Lognormal scale invariant random measures

In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with lognormal weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation; these measures fall under the scope of the Gaussian multiplicative chaos theory developed by J.P. Kahane in 1985 (or possibly extensions of this theory). As a by product, we also obtain an explicit characterization of the covariance structure of these measures. We also prove that qualitative properties such as long-range independence or isotropy can be read off the equation.Comment: 31 pages; Probability Theory and Related Fields (2012) electronic versio

Magnetic field relaxation in ferromagnetic Ising systems

We analyze the thermal magnetization reversal processes in magnetic grains. Two experiments are carried out: swtiching time and switching field experiments. In both cases, we find that the simulated behavior is coherent with existing experimental data (the streched exponent of the switching time experiment increases with the temperature and is superior to unity; there exists a master curve for the switching field experiment). Moreover, we simulated magnetic grains in a region of parameters where no experimental data are available. We find that the relaxation time distribution $P(\ln{\tau})$ is gaussian, and we find the existence of a strong field regime.Comment: 9 pages, 7 figures, J.M.M.

Markov properties of high frequency exchange rate data

We present a stochastic analysis of a data set consisiting of 10^6 quotes of the US Doller - German Mark exchange rate. Evidence is given that the price changes x(tau) upon different delay times tau can be described as a Markov process evolving in tau. Thus, the tau-dependence of the probability density function (pdf) p(x) on the delay time tau can be described by a Fokker-Planck equation, a gerneralized diffusion equation for p(x,tau). This equation is completely determined by two coefficients D_{1}(x,tau) and D_{2}(x,tau) (drift- and diffusion coefficient, respectively). We demonstrate how these coefficients can be estimated directly from the data without using any assumptions or models for the underlying stochastic process. Furthermore, it is shown that the solutions of the resulting Fokker-Planck equation describe the empirical pdfs correctly, including the pronounced tails.Comment: 29 pages, 19 eps figures, misprints corrected, under consideration for publication in Physica

Generalized scaling in fully developed turbulence

In this paper we report numerical and experimental results on the scaling properties of the velocity turbulent fields in several flows. The limits of a new form of scaling, named Extended Self Similarity(ESS), are discussed. We show that, when a mean shear is absent, the self scaling exponents are universal and they do not depend on the specific flow (3D homogeneous turbulence, thermal convection , MHD). In contrast, ESS is not observed when a strong shear is present. We propose a generalized version of self scaling which extends down to the smallest resolvable scales even in cases where ESS is not present. This new scaling is checked in several laboratory and numerical experiment. A possible theoretical interpretation is also proposed. A synthetic turbulent signal having most of the properties of a real one has been generated.Comment: 25 pages, plain Latex, figures are available upon request to the authors ([email protected], [email protected]

Characterisation and modelling of aging of composites

International audienceThe aim of this study was to better understand the aging of glass fibre-epoxy composites exposed to humid conditions and loading so as to predict its effects on the lifetimes of composite structures. Water diffusion in the material was initially determined by gravimetric methods under different conditions of relative humidity (r.h.) conditions. A fickian model of diffusion could describe the results obtained. The specimens, saturated at different levels, were mechanically characterised and tensile strengths and shear moduli were seen to decrease with water uptake. The effects of matrix cracking of the laminate on water absorption and its mechanical properties have also been studied. Differences between reversible and irreversible changes in properties were revealed and analysed in detail. A predictive model has been proposed by considering different sections throughout the thickness of the material. As a first step in modelling the diffusion process, the non-uniform water distribution across the composite for any conditions (temperature, humidity, aging time) are determined. The resulting mechanical properties of the material, as a function of the absorbed water concentration, are determined in each point. The model which is proposed enables the global behaviour of composite to be determined, at all stages of water absorption and matrix cracking, by calculating behaviour in each section of the composite through its thickness

Zeolites fit for a crown:Studying organic-framework host-guest interactions through thermogravimetric techniques

Every year millions of tons of zeolites are produced, being used as molecular sieves, hydrocracking catalysts, gas-capture materials and for emerging novel applications. There is a demand to synthesise new zeolites with bespoke frameworks, which are tailor-made for a chosen application. To achieve these ‘designer zeolites’ it is crucial to fully understand the host-guest interactions between organic additives and zeolitic frameworks. Here we have studied four different zeolites, synthesised with the same organic additive, 18-crown-6 ether, which show observable differences in the host-guest interactions. We demonstrate that the framework geometry dominates the decomposition temperature, enthalpy and mechanism. The zeolites show unique decomposition features, emphasising experimental differences in how the organic additive and framework interact.</p

Plume motion and large-scale circulation in a cylindrical Rayleigh-B\'enard cell

We used the time correlation of shadowgraph images to determine the angle $\Theta$ of the horizontal component of the plume velocity above (below) the center of the bottom (top) plate of a cylindrical Rayleigh-B\'enard cell of aspect ratio $\Gamma \equiv D/L = 1$ ($D$ is the diameter and $L \simeq 87$ mm the height) in the Rayleigh-number range $7\times 10^7 \leq R \leq 3\times 10^{9}$ for a Prandtl number $\sigma = 6$. We expect that $\Theta$ gives the direction of the large-scale circulation. It oscillates time-periodically. Near the top and bottom plates $\Theta(t)$ has the same frequency but is anti-correlated.Comment: 4 pages, 6 figure

Effects of electromagnetic waves on the electrical properties of contacts between grains

A DC electrical current is injected through a chain of metallic beads. The electrical resistances of each bead-bead contacts are measured. At low current, the distribution of these resistances is large and log-normal. At high enough current, the resistance distribution becomes sharp and Gaussian due to the creation of microweldings between some beads. The action of nearby electromagnetic waves (sparks) on the electrical conductivity of the chain is also studied. The spark effect is to lower the resistance values of the more resistive contacts, the best conductive ones remaining unaffected by the spark production. The spark is able to induce through the chain a current enough to create microweldings between some beads. This explains why the electrical resistance of a granular medium is so sensitive to the electromagnetic waves produced in its vicinity.Comment: 4 pages, 5 figure

Intermittency and the Slow Approach to Kolmogorov Scaling

From a simple path integral involving a variable volatility in the velocity differences, we obtain velocity probability density functions with exponential tails, resembling those observed in fully developed turbulence. The model yields realistic scaling exponents and structure functions satisfying extended self-similarity. But there is an additional small scale dependence for quantities in the inertial range, which is linked to a slow approach to Kolmogorov (1941) scaling occurring in the large distance limit.Comment: 10 pages, 5 figures, minor changes to mirror version to appear in PR