Kinetic decomposition for periodic homogenization problems

We develop an analytical tool which is adept for detecting shapes of oscillatory functions, is useful in decomposing homogenization problems into limit-problems for kinetic equations, and provides an efficient framework for the validation of multi-scale asymptotic expansions. We apply it first to a hyperbolic homogenization problem and transform it to a hyperbolic limit problem for a kinetic equation. We establish conditions determining an effective equation and counterexamples for the case that such conditions fail. Second, when the kinetic decomposition is applied to the problem of enhanced diffusion, it leads to a diffusive limit problem for a kinetic equation that in turn yields the effective equation of enhanced diffusion

Homogenization of linear transport equations in a stationary ergodic setting

We study the homogenization of a linear kinetic equation which models the evolution of the density of charged particles submitted to a highly oscillating electric field. The electric field and the initial density are assumed to be random and stationary. We identify the asymptotic microscopic and macroscopic profiles of the density, and we derive formulas for these profiles when the space dimension is equal to one.Comment: 24 page

DFIG-based wind turbine fault diagnosis using a specific discrete wavelet transform

International audienc

Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case

We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading terms of the asymptotic expansions for the eigenelements and verify the asymptotics

The Navier wall law at a boundary with random roughness

We consider the Navier-Stokes equation in a domain with irregular boundaries. The irregularity is modeled by a spatially homogeneous random process, with typical size \eps \ll 1. In a parent paper, we derived a homogenized boundary condition of Navier type as \eps \to 0. We show here that for a large class of boundaries, this Navier condition provides a O(\eps^{3/2} |\ln \eps|^{1/2}) approximation in $L^2$, instead of O(\eps^{3/2}) for periodic irregularities. Our result relies on the study of an auxiliary boundary layer system. Decay properties of this boundary layer are deduced from a central limit theorem for dependent variables

Sex differences in adrenal cortex beta-catenin immunolocalization of the Saharan gerbil, Libyan jird (Meriones libycus, Lichtenstein, 1823)

Background: The adrenal cortex provides adequate steroidogenic responses to environmental changes. However, in desert rodents, the adrenocortical activity varies according to several factors especially sex, age, and seasonal variations. Herein, we examined the sex differences in the adrenal cortex activity and explored the involvement of sex hormones in the regulation of this function in Libyan jird Meriones libycus. Materials and methods: Twenty-four adults male and female animals weighing 109-110g were captured in the breeding season and equally assigned into control and gonadectomised groups. Animal euthanasia was performed 50 days after the gonadectomy. Adrenal gland was processed for structural and immunohistochemistry study of β-catenin, whereas plasma was used for cortisol assay. Results: The results showed that female adrenal gland weight was heavier than male and gonadectomy reduced this dimorphism. The adrenal cortex thickness was greater in the female than in the male, mainly due to significant development of the zona fasciculata. Females presented higher cell density in fasciculata and reticularis zones. The plasma cortisol was higher in females than in males. The immunolocalization of β-catenin showed that the expression was particularly glomerular in both sexes. However, in the female, the immunostaining was present in the zona reticularis while it was absent in the control male. Orchiectomy reduced zona glomerulosa cell density and induced hypertrophy of zona reticularis characterized by strong β-catenin immunoreactivity. However, ovariectomy leads to hyperplastic expansion and high β-catenin expression in the zona glomerulosa associated with zona fasciculata and reticularis hypoplasia distinguished by weak β-catenin immunostaining. Conclusions: Results indicated that sex hormones had a major role in the regulation of the Saharan gerbil’s adrenal homeostasis by modulating β-catenin signaling. Androgens seem to inhibit the Wnt β-catenin pathway and estrogens are activators of the adrenal inner zones

A computational study of the influence of surface roughness on material strength

In machine component stress analysis, it usually assumed that the geometry specified in CAD provides a fair representation of the geometry of the real component. While in particular circumstances, tolerance information, such as minimum thickness of a highly stressed region, might be taken into consideration, there is no standard practice for the representation of surface quality. It is known that surface roughness significantly influences fatigue life, but for this to be useful in the context of life prediction, there is a need to examine the nature of surface roughness and determine how best to characterise it. Non-smooth geometry can be represented in mathematics by fractals or other methods, but for a representation to have a practical value for a manufactured component, it is necessary to accept that there is a lower limit to surface profile measurement resolution. Resolution and mesh refinement also play a part in any computational analysis undertaken to assess surface profile effects: in the analyses presented, a nominal axi-symmetric geometry has been taken, with a finite non-smooth region on the boundary. Various surface roughness representations are modelled, and the significance of the characterized surface roughness type is investigated. It is shown that the applied load gives rise to a nominally uni-axial stress state of 90% of the yield, although surface roughness features have the effect of modifying the load path, and give rise to localized regions of plasticity near to the surface. The material of the test model is assumed to be elasto-plastic, and the development and evolution of plastic zones formed within the geometry are shown for multiple load cycles

Weak and strong solutions of equations of compressible magnetohydrodynamics

International audienceThis article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions. Then, existence of strong solutions in the neighbourhood of equilibrium states is reviewed, in particular with the method of Kawashima and Shizuta. Finally, the special case of dimension one is highlighted : the use of Lagrangian coordinates gives a simpler system, which is solved by standard techniques

Réalisation d'un simulateur de gestion d'énergie électrique embarquée

L'objectif de l'article est la présentation d'un simulateur pour la gestion de l'énergie électrique embarquée à bord d'un véhicule. Ce simulateur se présente sous la forme d'une maquette pédagogique réalisée par des étudiants dans le cadre des projets du Master PROTEE (production et traitement de l'énergie électrique) de l'université de franche-comté. Il intègre des éléments issus de technologies récentes telles que l'alternodémareur qui équipe la Citroën C3, des supercondensateurs, un convertisseur d'énergie statique réversible (onduleur/redresseur), un volant d'inertie ainsi qu'une batterie classique. Ces divers éléments sont interconnectés entre eux de façon électrique ou mécanique. Le bon fonctionnement de l'ensemble a nécessité la réalisation de plusieurs cartes électroniques autour des microcontrôleurs PIC permettant l'exploitation dans un cadre pédagogique de la maquette. En effet, ces différentes cartes électroniques permettent de traiter les informations issues des différents capteurs, le contrôle du convertisseur statique, l'interface de dialogue avec l'utilisateur et un système informatique telle que dSPACE. Ces derniers sont introduits afin d'assurer, d'une part la supervision, la surveillance et la sûreté de fonctionnement de l'ensemble, et d'autre part, la mise en oeuvre de différentes stratégies de gestion de l'énergie. L'évaluation des différents rendements et puissances mécaniques et électriques mises en jeu est possible aussi bien en ligne qu'en différé puisque le système assure le stockage des différentes mesures. Ce projet est pluridisciplinaire et permet aux étudiants de faire le lien entre les différents modules enseignés en Master PROTEE