Publications

2012

• Prediction of Neuroprotective Treatment Efficiency Using a HRMAS NMR-Based Statistical Model of Refractory Status Epilepticus on Mouse: A Metabolomic Approach Supported by Histology
  
  • Fauvelle Florence
  • Carpentier Pierre
  • Dorandeu Frederic
  • Foquin Annie
  • Testylier Guy
  Journal of Proteome Research, American Chemical Society, 2012, 11 (7), pp.3782 - 3795. This work presents a model combining quantitative proton HRMAS NMR data and PLS-DA for neuropathology and neuroprotection evaluation. Metabolic data were also confronted to histopathological results obtained using the same experimental conditions. Soman, when not lethal, can induce status epilepticus (SE), brain damage, histological lesions, and profound cerebral metabolic disorders as revealed using 1 H HRMAS NMR. Our challenge was to evaluate delayed treatments, which could control refractory SE and avoid brain lesions. For this aim, we have built a statistical model of soman intoxication describing brain metabolite evolution during 7 days. We have then used this model to evaluate the efficiency of a combination of ketamine/atropine (KET/AS) administrated 1 and 2 h after SE induction, compared to the immediate anticonvulsant therapy midazolam/atropine sulfate (MDZ/AS). Furthermore, quantitation of HRMAS NMR data allowed us to follow individual evolution of 17 metabolites. N-Acetylaspartate, lactate, or taurine presented a long lasting disruption, while glutamine, alanine, glycerophosphocholine and myo-inositol showed disruptions for 3 days with a reversion at day 7. These changes were completely normalized by the administration of MDZ/AS. Interestingly, they were also almost completely reversed by KET/AS 1 h postsoman. This work suggests further the predictive interest of HRMAS and PLS-DA for neuropathology/neuroprotection studies and also confirms, on the metabolic aspects, the neuroprotective potentials of KET/AS combinations for the delayed treatment of soman-induced SE. (10.1021/pr300291d)
  DOI : 10.1021/pr300291d
• Finite element computation of elastic propagation modes in open stratified waveguides
  
  • Treyssede Fabien
  • Nguyen Khac-Long
  • Bonnet-Ben Dhia Anne-Sophie
  • Hazard Christophe
  , 2012, pp.1p.. Elastic guided waves are of interest for inspecting structures due to their ability to propagate over long distances. In several applications, the guiding structure is surrounded by a solid matrix that can be considered as unbounded. The physics of waves in open waveguides significantly differs from closed waveguides. Except for trapped modes, part of the energy is radiated in the surrounding medium, yielding attenuated modes along the axis called leaky modes (wavenumbers are then complex). From a numerical modeling point of view, the main difficulty lies in the unbounded nature of the geometry in the transverse direction. This difficulty is particularly severe due to the unusual behavior of leaky modes: while attenuating along the axis, such modes exponentially grow along the transverse direction. This behavior is seldom mentioned in the literature of elastic waveguides. Yet leaky modes have often been considered for NDT applications, which require waves of low attenuation in order to maximize the inspection range. A numerical approach is proposed for computing modes in open elastic waveguides, in the bidimensional case as a first step. The approach combines a semi-analytical finite element method with perfectly matched layers (PML). The technique of absorbing layers (AL) is also implemented, which consists in using large artificial layers of growing viscoelasticity. Numerical results are compared to analytical results. The efficiency of PML is compared to AL and parametric studies are briefly conducted in order to assess the convergence of both techniques. The physical meaning of leaky modes is also highlighted.
• A staggered discontinuous Galerkin method for wave propagation in media with dielectrics and meta-materials
  
  • Chung Eric T.
  • Ciarlet Patrick
  , 2012. Some electromagnetic materials exhibit, in a given frequency range, effective dielectric permittivity and/or magnetic permeability which are negative. In the literature, they are called negative index materials, left-handed materials or meta-materials. We propose in this paper a numerical method to solve a wave transmission between a classical dielectric material and a meta-material. The method we investigate can be considered as an alternative method compared to the method presented by the second author and co-workers. In particular, we shall use the abstract framework they developed to prove well-posedness of the exact problem. We recast this problem to fit later discretization by the staggered discontinuous Galerkin method developed by the first author and co-worker, a method which relies on introducing an auxiliary unknown. Convergence of the numerical method is proven, with the help of explicit inf-sup operators, and numerical examples are provided to show the efficiency of the method.
• On the wave equation with semilinear porous acoustic boundary conditions
  
  • Graber Philip Jameson
  • Said-Houari Belkacem
  Journal of Differential Equations, Elsevier, 2012, 252, pp.4898-4941. The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function. (10.1016/j.jde.2012.01.042)
  DOI : 10.1016/j.jde.2012.01.042
• Propagation in a periodic succession of slabs with mixed negative/positive index
  
