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In this paper, we study the uniqueness of solutions for diagonal hyperbolic systems in one space dimension. We present two uniqueness results. The first one is a global existence and uniqueness result of a continuous solution for strictly hyperbolic systems. The second one is a global existence and uniqueness result of a Lipschitz solution for hyperbolic systems not necessarily strictly hyperbolic. An application of these two results is shown in the case of the one-dimensional isentropic gas dynamics.

ano.nymous@ccsd.cnrs.fr.invalid (Ahmad El Hajj), Ahmad El Hajj

Nous présentons un environnement de génération automatique de simulations entièrement basé sur les technologies XML. Le langage de description proposé permet de décrire des objets mathématiques tels que des systèmes d'équations différentielles, des systèmes d'équations non-linéaires, des équations aux dérivées partielles en dimension 2, ou bien de simples courbes et surfaces. Il permet aussi de décrire les paramètres dont dépendent ces objets. Ce langage est indépendant du logiciel et permet donc de garantir la pérennité du travail des auteurs ainsi que leur mutualisation et leur réutilisation. Nous décrivons aussi l'architecture d'une «chaîne de compilation» permettant de transformer ces fichiers XML sous forme de scripts et de les faire fonctionner dans le logiciel Scilab.

ano.nymous@ccsd.cnrs.fr.invalid (Stéphane Mottelet), Stéphane Mottelet

The Hidden semi-Markov models (HSMMs) have been introduced to overcome the constraint of a geometric sojourn time distribution for the different hidden states in the classical hidden Markov models. Several variations of HSMMs have been proposed that model the sojourn times by a parametric or a nonparametric family of distributions. In this article, we concentrate our interest on the nonparametric case where the duration distributions are attached to transitions and not to states as in most of the published papers in HSMMs. Therefore, it is worth noticing that here we treat the underlying hidden semi–Markov chain in its general probabilistic structure. In that case, Barbu and Limnios (2008) proposed an Expectation–Maximization (EM) algorithm in order to estimate the semi-Markov kernel and the emission probabilities that characterize the dynamics of the model. In this paper, we consider an improved version of Barbu and Limnios' EM algorithm which is faster than the original one. Moreover, we propose a stochastic version of the EM algorithm that achieves comparable estimates with the EM algorithm in less execution time. Some numerical examples are provided which illustrate the efficient performance of the proposed algorithms.

ano.nymous@ccsd.cnrs.fr.invalid (Sonia Malefaki), Sonia Malefaki

This article concerns the study of the asymptotic properties of the maximum likelihood estimator (MLE) for the general hidden semi-Markov model (HSMM) with backward recurrence time dependence. By transforming the general HSMM into a general hidden Markov model, we prove that under some regularity conditions, the MLE is strongly consistent and asymptotically normal. We also provide useful expressions for the asymptotic covariance matrices, involving the MLE of the conditional sojourn times and the embedded Markov chain of the hidden semi-Markov chain.

ano.nymous@ccsd.cnrs.fr.invalid (Samis Trevezas), Samis Trevezas

The fast multipole method is an efficient technique to accelerate the solution of large scale 3D scattering problems with boundary integral equations. However, the fast multipole accelerated boundary element method (FM-BEM) is intrinsically based on an iterative solver. It has been shown that the number of iterations can significantly hinder the overall efficiency of the FM-BEM. The derivation of robust preconditioners for FM-BEM is now inevitable to increase the size of the problems that can be considered. The main constraint in the context of the FM-BEM is that the complete system is not assembled to reduce computational times and memory requirements. Analytic preconditioners offer a very interesting strategy by improving the spectral properties of the boundary integral equations ahead from the discretization. The main contribution of this paper is to combine an approximate adjoint Dirichlet to Neumann (DtN) map as an analytic preconditioner with a FM-BEM solver to treat Dirichlet exterior scattering problems in 3D elasticity. The approximations of the adjoint DtN map are derived using tools proposed in [40]. The resulting boundary integral equations are preconditioned Combined Field Integral Equations (CFIEs). We provide various numerical illustrations of the efficiency of the method for different smooth and non smooth geometries. In particular, the number of iterations is shown to be completely independent of the number of degrees of freedom and of the frequency for convex obstacles.

