Power law spectra and intermittent fluctuations due to uncorrelated Lorentzian pulses

A stochastic model for intermittent fluctuations due to a super-position of uncorrelated Lorentzian pulses is presented. For constant pulse duration, this is shown to result in an exponential power spectral density for the stationary process. A random distribution of pulse durations modifies the frequency spectrum and several examples are shown to result in power law spectra. The distribution of pulse durations does not influence the characteristic function and thus neither the moments nor the probability density function for the random variable. It is demonstrated that the fluctuations are intrinsically intermittent through a large excess kurtosis moment in the limit of weak pulse overlap. These results allow to estimate the basic properties of fluctuations from measurement data and describe the diversity of frequency spectra reported from measurements in magnetized plasmas.Comment: 12 pages, 4 figure

Intermittent fluctuations due to uncorrelated Lorentzian pulses

Fluctuations due to a super-position of uncorrelated Lorentzian pulses with a random distribution of amplitudes and duration times are considered. These are demonstrated to be strongly intermittent in the limit of weak pulse overlap, resulting in large skewness and flatness moments. The characteristic function and the lowest order moments are derived, revealing a parabolic relationship between the skewness and flatness moments. Numerical integration reveals the probability density functions in the case of exponential and Laplace distributed pulse amplitudes. This stochastic model describes the intermittent fluctuations and probability densities with exponential tails commonly observed in turbulent fluids and magnetized plasmas.Comment: 12 pages, 3 figure

Preface "Nonlinear processes in oceanic and atmospheric flows"

Nonlinear phenomena are essential ingredients in many oceanic and atmospheric processes, and successful understanding of them benefits from multidisciplinary collaboration between oceanographers, meteorologists, physicists and mathematicians. The present Special Issue on ``Nonlinear Processes in Oceanic and Atmospheric Flows'' contains selected contributions from attendants to the workshop which, in the above spirit, was held in Castro Urdiales, Spain, in July 2008. Here we summarize the Special Issue contributions, which include papers on the characterization of ocean transport in the Lagrangian and in the Eulerian frameworks, generation and variability of jets and waves, interactions of fluid flow with plankton dynamics or heavy drops, scaling in meteorological fields, and statistical properties of El Ni\~no Southern Oscillation.Comment: This is the introductory article to a Special Issue on "Nonlinear Processes in Oceanic and Atmospheric Flows'', published in the journal Nonlinear Processes in Geophysics, where the different contributions are summarized. The Special Issue itself is freely available from http://www.nonlin-processes-geophys.net/special_issue103.htm

Explicit towers of Drinfeld modular curves

We give explicit equations for the simplest towers of Drinfeld modular curves over any finite field, and observe that they coincide with the asymptotically optimal towers of curves constructed by Garcia and Stichtenoth.Comment: 10 pages. For mini-symposium on "curves over finite fields and codes" at the 3rd European Congress in Barcelona 7/2000 Revised to correct minor typographical and grammatical error

Kalikow-type decomposition for multicolor infinite range particle systems

We consider a particle system on $\mathbb{Z}^d$ with real state space and interactions of infinite range. Assuming that the rate of change is continuous we obtain a Kalikow-type decomposition of the infinite range change rates as a mixture of finite range change rates. Furthermore, if a high noise condition holds, as an application of this decomposition, we design a feasible perfect simulation algorithm to sample from the stationary process. Finally, the perfect simulation scheme allows us to forge an algorithm to obtain an explicit construction of a coupling attaining Ornstein's $\bar{d}$-distance for two ordered Ising probability measures.Comment: Published in at http://dx.doi.org/10.1214/12-AAP882 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

White dwarf cooling sequences and cosmochronology

The evolution of white dwarfs is a simple gravothermal process. This means that their luminosity function, i.e. the number of white dwarfs per unit bolometric magnitude and unit volume as a function of bolometric magnitude, is a monotonically increasing function that decreases abruptly as a consequence of the finite age of the Galaxy. The precision and the accuracy of the white dwarf luminosity functions obtained with the recent large surveys together with the improved quality of the theoretical models of evolution of white dwarfs allow to feed the hope that in a near future it will be possible to reconstruct the history of the different Galactic populations.Comment: Proceedings of the 40th Liege International Astrophysical Colloquium: Aging low mass stars: from red giants to white dwarf