  • Maurel Agnes
  • Ourir Abdelwaheb
  • Mercier Jean-François
  • Pagneux Vincent
  , 2012. Metamaterials are artificial materials engineered using periodic inclusions of small inhomogeneities to enact effective macroscopic behavior. Until recently, most studies considered only ideal systems and did not address the possible effects of disorder.The first step in this direction was made in [Phys. Rev. B 70, 245102, 2004] where it was shown that the presence of a single defect led to the appearance of a localized mode. Since then, more general model of alternating sequences of right and left handed layers with random parameters have been studied, notably in [M. V. Gorkunov et al., Phys. Rev. E 73, 056605, 2006; Phys. Rev. Lett. 99, 193902, 2007]. The authors have shown that the localization properties differ dramatically from those exhibited by conventional disordered materials. We study wave propagation in such stratified media both experimentally and theoretically. Experiments confirm that the properties of the attenuation length differ dramatically from those exhibited by conventional alternated layer materials, notably in the intermediate value of the wavelength. Analytical prediction of the attenuation length is in good agreement with the observations.
• A complete FE simulation tools for NDT inspections with piezoelectric transducers
  
  • Imperiale Sebastien
  • Marmorat Simon
  • Leymarie Nicolas
  • Chatillon Sylvain
  , 2012. An ultrasonic inspection system involves the generation, propagation and reception of short transient signals. Piezoelectric transducers and particularly phased arrays are increasingly used in ultrasonic Non Destructive Testing (NDT) because of their ability to focus or deflect an ultrasonic beam in parts of complex geometries. To accurately model the sensitivity in transmission and reception of such sensors, a transient Finite Element (FE) model has been developed including not only piezoelectric effects but also all electrical elements such as pulser/receiver system and cabling. A particular attention is devoted to the different boundary conditions used to model the emission and reception regimes of the sensor. The definition of the inspection domain is made easier by a decomposition domain technique allowing, in the same time, local time stepping and efficient absorbing layers to optimize calculation cost. In order to illustrate all the capabilities of this simulation tool, several cases of NDT inspections are then presented through the analysis of the ultrasonic beam snapshots and the electrical signal read on the receiver.
• T-coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients
  
  • Chesnel Lucas
  • Ciarlet Patrick
  , 2012. To solve variational indefinite problems, one uses classically the Banach-Necas-Babuška theory. Here, we study an alternate theory to solve those problems: T-coercivity. Moreover, we prove that one can use this theory to solve the approximate problems, which provides an alternative to the celebrated Fortin lemma. We apply this theory to solve the indefinite problem $div\sigma\nabla u = f$ set in $H^1_0$, with $\sigma$ exhibiting a sign change.
• Physical parameters for piano modeling
  
  • Chabassier Juliette
  • Duruflé Marc
  , 2012, pp.24. This document lists the physical parameters used by the authors when performing numerical simulations of the piano. We first give the parameters used for the soundboard and the air. Then, the hammer parameters are given. Finally, strings parameters are issued and two cases are considered : with (realistic) or without (virtual) wrapped strings. When the strings are considered wrapped, their length is the effective length measured on the reference piano, but we consider that they are made of a virtual material with a higher density. When the strings are considered unwrapped, the material is steel, and to achieve the very bass notes without increasing inharmonicity too much, we have increased the length up to almost 6 meters.
• High order asymptotics for the electromagnetic scattering from thin periodic layers : the 3D Maxwell case
  
  • Delourme Bérangère
  , 2012. This work deals with the scattering of electromagnetic waves by a thin periodic layer made of an array of regularly-spaced obstacles. The size of the obstacles and the spacing between two consecutive obstacles are of the same order $\delta$, which is much smaller than the wavelength of the incident wave. We provide a complete description of the asymptotic behavior of the solution with respect to the small parameter $\delta$: we use a method that mixes matched asymptotic expansions and homogenization techniques. We pay particular attention to the construction of the near field terms. Indeed, they satisfy electrostatic problems posed in an infinite 3D strip that require a careful analysis. Error estimates are carried out to justify the accuracy of our expansion
• Modélisation et simulation numérique d'un piano par modèles physiques
  
