Stability of Lie groupoid C*-algebras

In this paper we generalize a theorem of M. Hilsum and G. Skandalis stating that the $C^*$- algebra of any foliation of non zero dimension is stable. Precisely, we show that the C*-algebra of a Lie groupoid is stable whenever the groupoid has no orbit of dimension zero. We also prove an analogous theorem for singular foliations for which the holonomy groupoid as defined by I. Androulidakis and G. Skandalis is not Lie in general

Pseudodifferential extensions and adiabatic deformation of smooth groupoid actions

The adiabatic groupoid $\mathcal{G}_{ad}$ of a smooth groupoid $\mathcal{G}$ is a deformation relating $\mathcal{G}$ with its algebroid. In a previous work, we constructed a natural action of $\mathbb{R}$ on the C*-algebra of zero order pseudodifferential operators on $\mathcal{G}$ and identified the crossed product with a natural ideal $J(\mathcal{G})$ of $C^*(\mathcal{G}_{ad})$. In the present paper we show that $C^*(\mathcal{G}_{ad})$ itself is a pseudodifferential extension of this crossed product in a sense introduced by Saad Baaj. Let us point out that we prove our results in a slightly more general situation: the smooth groupoid $\mathcal{G}$ is assumed to act on a C*-algebra $A$. We construct in this generalized setting the extension of order $0$ pseudodifferential operators $\Psi(A,\mathcal{G})$ of the associated crossed product $A\rtimes \mathcal{G}$. We show that $\mathbb{R}$ acts naturally on $\Psi(A,\mathcal{G})$ and identify the crossed product of $A$ by the action of the adiabatic groupoid $\mathcal{G}_{ad}$ with an extension of the crossed product $\Psi(A,\mathcal{G})\rtimes \mathbb{R}$. Note that our construction of $\Psi(A,\mathcal{G})$ unifies the ones of Connes (case $A=\mathbb{C}$) and of Baaj ($\mathcal{G}$ is a Lie group).Comment: appears in Bulletin des sciences math\'ematiques (2015

Numerical analysis of a penalization method for the three-dimensional motion of a rigid body in an incompressible viscous fluid

We present and analyze a penalization method wich extends the the method of [1] to the case of a rigid body moving freely in an incompressible fluid. The fluid-solid system is viewed as a single variable density flow with an interface captured by a level set method. The solid velocity is computed by averaging at avery time the flow velocity in the solid phase. This velocity is used to penalize the flow velocity at the fluid-solid interface and to move the interface. Numerical illustrations are provided to illustrate our convergence result. A discussion of our result in the light of existing existence results is also given. [1] Ph. Angot, C.-H. Bruneau and P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows, Numer. Math. 81: 497--520 (1999)Comment: 23 page

Can we predict community-wide effects of herbicides from toxicity tests on macrophyte species?

Macrophyte communities play an essential role in the way freshwater ecosystems function. It is thus of great concern to understand how environmental factors, especially anthropogenic ones, influence their composition and diversity. The aim of this study was to examine whether the effects of a herbicide mixture (50% atrazine, 35% isoproturon, 15% alachlor) on single macrophyte species can be used to predict its impact at a community level. In a first experiment we tested the sensitivity of six species (Azolla filiculoides, Ceratophyllum demersum, Elodea canadensis, Lemna minor, Myriophyllum spicatum and Vallisneria spiralis) grown separately and exposed to 0.6–600 gL−1 of the herbicide mixture. In a second experiment, conducted in microcosms, we tested the effects of herbicides on macrophyte assemblages composed of the same six species exposed to 0, 6 or 60 gL−1 of the herbicide mixture. Species grown separately exhibited growth inhibition at 60 and 600 gL−1. At 600 gL−1 the sensitivity differed significantly between species. V. spiralis was the most resistant species, C. demersum, M. spicatum and E. canadensis exhibited intermediate sensitivities, and A. filiculoides and L. minor were the most sensitive species. In microcosms, community biomass and Shannon evenness index were reduced after 8 weeks at 60 gL−1. Communities also exhibited changes in their composition: the relative and absolute abundance of C. demersum increased at 6 gL−1, while the relative abundance of V. spiralis increased at 60 gL−1. These results are in agreement with the individual responses of these species to the herbicides. It is therefore concluded that short-term effects of herbicides on simple macrophyte communities can be predicted from the sensitivity of individual species. However, further investigations are required to examine whether longer term effects can be predicted as well, especially in more complex communities

Lie groupoids, pseudodifferential calculus and index theory

Alain Connes introduced the use of Lie groupoids in noncommutative geometry in his pioneering work on the index theory of foliations. In the present paper, we recall the basic notion involved: groupoids, their C*-algebras, their pseudodifferential calculus... We review several recent and older advances on the involvement of Lie groupoids in noncommutative geometry. We then propose some open questions and possible developments of the subject

