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.      

Resolution numerique de quelques problemes raides en mecanique des milieux faiblement compressibles

This paper deals with the numerical approximation of some «stiff» problems by asymptotic expansion of the solution. The model problem is the stationary linearized equation of slightly compressible fluids: $$\begin{gathered} \ll Find u_\varepsilon \varepsilon \left[ {H_0^1 (\Omega )} \right]^n s.t. \hfill \\ - \mu \Delta u_\varepsilon - \frac{1}{\varepsilon } grad div u_\varepsilon = f in \Omega \gg \hfill \\ \end{gathered} $$ where ∈ is asmall parameter; numerical treatment of the problem is thus difficult («stiff» problem). We establish existence and unicity of an asymptotic expansion foru, and use it to computeu. In the usual cases, with small divergence, the numerical results are far better than those obtained by direct discretisation of the problem. We also construct asymptotic expansions for the solutions of some nonlinear or non-stationary related problems.     

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.     

Analyse numerique du champ magnetique d'un alternateur par elements finis et sur-relaxation ponctuelle non lineaire

The purpose of this paper is to study a method of solution of the two-dimensional non-linear partial differential equation describing the magnetic state in the cross-section of an alternator.The method used is based on the combination of finite element technique with various non-linear successive point overrelaxation algorithms. We obtain a method which is very robust and efficient and gives the possibility of solving easily, even on middle-size computers, the previous problem on complicated geometries. Convergence proofs for the finite element approximation and iterative algorithms are given.     

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.     

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.     

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).