  • Chabassier Juliette
  , 2012. Cette étude porte sur la modélisation et la simulation numérique d'un piano, en domaine temporel, par modèles phy- siques. Nous souhaitons rendre compte du comportement vibratoire et acoustique du piano, en prenant en compte les éléments principaux qui contribuent à la production du son. La table d'harmonie est modélisée par une équation bidimensionnelle de plaque épaisse, le système de Reissner Mindlin, pour un matériau orthotrope et hétérogène, dont l'amortissement dépend de la fréquence. Grâce aux équations de la vibroacoustique, la table rayonne dans l'air, dans lequel on souhaite calculer le champ acoustique complet autour de la ceinture du piano, que l'on suppose rigide. La table d'harmonie est d'autre part sollicitée par les cordes, à travers le chevalet où elles présentent un léger angle par rapport au plan horizontal. Chaque corde est modélisée par un système d'équations monodimensionnelles amorties dans lequel on prend en compte non seulement les ondes transversales excitées par le marteau, mais aussi la raideur à travers les ondes de cisaillement, ainsi que le couplage avec les ondes longi- tudinales provenant de la prise en compte des non linéarités géométriques. Le marteau est lancé avec une vitesse initiale vers un chœur de cordes, contre lequel il s'écrase avant d'être repoussé par les cordes. La force d'interaction dépend de façon non linéaire de l'écrasement du marteau.Le modèle complet de piano, que l'on souhaite résoudre numériquement, consiste donc en un système couplé d'équations aux dérivées partielles, dont chacune revêt des difficultés de nature différente : la corde est régie par un système d'équations non linéaires, la table d'harmonie est soumise à un amortissement dépendant de la fréquence, la propagation acoustique requiert un très grand nombre d'inconnues; auxquelles s'ajoute la difficulté inhérente aux couplages. D'une part, la stabilité numérique du schéma discret peut être compromise par la présence d'équations non linéaires et de nombreux couplages. Une méthode efficace pour garantir cette stabilité a priori est de construire un schéma qui conserve, ou dissipe, un équivalent discret de l'énergie physique d'un pas de temps au suivant. Une contribution majeure de ce travail a été de développer des schémas préservant une énergie discrète pour une classe de systèmes non linéaires dans laquelle s'inscrit le modèle de corde. D'autre part, afin d'augmenter l'efficacité de la méthode et de réduire le coût des calculs numériques, il est souhaitable de mettre à jour de façon découplée les inconnues liées aux différentes parties du problème, sur lesquelles la discrétisation en temps est faite de façon différente, afin de s'adapter aux spécificités de chacune. L'introduction de multiplicateurs de Lagrange nous permet de réaliser ce découplage artificiel grâce à des compléments de Schur adaptés. L'utilisation du code de calcul en situation réaliste montre le potentiel d'une telle modélisation d'un piano complet en domaine temporel. Au delà de très bien reproduire les mesures, il est possible d'étudier l'influence de certains phénomènes physiques (corde raide, non linéaire), de la géométrie ou encore des matériaux utilisés sur le comportement vibratoire général du piano, et sur le son en particulier. L'enrichissement spectral, ainsi que l'apparition des " partiels fantômes " et du précurseur non linéaire sont clairement mis en évidence pour les grandes amplitudes de jeu, soulignant l'intérêt de notre approche dans la compréhension du fonctionnement de l'instrument.
• T-coercivity: application to the discretization of Helmholtz-like problems
  
  • Ciarlet Patrick
  , 2012. To solve variational indefinite problems, a celebrated tool is the Banach-Nečas- Babuška theory, which relies on the inf-sup condition. Here, we choose an alternate theory, T-coercivity. This theory relies on explicit inf-sup operators, both at the continuous and discrete levels. It is applied to solve Helmholtz-like problems in acoustics and electromagnetics. We provide simple proofs to solve the exact and discrete problems, and to show convergence under fairly general assumptions. We also establish sharp estimates on the convergence rates.
• Uniform boundary stabilization of a wave equation with nonlinear acoustic boundary conditions and nonlinear boundary damping
  
  • Graber Philip Jameson
  Journal of Evolution Equations, Springer Verlag, 2012, 12, pp.141-164. We consider a wave equation with nonlinear acoustic boundary conditions. This is a nonlinearly coupled system of hyperbolic equations modeling an acoustic/structure interaction, with an additional boundary damping term to induce both existence of solutions as well as stability. Using the methods of Lasiecka and Tataru for a wave equation with nonlinear boundary damping, we demonstrate well-posedness and uniform decay rates for solutions in the finite energy space, with the results depending on the relationship between (i) the mass of the structure, (ii) the nonlinear coupling term, and (iii) the size of the nonlinear damping. We also show that solutions (in the linear case) depend continuously on the mass of the structure as it tends to zero, which provides rigorous justification for studying the case where the mass is equal to zero. (10.1007/s00028-011-0127-x)
  DOI : 10.1007/s00028-011-0127-x
• Wave propagation in locally perturbed periodic media (case with absorption): Numerical aspects
  
