Resolution numerique d'un probleme de controle optimal d'un couplage des equations de navier-stokes et celle de la chaleur

We study by the method of artificial compressibility the numerical solution of an optimal control problem of a system governed by the Navier-Stokes equations coupled with the heat-equation. The control problem is of boundary control—final observation type. A system of equations and an inequality characterizing the optimal control gives rise to an algorithm which permits us to calculate a control satisfying a necessary condition for optimality. The algorithm will be approximated by finite difference schemes based on the fractional step method. We prove the stability and the convergence of the schemes and the convergence of the algorithm. Finally we present some numerical results illustrating the proposed method.     

Etude theorique et numerique de deux problemes couples stefan-transport; Application au stockage thermique

In this paper, we study a model of thermal energy storage by solid-liquid phase change. Writing the equations reveals Stefan problems and Transport equations. Reducing them to a variational formulation, we get some results about the existence and uniqueness of solutions using different properties of variational inequalities. Then we propose two finite difference methods of approximation (explicit and implicit) and numerical results.      

Etude numerique d'un probleme de stokes intervenant en oceanographie

The purpose of this paper is a study of a three-dimensional model used to compute wind-drift ocean currents. Non linear terms are neglected. The movement is governed by Stokes equations. Some simplifications are justified by the ratio of the vertical scale to the horizontal scale for oceanic problems. A method of separation of variables and expansion in Fourier series is used in order to reduce the three-dimensional problem to a two-dimensional one. Existence and uniqueness of the solution is proved for these two problems. The two-dimensional set of equations is discretized by a finite difference method. Numerical experiments have been carried out to determine the stationary wind-drift circulation in the upper layer of the Equatorial Atlantic Ocean. Currents at ahy depth are computed as well as surface elevation.      

Analyse des problemes de geometrie et apprentissage de la preuve au secondaire

Résumé

Le présent article rend compte de l'élaboration d'une grille d'analyse des problèmes de géométrie, et de sa mise à l'épreuve par la classification des problèmes et exercices de géométrie synthétique dans une collection de manuels du secondaire parmi les plus utilisées au Québec. Le cadre conceptuel sur lequel s'appuie cette élaboration s'inspire principalement des travaux de Balacheff (1987), Barbin (1988), Brousseau (1998), Hanna (1995) et Rouche (1989), et débouche sur une typologie des preuves de géométrie. La classification des problèmes à partir de cette grille et l'analyse qui en découle nous a permis de conclure sur les aspects de l'apprentissage de la preuve que nous évaluons comme mal ? gérés ? dans la collection : transition non suffisamment graduelle du sensible au formel (peu de problèmes qui sollicitent une validation hybride, niveau de formalisation trop longtemps stationnaire), prépondérance des applications directes et des déductions locales sur les séquences déductives, intérêt et mode de présentation des résultats qui ne favorisent pas une ? attitude de preuve ?.     

Analyse numerique du probleme des ondes longues en eau peu profonde

This paper deals with the study of the problem of long waves in shallow water, when viscesity is taken into account. Existence and uniqueness of the solution are established. For the numerical treatment, an implicit scheme is proposed together with results of stability and convergence.

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Le présent travail a été réalisé au Laboratoire de Matématiques Appliquees de l'Université Scientitique et Médicale de Grenoble (France).     

Methode d'etude numerique des champs physiques. Application a la determination de l'effet hall dans des plaques rectangulaires

The authors describe in this paper a digital method, which by conserving the representation of the fields by finite difference equations, allows to reduce considerably the work necessary to determine those fields and makes it possible to solve those problems on digital computers with low capacity. They make therefore use of the technique of the flow graphs.     

Construction d’approximations des espaces de sobolev sur des reseaux en simplexes

The purpose of the present paper is to construct approximations of the So bolev spacesW ^m,p (Ω) by piecewise polynomial functions on sets of simplexes of the Euclidean spaceR ⁿ. These approximations are obtained by repeated convolution of the characteristic function of the unit hypercube ofR ⁿ with a positive measure. Although they involve polynomials of lower degree, they yield the same accuracy as the approximations on rectaugular nets usually adopted. Moreover when used for the approximate solution of variational boundary value problems, they lead to systems of linear equations with matrices where the diagonals with non-vanishing elements are less numerous; their number is reduced from (2m+1) ⁿ , for approximations on rectangular nets, to2(2m) ⁿ?(2m?1)ⁿ for approximations on simplexes nets. The gain thus realised cannot be improved when one requires that these approximations verify a commutation property with differentiation operators.     

Politique des banques de données en sciences humaines et sociales

Sans résumé Serge Cacaly works at the Ministry of Education, he is a specialist of databanks at DBMIST (Direction des Bibliothèques, des Musées et de l'Information Scientifique et Technique) where he is responsible for the sector “Humanities & the Social Sciences”.     

Apport de la teledetection a l'etude des plaques de sols nus en zone soudanienne (Burkina-Faso)

L'imagerie satellitale haute resolution SPOT est utilisee pour detecter les plaques de sols nus en zone de savane soudanienne. L'objectif hydrologique de cette determination est de mieux comprendre en quoi la presence ou l'absence de ces plaques explique la genese des ruissellements dans les petits bassins versants: contribution au transfert d'eau continu entre le versant elementaire et le bas-fond et genese de debits de crues extremes. La precision de la cartographie est appreciee a partir de documents de terrain detailles (echelle 1/10,000) servant de reference pour connaitre la repartition, le nombre, la surface et la forme des plaques. La qualite d'estimation est evaluee en separant erreur geometrique fonction de la resolution utilisee, et erreur radiometrique fonction des canaux utilises et de la date de l'image. Pour cet objectif thematique, les images SPOT XS paraissent alors suffisamment precises pour detecter les plaques de sols nus (taille minimale des plaques 0.25ha) a partir d'une image de saison des pluies (grand contraste entre sols nus et cultures). L'application porte sur un petit bassin versant du Burkina Faso (Imiga, 12km²).     

