Publications

2012

• Numerical Algorithms for a Variational Problem of the Spatial Segregation of Reaction-Diffusion Systems
  
  • Arakelyan Avetik
  • Bozorgnia Farid
  , 2012. In this paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support, which are governed by a minimization problem. We use quantitative properties of both solutions and free boundaries to derive our scheme. Furthermore, the proof of convergence of the numerical method is given in some particular cases. We also apply our numerical simulations for the spatial segregation limit of diffusive Lotka-Volterra models in presence of high competition and inhomogeneous Dirichlet boundary conditions. We discuss numerical implementations of the resulting approach and present computational tests.
• 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.
• 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.
• 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.
• 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.
• Transparent boundary conditions for evolution equations in infinite periodic strips
  
  • Coatléven Julien
  SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2012, 34 (3), pp.1563-1583. We consider the solution of a generic equation $\gamma\rho(\mathbf{x})\partial^p_tu(\mathbf{x},t)-\Delta u(\mathbf{x},t) +V(\mathbf{x})u(\mathbf{x},t) = f(\mathbf{x},t)$, $\mathbf{x} = (x,y)$, for $t>0$, $p=1,2$ in a domain $\Omega$ which is infinite in $x$ and bounded in $y$. We assume that $f(\cdot,t)$ is supported for all $t>0$ in $\Omega_0 = \{\mathbf{x} \in \Omega \; | \; -a_- < x < a_+\}$ and that $\rho(\mathbf{x})$ and $V(\mathbf{x})$ are x-periodic in $\Omega \setminus \Omega_0$. We consider the associated $\theta$-scheme in time, to obtain a semidiscretized problem. We then show how to obtain for each time step exact boundary conditions on the vertical segments, $\Gamma_0^- = \{\mathbf{x}\in \Omega\; | \; x=-a_-\}$ and $\Gamma_0^+ = \{\mathbf{x}\in \Omega \;| \; x=a_+\}$, that will enable us to find the solution on $\Omega_0 \cup \Gamma_0^+ \cup \Gamma_0^-$. Then the solution can be extended in $\Omega$ in a straightforward manner from the values on $\Gamma_0^-$ and $\Gamma_0^+$. The method is based on the solution of local problems on a single periodicity cell, solved during an initialization step. The exact boundary conditions as well as the extension operators can be obtained for each time step through elementary computations using the solution of these local cell problems. (10.1137/110838030)
  DOI : 10.1137/110838030
• Interior transmission eigenvalue problem for Maxwell's equations: The T-coercivity as an alternative approach
  
  • Chesnel Lucas
  Inverse Problems, IOP Publishing, 2012, 28 (6). In this paper, we examine the interior transmission problem for Maxwells equations in the case where both and , the physical parameters of the scattering medium, differ from 0 and 0 modelling the background medium. Using the T-coercivity method, we propose an alternative approach to the classical techniques to prove that this problem is of Fredholm type and that the so-called transmission eigenvalues form at most a discrete set. The T-coercivity approach allows us to deal with cases where 0 and 0 can change sign. We also provide results of localization and FaberKrahn-type inequalities for the transmission eigenvalues. © 2012 IOP Publishing Ltd. (10.1088/0266-5611/28/6/065005)
  DOI : 10.1088/0266-5611/28/6/065005
• On Simultaneous Identification of the Shape and Generalized Impedance Boundary Condition in Obstacle Scattering
  
  • Bourgeois Laurent
  • Chaulet Nicolas
  • Haddar Houssem
  SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2012, 34 (3), pp.A1824-A1848. We consider the inverse obstacle scattering problem of determining both the shape and the "equiva- lent impedance" from far field measurements at a fixed frequency. In this work, the surface impedance is represented by a second order surface differential operator (refer to as generalized impedance boundary condition) as opposed to a scalar function. The generalized impedance boundary condition can be seen as a more accurate model for effective impedances and is widely used in the scattering problem for thin coatings. Our approach is based on a least square optimization technique. A major part of our analysis is to characterize the derivative of the cost function with respect to the boundary and this complex surface impedance configuration. In particular, we provide an extension of the notion of shape derivative to the case where the involved impedance parameters do not need to be surface traces of given functions, which leads (in general) to a non-vanishing tangential boundary perturbation. The efficiency of considering this type of derivative is illustrated by several 2D numerical experiments based on a (classical) steepest descent method. The feasibility of retrieving both the shape and the impedance parameters is also discussed in our numerical experiments. (10.1137/110850347)
  DOI : 10.1137/110850347
• Usual Anderson localization restored in bilayered left- and right-handed structures
  
  • Maurel Agnès
  • Ourir Abdelwaheb
  • Mercier Jean-François
  • Pagneux Vincent
  Physical Review B: Condensed Matter and Materials Physics (1998-2015), American Physical Society, 2012, 85 (20). We present a study of the attenuation length in a one-dimensional array of alternating left- and right-handed materials in which both the permittivities and the permeabilities are disordered. This type of structure has been shown to present an anomaly in the attenuation length when only permeabilities are disordered. We derive a simple analytical expression of the attenuation length, when the disorder in the refraction index is due to perturbations in both the permeability and the permittivity. Our expression is able to explain the transition to the anomalous behavior when perturbation only in the permeability or only in the permittivity is considered. Besides, we show that the anomaly is dramatically affected when considering perturbations in permeability and permittivity. The coupling effects are able to restore the ordinary localization length. © 2012 American Physical Society. (10.1103/physrevb.85.205138)
  DOI : 10.1103/physrevb.85.205138
• Sensitivity analysis of energy contracts management problem by stochastic programming techniques
  