  • Fliss Sonia
  • Joly Patrick
  Journal of Computational Physics, Elsevier, 2012, 231 (4), pp.1244-1271. We are interested in the numerical simulation of wave propagation in media which are a local perturbation of an infinite periodic one. The question of finding artificial boundary conditions to reduce the actual numerical computations to a neighborhood of the perturbation via a DtN operator was already developed in at the continuous level. We deal in this article with the numerical aspects associated to the discretization of the problem. In particular, we describe the construction of discrete DtN operators that relies on the numerical solution of local cell problems, non stationary Ricatti equations and the discretization of non standard integral equations in Floquet variables. © 2011 Elsevier Inc. (10.1016/j.jcp.2011.10.007)
  DOI : 10.1016/j.jcp.2011.10.007
• First and second order necessary conditions for stochastic optimal control problems
  
  • Bonnans Joseph Frédéric
  • Silva Francisco J.
  Applied Mathematics and Optimization, Springer Verlag (Germany), 2012, 65 (3), pp.403-439. In this work we consider a stochastic optimal control problem with either convex control constraints or finitely many equality and inequality constraints over the final state. Using the variational approach, we are able to obtain first and second order expansions for the state and cost function, around a local minimum. This fact allows us to prove general first order necessary condition and, under a geometrical assumption over the constraint set, second order necessary conditions are also established. We end by giving second order optimality conditions for problems with constraints on expectations of the final state.
• Time-Harmonic Acoustic Scattering in a Complex Flow: a Full Coupling Between Acoustics and Hydrodynamics
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Mercier Jean-François
  • Millot Florence
  • Pernet Sébastien
  • Peynaud Emilie
  Communications in Computational Physics, Global Science Press, 2012, 11 (2), pp.555-572. For the numerical simulation of time harmonic acoustic scattering in a complex geometry, in presence of an arbitrary mean flow, the main difficulty is the coexistence and the coupling of two very different phenomena: acoustic propagation and convection of vortices. We consider a linearized formulation coupling an augmented Galbrun equation (for the perturbation of displacement) with a time harmonic convection equation (for the vortices). We first establish the well-posedness of this time harmonic convection equation in the appropriate mathematical framework. Then the complete problem, with Perfectly Matched Layers at the artificial boundaries, is proved to be coercive + compact, and a hybrid numerical method for the solution is proposed, coupling finite elements for the Galbrun equation and a Discontinuous Galerkin scheme for the convection equation. Finally a 2D numerical result shows the efficiency of the method. (10.4208/cicp.221209.030111s)
  DOI : 10.4208/cicp.221209.030111s
• Control of Nonholonomic Systems and Sub-Riemannian Geometry
  
  • Jean Frédéric
  , 2012. Nonholonomic systems are control systems which depend linearly on the control. Their underlying geometry is the sub-Riemannian geometry, which plays for these systems the same role as Euclidean geometry does for linear systems. In particular the usual notions of approximations at the first order, that are essential for control purposes, have to be defined in terms of this geometry. The aim of these notes is to present these notions of approximation and their link with the metric tangent structure in sub-Riemannian geometry.
• Source point discovery through high frequency asymptotic time reversal
  
  • Benamou Jean-David
  • Collino Francis
  • Marmorat Simon
  Journal of Computational Physics, Elsevier, 2012, 231, pp.4643-4661. (10.1016/j.jcp.2012.03.012)
  DOI : 10.1016/j.jcp.2012.03.012
• Complete Radiation Boundary Conditions for Convective Waves
  
  • Hagstrom Thomas
  • Bécache Eliane
  • Givoli Dan
  • Stein Kurt
  Communications in Computational Physics, Global Science Press, 2012, 11 (2), pp.610-628. Local approximate radiation boundary conditions of optimal efficiency for the convective wave equation and the linearized Euler equations in waveguide geometry are formulated, analyzed, and tested. The results extend and improve for the convective case the general formulation of high-order local radiation boundary condition sequences for anisotropic scalar equations developed in [4]. (10.4208/cicp.231209.060111s)
  DOI : 10.4208/cicp.231209.060111s
• About Fokker-Planck equation with measurable coefficients and applications to the fast diffusion equation
  
