Drapage géométrique des compositesGeometrical draping of composite fabrics

This paper presents a study devoted to the composite fabric shaping simulation in finite strain analysis. We introduce a new geometrical approach based on the fishnet method for which the deformation of a fabric mesh element consists in a pure trellis effect. Such a fabric mesh element is then defined by a curved quadrilateral whose edges are geodesic lines with the same length plotted onto the surface to drape. Given three vertices of the fabric mesh element on the surface, we propose an optimization algorithm to define the fourth vertex of the fabric mesh element. This algorithm allows us to drape the surface using an advancing front approach from the data of an initial impact point between the fabric and the surface and the initial fibre directions at this point. A numerical draping simulation example using this approach is given. To cite this article: H. Borouchaki, A. Cherouat, C. R. Mecanique 331 (2003).     

Numerical Analysis of Heat Transfer for Cooling of Photovoltaic Cells

Photovoltaic cells are devices which convert solar radiation directly into electricity. However, solar radiation increases the photovoltaic cells temperature [1] [2]. The temperature has an influence on the degradation of the cell efficiency and the lifetime of a PV cell. This work reports on a cooling water technique for cells, whereby the cooling system was placed at the front surface of the cells to dissipate away excess heat and to block unwanted radiation. Using water as a cooling medium for the cells, the overheating of closed panel is greatly reduced without prejudicing luminosity and water acts as a filter to remove a portion of solar spectrum in the infrared band but allows transmission of the visible spectrum most useful for the PV operation. The aims of this study are to develop a 3D thermal model to simulate the cooling and heat transfer in Photovoltaic panel and recommend a cooling technique for the PV panel. In order to have a good estimation for the temperature distribution, the three-dimensional flow and heat transfer across the cooling block is investigated numerically by solving the continuity, momentum and energy equations using FLUENT. The second objective of this work is to study the influence of the geometrical dimensions of the panel, water mass flow rate and water inlet temperature on the flow distribution and the solar panel temperature. The results obtained by the model are compared with experimental results from testing the prototype of the cooling device. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Carleman inequalities for the heat equation in singular domains

We consider the Cauchy problem associated to the heat equation firstly in a plane domain with a reentrant corner, then in a cracked domain. By constructing a weight function, we show a result of null controllability using Carleman estimates.     

Asymptotic inference of unstable periodic ARCH processes

This paper studies asymptotic properties of the quasi maximum likelihood and weighted least squares estimates (QMLE and WLSE) of the conditional variance slope parameters of a strictly unstable ARCH model with periodically time varying coefficients (PARCH in short). The model is strictly unstable in the sense that its parameters lie outside the strict periodic stationarity domain and its boundary. Obtained from the regression form of the PARCH, the WLSE is a variant of the least squares method weighted by the square of the conditional variance evaluated at any fixed value in the parameter space. In calculating the QMLE and WLSE, the conditional variance intercepts are set to any arbitrary values not necessarily the true ones. The theoretical finding is that the QMLE and WLSE are consistent and asymptotically Gaussian with the same asymptotic variance irrespective of the fixed conditional variance intercepts and the weighting parameters. So because of its numerical complexity, the QMLE may be dropped in favor of the WLSE which enjoys closed form.     

Tail product-limit process for truncated data with application to extreme value index estimation

A weighted Gaussian approximation to tail product-limit process for Pareto-like distributions of randomly right-truncated data is provided and a new consistent and asymptotically normal estimator of the extreme value index is introduced. A simulation study is carried out to evaluate the finite sample behavior of the proposed estimator and compare it to that recently proposed by Gardes and Stupfler (TEST 24, 207–227, 2015). Also, a new approach of estimating extreme quantiles, under random right truncation, is derived and applied to a real dataset of lifetimes of automobile brake pads.     

