Continuous nonlinear eigenvalue solver with applications to the design of electro/magnetorheological sandwich structures

International audienceSmart sandwich structures comprising an electro-or a magnetorheo-logical material have the potential to attenuate vibration over a wide range of frequencies. The analysis of their vibration behaviour with respect to the continuous variation of the field intensity is thus a major challenge for research and industry to maximize damping treatments. The numerical higher order homotopy method we propose models the effects of a continuous variation of the field intensity on resonant frequencies and loss factors by means of Taylor expansions. Comparisons between our continuous approach and the classical incremental method are proposed for state of the art sandwich beams and plate structures comprising ER/MR fluids to highlight the benefits of our continuous methods in terms of maximal damping determination

Quantum nature of the critical points of substances

Thermodynamics of chemical elements, based on the two-component electron-nuclear plasma model shows that the critical parameters for the liquid-vapor transition are the quantum values for which the classical limit is absent.Comment: 4 pages, no figure

Mathematical modeling of bioremediation of trichloroethylene in aquifers

AbstractTrichloroethylene (TCE) is a very common contaminant of groundwater. It is used as an industrial solvent and is frequently poured into the soil. There exist bacteria that can degrade TCE. In contrast with most cases of bioremediation, the bacteria that degrade TCE do not use it as a carbon source. Instead the bacteria produce an enzyme to metabolize methane. This enzyme can degrade other organics including TCE. In this paper we model in situ bioremediation of TCE in an aquifer by using two species of bacteria: one that forms biobarriers to restrict the movement of TCE and the second one to reduce TCE. The model includes flow of water, transport of TCE and the nutrients, bacterial growth and degradation of TCE. Nonstandard numerical methods are used to discretize the equations. Some results are presented

Do the generalized polynomial chaos and Fröbenius methods retain the statistical moments of random differential equations?

The aim of this paper is to explore whether the generalized polynomial chaos (gPC) and random Fröbenius methods preserve the first three statistical moments of random differential equations. There exist exact solutions only for a few cases, so there is a need to use other techniques for validating the aforementioned methods in regards to their accuracy and convergence. Here we present a technique for indirectly study both methods. In order to highlight similarities and possible differences between both approaches, the study is performed by means of a simple but still illustrative test-example involving a random differential equation whose solution is highly oscillatory. This comparative study shows that the solutions of both methods agree very well when the gPC method is developed in terms of the optimal orthogonal polynomial basis selected according to the statistical distribution of the random input. Otherwise, we show that results provided by the gPC method deteriorate severely. A study of the convergence rates of both methods is also included.This work has been partially supported by the Spanish M.C.Y.T. grants MTM2009-08587, DPI2010-20891-C02-01 as well as the Universitat Politecnica de Valencia grants PAID06-11 (ref. 2070) and PAID00-11 (ref. 2753).Chen Charpentier, BM.; Cortés López, JC.; Romero Bauset, JV.; Roselló Ferragud, MD. (2013). Do the generalized polynomial chaos and Fröbenius methods retain the statistical moments of random differential equations?. Applied Mathematics Letters. 26(5):553-558. doi:10.1016/j.aml.2012.12.013S55355826

Méthode d'auto-fuzzyfication par analyse des typicalités sur des lots de données réduits

Cet article expose une méthode de fuzzyfication automatique pour un classificateur à base de règles linguistiques floues. Elle s'appuie sur l'analyse des scores de typicalité des attributs caractérisant les formes à classer. La méthode proposée est appliquée à la reconnaissance de couleur sur des avivés. L'utilisation d'un classificateur flou n'étant pas aisée pour des non experts, l'industrialisation d'une telle méthode nécessite une simplification des phases de réglages. En outre, le cadre applicatif spécifique de cette étude ne permet d'avoir à disposition qu'une quantité de données réduite pour réaliser la phase d'apprentissage. Les scores de typicalité des attributs présentent l'avantage de discriminer les plages de valeurs associées à chaque classe couleur de sortie. L'étude des corrélations de ces typicalités améliore la fuzzyfication des paramètres et les essais réalisés sur des lots de données « industrielles » montrent l'augmentation du taux de reconnaissance. Ces taux sont comparés à ceux obtenus à partir d'une fuzzyfication équirépartie. Par ailleurs, une diminution du nombre de règles floues générées dans le modèle est constatée. Les temps de traitements en généralisation sont ainsi réduits

