Non-trapping condition for semiclassical Schrödinger operators with matrix-valued potentials.
Nontrivial solutions for Monge-Ampère type operators in convex domains.
Non-unitary scattering and capture. II. Quantum dynamical semigroup theory
Normal form of the wave group and inverse spectral theory
This talk will describe some results on the inverse spectral problem on a compact riemannian manifold (possibly with boundary) which are based on V. Guillemin's strategy of normal forms. It consists of three steps : first, put the wave group into a normal form around each closed geodesic. Second, determine the normal form from the spectrum of the laplacian. Third, determine the metric from the normal form. We will try to explain all three steps and to illustrate with simple examples such as surfaces...
Note on spectral theory of nonlinear operators: Extensions of some surjectivity theorems of Fučík and Nečas
Nouvelle interprétation de la formule des traces de Selberg
Nouvelles propriétés des courbes et relation de dispersion en élasticité linéaire
In the case of an elastic strip we exhibit two properties of dispersion curves λn,n ≥ 1, that were not pointed out previously. We show cases where λ'n(0) = λ''n(0) = λ'''n(0) = 0 and we point out that these curves are not automatically monotoneous on . The non monotonicity was an open question (see [2], for example) and, for the first time, we give a rigourous answer. Recall the characteristic property of the dispersion curves: {λn(p);n ≥ 1} is the set of eigenvalues of Ap, counted with their...
Nouvelles propriétés des courbes et relations de dispersion en élasticité linéaire
Noyau, résolvante et valeurs propres d'une classe d'opérateurs elliptiques et dégénérés
Noyaux d'Agmon
Numerical analysis of the adiabatic variable method for the approximation of the nuclear hamiltonian
Many problems in quantum chemistry deal with the computation of fundamental or excited states of molecules and lead to the resolution of eigenvalue problems. One of the major difficulties in these computations lies in the very large dimension of the systems to be solved. Indeed these eigenfunctions depend on variables where stands for the number of particles (electrons and/or nucleari) in the molecule. In order to diminish the size of the systems to be solved, the chemists have proposed many...
Numerical Analysis of the Adiabatic Variable Method for the Approximation of the Nuclear Hamiltonian
Many problems in quantum chemistry deal with the computation of fundamental or excited states of molecules and lead to the resolution of eigenvalue problems. One of the major difficulties in these computations lies in the very large dimension of the systems to be solved. Indeed these eigenfunctions depend on 3n variables where n stands for the number of particles (electrons and/or nucleari) in the molecule. In order to diminish the size of the systems to be solved, the chemists have proposed...
Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models
In this article, we provide a priorierror estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsäcker (TFW) model and for the spectral discretization of the periodic Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the electronic ground state energy and density of molecular systems in the condensed phase. The TFW model is strictly convex with respect to the...
Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models
In this article, we provide a priori error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsäcker (TFW) model and for the spectral discretization of the periodic Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the electronic ground state energy and density of molecular systems in the condensed phase. The TFW model is strictly convex with respect to the...
Numerical calculation of the essential spectrum of a Laplacian.
Numerical implementation of coherence for the example of the "Swiss Cross".
Numerical simulations for nodal domains and spectral minimal partitions
We recall here some theoretical results of Helffer et al. [Ann. Inst. H. Poincaré Anal. Non Linéaire (2007) doi:10.1016/j.anihpc.2007.07.004] about minimal partitions and propose numerical computations to check some of their published or unpublished conjectures and exhibit new ones.
Obere Schranken für Eigenfunktionen eines Operators - ... + q.
Observability properties of a semi-discrete 1d wave equation derived from a mixed finite element method on nonuniform meshes
The goal of this article is to analyze the observability properties for a space semi-discrete approximation scheme derived from a mixed finite element method of the 1d wave equation on nonuniform meshes. More precisely, we prove that observability properties hold uniformly with respect to the mesh-size under some assumptions, which, roughly, measures the lack of uniformity of the meshes, thus extending the work [Castro and Micu, Numer. Math.102 (2006) 413–462] to nonuniform meshes. Our results...
On a Class of non Linear Schrödinger Equations with non Local Interaction.