Le nombre des diviseurs d'un entier dans les progressions arithmétiques

Let d_k,?(n) be the function number of divisors of the integer n?1, in arithmetic progressions {?+mk}, with 1???k and ?,k coprime, and let F(n;k,?) defined as follows:

$\text{F(n;k,?)=}\text{ln}\text{d}{}_{\mathrm{k,?}}\text{(n)}\text{ln}\text{(?(k)}\text{ln}\text{n)}\text{ln}\text{2}\text{ln}\text{n}\text{.}$

In this Note, we study and give the structure of d_k,?-superior, highly composite numbers, which generalize those defined by S. Ramanujan. We prove that F(n;k,?) reaches its maximum among these numbers. We give it explicitly for k=2,…,13. This generalizes the study of Nicolas and Robin, in which the case k=1 is treated. To cite this article: A. Derbal, A. Smati, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Synthesis of hydroxy-substituted aza-analogues of antitumor anthrapyrazoles

Synthetic routes have been developed which lead to ring-hydroxylated aza-analogues of antitumor anthrapyrazoles, namely, 2,5-bis[(aminoalkyI)amino] substituted 10-hydroxymdazolo[3,4-fg]isoquinolin-6(2H)-ones 1 and 7-hydroxyindazolo[4,3-gh]isoquinolin-6(2H)-ones 2 . The regiospecific synthesis of 6,9-dihalo-4-hydroxybenz[g]isoquinolines 3 and 4 has been accomplished. Intermediate 3 was constructed in a multistep process involving Diels-Alder chemistry of benzoylacrylates whereas 4 was assembled using Ni(II) mediated coupling of methyl 3-chloro-5-methoxyisonicotinate ( 15b ) with the organic zinc reagent 18 derived from 2-fluoro-5-chlorobenzyl bromide ( 17 ). After protection of the hydroxy group with a p-methoxybenzyl moiety, the different nucleofugacities of the leaving groups present in 10 and 20 allowed sequential displacements by substituted hydrazines and amines, respectively, to lead to the desired p-methoxybenzyl protected analogues 12 and 22 . Deprotection led to the side arm modified compounds 1 and 2 . The displacements of 21a and 21b with N,N-dimethylethylenediamine also led to the tri[(aminoalkyl)amino]substituted analogues 23a and 23b , respectively, which arose from further S_NAr substitutions of the p-methoxybenzyloxy group.     

Electrical properties and Pockels effect in BaTiO_{3}/SrTiO_{3} superlattices

The electrical and linear electro-optical properties of BaTiO $_{3}$ (BT)/SrTiO $_{3}$ (ST) superlattices epitaxially grown on ST substrate are theoretically investigated using a microscopic quantum mechanical model based on the orbital approximation in correlation with the dipole–dipole interaction. Both the first-, second-, and third-order electronic polarizabilities were considered in this calculation in order to obtain accurate results for both the spontaneous local electric field, spontaneous polarization, relative dielectric constant, and linear electro-optic coefficients (Pockels constants) of BT/ST superlattices. The calculations show that the spontaneous local electric field, spontaneous polarization and linear electro-optic coefficients of BT/ST superlattices increase with their content in BT while the relative dielectric constant increases with their content in ST. Moreover, we have shown that significant enhancement of the linear electro-optic coefficients can be achieved in BT/ST superlattices. This enhancement, which concerns the ST as well as the BT layers, arises from the combined effects of strain, induced in the BT layers by the epitaxial growth, and internal polarizing electric field originating in the BT layers and acting on the electronic clouds of the polarizable constituent ions of the system.     

Remaillage adaptatif pour la mise en forme des tôles minces

Problems associated with finite element simulation of the forming processes are characterized by large elastoplastic deformations, evolutive contact with friction, geometrical nonlinearities inducing a severe distortion of the computational mesh of the domain. In this case, frequent remeshing of the deformed domain during computation are necessary to obtain an accurate solution and complete the computation until the termination of the numerical simulation process. This Note presents a new adaptive remeshing method of thin sheets for numerical simulation of metal forming processes. The proposed method is based on geometrical criteria and does not use the geometry of the forming tools. It is integrated in a computational environment using the ABAQUS solver. Numerical examples are given to show the efficiency of our approach. To cite this article: L. Moreau et al., C. R. Mecanique 333 (2005).