Fluctuation-dissipation relation on a Melde string in a turbulent flow, considerations on a "dynamical temperature"

3,5 new printed pagesWe report on measurements of the transverse fluctuations of a string in a turbulent air jet flow. Harmonic modes are excited by the fluctuating drag force, at different wave-numbers. This simple mechanical probe makes it possible to measure excitations of the flow at specific scales, averaged over space and time: it is a scale-resolved, global measurement. We also measure the dissipation associated to the string motion, and we consider the ratio of the fluctuations over dissipation (FDR). In an exploratory approach, we investigate the concept of {\it effective temperature} defined through the FDR. We compare our observations with other definitions of temperature in turbulence. From the theory of Kolmogorov ($1941$), we derive the exponent $-11/3$ expected for the spectrum of the fluctuations. This simple model and our experimental results are in good agreement, over the range of wave-numbers, and Reynolds number accessible ($74000 \leq Re \leq 170000$)

Combinatorial Conversion and Moment Bisimulation for Stochastic Rewriting Systems

We develop a novel method to analyze the dynamics of stochastic rewriting systems evolving over finitary adhesive, extensive categories. Our formalism is based on the so-called rule algebra framework and exhibits an intimate relationship between the combinatorics of the rewriting rules (as encoded in the rule algebra) and the dynamics which these rules generate on observables (as encoded in the stochastic mechanics formalism). We introduce the concept of combinatorial conversion, whereby under certain technical conditions the evolution equation for (the exponential generating function of) the statistical moments of observables can be expressed as the action of certain differential operators on formal power series. This permits us to formulate the novel concept of moment-bisimulation, whereby two dynamical systems are compared in terms of their evolution of sets of observables that are in bijection. In particular, we exhibit non-trivial examples of graphical rewriting systems that are moment-bisimilar to certain discrete rewriting systems (such as branching processes or the larger class of stochastic chemical reaction systems). Our results point towards applications of a vast number of existing well-established exact and approximate analysis techniques developed for chemical reaction systems to the far richer class of general stochastic rewriting systems

La gestion des groupes de variables en recherche directe

RÉSUMÉ La Recherche par Coordonnées (CS), la Recherche par Motifs Généralisée (GPS) et la Recherche Directe sur Treillis Adaptatif (MADS) sont des exemples d’algorithmes robustes en optimisation non lin´eaire et non lisse. Afin d’améliorer la solution courante, ces méthodes utilisent des directions d’exploration qui affectent soit une seule variable à la fois (CS), soit plusieurs variables à la fois (GPS et MADS). Nous nous proposons ici de formaliser et généraliser ces approches, à travers le concept de “groupes” de variables : chaque groupe, gérée par l’algorithme de manière ´evolutive, génère des points d’essai en ne modifiant que les variables le concernant. Cela permet la construction d’un voisinage particulier potentiellement fructueux : dans le cas de variables de positionnement par exemple, cela permet de d´eplacer des objets ou des collections d’objets de manière individuelle. On utilise pour cette étude le logiciel NOMAD développé par Le Digabel (2009), qui est une implémentation écrite en C++ des tout derniers algorithmes de ce type, à savoir BIMADS et ORTHOMADS, respectivement introduits par Audet et al. (2008d) et Abramson et al. (2009b). Ces méthodes sont conçues pour l’optimisation de boîtes noires : les évaluations des fonctions relatives aux objectifs et contraintes sont le résultat d’un processus opaque, typiquement un code informatique. Par conséquent, ces fonctions peuvent ˆetre non lisses, non linéaires, non convexes ou discontinues, avec possiblement des domaines de d´efinition très fragmentés. Nous souhaitons également nous atteler à la résolution de problématiques concrètes liées à ce type d’optimisation : nous traiterons en particulier le cas d’un problème de localisation de balises à rayonnement gamma, sur des cartes en deux dimensions à domaines réalisables très fragmentés. Ce projet, mené en collaboration avec l’Institut de recherche d’HYDROQUE BEC (IREQ), vise à améliorer la pr´ecision de l’estimation du manteau neigeux et de l’équivalent Eau-Neige, afin de gérer les prévisions hydriques tout au long de l’année, et plus particulièrement aux moments critiques tels que la fonte des neiges printanière.----------Abstract Coordinate Search (CS), Generalized Pattern Search (GPS) and Mesh Adaptive Direct Search (MADS) are examples of robust algorithms for nonsmooth nonlinear optimization. To improve the current solution, these methods use exploratory directions that affect either a single variable at a time (CS), or several variables at once (GPS and MADS). We will formalize and generalize these approaches, through the concept of “groups” of variables : each group, managed by the algorithm dynamically, generates trial points by only changing the variables concerning them. This allows the construction of a particular and potentially fruitful neighborhood : for example, in the case of positioning variables, the algorithm can move objects or collections of objects sequentially. We use for this research the software NOMAD developed by Le Digabel (2009), which is an C++ implementation of the very latest MADS algorithms, namely BIMADS and ORTHOMADS, respectively introduced by Audet et al. (2008d) and Abramson et al. (2009b). These methods are designed for blackbox optimization : the evaluations of the objective and constraint functions are the result of an opaque process, typically a computer code. Therefore, these functions may be nonsmooth, non-linear, non-convex or discontinuous, with possibly highly fragmented domains. We aim to solve practical issues linked to this type of optimization : we will focus on the case of a gamma-monitoring beacons location problem, on two-dimensional maps with very fragmented domains. This project, in collaboration with the Research Institute of HYDRO-QUEBEC (IREQ), aims to improve the snowpack estimate accuracy in order to manage the hydrological forecast throughout the year, especially at critical times such as spring snowmelt

