Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models

We provide a priori error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizs\"{a}cker (TFW) model and for the spectral discretization of the Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the ground state energy and density of molecular systems in the condensed phase. The TFW model is stricly convex with respect to the electronic density, and allows for a comprehensive analysis. This is not the case for the Kohn-Sham LDA model, for which the uniqueness of the ground state electronic density is not guaranteed. Under a coercivity assumption on the second order optimality condition, we prove that for large enough energy cut-offs, the discretized Kohn-Sham LDA problem has a minimizer in the vicinity of any Kohn-Sham ground state, and that this minimizer is unique up to unitary transform. We then derive optimal a priori error estimates for the spectral discretization method.Comment: 50 page

Synthesis, metal complexation and biological evaluation of a novel semi-rigid bifunctional chelating agent for 99mTc labelling

A novel bifunctional chelating agent bearing an aromatic ring has been synthesised and characterised. This ligand formed well-defined oxorhenium complexes. The analogous 99mTcO-complex was obtained in an excellent yield with high radiochemical purity (>95%). The biodistribution of the 99mTo-complex after intravenous injection studied in normal rats showed that the activity was excreted mainly via renal-urinary pathway indicating its use for labelling peptides with 99mTc

Flexibilités et systèmes d'information

Face à la croissance combinée de l'incertitude et de la réactivité requise, les dirigeants attendent de leurs dispositifs opérationnels qu'ils se révèlent capables de flexibilité. Après avoir proposé plusieurs clarifications sur ce concept, nous analysons son application au champ des systèmes d'information (SI). Une analyse ontologique et téléologique de celui-ci nous permet de tester les effets de plusieurs types de variations des conditions opérationnelles sur le SI singulier de telle ou telle entreprise. Ces variations peuvent trouver leur origine au sein de l'entreprise elle-même ou dans son environnement, et elles peuvent être de diverses natures (éco-industrielles, technologiques, ...). L'identification des choix d'architecture ( infrastructures, applications, bases de données,...) et de gouvernance (internalisée, externalisée, mixte) met en évidence le rôle central des compétences et des capacités d'apprentissage des acteurs, notamment celles des directions générales et des directions des systèmes d'information, mais également celles de l'organisation en tant que telle.Flexibilité;système d'information;variation des conditions opérationnelles;architectures;gouvernance

Combining Analytic Preconditioner and Fast Multipole Method for the 3-D Helmholtz Equation

International audienceThe paper presents a detailed numerical study of an iterative solution to 3-D sound-hard acoustic scattering problems at high frequency considering the Combined Field Integral Equation (CFIE). We propose a combination of an OSRC preconditioning technique and a Fast Multipole Method which leads to a fast and efficient algorithm independently of both a frequency increase and a mesh refinement. The OSRC-preconditioned CFIE exhibits very interesting spectral properties even for trapping domains. Moreover, this analytic preconditioner shows highly-desirable advantages: sparse structure, ease of implementation and low additional computational cost. We first investigate the numerical behavior of the eigenvalues of the related integral operators, CFIE and OSRC-preconditioned CFIE, in order to illustrate the influence of the proposed preconditioner. We then apply the resolution algorithm to various and significant test-cases using a GMRES solver. The OSRC-preconditioning technique is combined to a Fast Multipole Method in order to deal with high-frequency 3-D cases. This variety of tests validates the effectiveness of the method and fully justifies the interest of such a combination

Numerical analysis of nonlinear eigenvalue problems

International audienceWe provide a priori error estimates for variational approximations of the ground state eigenvalue and eigenvector of nonlinear elliptic eigenvalue problems . We focus in particular on the Fourier spectral approximation (for periodic problems) and on the P1 and P2 finite-element discretizations. Our analysis extends to the case of nonlinear eigenproblems the classical results about the comparative speeds of convergence of the eigenvalues with respect to the eigenvectors in the H1- norm. We show that under some assumptions we recover a standard result for linear elliptic eigenvalue problems

Two-grid methods for a class of nonlinear elliptic eigenvalue problems

In this paper, we introduce and analyze some two-grid methods for nonlinear elliptic eigenvalue problems of the form −div(A∇u)+Vu+ f (u 2)u = λ u, u L 2 = 1. We provide a priori error estimates for the ground state energy, the eigenvalue λ , and the eigenfunction u, in various Sobolev norms. We focus in particular on the Fourier spectral approximation (for periodic boundary conditions), and on the P 1 and P 2 finite element discretizations (for homogeneous Dirichlet boundary conditions), taking numerical integration errors into account. Finally, we provide numerical examples illustrating our analysis

Ethylenediamine- and propylenediaminediacetic acid derivatives as ligands for the "fac-[M(CO)3]+" core (M = Re, 99mTc)

The reaction of Re(CO)5Cl with o- or p-N-(nitrophenyl)ethylenediaminediacetic acid (H2L1, H2L2) and o- or p-N-(nitrophenyl)propylenediaminediacetic acid (H2L3, H2L4) in methanol leads to the formation of stable anionic [Et3NH][Re(CO)3(L)]·H2O complexes 1-4. These compounds have been characterized by means of IR, mass spectrometry, elemental analysis, NMR and conductimetry, as well as X-ray crystallography for 2 and 3. The [Re(CO)3]+ moiety is coordinated via the nitrogen of the iminodiacetic acid unit and two oxygens of monodentate carboxylate groups. In each case, the nitro group of the aromatic ring remains uncoordinated. The analogous technetium-99m complexes 1' and 3' were also prepared quantitatively by the reaction of H2L1 and H2L3, respectively, with the fac-[99mTc(CO)3(H2O)3]+ precursor in ethanol. The corresponding Re and 99mTc compounds were shown to possess the same structure by means of HPLC studies. The high affinity of these ligands for the Tc(I) or Re(I) core, coupled with the easiness of their derivatization (by reduction of the nitro group in amino group), implies that the utilization of this ligand system to develop target-specific radiopharmaceuticals for diagnosis and therapy is promising

A perturbation-method-based a posteriori estimator for the planewave discretization of nonlinear Schrödinger equations

International audienceIn this Note, we propose a new method, based on perturbation theory, to post-process the planewave approximation of the eigenmodes of periodic Schrödinger operators. We then use this post-processing to construct an accurate a posteriori estimator for the approximations of the (nonlinear) Gross--Pitaevskii equation, valid at each step of a self-consistent procedure. This allows us to design an adaptive algorithm for solving the Gross-Pitaevskii equation, which automatically refines the discretization along the convergence of the iterative process, by means of adaptive stopping criteria

A perturbation-method-based post-processing for the planewave discretization of Kohn–Sham models

International audienceIn this article, we propose a post-processing of the planewave solution of the Kohn–Sham LDA model with pseudopotentials. This post-processing is based upon the fact that the exact solution can be interpreted as a perturbation of the approximate solution, allowing us to compute corrections for both the eigenfunctions and the eigenvalues of the problem in order to increase the accuracy. Indeed, this post-processing only requires the computation of the residual of the solution on a finer grid so that the additional computational cost is negligible compared to the initial cost of the planewave-based method needed to compute the approximate solution. Theoretical estimates certify an increased convergence rate in the asymptotic convergence range. Numerical results confirm the low computational cost of the post-processing and show that this procedure improves the energy accuracy of the solution even in the pre-asymptotic regime which comprises the target accuracy of practitioners