École normale supérieure de Cachan

About: École normale supérieure de Cachan is a education organization based out in Cachan, Île-de-France, France. It is known for research contribution in the topics: Decidability & Nonlinear system. The organization has 2717 authors who have published 5585 publications receiving 175925 citations.

The normal flux method at the boundary for multidimensional finite volume approximations in CFD

Abstract: This paper presents a general method for imposing boundary conditions in the context of hyperbolic systems of conservation laws. This method is particularly well suited for approximations in the framework of Finite Volume Methods in the sense that it computes directly the normal flux at the boundary. We generalize our approach to nonconservative hyperbolic systems and discuss both the characteristic and the noncharacteristic cases. We present several applications to models occurring in Computational Fluid Mechanics like the Euler equations for compressible inviscid fluids with real equation of state, shallow water equations, magnetohydrodynamics equations and two fluid models.

Directional emission of stadium-shaped microlasers

Abstract: The far-field emission of two-dimensional stadium-shaped dielectric cavities is investigated. Microlasers with such shape present a highly directional emission. We provide experimental evidence of the dependence of the emission directionality on the shape of the stadium, in good agreement with ray numerical simulations. We develop an analytical geometrical optics model which permits to account for the main observed features. Wave numerical calculations confirm the results.

Nonlinear modeling of scattered multivariate data and its application to shape change

Abstract: We are given a set of points in a space of high dimension. For instance, this set may represent many visual appearances of an object, a face, or a hand. We address the problem of approximating this set by a manifold in order to have a compact representation of the object appearance. When the scattering of this set is approximately an ellipsoid, then the problem has a well-known solution given by principal components analysis (PCA). However, in some situations like object displacement learning or face learning, this linear technique may be ill-adapted and nonlinear approximation has to be introduced. The method we propose can be seen as a nonlinear PCA (NLPCA), the main difficulty being that the data are not ordered. We propose an index which favors the choice of axes preserving the closest point neighborhoods. These axes determine an order for visiting all the points when smoothing. Finally, a new criterion, called "generalization error", is introduced to determine the smoothing rate, that is, the knot number for the spline fitting. Experimental results conclude this paper: The method is tested on artificial data and on two databases used in visual learning.