  • Cen Zhihao
  • Bonnans J. Frederic
  • Christel Thibault
  , 2012, 12 (2012), pp.447-471.. We consider a model of medium-term commodity contracts management. Randomness takes place only in the prices on which the commodities are exchanged whilst state variable is multi-dimensional. In our previous article, we proposed an algorithm to deal with such problem, based on quantization of random process and a dual dynamic programming type approach. We obtained accurate estimates of the optimal value and a suboptimal strategy from this algorithm. In this paper, we analyse the sensitivity with respect to parameters driving the price model. We discuss the estimate of marginal price based on the Danskin's theorem. Finally, some numerical results applied to realistic energy market problems have been performed. Comparisons between results obtained by our algorithm and other classical methods are provided and evidence the accuracy of the estimate of marginal prices.
• Solving multi-stage stochastic mixed integer linear programs by the dual dynamic programming approach
  
  • Cen Zhihao
  , 2012. We consider a model of medium-term commodity contracts management. Randomness takes place only in the prices on which the commodities are exchanged, whilst state variable is multi-dimensional, and decision variable is integer. In our previous article, we proposed an algorithm based on the quantization of random process and a dual dynamic programming type approach to solve the continuous relaxation problem. In this paper, we study the multi-stage stochastic mixed integer linear program (SMILP) and show the difficulty when using dual programming type algorithm. We propose an approach based on the cutting plane method combined with the algorithm in our previous article, which gives an upper and a lower bound of the optimal value and a sub-optimal integer solution. Finally, a numerical test on a real problem in energy market is provided.
• Operator Factorization for Multiple-Scattering Problems and an Application to Periodic Media
  
  • Coatléven Julien
  • Joly Patrick
  Communications in Computational Physics, Global Science Press, 2012, 11 (2), pp.303-318. This work concerns multiple-scattering problems for time-harmonic equations in a reference generic media. We consider scatterers that can be sources, obstacles or compact perturbations of the reference media. Our aim is to restrict the computational domain to small compact domains containing the scatterers. We use Robin-to-Robin (RtR) operators (in the most general case) to express boundary conditions for the interior problem. We show that one can always factorize the RtR map using only operators defined using single-scatterer problems. This factorization is based on a decomposition of the diffracted field, on the whole domain where it is defined. Assuming that there exists a good method for solving single-scatterer problems, it then gives a convenient way to compute RtR maps for a random number of scatterers.
• An elementary introduction to the construction and the analysis of Perfectly Matched Layers for time domain wave propagation
  
  • Joly Patrick
  SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada, Springer, 2012, 57, pp.5-48.
• T-coercivity for scalar interface problems between dielectrics and metamaterials
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Chesnel Lucas
  • Ciarlet Patrick
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2012, 46, pp.1363-1387. Some electromagnetic materials have, in a given frequency range, an effective dielectric permittivity and/or a magnetic permeability which are real-valued negative coefficients when dissipation is neglected. They are usually called metamaterials. We study a scalar transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of R^d, with d=2,3. Our aim is to characterize occurences where the problem is well-posed within the Fredholm (or coercive + compact) framework. For that, we build some criteria, based on the geometry of the interface between the dielectric and the metamaterial. The proofs combine simple geometrical arguments with the approach of T-coercivity, introduced by the first and third authors and co-worker. Furthermore, the use of localization techniques allows us to derive well-posedness under conditions that involve the knowledge of the coefficients only near the interface. When the coefficients are piecewise constant, we establish the optimality of the criteria. (10.1051/m2an/2012006)
  DOI : 10.1051/m2an/2012006
• On the use of sampling methods to identify cracks in acoustic waveguides
  
  • Bourgeois Laurent
  • Lunéville Éric
  Inverse Problems, IOP Publishing, 2012, 28 (10), pp.105011.1-105011.18. We consider the identification of cracks in an acoustic 2D/3D waveguide with the help of sampling methods such as the linear sampling method or the factorization method. A modal version of these sampling methods is used. Our paper emphasizes the fact that if one a priori knows the type of boundary condition which actually applies on the crack, then we shall adapt the formulation of our sampling method to such boundary conditions in order to improve the efficiency of the method. The need for such adaptation is proved theoretically and illustrated numerically with the help of 2D examples. We also show by using our modal formulation that the factorization method is applicable in a waveguide with the same data as the linear sampling method. © 2012 IOP Publishing Ltd. (10.1088/0266-5611/28/10/105011)
  DOI : 10.1088/0266-5611/28/10/105011
• Propagation of guided waves through weak penetrable scatterers
  
  • Maurel Agnes
  • Mercier Jean-François
  Journal of the Acoustical Society of America, Acoustical Society of America, 2012, 131 (3), pp.1874-1889. The scattering of a scalar wave propagating in a waveguide containing weak penetrable scatterers is inspected in the Born approximation. The scatterers are of arbitrary shape and present a contrast both in density and in wavespeed (or bulk modulus), a situation that can be translated in the context of SH waves, water waves, or transverse electric/transverse magnetic polarized electromagnetic waves. For small size inclusions compared to the waveguide height, analytical expressions of the transmission and reflection coefficients are derived, and compared to results of direct numerical simulations. The cases of periodically and randomly distributed inclusions are considered in more detail, and compared with unbounded propagation through inclusions. Comparisons with previous results valid in the low frequency regime are proposed. © 2012 Acoustical Society of America. (10.1121/1.3682037)
  DOI : 10.1121/1.3682037