Detecting vorticity filaments using wavelet analysis: About the statistical contribution of vorticity filaments to intermittency in swirling turbulent flows

Swirling turbulent flows display intermittent pressure drops associated with intense vorticity filaments. Using the wavelet transform modulus maxima representation of pressure fluctuations, we propose a method of characterizing these pressure drop events from their time-scale properties. This method allows us to discriminate fluctuations induced by just formed (young) as well as by burst (old) filaments from background pressure fluctuations. The statistical characteristics of these filaments (core size, waiting time) are analyzed in details and compared with previously reported experimental and numerical findings. Their intermittent occurrence is found to be governed by a pure Poisson's law, the hallmark of independent events. Then we apply the wavelet transform modulus maxima (WTMM) method to the background pressure fluctuations. This study reveals that, once removed all the filaments, the “multifractal” nature of pressure fluctuations still persists. This is a clear indication that the statistical contribution of the filaments is not important enough to account for the intermittency phenomenon in turbulents flows. Received 27 July 1998 and Received in final form 23 November 1998     

A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and anisotropic random rough surfaces

We generalize the so-called wavelet transform modulus maxima (WTMM) method to multifractal image analysis. We show that the implementation of this method provides very efficient numerical techniques to characterize statistically the roughness fluctuations of fractal surfaces. We emphasize the wide range of potential applications of this wavelet-based image processing method in fundamental as well as applied sciences. This paper is the first one of a series of three articles. It is mainly devoted to the methodology and to test applications on random self-affine surfaces (e.g., isotropic fractional Brownian surfaces and anisotropic monofractal rough surfaces). Besides its ability to characterize point-wise regularity, the WTMM method is definitely a multiscale edge detection method which can be equally used for pattern recognition, detection of contours and image denoising. Paper II (N. Decoster, S.G. Roux, A. Arnéodo, to be published in Eur. Phys. J. B 15 (2000)) will be devoted to some applications of the WTMM method to synthetic multifractal rough surfaces. In paper III (S.G. Roux, A. Arnéodo, N. Decoster, to be published in Eur. Phys. J. 15 (2000)), we will report the results of a comparative experimental analysis of high-resolution satellite images of cloudy scenes. Received 8 July 1999     

Modelling fluctuations of financial time series: from cascade process to stochastic volatility model

In this paper, we provide a simple, “generic” interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as recently observed in reference [23], naturally emerge. We then propose a simple solvable “stochastic volatility” model for return fluctuations. This model is able to reproduce most of recent empirical findings concerning financial time series: no correlation between price variations, long-range volatility correlations and multifractal statistics. Moreover, its extension to a multivariate context, in order to model portfolio behavior, is very natural. Comparisons to real data and other models proposed elsewhere are provided. Received 22 May 2000     

Two interacting particles in a disordered chain I: Multifractality of the interaction matrix elements

For N interacting particles in a one dimensional random potential, we study the structure of the corresponding network in Hilbert space. The states without interaction play the role of the “sites”. The hopping terms are induced by the interaction. When the one body states are localized, we numerically find that the set of directly connected “sites” is multifractal. For the case of two interacting particles, the fractal dimension associated to the second moment of the hopping term is shown to characterize the Golden rule decay of the non interacting states and the enhancement factor of the localization length. Received: 17 April 1998 / Accepted: 14 May 1998     

Three-dimensional wavelet-based multifractal method: the need for revisiting the multifractal description of turbulence dissipation data

We generalize the wavelet transform modulus maxima (WTMM) method to multifractal analysis of 3D random fields. This method is calibrated on synthetic 3D monofractal fractional Brownian fields and on 3D multifractal singular cascade measures as well as their random function counterpart obtained by fractional integration. Then we apply the 3D WTMM method to the dissipation field issued from 3D isotropic turbulence simulations. We comment on the need to revisit previous box-counting analyses which have failed to estimate correctly the corresponding multifractal spectra because of their intrinsic inability to master nonconservative singular cascade measures.     

A generalized spin model of financial markets

We reformulate the Cont-Bouchaud model of financial markets in terms of classical “super-spins” where the spin value is a measure of the number of individual traders represented by a portfolio manager of an investment agency. We then extend this simplified model by switching on interactions among the super-spins to model the tendency of agencies getting influenced by the opinion of other managers. We also introduce a fictitious temperature (to model other random influences), and time-dependent local fields to model a slowly changing optimistic or pessimistic bias of traders. We point out close similarities between the price variations in our model with N super-spins and total displacements in an N-step Levy flight. We demonstrate the phenomena of natural and artificially created bubbles and subsequent crashes as well as the occurrence of “fat tails” in the distributions of stock price variations. Received 13 October 1998     

A note on the screening of hydrodynamic interactions, in electrophoresis, and in porous media

We consider two situations where hydrodynamic interactions are said to be “screened”: hydrodynamics in a gel or in a porous medium, and electrophoresis in an electrolyte. We focus on the corresponding Green functions, and show that the flow fields are similar in the two cases. Contrarily to statements often made, the fluid velocity decays algebraically with distance (), i.e. not exponentially. We point out that the pressure fields are different in the two cases. Received 23 March 2000