Identification of internal cracks in a three-dimensional solid body via Steklov–Poincaré approaches

This Note deals with the identification of internal planar cracks inside a three-dimensional elastic body via two approaches relying on domain decomposition using elastostatic measurements. These approaches consist in recasting the problem in terms of primal or dual Steklov–Poincaré equations. The primal approach is a straightforward continuation to the elastic Cauchy problem of the work presented in J. Ben Abdallah (2007) [1] which is devoted to the Cauchy problem for the scalar Laplace equation. The numerical performances of these formulations are compared.     

SAXS studies of blends of high- and low-density polyethylene

It is shown that in blends of PE having different melting temperatures the morphology depends drastically on the cooling rate. In these heterogeneous PE, the correlation relationship L = r between the long period L of the solid state and the dimension of the coils r in the liquid state is observed only in rapidly quenched materials. In slowcooled materials the SAXS spectra are interpreted in terms of segregation of two types of PE, on a scale of the order of the dimension of the coils, the arrangement of the crystalline lamellae being paracrystalline and statistical.     

A cell cycle model and translation semigroups

First are given results on the norm-continuity of translation semigroups and their asymptotic behavior. Secondly a cell cycle model is studied from the point of view of linear translation semigroups theory. Existence and norm-continuity of the solution semigroup and the property of exponential asynchronous growth are established for this model.     

Effects of blowing through a porous strip in a turbulent channel flow

An experimental investigation is performed on a fully developed turbulent channel flow with local injection through a porous strip. The Reynolds number based on the channel half-width was set to 5000. In addition to the no blowing case, measurements are made for three different blowing rates σ = 0.22, 0.36 and 0.58 (where σ is the ratio of momentum flux gain due to the blowing and momentum flux of the incoming channel flow). Measurements carried out with hot-wire anemometry reveal that injection strongly affects both the velocity profiles and the turbulence characteristics. The injection decreases the skin friction coefficient and increases all the Reynolds stresses downstream the blowing strip. The turbulence structure and the bursting phenomena were examined using space-time correlations measurements and conditional analysis. It is found that the injection increases the frequency of occurrence of the bursts.     

A novel process for the fabrication of nanoporous apatites from Moroccan phosphate rock

Naturally-abundant Moroccan phosphate (Bengurir ores) was used as a source for calcium and phosphorus precursors for the synthesis of nanoporous apatites, following a dissolution–precipitation method. The influence of temperature, ripening time and solvent nature on the crystal growth of apatite was investigated. For all products, poorly crystalline apatite phases were obtained after drying, exhibiting a mesoporous structure with specific surface area up to 150 m² g⁻¹. These materials could be converted into a pure crystalline hydroxyapatite phase after treatment at 800 °C. This simple, eco-friendly and cheap procedure may be useful for the future development of sorbents for water treatment.     

Path integral treatment of a noncentral electric potential

We present a rigorous path integral treatment of a dynamical system in the axially symmetric potential $V(r,\theta ) = V(r) + \tfrac{1} {{r^2 }}V(\theta ) $ . It is shown that the Green’s function can be calculated in spherical coordinate system for $V(\theta ) = \frac{{\hbar ^2 }} {{2\mu }}\frac{{\gamma + \beta \sin ^2 \theta + \alpha \sin ^4 \theta }} {{\sin ^2 \theta \cos ^2 \theta }} $ . As an illustration, we have chosen the example of a spherical harmonic oscillator and also the Coulomb potential for the radial dependence of this noncentral potential. The ring-shaped oscillator and the Hartmann ring-shaped potential are considered as particular cases. When α = β = γ = 0, the discrete energy spectrum, the normalized wave function of the spherical oscillator and the Coulomb potential of a hydrogen-like ion, for a state of orbital quantum number l ≥ 0, are recovered.     

Stabilité du caractère kählérien transverse

Soient $\mathcal{F}$ un feuilletage hermitien homologiquement orientable sur une variété compacteM et $\mathcal{F}_t $ une déformation de $\mathcal{F}$ à type différentiable fixé paramétrée par un voisinageT de 0 dans ? ^d par des feuilletages transversalement holomorphes. On suppose que la métrique hermitienne transverse σ de $\mathcal{F} = \mathcal{F}_0 $ est kählérienne. On montre qu’il exist ε>0 tel que pour toutt∈T, |t|<ε le feuilletage $\mathcal{F}_t $ possède une métrique kählérienne transverseσ _t telle queσ ₀=σ; en plusσ _t dépend différentiablement det pour |t|<ε.     

Test d'hétéroscédasticité quand les covariables sont fonctionnelles

We present in this paper a consistent nonparametric test for heteroscedasticity when data are of functional kind. The latter is constructed by evaluating the difference between the conditional and unconditional variances. We show the asymptotic normality of the statistical test under the null hypothesis. In addition, we prove that this test is consistent against all deviations from homoscedasticity condition.     

Structure and thermal behaviors of Moroccan phosphate rock (Bengurir)

Moroccan phosphate ores have important phosphate reserves, thus makes possible to distinguish three main layers: submittal, principal and basal. A characterization of the ore was carried out to determine the mineralogical and chemical characteristics. Thermal analysis, infrared and NMR techniques were used to study the thermal and structure behaviors of the organic matter in Moroccan phosphate from Bengurir. The TG analysis showed that the investigated mineral exhibited 7 mass% as total mass loss. The calcination-separation enrichment of carbonate-phosphorite ores from Bengurir region (Morocco) has been studied.