Antioxidant activity of rosemary extracts in solution and embedded in polymeric systems

The rosemary extract was encapsulated in polyethylene or in covalently-based network gels. The covalent gels were obtained by the reaction of isocyanate end-capped polyethylene glycol (PEG) with β-cyclodextrin or glycerol. The 2,2-diphenyl-1-picrylhydrazyl (DPPH) assay was used to evaluate the antioxidant activity (AA) of rosemary extract entrapped in polymeric structures and in ethanol or water solutions. The AA of the rosemary extract was determined using a DPPH radical for samples prepared in ethanol, and a water-soluble derivative, the sulphonated DPPH radical (DPPH-SO₃Na), for the rosemary extract in water. Formulation of the rosemary extract in polymeric gels ensures a rapid release which determines the AA values similar to those in solution.     

Fuzzy supervised neurocontrol of electrohydraulic servos

The work presents theoretical and experimental investigations concerning the neuro-fuzzy control of electrohydraulic servos. The control algorithm is built around a neurocontroller designed to optimize a performance index. Whenever the neurocontrol saturates or a system performance parameter decreases, the control scheme switches to a feasible and reliable fuzzy logic control. In accordance with simulation studies developed in previous works of the authors, the neuro-fuzzy controlled system proves often to be better than the corresponding classical PI or LQG systems. We emphasize that the entire control synthesis is thought as a model free approach, thus ensuring reduced design complexity and focusing on increased system robustness. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

New constructions of domain decomposition methods for systems of PDEs

We propose new domain decomposition methods for systems of partial differential equations in two and three dimensions. The algorithms are derived with the help of the Smith factorization. This could also be validated by numerical experiments. To cite this article: V. Dolean et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

4-(Azulen-1-yl) six-membered heteroaromatics substituted in 2- and 6- positions with 2-(2-furyl)vinyl, 2-(2-thienyl)vinyl or 2-(3-thienyl)vinyl moieties

The synthesis of pyrylium and pyridinium salts and pyridines with azulene-1-yl moieties in position 4 and two 2-heteroarylvinyl groups in positions 2 and 6 was accomplished. The pyrylium salts were obtained starting from pyranones and pyridines could be prepared from these salts by treating them with ammonium acetate. The general procedures for the synthesis of pyridinium salts, which occur with good results in less delocalized electronic systems, do not take place when applied to the above obtained pyrylium salts. Therefore, as starting material 4-(azulen-1-yl)-1-(n-butyl)-2,6-dimethylpyridinium perchlorate was used, which was condensed with heteroarylcarboxaldehydes. These compounds were completely characterized and some of their spectra were discussed. Their interaction with some metal ions was revealed, observing an affinity better than in the case of simple azulenepyridines. In the last part of the paper are presented redox potentials for several pyrylium salts and pyridines in comparison with those of the nonvinylogated derivatives.     

A domain decomposition method for solving the three-dimensional time-harmonic Maxwell equations discretized by discontinuous Galerkin methods

We present here a domain decomposition method for solving the three-dimensional time-harmonic Maxwell equations discretized by a discontinuous Galerkin method. In order to allow the treatment of irregularly shaped geometries, the discontinuous Galerkin method is formulated on unstructured tetrahedral meshes. The domain decomposition strategy takes the form of a Schwarz-type algorithm where a continuity condition on the incoming characteristic variables is imposed at the interfaces between neighboring subdomains. A multifrontal sparse direct solver is used at the subdomain level. The resulting domain decomposition strategy can be viewed as a hybrid iterative/direct solution method for the large, sparse and complex coefficients algebraic system resulting from the discretization of the time-harmonic Maxwell equations by a discontinuous Galerkin method.     

A robust two-level domain decomposition preconditioner for systems of PDEs

Coarse spaces are instrumental in obtaining scalability for domain decomposition methods. However, it is known that most popular choices of coarse spaces perform rather weakly in presence of heterogeneities in the coefficients in the partial differential equations, especially for systems. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems which isolate the terms responsible for slow convergence. We give a general theoretical result and then some numerical examples on a heterogeneous elasticity problem.     

Solving generalized eigenvalue problems on the interfaces to build a robust two-level FETI method

FETI is a very popular method, which has proved to be extremely efficient on many large-scale industrial problems. One drawback is that it performs best when the decomposition of the global problem is closely related to the parameters in equations. This is somewhat confirmed by the fact that the theoretical analysis goes through only if some assumptions on the coefficients are satisfied. We propose here to build a coarse space for which the convergence rate of the two-level method is guaranteed regardless of any additional assumptions. We do this by identifying the problematic modes using generalized eigenvalue problems.     

Locally implicit discontinuous Galerkin method for time domain electromagnetics

In the recent years, there has been an increasing interest in discontinuous Galerkin time domain (DGTD) methods for the solution of the unsteady Maxwell equations modeling electromagnetic wave propagation. One of the main features of DGTD methods is their ability to deal with unstructured meshes which are particularly well suited to the discretization of the geometrical details and heterogeneous media that characterize realistic propagation problems. Such DGTD methods most often rely on explicit time integration schemes and lead to block diagonal mass matrices. However, explicit DGTD methods are also constrained by a stability condition that can be very restrictive on highly refined meshes and when the local approximation relies on high order polynomial interpolation. An implicit time integration scheme is a natural way to obtain a time domain method which is unconditionally stable but at the expense of the inversion of a global linear system at each time step. A more viable approach consists of applying an implicit time integration scheme locally in the refined regions of the mesh while preserving an explicit time scheme in the complementary part, resulting in an hybrid explicit–implicit (or locally implicit) time integration strategy. In this paper, we report on our recent efforts towards the development of such a hybrid explicit–implicit DGTD method for solving the time domain Maxwell equations on unstructured simplicial meshes. Numerical experiments for 3D propagation problems in homogeneous and heterogeneous media illustrate the possibilities of the method for simulations involving locally refined meshes.     

A two level domain decomposition preconditioner based on local Dirichlet-to-Neumann maps

Coarse grid correction is a key ingredient in order to have scalable domain decomposition methods. In this Note we construct the coarse grid space using the low frequency modes of the subdomain DtN (Dirichlet–Neumann) maps, and apply the obtained two-level preconditioner to the linear system arising from an overlapping domain decomposition. Our method is suitable for the parallel implementation and its efficiency is demonstrated by numerical examples on problems with high heterogeneities.