Rarefaction indices

There are at least two indices used to measure the size of bounded sets of n of zero measure—Hausdorff dimension (see [4] for a definition), and the density index [7

On various multifractal spectra

International audienceWe introduce two classes of multifractal spectra, called respectively dimension and continuous spectra. Dimension spectra offer an interesting alternative to the classical Hausdorff spectrum: They are much easier to estimate yet still give relevant information about the geometry of the H¨older function. Continuous spectra are a generalization of the large deviation spectrum that allow to obtain partition free results. Both classes of spectra allow to perform efficient multifractal analysis in an experimental framewor

Continuous Large Deviation Multifractal Spectrum: Definition and Estimation

International audienceThe 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 Hölder exponent is equal to a Höder 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

Modeling carbon black reinforcement in rubber compounds

General hypotheses of the model -- Microscopic interaction between aggregates -- Idealized response of the microscopic model -- Statistical description