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

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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

Magnetic Flux Density Measurement in Permanent Magnet Synchronous Machines

International audience— This paper describes two measurement techniques of the air gap flux density in a small permanent magnet synchronous machine. The first method is based of the harmonic analysis of the induced voltage in a search coil placed on the inner periphery of the stator, while the second relies on the analysis of the induced voltage in the stator windings. Accurate results can be achieved since the measurement procedure relies only on well defined electrical quantities regardless of the dimensions of the machine. A further appreciation of the accuracy of the proposed measurement procedures can be confirmed by the reconstruction of the stator induced voltages. Although each method has its own merit in terms of field sensing, they are basically identical; nonetheless they enable a cross comparison of the measured results