Random Wavelet Series: Theory and Applications

Random Wavelet Series form a class of random processes with multifractal properties. We give three applications of this construction. First, we synthesize a random function having any given spectrum of singularities satisfying some conditions (but including non-concave spectra). Second, these processes provide examples where the multifractal spectrum coincides with the spectrum of large deviations, and we show how to recover it numerically. Finally, particular cases of these processes satisfy a generalized selfsimilarity relation proposed in the theory of fully developed turbulence.Comment: To appear in Annales Math\'ematiques Blaise Pasca

Fourier integrals operators on lie groupoids

As announced in [12], we develop a calculus of Fourier integral G-operators on any Lie groupoid G. For that purpose, we study convolability and invertibility of Lagrangian conic submanifolds of the symplectic groupoid T * G. We also identify those Lagrangian which correspond to equivariant families parametrized by the unit space G (0) of homogeneous canonical relations in (T * Gx \ 0) x (T * G x \ 0). This allows us to select a subclass of Lagrangian distributions on any Lie groupoid G that deserve the name of Fourier integral G-operators (G-FIO). By construction, the class of G-FIO contains the class of equivariant families of ordinary Fourier integral operators on the manifolds Gx, x $\in$ G (0). We then develop for G-FIO the first stages of the calculus in the spirit of Hormander's work. Finally, we work out an example proving the efficiency of the present approach for studying Fourier integral operators on singular manifolds

Influence of activated carbons on the kinetics and mechanisms of aromatic molecules ozonation

Companies have been looking for new methods for treating toxic or refractory wastewaters; which can mainly be used prior to or after or in connexion with biological treatment processes.This paper compares conventional ozone oxidation with activatedcarbon (AC) promoted ozone oxidation, which helps developing a mechanism involving HOradical dot radical. For a compound which is quite easy to oxidise, like 2,4-dichlorophenol (2,4-DCP) conventional ozonation is efficient enough to remove the initial molecule. The mechanism involved mainly consists of an electrophilic attack on the aromatic ring, which is activated by the donor effect of the –OH group, then followed by a 1,3 dipolar cycloaddition (Criegee mechanism) that leads to aliphatic species, mainly carboxylic acids. Yet, the addition of AC, through the presence of HOradical dot radical, enhances the removal of these species which are more refractory.For a refractory compound like nitrobenzene (NB), with a de-activatedaromatic ring because of the attractive effect of –NO2, conventional ozonation is inefficient. On the contrary, this molecule can be quite easily removed with AC promoted oxidation and it is found that the mechanism (electrophilic attack followed by a 1,3 dipolar cycloaddition) is quite similar to the one corresponding to conventional ozonation, but with less selectivity.For both molecules, a mass balance has established that the by-products accounting for more than 75% of the remaining COD can be quantified. A significant part is composed of carboxylic acids (acetic, oxalic, etc.), which could afterwards be easily removed in an industrial wastewater treatment process followed by a final biological treatment step

The HyperBagGraph DataEdron: An Enriched Browsing Experience of Multimedia Datasets

Traditional verbatim browsers give back information in a linear way according to a ranking performed by a search engine that may not be optimal for the surfer. The latter may need to assess the pertinence of the information retrieved, particularly when s$\cdot$he wants to explore other facets of a multi-facetted information space. For instance, in a multimedia dataset different facets such as keywords, authors, publication category, organisations and figures can be of interest. The facet simultaneous visualisation can help to gain insights on the information retrieved and call for further searches. Facets are co-occurence networks, modeled by HyperBag-Graphs -- families of multisets -- and are in fact linked not only to the publication itself, but to any chosen reference. These references allow to navigate inside the dataset and perform visual queries. We explore here the case of scientific publications based on Arxiv searches.Comment: Extension of the hypergraph framework shortly presented in arXiv:1809.00164 (possible small overlaps); use the theoretical framework of hb-graphs presented in arXiv:1809.0019

Strong dynamical effects during stick-slip adhesive peeling

We consider the classical problem of the stick-slip dynamics observed when peeling a roller adhesive tape at a constant velocity. From fast imaging recordings, we extract the dependencies of the stick and slip phases durations with the imposed peeling velocity and peeled ribbon length. Predictions of Maugis and Barquins [in Adhesion 12, edited by K.W. Allen, Elsevier ASP, London, 1988, pp. 205--222] based on a quasistatic assumption succeed to describe quantitatively our measurements of the stick phase duration. Such model however fails to predict the full stick-slip cycle duration, revealing strong dynamical effects during the slip phase.Comment: Soft Matter 201

Oxidation of nitrobenzene by ozone in the presence of faujasite zeolite in a continuous flow gas–liquid–solid reactor

This work investigates the oxidation of nitrobenzene (NB) by ozone in the presence of faujasite zeolite. Experiments were carried out in a gas–liquid–solid reactor were ozone transfer and NB oxidation took place at the same time. Three configurations of the reactor were compared: empty, filled with inert glass beads and filled with faujasite pellets. First, ozone transfer coefficient (kLa) and decomposition rate constant (kC) were determined for each configuration. In presence of solid, kLa was 2.0 to 2.6 times higher and kC was 5.0 to 6.4 times higher compared to the empty reactor. Then, the various configurations were evaluated in terms of NB removal and chemical oxygen demand (COD) decrease. The faujasite reactor showed higher removal of NB and decrease of COD compared to other configurations under the same conditions suggesting that the faujasite increases the oxidation rate of NB. Oxidation of NB in presence of faujasite also proved to be limited by the transfer of ozone from the gas to the liquid phase

Adsorption of Nitrobenzene from Water onto High Silica Zeolites and Regeneration by Ozone

This work investigates the removal of nitrobenzene (NB), a model pollutant from water, by combining adsorption onto zeolites and regeneration with ozone. The adsorption equilibrium isotherms of NB onto zeolites enabled the best adsorbent to be selected and zeolites with a high Si/Al ratio were the most efficient. The adsorption capacity depended on the Si/Al ratio and on the pore size. In a sequential process coupling adsorption and oxidation by ozone, NB was completely removed from water and the initial adsorption capacity of the zeolite was totally restored. Although no catalytic effect was noticed, the adsorption produced locally high concentrations, thus enhancing the oxidation rate for NB