Couplage de deux milieux hétérogènes multiplicateurs de neutrons

Summary The object of several studies has been the analyzing of heterogeneous mediums which multiply neutrons, and which cannot be assimilated in homogeneous ones.These studies always postulate that the isolated medium is infinite, and never permit treating a multimedium assembly. We resolve this problem by the intermediary of a simplified model, equivalent to the real one. Considering successively all the isolated medium and using the calculating method of heterogeneous mediums, the equivalent conditions are established. A safety calculation, for the exponential experiment of the EPUL, shows the use of this method.

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Subside du Fonds National Suisse de la Recherche Scientifique, N° A 183.     

Méthodes de calcul des milieux hétérogènes multiplicateurs de neutrons.—Application à un système de 5 sources de neutrons au plutonium-béryllium dans un modérateur de graphite

Summary In the field of nuclear engineering, heterogeneous systems are generally preferred to homogeneous ones. Therefore, difficulties arise while computing critical sizes. It is possible to avoid them by considering the heterogeneous media as homogeneous ones, and by properly defining the characteristics of the latter. Such a method cannot be used in the case of a small number of fissionable pieces, placed in an infinite homogeneous moderator. We compare two methods solving this problem: the heterogeneous method ofFeinberg, and the heterogeneous method of auxiliary coupling sources.

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Subside du Fonds National Suisse de la Recherche Scientifique, N^o A 183.     

Sur les rotations barotropes des masses fluides hétérogènes

Sans résumé     

Une méthode géométrique élémentaire pour l’étude de certaines questions de la théorie des courbes planes

Sans résumé Une partie du présent travail est la reproduction d’un article paru dans Arkiv f?r mathematik, astronomi och fysik (utg. af K. Sv. Vet.-Akademien, Stockholm), Bd. 1, p. 681.     

Les fonctions asymptotiquement presque-périodiques d'une variable entière et leur application à l'étude de l'itération des transformations continues

Sans résumé     

Nouvelle méthode d'édifier la géométrie plane de Bolyai et de Lobatchefski

Sans résumé     

Comportement asymptotique des solutions du système de l'élasticité linéarisée anisotrope hétérogène dans des cylindres minces

We study the convergence of the solution u^ɛ of an anisotropic, heterogeneous, linearized elasticity problem in a cylinder, the diameter of which tends to zero. We prove in particular that u^ɛ − (u + ɛv + ɛ²w) strongly converges to zero (in a sense which will be specified), where (u, v, w) is the unique solution of an elliptic system of partial differential equations.     

Interpolation transfinie sur le triangle,le tétraèdre et le pentaèdre. Application à la création de maillages et à la condition de Dirichlet

The Lagrange's interpolation L(ν) of a function ν on a polyhedron K is defined from the values of the function at points p_i of the boundary Γ(K) and ℒ(ν)(p_i) = ν(p_i) at these points. The transfinite interpolation is defined in the same way, but on the whole boundary Γ(K). Three new transfinite interpolations of degree one on the triangle, tetrahedron, and pentahedron are added to the Gordon and Hall's transfinite interpolations on the quadrangle and hexaedron. All these interpolations leave the polynomials of degree ≤1 invariant. The applications to the generation of regular meshes and the possibility of exactly taking into account the Dirichlet boundary condition, show the usefulness of these transfinite interpolations.     

Convergence de modèles moléculaires vers des modèles de mécanique des milieux continus

The work we present here is focused on the justification of continuum mechanics as a natural asymptotic of molecular theories when the interatomic distance goes to zero. We give a sound theoretical ground to existing models, and derive and next study (apparently) new ones.     

Approximation du problème de contact unilatéral par la méthode des éléments finis avec joints

The purpose of this Note is to extend the mortar finite element method to handle the unilateral contact model between two deformable bodies. The corresponding variational inequality is approximated using finite elements with meshes which do not fit on the contact zone. The mortar technique allows us to match (independent) discretizations within each solid and to express the contact conditions in a satisfying way. Then, we carry out a numerical analysis of the algorithm and, using a bootstrap argument, we give an upper bound of the convergence rate similar to that already obtained for compatible grids.