Design and analysis of a Schwarz coupling method for a dimensionally heterogeneous problem

In the present work, we propose and analyse an efficient iterative coupling method for a dimensionally heterogeneous problem. We consider the case of a 2D Laplace equation with non‐symmetric boundary conditions coupled with a corresponding 1D Laplace equation. We first show how to obtain the 1D model from the 2D one by integration along one direction, by analogy with the link between shallow water equations and the Navier–Stokes system. Then we focus on the design of a Schwarz‐like iterative coupling method. We discuss the choice of boundary conditions at coupling interfaces. We prove the convergence of such algorithms and give some theoretical results related to the choice of the location of the coupling interface, and to the control of the difference between a global 2D reference solution and the 2D coupled solution. These theoretical results are illustrated numerically. Copyright © 2014 John Wiley & Sons, Ltd.     

New reaction of formation of the fused tricyclic bispyrroloquinone ring system

A one-pot procedure to difunctionalized fused tricyclic bispyrroloquinone derivatives involving the condensation of N-tosylindoledione and α-ketoamines is described.     

Coexistence of Two Different Distorted Octahedral [MnF6]3− Sites in K3[MnF6]: Manifestation in Spectroscopy and Magnetism

As a consequence of the static Jahn-Teller effect of the ⁵E ground state of Mn^III in cubic structures with octahedral parent geometries, their octahedral coordination spheres become distorted. In the case of six fluorido ligands, [MnF₆]³⁻ anions with two longer and four shorter Mn−F bonds making elongated octahedra are usually observed. Herein, we report the synthesis of the compound K₃[MnF₆] through a high-temperature approach and its crystallization by a high-pressure/high-temperature route. The main structural motifs are two quasi-isolated, octahedron-like [MnF₆]³⁻ anions of quite different nature compared to that met in ideal octahedral Mn^III Jahn-Teller systems. Owing to the internal electric field of C_i symmetry dominated by the next-neighbour K⁺ ions acting on the Mn^III sites, both sites, the pseudo-rhombic (site 1) and the pseudo-tetragonally elongated (site 2) [MnF₆]³⁻ anions are present in K₃[MnF₆]. The compound was characterized by single-crystal and powder X-ray diffraction, and magnetometry as well as by FTIR, Raman, and ligand field spectroscopy. A theoretical interpretation of the electronic structure and molecular geometry of the two Mn sites in the lattice is given by using a vibronic coupling model with parameters adjusted from multireference ab-initio cluster calculations.     

Role of reactive species in processing materials at laboratory temperature by spray plasma devices

Processing the aerosol of metal salts in non-equilibrium plasma represents a promising technique that combines the advantages of spray pyrolysis with the high reactivity of plasmas at nearlaboratory temperature in order to produce mixed-oxides and perovskite materials. The aim of this paper is to describe the principles of this new technique and to present the various applications and latest developments. This technique’s capacity to deposit various mixed metal oxides with precise stoichiometry is demonstrated. It is shown that oxidant plasma species play a key role in the chemical transformation of starting materials into oxides at laboratory temperature, while the configuration of the reactor determines the morphology and texture of the deposited layers. Two different reactor configurations are presented. The porous layers of La _x Sr_1−x MnO₃ as the cathode for fuel cells were synthesised in a wave shock reactor configuration, while nanostructured ZnO-Al layers to form a transparent conductive cathode for photovoltaic cells were deposited in the spray plasma reactor of the latest generation for this technique. The experimental results emphasise the role of plasma species in the rate of chemical reactions and in the chemical composition of the deposited layers.     

MODELISATION DE MACROCYCLES BICY CLOPHOSPHORANIQUES

Abstract

La modélisation de 14 macrocycles bicyclophosphoraniques des types I, II et III a été réussie à l'aide du programme Biosym. V95 basé sur le champ de forces ESFF et utilisant les deux modules Insight II et Discover 3.

Molecular modeling of 14 bicyclophosphoranic macrocycles I, II and III has been carried out using Biosym V95 program based on the ESFF forcefield and including the modules Insight II and Discover 3.     

Dichotomous Hamiltonians with unbounded entries and solutions of Riccati equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.     

Strategic analysis of the dairy transportation problem

The dairy transportation problem (DTP) consists of determining the best routes to be performed for collecting milk from farms and delivering it to processing plants. We study the particular case of the province of Quebec, where the Fédération des producteurs de lait du Québec is responsible for negotiating the transportation costs on behalf of producers. Several issues are highlighted in the actual process of designing contracts such as using historical data. We propose an approach based on scenario analysis that consists of revising both the steps and the information used to construct the routes. We develop a generalized tabu search algorithm that integrates the different characteristics of the DTP.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.