Stochastic Analysis of the Eigenvalue Problem for Mechanical Systems Using Polynomial Chaos Expansion: Application to a Finite Element Rotor

International audienceThis paper proposes to use a polynomial chaos expansion approach to compute stochastic complex eigenvalues and eigenvectors of structures including damping or gyroscopic effects. Its application to a finite element rotor model is compared to Monte Carlo simulations. This lets us validate the method and emphasize its advantages. Three different uncertain configurations are studied. For each, a stochastic Campbell diagram is proposed and interpreted and critical speeds dispersion is evaluated. Furthermore, an adaptation of the Modal Accordance Criterion is proposed in order to monitor the eigenvectors dispersion

Mineral studies in enamel, an exemplary model system at the interface between physics, chemistry and medical sciences

AbstractEnamel is an exemplary material for physicochemical analyses of biological mineral. Hereditary and environmental enamel defects as well as secondary decay processes induce degradation and destruction of enamel matter. This exceptional mineralized tissue is unable to regenerate due to the loss of the cell forming enamel: the ameloblasts. Deciphering mechanisms of enamel degradation represent a scientific challenge of economic interest. The interface between physics, chemistry, and biomedical science has been initiated for a long time. An updated review of a classical and routinely available set of different techniques is proposed to illustrate the interface between oral sciences and physico-chemistry. Research in this field has greatly evolved over the past decade thanks to various extremely sensitive techniques in Materials Science available for translational research in biomedicine

Steady-state response of a random dynamical system described with Padé approximants and random eigenmodes

Designing a random dynamical system requires the prediction of the statistics of the response, knowing the random model of the uncertain parameters. Direct Monte Carlo simulation (MCS) is the reference method for propagating uncertainties but its main drawback is the high numerical cost. A surrogate model based on a polynomial chaos expansion (PCE) can be built as an alternative to MCS. However, some previous studies have shown poor convergence properties around the deterministic eigenfrequencies. In this study, an extended Pade approximant approach is proposed not only to accelerate the convergence of the PCE but also to have a better representation of the exact frequency response, which is a rational function of the uncertain parameters. A second approach is based on the random mode expansion of the response, which is widely used for deterministic dynamical systems. A PCE approach is used to calculate the random modes. Both approaches are tested on an example to check their efficiency

Shedding Light on the Chemical Diversity of Ectopic Calcifications in Kidney Tissues: Diagnostic and Research Aspects

In most industrialized countries, different epidemiologic studies show that chronic renal failure is dramatically increasing. Such major public health problem is a consequence of acquired systemic diseases such as type II diabetes, which is now the first cause for end stage renal failure. Furthermore, lithogenic diseases may also induce intratubular crystallization, which may finally result in end-stage renal failure (ESRF). Up to now, such rare diseases are often misdiagnosed. In this study, based on twenty four biopsies, we show that SR µFTIR (Synchrotron Radiation-µFourier transform infrared) spectroscopy constitutes a significant opportunity to characterize such pathological µcalcifications giving not only their chemical composition but also their spatial distribution in the tissues. This experimental approach offers new opportunities to the clinicians to describe at the cell level the physico-chemical processes leading to the formation of the pathological calcifications which lead to ESRF

FAM20A Gene Mutation: Amelogenesis or Ectopic Mineralization?

Background and objective:FAM20A gene mutations result in enamel renal syndrome (ERS) associated with amelogenesis imperfecta (AI), nephrocalcinosis, gingival fibromatosis, and impaired tooth eruption. FAM20A would control the phosphorylation of enamel peptides and thus enamel mineralization. Here, we characterized the structure and chemical composition of unerupted tooth enamel from ERS patients and healthy subjects.Methods: Tooth sections were analyzed by Scanning Electron Microscopy (SEM), Energy Dispersive Spectroscopy (EDS), X-Ray Diffraction (XRD), and X-Ray Fluorescence (XRF).Results: SEM revealed that prisms were restricted to the inner-most enamel zones. The bulk of the mineralized matter covering the crown was formed by layers with varying electron-densities organized into lamellae and micronodules. Tissue porosity progressively increased at the periphery, ending with loose and unfused nanonodules also observed in the adjoining soft tissues. Thus, the enamel layer covering the dentin in all ERS patients (except a limited layer of enamel at the dentino-enamel junction) displayed an ultrastructural globular pattern similar to one observed in ectopic mineralization of soft tissue, notably in the gingiva of Fam20a knockout mice. XRD analysis confirmed the existence of alterations in crystallinity and composition (vs. sound enamel). XRF identified lower levels of calcium and phosphorus in ERS enamel. Finally, EDS confirmed the reduced amount of calcium in ERS enamel, which appeared similar to dentin.Conclusion: This study suggests that, after an initial normal start to amelogenesis, the bulk of the tissue covering coronal dentin would be formed by different mechanisms based on nano- to micro-nodule aggregation. This evocated ectopic mineralization process is known to intervene in several soft tissues in FAM20A gene mutant