Random integrals and correctors in homogenization

International audienceThis paper concerns the homogenization of a one-dimensional elliptic equation with oscillatory random coefficients. It is well-known that the random solution to the elliptic equation converges to the solution of an effective medium elliptic equation in the limit of a vanishing correlation length in the random medium. It is also well-known that the corrector to homogenization, i.e., the difference between the random solution and the homogenized solution, converges in distribution to a Gaussian process when the correlations in the random medium are sufficiently short-range. Moreover, the limiting process may be written as a stochastic integral with respect to standard Brownian motion. We generalize the result to a large class of processes with long-range correlations. In this setting, the corrector also converges to a Gaussian random process, which has an interpretation as a stochastic integral with respect to fractional Brownian motion. Moreover, we show that the longer the range of the correlations, the larger is the amplitude of the corrector. Derivations are based on a careful analysis of random oscillatory integrals of processes with long-range correlations. We also make use of the explicit expressions for the solutions to the one-dimensional elliptic equation

Experimental investigation of rotating waves as a rotating stall inception indication in compressors

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1989.Includes bibliographical references (leaves 85-87).by Vincent Hubert Garnier.M.S

An experimental evaluation of two effective medium theories for ultrasonic wave propagation in concrete

9 pagesInternational audienceThis study compares ultrasonic wave propagation modeling and experimental data in concrete. As a consequence of its composition and manufacturing process, this material has a high elastic scattering (sand and aggregates) and air (microcracks and porosities) content. The behavior of the "Waterman-Truell" and "Generalized Self Consistent Method" dynamic homogenization models are analyzed in the context of an application for strong heterogeneous solid materials, in which the scatterers are of various concentrations and types. The experimental validations of results predicted by the models are carried out by making use of the phase velocity and the attenuation of longitudinal waves, as measured by an immersed transmission setup. The test specimen material has a cement-like matrix containing spherical inclusions of air or glass, with radius close to the ultrasonic wavelength. The models are adapted to the case of materials presenting several types of scattering particle, and allow the propagation of longitudinal waves to be described at the scale of materials such as concrete. The validity limits for frequency and for particle volume ratio can be approached through a comparison with experimental data. The potential of these homogenization models for the prediction of phase velocity and attenuation in strongly heterogeneous solids is demonstrated

Effects of the nature of the doping salt and of the thermal pre-treatment and sintering temperature on spark plasma sintering of transparent alumina

A slurry of a-Al2O3 was doped with Mg, Zr and La nitrates or chlorides, in various amounts in the range 150-500 wt ppm and then freeze-dried to produce nanosized doped powder (~150 nm). The powder was sintered by SPS to yield transparent polycrystalline alpha alumina. The influence of the nature of the doping element and the starting salt, the thermal treatment before sintering and the sintering emperature on the transparency of the ceramics were investigated. The transparency of the ceramics of nanosized Al2O3 was shown to depend mainly on the way the powder was prepared, the nature of the doping salt also had an effect. Finally, a high real inline transmittance, reaching 48.1% was achieved after optimization

Identification de modèles LPV : application à la modélisation pluie/débit d'un bassin versant viticole

International audienceL'identification de la relation pluie/débit dans un bassin versant pour la prédiction de débit est un problème stimulant de par la difficulté à caractériser un modèle les décrivant dans leur ensemble. Les modèles conceptuels, basés sur les lois et modèles hydrauliques simples sont sou- vent limités dans la précision de la prédiction qu'ils offrent. L'objectif de cet article est d'une part de montrer l'intérêt des modèles non linéaires de type Linéaires à Paramètres Variants (LPV) par rapport aux modèles linéaires, ainsi que la différence de qualité dans les résultats obtenus selon la méthode employée pour l'identification d'un modèle donné. D'autre part, cet article propose et analyse plusieurs variables de séquencement dont dépendent les paramètres variants des modèles LPV pour représenter les bassins versants ruraux

A new data-based modelling method for identifying parsimonious nonlinear rainfall/flow models

International audienceThe identification of rainfall/runoff relationship is a challenging issue, mainly because of the complexity to find a suitable model for a whole given catchment. Conceptual hydrological models fail to describe correctly the dynamic changes of the system for different rainfall events (e.g. intensity or duration). However, the need for such relationship grows with the water pollution increase in agricultural regions. Lately, a well-known type of model in the control field appears to be a suitable candidate for water processes identification: the Linear Parameter Varying (LPV) models. This paper depicts a novel refined instrumental variable based method for the identification of Input/Output LPV models and this algorithm is applied to identify a parsimonious nonlinear rainfall/flow model of a 42 ha vineyard catchment located in Alsace, France