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

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

The global picture of self-similar and not self-similar decay in Burgers Turbulence

This paper continue earlier investigations on the decay of Burgers turbulence in one dimension from Gaussian random initial conditions of the power-law spectral type $E_0(k)\sim|k|^n$. Depending on the power $n$, different characteristic regions are distinguished. The main focus of this paper is to delineate the regions in wave-number $k$ and time $t$ in which self-similarity can (and cannot) be observed, taking into account small-$k$ and large-$k$ cutoffs. The evolution of the spectrum can be inferred using physical arguments describing the competition between the initial spectrum and the new frequencies generated by the dynamics. For large wavenumbers, we always have $k^{-2}$ region, associated to the shocks. When $n$ is less than one, the large-scale part of the spectrum is preserved in time and the global evolution is self-similar, so that scaling arguments perfectly predict the behavior in time of the energy and of the integral scale. If $n$ is larger than two, the spectrum tends for long times to a universal scaling form independent of the initial conditions, with universal behavior $k^2$ at small wavenumbers. In the interval $2<n$ the leading behaviour is self-similar, independent of $n$ and with universal behavior $k^2$ at small wavenumber. When $1<n<2$, the spectrum has three scaling regions : first, a $|k|^n$ region at very small $k$\ms1 with a time-independent constant, second, a $k^2$ region at intermediate wavenumbers, finally, the usual $k^{-2}$ region. In the remaining interval, $n<-3$ the small-$k$ cutoff dominates, and $n$ also plays no role. We find also (numerically) the subleading term $\sim k^2$ in the evolution of the spectrum in the interval $-3<n<1$. High-resolution numerical simulations have been performed confirming both scaling predictions and analytical asymptotic theory.Comment: 14 pages, 19 figure

Automates de gaz sur réseaux. Aspects théoriques et simulations

Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe

Lattice gas hydrodynamics

info:eu-repo/semantics/publishe

Transport et fluctuations de densité dans les systèmes désordonnés (applications à la dispersion atmosphétique)

Le transport turbulent de particules est un phénomène important qui intervient dans de nombreux processus naturels et industriels. Comprendre ses propriétés et, en particulier, la création de grandes fluctuations de densité, est fondamental pour améliorer les modèles et affiner les prévisions. Cela représente de nombreux enjeux économiques, environnementaux et de santé. Une étude Lagrangienne de la séparation de paires de traceurs a été menée en s'appuyant sur l'analyse des données de simulations numériques à très haute résolution. Elle a permis de souligner les défaillances des approches de type champ moyen qui sont à la base des modèles les plus couramment utilisés. Pour la séparation, on constate que la transition entre le régime balistique de Batchelor et le régime explosif de Richardson a lieu à des temps données par le temps moyen de dissipation de l'énergie cinétique turbulente. Aussi, il est montré que la loi de Richardson peut s'interpréter comme un comportement diffusif des différences de vitesse. Des arguments phénoménologiques permettent d'interpréter cet effet par la décorrélation de différences d'accélération et la stationnarité aux temps longs du taux local de transfert d'énergie cinétique. Les moments d'ordres élevés de la séparation et de la vitesse sont aussi étudiés pour aborder la question des événements violents dans la distribution des distances. Enfin, un modèle d'éjection de masse est proposé et utilisé pour examiner les fluctuations de la densité de particules lourdes transportées dans un environnement aléatoire.The turbulent transport of particles is an important phenomena which appears in many natural and industrial processes. Understanding its properties, and, in particular, the creation of strong density fluctuations, is fundamental to improve models and refine forecasts. This can lead to significant benefits in issues related to economics, the environmental and health. A Lagrangian study of the tracer pair separation was carried out with the help of high resolution data analysis. This allowed us to point out the weaknesses of the mean-field approaches on which most models are based. For the separation, it is found that the transition from the regime of Batchelor (or ballistic) to that of Richardson (or explosive) occurs at times given by those typical of the turbulent kinetic energy dissipation. It is also found that Richardson s law can be reinterpreted in terms of diffusive behaviour of the velocity differences. Phenomenological arguments allow us to explain this effect through the decorrelation of the acceleration differences and the stationarity of the kinetic energy transfer ratio at large times. The high-order moments of both separation and velocity are also investigated to address the question of "violent events" in the distribution of the distances. Finally, a one-dimensional mass ejection model is proposed and used to examine the density fluctuations of heavy particles transported by the random environment.NICE-BU Sciences (060882101) / SudocSudocFranceF

Vortex Interactions in 2-D Lattice Gas Automata

info:eu-repo/semantics/publishe