrices we use a recently developed technique to lift the degeneracy at zero
in the spectrum and find a significant signature of critical behavior even in
this case as compared to high temperature results which tend to those of random
matrix models.Comment: 4 pages, 5 figure

### Random Sequential Adsorption of Objects of Decreasing Size

We consider the model of random sequential adsorption, with depositing
objects, as well as those already at the surface, decreasing in size according
to a specified time dependence, from a larger initial value to a finite value
in the large time limit. Numerical Monte Carlo simulations of two-dimensional
deposition of disks and one-dimensional deposition of segments are reported for
the density-density correlation function and gap-size distribution function,
respectively. Analytical considerations supplement numerical results in the
one-dimensional case. We investigate the correlation hole - the depletion of
correlation functions near contact and, for the present model, their vanishing
at contact - that opens up at finite times, as well as its closing and
reemergence of the logarithmic divergence of correlation properties at contact
in the large time limit.Comment: Submitted for publicatio

### Noise in laser speckle correlation and imaging techniques

We study the noise of the intensity variance and of the intensity correlation
and structure functions measured in light scattering from a random medium in
the case when these quantities are obtained by averaging over a finite number N
of pixels of a digital camera. We show that the noise scales as 1/N in all
cases and that it is sensitive to correlations of signals corresponding to
adjacent pixels as well as to the effective time averaging (due to the finite
sampling time) and spatial averaging (due to the finite pixel size). Our
results provide a guide to estimation of noise level in such applications as
the multi-speckle dynamic light scattering, time-resolved correlation
spectroscopy, speckle visibility spectroscopy, laser speckle imaging etc.Comment: submitted 14 May 201

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