Color sorting system by fuzzy sensor

This article presents a color recognition system formalized under the fuzzy sensor concept. The main objective is to improve the color classification of wooden boards. Our study relates the development of an industrial vision system allowing the recognition of gradual colors. This context imposes a strong reliability constraint, because the currently used sensors are not always enough robust. Then, we are interested in techniques which improve the taking into account of the physical measure imprecision and the uncertainty concerning the definition of the wood color by a Human, the color classes being always neither identified nor separated. Moreover, the different users can have different perceptions of them. Besides, the vision system must be easy to tune. To carry out such a system, we propose to base the fuzzy sensor on a classification method with fuzzy linguistic rules (Fuzzy Reasoning Classifier) which main advantages reside in its generalization capacity from small training data sets and in the interpretability of its rule set. The obtained results show the efficiency of our intelligent sensor.Cet article présente un système de reconnaissance couleur formalisé sous le concept de capteur flou. L’objectif principal est d’améliorer la classification couleur de planches de bois. Notre étude concerne le développement d’un système de vision industriel permettant la reconnaissance de couleurs graduelles. Ce contexte impose une contrainte forte de fiabilité, les capteurs utilisés aujourd’hui n’étant pas toujours suffisamment robustes. Ainsi, nous nous sommes intéressés à des techniques qui améliorent la prise en compte des imprécisions des mesures physiques et la subjectivité concernant la définition de la couleur du bois par l’Homme, les classes de couleur n’étant jamais bien identifiées ni séparées. De plus, les différents utilisateurs peuvent en avoir des perceptions différentes. Par ailleurs, et dans ce contexte particulier, un système de vision doit être simple à régler. Pour réaliser un tel système, nous proposons de baser le capteur flou sur une méthode de classification par règles linguistiques floues (Fuzzy Reasoning Classifier) dont les principaux avantages résident dans sa capacité de généralisation à partir de lot de données réduits en apprentissage et dans l’interprétabilité de sa base de règles. Les résultats que nous obtenons montrent l’efficacité de notre capteur intelligent

A simple model of immune and muscle cell crosstalk during muscle regeneration

Muscle injury during aging predisposes skeletal muscles to increased damage due to reduced regenerative capacity. Some of the common causes of muscle injury are strains, while other causes are more complex muscle myopathies and other illnesses, and even excessive exercise can lead to muscle damage. We develop a new mathematical model based on ordinary differential equations of muscle regeneration. It includes the interactions between the immune system, healthy and damaged myonuclei as well as satellite cells. Our new mathematical model expands beyond previous ones by accounting for 21 specific parameters, including those parameters that deal with the interactions between the damaged and dead myonuclei, the immune system, and the satellite cells. An important assumption of our model is the replacement of only damaged parts of the muscle fibers and the dead myonuclei. We conduce systematic sensitivity analysis to determine which parameters have larger effects on the model and therefore are more influential for the muscle regeneration process. We propose additional validation for these parameters. We further demonstrate that these simulations are species-, muscle-, and age-dependent. In addition, the knowledge of these parameters and their interactions, may suggest targeting or selecting these interactions for treatments that accelerate the muscle regeneration process

Appariement couleur de planches de bois par inférence floue

Cet article présente une méthode de classification de couleurs sur des planches de bois à partir d'un mécanisme à base de systèmes d'inférences floues implémenté à travers l'algorithme d'Ishibuchi-Nozaki-Tanaka. Le raisonnement flou permet de prendre en compte la subjectivité de la perception des couleurs au sein d'un produit « bois ». De plus, les informations extraites des images ne peuvent pas être considérées comme précises et certaines. L'utilisation de notre méthode améliore les taux de reconnaissance en apprentissage et en généralisation dans la classification des couleurs du bois, mais aussi sur le benchmark IRIS

Thermal Diffusion of a Two Layer System

In this paper thermal conductivity and thermal diffusivity of a two layer system is examined from the theoretical point of view. We use the one dimensional heat diffusion equation with the appropriate solution in each layer and boundary conditions at the interfaces to calculate the heat transport in this bounded system. We also consider the heat flux at the surface of the samle as boundary condition instead of using a fixed tempertaure. From this, we obtain an expression for the efective thermal diffusivity of the composite sample in terms of the thermal diffusivity of its constituent materials whithout any approximations.Comment: 16 pages, 1 figure, RevTeX v. 3.0 macro packag