The Hurst Exponent of Fermi GRBs

Using a wavelet decomposition technique, we have extracted the Hurst exponent for a sample of 46 long and 22 short Gamma-ray bursts (GRBs) detected by the Gamma-ray Burst Monitor (GBM) aboard the Fermi satellite. This exponent is a scaling parameter that provides a measure of long-range behavior in a time series. The mean Hurst exponent for the short GRBs is significantly smaller than that for the long GRBs. The separation may serve as an unbiased criterion for distinguishing short and long GRBs.Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Societ

Numerical Schemes for Rough Parabolic Equations

This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0, 1) perturbed by a non-linear rough signal. It is the continuation of [8, 7], where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H \textgreater{} 1/3.Comment: Applied Mathematics and Optimization, 201

Multifractal stationary random measures and multifractal random walks with log-infinitely divisible scaling laws

We define a large class of continuous time multifractal random measures and processes with arbitrary log-infinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined log-normal Multifractal Random Walk (MRW) [Bacry-Delour-Muzy] and the log-Poisson "product of cynlindrical pulses" [Barral-Mandelbrot]. Our construction is based on some ``continuous stochastic multiplication'' from coarse to fine scales that can be seen as a continuous interpolation of discrete multiplicative cascades. We prove the stochastic convergence of the defined processes and study their main statistical properties. The question of genericity (universality) of limit multifractal processes is addressed within this new framework. We finally provide some methods for numerical simulations and discuss some specific examples.Comment: 24 pages, 4 figure

Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series

Notwithstanding the significant efforts to develop estimators of long-range correlations (LRC) and to compare their performance, no clear consensus exists on what is the best method and under which conditions. In addition, synthetic tests suggest that the performance of LRC estimators varies when using different generators of LRC time series. Here, we compare the performances of four estimators [Fluctuation Analysis (FA), Detrended Fluctuation Analysis (DFA), Backward Detrending Moving Average (BDMA), and centred Detrending Moving Average (CDMA)]. We use three different generators [Fractional Gaussian Noises, and two ways of generating Fractional Brownian Motions]. We find that CDMA has the best performance and DFA is only slightly worse in some situations, while FA performs the worst. In addition, CDMA and DFA are less sensitive to the scaling range than FA. Hence, CDMA and DFA remain "The Methods of Choice" in determining the Hurst index of time series.Comment: 6 pages (including 3 figures) + 3 supplementary figure

Renormalization flow for extreme value statistics of random variables raised to a varying power

Using a renormalization approach, we study the asymptotic limit distribution of the maximum value in a set of independent and identically distributed random variables raised to a power q(n) that varies monotonically with the sample size n. Under these conditions, a non-standard class of max-stable limit distributions, which mirror the classical ones, emerges. Furthermore a transition mechanism between the classical and the non-standard limit distributions is brought to light. If q(n) grows slower than a characteristic function q*(n), the standard limit distributions are recovered, while if q(n) behaves asymptotically as k.q*(n), non-standard limit distributions emerge.Comment: 21 pages, 1 figure,final version, to appear in Journal of Physics

On the magnetic fields generated by experimental dynamos

We review the results obtained by three successful fluid dynamo experiments and discuss what has been learnt from them about the effect of turbulence on the dynamo threshold and saturation. We then discuss several questions that are still open and propose experiments that could be performed to answer some of them.Comment: 40 pages, 13 figure

Solar Wind Turbulence and the Role of Ion Instabilities

International audienc

Study of reconnection-associated multi-scale fluctuations with Cluster and Double Star

The objective of the paper is to asses the specific spectral scaling properties of magnetic reconnection associated fluctuations/turbulence at the Earthward and tailward outflow regions observed simultaneously by the Cluster and Double Star (TC-2) spacecraft on September 26, 2005. Systematic comparisons of spectral characteristics, including variance anisotropy and scale-dependent spectral anisotropy features in wave vector space were possible due to the well-documented reconnection events, occurring between the positions of Cluster (X = -14--16 $R_e$) and TC-2 (X = -6.6 $R_e$). Another factor of key importance is that the magnetometers on the spacecraft are similar. The comparisons provide further evidence for asymmetry of physical processes in Earthward/tailward reconnection outflow regions. Variance anisotropy and spectral anisotropy angles estimated from the multi-scale magnetic fluctuations in the tailward outflow region show features which are characteristic for magnetohydrodynamic cascading turbulence in the presence of a local mean magnetic field. The multi-scale magnetic fluctuations in the Earthward outflow region are exhibiting more power, lack of variance and scale dependent anisotropies, but also having larger anisotropy angles. In this region the magnetic field is more dipolar, the main processes driving turbulence are flow breaking/mixing, perhaps combined with turbulence ageing and non-cascade related multi-scale energy sources.Comment: 30 pages, 6 figure

“Savages Who Speak French”: Folklore, Primitivism and Morals in Robert Hertz

Hertz's analysis of the Alpine cult of Saint Besse apparently marks a break from his studies of death, sin and the left to folkloric studies. This analysis helps one to understand the personality of Robert Hertz. His sociological curiosity about folklore reveals his ambiguous position in social sciences at the beginning of the twentieth century. His text appears to be a variation from the Durkheimian norm, but another reading could suggest that Hertz continued and went beyond Durkheimian thought to something between sociology of the modern world and engaged socialism. Through this study, Hertz linked his political ideals, his work in ethnology and his desire for social involvement. The cult of Saint Besse perpetuated as much religious tradition as local identity. The Alpine people were presented in the text as wilful perpetuators of an ideal social order, whose loss for his contemporary city dwellers Hertz feared. The alpine Other, marked by a material and moral backwardness, represented for activist and socialist Hertz one of the paths of balanced social organization that stabilized the identity of a group across time if it fit rather well into the folkloric stereotypes of the beginning of the twentieth century. Finally, by linking events in Herz's life (e.g., the accidental Alpine death of his father), this article suggests that the legend of Saint Besse embodied several recurring motifs in Hertz' career: the accidental deaths of saint and father by falls, the military role of the saint and of Hertz himself