Caracteristiques des explications orales en classe de mathematiques : Construction d'un cadre d'analyse pour rendre compte de la pratique des futurs enseignants et futures enseignantes de mathematiques du secondaire 1

Résumé:

De nombreuses études font ressortir l'importance des explications orales des enseignants et enseignantes de mathématiques pour l'apprentissage des élèves. Cette compétence à expliquer les mathématiques en classe apparaît donc centrale à la formation des enseignants et enseignantes. Afin de mieux rendre compte de la construction de cette compétence chez les futurs enseignants et futures enseignantes de mathématiques du secondaire, nous avons élaboré un cadre d'analyse permettant de situer différentes caractéristiques des explications orales. Ce cadre d'analyse a été mis à l'essai, à titre d'exemple illustratif, lors de l'analyse des pratiques de deux futurs enseignants. L'analyse permet de tracer un portrait caractéristique des explications orales pour ces deux futurs enseignants et montre l'intérêt que présente ce cadre d'analyse pour la compréhension des pratiques d'enseignement — tout en suscitant et orientant certaines réflexions pour la formation des enseignants et enseignantes de mathématiques. La façon qu'ont les futurs enseignants et futures enseignantes de ?parler? les mathématiques en classe nous en dit long, en effet, sur leur enseignement et leur compréhension de ce que représente pour eux l'enseignement et l'apprentissage des mathématiques.     

Utilisation de la méthode des éléments finis en mécanique des fluides,II

Sans résumé La première partie, avec la Bibliographie, a parue dans le vol. XII, fasc. IV, pag. 405–441.     

Utilisation de la méthode des éléments finis en mécanique des fluides,I

An analysis is made of the possibility of building divergence free elements for the approximation of the Navier-Stokes equations of an incomprensible fluid. Two types of appoximation are considered. In the first real divergence free elements are considered. Many examples are given and error bounds are derived. It is shown that 0 (h ⁴) precision can be obtained using fourth degree polynomials. In the second type of approximation the incompressibility condition is satisfied only in the average. Two and three dimensional examples are given, using respectively second and third order polynomials. A possible numerical scheme is proposed for the case the steady-state linearized Stokes problem. Experimental evidence shows that it can be also used in the general non-linear case. Simple numerical results are presented for the cavity problem in two dimensions.

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Ce travail a été rendu possible en partie grace à une subvention du Conseil National de la Recherche du Canada.     

Comparaison de differentes methodes de traitement par analyses en composantes principales des donnees Thematic Mapper de LANDSAT-5 appliquees al'inventaire forets mediterranneennes du sud de la France

Abstract

The existence of remotely sensed data with high spatial resolution, like the ones produced by the Thematic Mapper of LANDSAT, set the problem of the reduction of the number of spectral dimensions to be analysed. The work presented hereby is in this context and aims to compare the performances of the supervized classification applied to the perception of forested and sub-forested mediterranean ecosystems processed with: original TM data selected only under spectral consideration; components factors provided by a classical Principal Component Analysis (PCA); components factors provided by a selective Principal Component Analysis (PCA). The analysis of the results shows that the classification done using the three axes extracted by a classical Principal Component Analysis of the six Thematic Mapper bands gives better results than all the other combinations (original data or data provided by selective PCA). On the other hand, and for all the classifications processed, it appears that the performances are excellent (near 90 per cent) for units representing stable systems, climatic or definitely degraded. At the opposite end, performances are quite good (near 60 per cent) for the evolutive systems (in regression or progression).     

Utilisation des donnees du moyen infrarouge de Landsat Thematic Mapper pour la mise en evidence des coupes rases sur le Massif Forestier Landais

The aim of this study is to test the feasibility of the detection and mapping of annual clearcuts from Landsat Thematic Mapper data over the forested region les Landes, in the south-west of France ( about 1 million hectares covered by uniform age monospecific forest stands of maritime pine) Two Landsat TM images acquired in summer 1985 and 1986 were used. The radiometric changes following a clearcut are analysed and compared to the changes following up other types of evolution, on a test area representing 200000ha. Newly clear felled stands showed strong increase in their mean radiometric level in the visible as well as in the middle infrared, but no clear variation in the near-infrared was found. Results of supervised image classifications using three different band combinations were compared to evaluate the potential contribution of the nearinfrared combined with the middle infrared for the detection of annual clear fellings. The following multi-temporal combinations were used: (TM–5–85, TM5– 86), (TM–5–85, TM–5–86, TM–4–86), (TM–5–85, TM–4–85, TM–5–86, TM–4–86). The combinations using the middle infrared alone led to the best identification of new clearcuts harvested between 1985 and 1986, but the commissionerror was high (about 25 per cent). The main confusion was observed on old clearcuts which were reforested between 1985 and 1986. In order to propose a global method for mapping and estimating the annual clearcuts over the whole Landes region, it is necessary to test whether the results are reproducible when images acquired at very different dates are used. Moreover, the cartographic accuracy must be controlled and improved. Effects of thinnings, which are not studied here, must also be taken into account. Then, we can propose a global system for monitoring regional forest resources.