122 research outputs found
A Frequency-selective Filter for Short-Length Time Series
An effective and easy-to-implement frequency filter is designed by convolving a Hamming window with the ideal rectangular filter response function. Three other filters, Hodrick-Prescott, Baxter-King, and Christiano-Fitzgerald, are critically reviewed. The behavior of the Hamming-windowed filter is compared to the others through their frequency responses and their application to both an artificial, known-structure series and to the Euro zone quarterly GDP series. The Hamming-windowed filter has almost no leakage and is thus much better than the others in eliminating high-frequency components and has a significantly flatter bandpass response. Its low-frequency behavior demonstrates better removal of undesired long-term components. These improvements are particularly evident when working with short-length time series, such as are common in macroeconomics. The proposed filter is stationary, symmetric, uses all the information contained in the raw data, and stationarizes series integrated up to order two. It thus proves to be a good candidate for extracting frequency-defined business-cycle componentsspectral analysis, bandpass filtering
Negative magnetic eddy diffusivities from test-field method and multiscale stability theory
The generation of large-scale magnetic field in the kinematic regime in the
absence of an alpha-effect is investigated by following two different
approaches, namely the test-field method and multiscale stability theory
relying on the homogenisation technique. We show analytically that the former,
applied for the evaluation of magnetic eddy diffusivities, yields results that
fully agree with the latter. Our computations of the magnetic eddy diffusivity
tensor for the specific instances of the parity-invariant flow-IV of G.O.
Roberts and the modified Taylor-Green flow in a suitable range of parameter
values confirm the findings of previous studies, and also explain some of their
apparent contradictions. The two flows have large symmetry groups; this is used
to considerably simplify the eddy diffusivity tensor. Finally, a new analytic
result is presented: upon expressing the eddy diffusivity tensor in terms of
solutions to auxiliary problems for the adjoint operator, we derive relations
between magnetic eddy diffusivity tensors that arise for opposite small-scale
flows v(x) and -v(x).Comment: 29 pp., 19 figures, 42 reference
Bifractality of the Devil's staircase appearing in the Burgers equation with Brownian initial velocity
It is shown that the inverse Lagrangian map for the solution of the Burgers
equation (in the inviscid limit) with Brownian initial velocity presents a
bifractality (phase transition) similar to that of the Devil's staircase for
the standard triadic Cantor set. Both heuristic and rigorous derivations are
given. It is explained why artifacts can easily mask this phenomenon in
numerical simulations.Comment: 12 pages, LaTe
Going forth and back in time: a fast and parsimonious algorithm for mixed initial/final-value problems
We present an efficient and parsimonious algorithm to solve mixed
initial/final-value problems. The algorithm optimally limits the memory storage
and the computational time requirements: with respect to a simple forward
integration, the cost factor is only logarithmic in the number of time-steps.
As an example, we discuss the solution of the final-value problem for a
Fokker-Planck equation whose drift velocity solves a different initial-value
problem -- a relevant issue in the context of turbulent scalar transport.Comment: 12 pages, 4 figure
Fluctuations of energy injection rate in a shear flow
We study the instantaneous and local energy injection in a turbulent shear
flow driven by volume forces. The energy injection can be both positive and
negative. Extremal events are related to coherent streaks. The probability
distribution is asymmetric, deviates slightly from a Gaussian shape and depends
on the position in shear direction. The probabilities for positive and negative
injection are exponentially related, but the prefactor in the exponent varies
across the shear layer.Comment: 10 pages, 4 Postscript figure
Pdf's of Derivatives and Increments for Decaying Burgers Turbulence
A Lagrangian method is used to show that the power-law with a -7/2 exponent
in the negative tail of the pdf of the velocity gradient and of velocity
increments, predicted by E, Khanin, Mazel and Sinai (1997 Phys. Rev. Lett. 78,
1904) for forced Burgers turbulence, is also present in the unforced case. The
theory is extended to the second-order space derivative whose pdf has power-law
tails with exponent -2 at both large positive and negative values and to the
time derivatives. Pdf's of space and time derivatives have the same
(asymptotic) functional forms. This is interpreted in terms of a "random Taylor
hypothesis".Comment: LATEX 8 pages, 3 figures, to appear in Phys. Rev.
Single-point velocity distribution in turbulence
We show that the tails of the single-point velocity probability distribution
function (PDF) are generally non-Gaussian in developed turbulence. By using
instanton formalism for the Navier-Stokes equation, we establish the relation
between the PDF tails of the velocity and those of the external forcing. In
particular, we show that a Gaussian random force having correlation scale
and correlation time produces velocity PDF tails at . For a short-correlated forcing
when there is an intermediate asymptotics at .Comment: 9 pages, revtex, no figure
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