Evaluation of a TiO2 photocatalysis treatment on nitrophenols and nitramines contaminated plant wastewaters by solid-phase extraction coupled with ESI HPLC–MS

Nitration reactions of aromatic compounds are commonly involved in different industrial processes for pharmaceutical, pesticide or military uses. For many years, most of the manufacturing sites used lagooning systems to treat their process effluents. In view of a photocatalytic degradation assay, the wastewater of a lagoon was investigated by using HPLC coupled with mass spectrometry. The wastewater was highly concentrated in RDX (hexahydro-1,3,5-trinitro-1,3,5-triazine), HMX (octahydro- 1,3,5,7-tetranitro-1,3,5,7-tetrazocine) and two herbicides Dinoterb (2-tert-butyl-4,6-dinitrophenol) and Dinoseb (2-sec-butyl-4,6-dinitrophenol). First of all, an analytical method using solid-phase extraction (SPE) combined with HPLC ESI MS/MS was put in work for identification and titration of RDX, HMX and the two dinitrophenols in a complex natural matrix. Then, the UV/TiO2 treatment was investigated for pollutants removal. Dinitrophenolic compoundswere significantly degraded after a 8-h-exposition of the wastewater/TiO2 suspension, whereas RDX and HMX were poorly affected

Régulation du système cardio-vasculaire par le système nerveux autonome à court terme : une revue des modèles

Projet SOSSODans ce rapport on examine différents types de modèle qui portent sur la régulation à court terme du système cardiovasculaire par le système nerveux autonome. Par court terme, on entend les interactions qui se passent en moins de 20 secondes. Tous les modèles passés en revue s'appuient sur l'analyse spectrale des variabilités cardiovasculaires pour comparer les simulations avec des données réelles. Le but ultime est de mieux comprendre la régulation des variables cardiovasculaires et de fournir aux médecins spécialistes un outil d'aide au diagnostic

Behavior of nanoparticle clouds around a magnetized microsphere under magnetic and flow fields

When a micron-sized magnetizable particle is introduced into a suspension of nanosized magnetic particles, the nanoparticles accumulate around the microparticle and form thick anisotropic clouds extended in the direction of the applied magnetic field. This phenomenon promotes colloidal stabilization of bimodal magnetic suspensions and allows efficient magnetic separation of nanoparticles used in bioanalysis and water purification. In the present work, size and shape of nanoparticle clouds under the simultaneous action of an external uniform magnetic field and the flow have been studied in details. In experiments, dilute suspension of iron oxide nanoclusters (of a mean diameter of 60 nm) was pushed through a thin slit channel with the nickel microspheres (of a mean diameter of 50$\mu$m) attached to the channel wall. The behavior of nanocluster clouds was observed in the steady state using an optical microscope. In the presence of strong enough flow, the size of the clouds monotonically decreases with increasing flow speed in both longitudinal and transverse magnetic fields. This is qualitatively explained by enhancement of hydrodynamic forces washing the nanoclusters away from the clouds. In the longitudinal field, the flow induces asymmetry of the front and the back clouds. To explain the flow and the field effects on the clouds, we have developed a simple model based on the balance of the stresses and particle fluxes on the cloud surface. This model, applied to the case of the magnetic field parallel to the flow, captures reasonably well the flow effect on the size and shape of the cloud and reveals that the only dimensionless parameter governing the cloud size is the ratio of hydrodynamic-to-magnetic forces - the Mason number. At strong magnetic interactions considered in the present work (dipolar coupling parameter $\alpha \geq 2$), the Brownian motion seems not to affect the cloud behavior

Le lagon sud-ouest de la Nouvelle-Calédonie : observations préalables à la cartographie bionomique des fonds meubles

Depuis 1984, l'ORSTOM a entrepris des études sur le benthos des fonds meubles du lagon de Nouvelle Calédonie. Ce document expose la méthode utilisée pour réaliser une cartographie bionomique à partir des resultats obtenus par dragages. La liste des espèces collectées dans les 489 stations du lagon sud-ouest sont présentées. Un résumé des études antérieures sur le benthos de la région est esquissé, ainsi qu'une description sommaire des caractéristiques physiques du lagon sud-ouest. Quelques informations préliminaires sur les grands types de fonds et les principaux peuplements sont commentées et cartographiées. Des cartes de répartitions sont fournies pour les espèces les plus fréquentes parmi les mollusques et les echinodermes. Des comparaisons biogéographiques sont faites avec les études réalisées à Madagascar, sur la Grande Barrière de Corail australienne et en Polynésie Française. (Résumé d'auteur