This paper demonstrates that intermittent magnetic field fluctuations in the plasma sheet exhibit transitory, localized, and multi-scale features. We propose a multifractal based algorithm, which quantifies intermittence on the basis of the statistical distribution of the 'strength of burstiness', estimated within a sliding window. Interesting multi-scale phenomena observed by the Cluster spacecraft include large scale motion of the current sheet and bursty bulk flow associated turbulence, interpreted as a cross-scale coupling (CSC) process.

Multi-scale magnetic field intermittence in the plasma sheet

We study several extensions of Besov spaces; these extensions include the oscillation spaces Ops,s’which take into account correlations between the positions of large wavelet coefficients through the scales and, more generally, spaces defined through the distributions of suprema of wavelet coefficients on wavelet subtrees. These spaces are independent of the particular wavelet basis chosen. Examples of applications will be taken from image processing and multifractal analysis.

Beyond Besov Spaces, Part 2: Oscillation Spaces

Response time series with a non-Gaussian distribution and long-range dependent dynamics have been reported for several cognitive tasks. Conventional monofractal analyses numerically define a long-range dependency as a single scaling exponent, but they assume that the response times are Gaussian distributed. Ihlen and Vereijken (Journal of Experimental Psychology: General, 139, 436-463, 2010) suggested multifractal extensions of the conventional monofractal analyses that are more suitable when the response time has a non-Gaussian distribution. Multifractal analyses estimate a multifractal spectrum of scaling exponents that contain the single exponent estimated by the conventional monofractal analyses. However, a comparison of the performance of multifractal analyses with behavioral variables has not yet been addressed. The present study compares the performance of seven multifractal analyses. The multifractal analyses were tested on multiplicative cascading noise that generates time series with a predefined multifractal spectrum and with a structure of variation that mimics intermittent response time variation. Time series with 1,024 and 4,096 samples were generated with additive noise and multiharmonic trends of two different magnitudes (signal-to-noise/trend ratio; 0.33 and 1). The results indicate that all multifractal analysis has individual pros and cons related to sample size, multifractality, and the presence of additive noise and trends in the response time series. The summary of pros and cons of the seven multifractal analyses provides a guideline for the choice of multifractal analyses of response time series and other behavioral variables.

/pdf/multifractal-analyses-of-response-time-series-a-comparative-1tvtzalopz.pdf

Multifractal analyses of response time series: A comparative study

In order to contribute to the understanding of solar wind/magnetosphere interactions the multifractal scaling properties of high-latitude geomagnetic fluctuations observed at the Thule observatory have been studied. Using the local observatory data and the present experimental knowledge only it seems hard to characterize directly the, presumably intermittent, mesoscale energy accumulation and dissipation processes taking place at the magnetotail, auroral region, etc. Instead a positive probability measure, describing the accumulated local geomagnetic signal energy content at the given time scales has been introduced and its scaling properties have been studied. There is evidence for the multifractal nature of the so defined intermittent field e, a result obtained by using the recently introduced technique of large deviation multifractal spectra. This technique allows us to describe the geomagnetic fluctuations locally in time by means of singularity exponents α, which represent a generalization of the local degree of differentiability and characterize the power-law scaling dependence of the introduced measure on resolution. A global description of the geomagnetic fluctuations is insured by the spectrum of exponents f(α) which represents a rate function quantifying the deviations of the observed singularities α from the expected value. The results show that there exists a multifractal counterpart of the previously reported spectral break and different types of f(α) spectra describe the fluctuations in direct dissipation or loading/unloading regimes of the solar wind-magnetosphere interaction. On the time scale of substorms and storms the multifractal structure of the loading-unloading mode fluctuations seems to be analogous to the simple multiplicative P-model, while the f(α) spectra in direct dissipation regime are close but not equal to the features of a uniform distribution. Larger deviations from the multiplicative model are observed when the influence of the solar wind fluctuations is examined. On this basis it is expected that an extended multifractal analysis of the singularity structure of near-Earth plasma system fluctuations would lead to improved geomagnetic diagnosis of the magnetospheric dynamics.

/pdf/on-multifractality-of-high-latitude-geomagnetic-fluctuations-10kypxekoc.pdf

On multifractality of high-latitude geomagnetic fluctuations

Multifractal modelling of electrochemical noise in corrosion of carbon steel

The large deviation multifractal spectrum gives important statistical informations on irregular measures. However it is difficult to estimate. In this paper, we propose two new definitions of the large deviation spectrum better adapted to the design of various estimators. They rely on the computation of the Lebesgue measure of the reunion of all intervals of same size whose coarse grain Holder exponent is equal to a Hoder exponent. In particular, we introduce the continuous large deviation spectrum for which we construct different estimators. We finally show some numerical results obtained on both deterministic and random synthetical signals.

https://hal.inria.fr/inria-00592418/document

Continuous Large Deviation Multifractal Spectrum: Definition and Estimation

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Continuous Large Deviation Multifractal Spectrum: Definition and Estimation