  • Belaribi Nadia
  • Russo Francesco
  Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2012, 17 (84), pp.1-28. The object of this paper is the uniqueness for a $d$-dimensional Fokker-Planck type equation with non-homogeneous (possibly degenerated) measurable not necessarily bounded coefficients. We provide an application to the probabilistic representation of the so called Barenblatt solution of the fast diffusion equation which is the partial differential equation $\partial_t u = \partial^2_{xx} u^m$ with $m\in(0,1)$. Together with the mentioned Fokker-Planck equation, we make use of small time density estimates uniformly with respect to the initial condition
• d-Transversals of Stable Sets and Vertex Covers in Weighted Bipartite Graphs
  
  • Bentz Cédric
  • Costa Marie-Christine
  • Picouleau Christophe
  • Ries Bernard
  • de Werra Dominique
  Journal of Discrete Algorithms, Elsevier, 2012, 17, pp.95-102. (10.1016/j.jda.2012.06.002)
  DOI : 10.1016/j.jda.2012.06.002
• A preconditioned 3-D multi-region fast multipole solver for seismic wave propagation in complex geometries
  
  • Chaillat Stéphanie
  • Semblat Jean-François
  • Bonnet Marc
  Communications in Computational Physics, Global Science Press, 2012, 11, pp.594-609. The analysis of seismic wave propagation and amplification in complex geological structures requires efficient numerical methods. In this article, following up on recent studies devoted to the formulation, implementation and evaluation of 3-D single- and multi-region elastodynamic fast multipole boundary element methods (FM-BEMs), a simple preconditioning strategy is proposed. Its efficiency is demonstrated on both the single- and multi-region versions using benchmark examples (scattering of plane waves by canyons and basins). Finally, the preconditioned FM-BEM is applied to the scattering of plane seismic waves in an actual configuration (alpine basin of Grenoble, France), for which the high velocity contrast is seen to significantly affect the overall efficiency of the multi-region FM-BEM. (10.4208/cicp.231209.030111s)
  DOI : 10.4208/cicp.231209.030111s
• Solving the Homogeneous Isotropic Linear Elastodynamics Equations Using Potentials and Finite Elements. The Case of the Rigid Boundary Condition
  
  • Burel Aliénor
  • Imperiale Sébastien
  • Joly Patrick
  Numerical Analysis and Applications, Springer, 2012, 5 (2), pp.136-143. In this article, elastic wave propagation in a homogeneous isotropic elastic medium with rigid boundary is considered. A method based on the decoupling of pressure and shear waves via the use of scalar potentials is proposed. This method is adapted to a finite elements discretization, which is discussed. A stable, energy preserving numerical scheme is presented, as well as 2D numerical results. (10.1134/S1995423912020061)
  DOI : 10.1134/S1995423912020061
• Perfectly Matched Layer with Mixed Spectral Elements for the Propagation of Linearized Water Waves
  
  • Cohen Gary
  • Imperiale Sébastien
  Communications in Computational Physics, Global Science Press, 2012, 11 (2), pp.285-302. After setting a mixed formulation for the propagation of linearized water waves problem, we define its spectral element approximation. Then, in order to take into account unbounded domains, we construct absorbing perfectly matched layer for the problem. We approximate these perfectly matched layer by mixed spectral elements and show their stability using the 'frozen coefficient' technique. Finally, numerical results will prove the efficiency of the perfectly matched layer compared to classical absorbing boundary conditions. (10.4208/cicp.201109.261110s)
  DOI : 10.4208/cicp.201109.261110s
• Approximate Models for Wave Propagation Across Thin Periodic Interfaces
  
  • Delourme Bérangère
  • Haddar Houssem
  • Joly Patrick
  Journal de Mathématiques Pures et Appliquées, Elsevier, 2012, 98 (1), pp.28-71. This work deals with the scattering of acoustic waves by a thin ring that contains regularly spaced inhomogeneities. We first explicit and study the asymptotic of the solution with respect to the period and thickness of the inhomogeneities using so-called matched asymptotic expansions. We then build simplified models replacing the thin ring with Approximate Transmission Conditions that are accurate up to third order with respect to the layer width. We pay particular attention to the study of these approximate models and the quantification of their accuracy. (10.1016/j.matpur.2012.01.003)
  DOI : 10.1016/j.matpur.2012.01.003
• Error estimates for 1D asymptotic models in coaxial cables with non-homogeneous cross-section
  
  • Imperiale Sébastien
  • Joly Patrick
  Advances in Applied Mechanics, New York ; London ; Paris [etc] : Academic Press, 2012, xx. This paper is the first contribution towards the rigorous justification of asymptotic 1D models for the time-domain simulation of the propagation of electromagnetic waves in coaxial cables. Our general objective is to derive error estimates between the "exact" solution of the full 3D model and the "approximate" solution of the 1D model known as the Telegraphist's equation. (10.4208/aamm.12-12S06)
  DOI : 10.4208/aamm.12-12S06