Elaboration et caractérisation de phases cristal liquides de suspensions de rutile (TiO2). Propriétés physiques anisotropes

TiO2 rutile nanorods of average length L = 160 +/- 40 nm and average diameter D = 15 +/- 5 nm have been synthesized through a seed-mediated growth process by TiCl4 hydrolysis in concentrated acidic solution, inspired of a Chimie Douce method. These nanorods were dispersed in water to yield stable (aggregation-free) colloidal aqueous suspensions. At volume fractions phy > 3%, the suspensions spontaneously display a phase separation into an isotropic liquid phase and a liquid-crystalline phase identified as nematic by X-ray scattering. At phy > 12 %, the suspensions form a nematic single phase, with large order parameter, S = 0.75 +/- 0.05. Very well aligned rutile films on glass substrate were produced by spin-coating and their photocatalytic properties were examined by monitoring the decomposition of methylene blue under UV-light. We found that UV-light polarized along the quadratic axis of the rutile nanorods was most efficient for this photocatalytic reaction. Some experiments of conduction have been performed. TiO2 rutile is a semi conductor with, for the bulk, a gap of around 3 eV. As in the photocatalytic studies, the polarized UV-light has a huge influence on the charge transport. A Schottky diode behaviour has been observed and explained. Irradiation in the visible spectrum has been shown to have no consequence on the properties of conduction. Rutile films have been also characterized to estimate the correction for the gap of anisotropic nanoparticles. Finally, a thermal study and a comparison with a monocrystal have been done.Les phases cristal-liquides minérales se situent à l'interface de la chimie colloïdale, de la physique de la matière molle et de la physique du solide. Largement utilisées dans l'industrie, les nanoparticules de TiO2 de variété rutile sont des candidates de choix à une étude visant à relier propriétés du matériau massif et propriétés d'une assemblée orientée de petits objets anisotropes.Le travail présenté montrera comment il est possible d'élaborer par Chimie Douce des nanoparticules anisotropes afin d'obtenir en milieu aqueux une mésophase, de nature nématique, et de la caractériser. De plus, des suspensions de bâtonnets, même relativement diluées, s'orientent sous cisaillement, ce qui permet de produire par spin-coating des films anisotropes. Ces films sont des échantillons de choix pour effectuer des mesures, sous irradiation ultraviolette, de photocatalyse d'espèces organiques dissoutes ou encore de photoconduction. Ces mesures peuvent être comparées avec les résultats obtenus à l'aide d'un monocristal de TiO2 présentant les mêmes facettes cristallographique [110] que les nanoparticules.Un film orienté de bâtonnets de rutile présente naturellement des propriétés anisotropes. En outre, nous avons mis en évidence une forte dépendance des propriétés catalytiques et de la conductivité électronique avec la polarisation de l'irradiation ultra-violette. Nous montrerons dans quelle mesure la théorie des bandes permet d'expliquer ces effets

Analyse dynamique de structures comportant des paramètres incertains

Dans le cadre de la mobilisation de structures comportant des paramètres incertains, on s'intéresse aux caractéristiques des réponses statiques et dynamiques de systèmes mécaniques. On distingue dans cette étude le cas de paramètres aléatoires à loi de probabilité connue et le cas de variables dont on ne connaît que les bornes. Dans cette optique, on s'applique dans une première partie à décrire les réponses dynamiques, aussi bien les fonctions de transfert que les modes propres, de structures comportant des paramètres modélisés comme des variables aléatoires. Pour ce faire, on utilise une méthode de projection sur une base de polynômes orthogonaux (chaos polynomial), qui permet d'obtenir les caractéristiques principales des réponses. Dans une deuxième partie, on utilise l'arihmétique des intervalles pour résoudre les problèmes statiques et dynamiques. Après avoir proposé une formulation adaptée à la modélisation des systèmes mécaniques, on reformule un algorithme de résolution de systèmes linéaires intervalles, qu'on utilise alors pour trouver les enveloppes des réponses cherchées.We are interested in the modelling of structures with uncertain parameters. We focus on the characteristics of static and dynamic responses of such mechanical systems. We distinguish in this study two cases : first, the case of random parameters with a known probability law and second the case of variables of which only the bounds are known. In a first part, we investigate the case of structures with uncertain parameters modelled as random variables. We are particularly interested in the dynamic responses, as well the frequency response functions as the eigenmodes. An inovative method is carried out, which consists in a projection on orthogonal polynomial (polynomial chaos) that leads to the main stochastic characteristics of the responses. In a second part, we use the interval arithmetic to solve static and dynamic problems. We first propose an adapted formulation of the mathematical problems with respect to the finite element modeling of mechanical systems. We then introduce a new formulation of an iterative algorithm that leads to enveloppes of responses for interval linear systems.LYON-Ecole Centrale (690812301) / SudocSudocFranceF

High Prevalence of Opaline Silica in Urinary Stones From Burkina Faso REPLY

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