ano.nymous@ccsd.cnrs.fr.invalid (Stéphanie Chaillat), Stéphanie Chaillat

Concise formulae are given for the cumulant matrices of a random vector up to order 6. In addition to usual matrix operations, they involve only the Kronecker product, the vec operator, and the commutation matrix. Orders 5 and 6 are provided here for the first time; the same method as provided in the paper can be applied to compute higher orders. An immediate consequence of these formulae is to return 1) upper bounds on the rank of the cumulant matrices and 2) the expression of the sixth-order moment matrix of a Gaussian vector. Due to their conciseness, the proposed formulae also have a computational advantage as compared to the repeated use of Leonov and Shiryaev formula.

ano.nymous@ccsd.cnrs.fr.invalid (Hanany Ould-Baba), Hanany Ould-Baba

The paper addresses the separation of multidimensional sources, with possibly different dimensions, by means of higher-order cumulant matrices. First, it is rigorously proved, in a general setting, that contracted cumulant matrices of any order are all block-diagonalizable in the same basis. Second, a family of joint block-diagonalization algorithms is proposed that separate multidimensional sources by combining contracted cumulant matrices of arbitrary orders. Third, a specific solution is given to determine the source dimensions when they are unknown but all different. The performances of the proposed algorithms are compared between them and with algorithms of the literature based on orders 3 and 6.

ano.nymous@ccsd.cnrs.fr.invalid (Hanany Ould-Baba), Hanany Ould-Baba

Topological optimization of networks is a complex multi-constraint and multi-criterion optimisation problem in many real world fields (telecommunications, electricity distribution etc.). This paper describes an heuristic algorithm using Binary Decisions Diagrams (BDD) to solve the reliable communication network design problem (RCND) \cite{ga1}. The aim is to design a communication network topology with minimal cost that satisfies a given reliability constraint.

ano.nymous@ccsd.cnrs.fr.invalid (Gary Hardy), Gary Hardy

The aim of our work is to reconstruct an inclusion immersed in a fluid flowing in a larger bounded domain via a boundary measurement. Here the fluid motion is assumed to be governed by the Stokes equations. We study the inverse problem thanks to the tools of shape optimization by minimizing a Kohn-Vogelius type cost functional. We first characterize the gradient of this cost functional in order to make a numerical resolution. Then, in order to study the stability of this problem, we give the expression of the shape Hessian. We show the compactness of the Riesz operator corresponding to this shape Hessian at a critical point which explains why the inverse problem is ill-posed. Therefore we need some regularization methods to solve numerically this problem. We illustrate those general results by some explicit calculus of the shape Hessian in some particular geometries. In particular, we solve explicitly the Stokes equations in a concentric annulus. Finally, we present some numerical simulations using a parametric method.

ano.nymous@ccsd.cnrs.fr.invalid (Fabien Caubet), Fabien Caubet

We construct and analyze a family of well-conditioned boundary integral equations for the Krylov iterative solution of three-dimensional elastic scattering problems by a bounded rigid obstacle. We develop a new potential theory using a rewriting of the Somigliana integral representation formula. From these results, we generalize to linear elasticity the well-known Brakhage-Werner and Combined Field Integral Equation formulations. We use a suitable approximation of the Dirichlet-to-Neumann (DtN) map as a regularizing operator in the proposed boundary integral equations. The construction of the approximate DtN map is inspired by the On-Surface Radiation Conditions method. We prove that the associated integral equations are uniquely solvable and possess very interesting spectral properties. Promising analytical and numerical investigations, in terms of spherical harmonics, with the elastic sphere are provided.

ano.nymous@ccsd.cnrs.fr.invalid (Marion Darbas), Marion Darbas

Dans ce travail je présente une étude unifiée basée sur l'estimation du maximum de vraisemblance pour des modèles markoviens, semi-markoviens et semi-markoviens cachés. Il s'agit d'une étude théorique des propriétés asymptotiques de l'EMV des modèles mentionnés ainsi que une étude algorithmique. D'abord, nous construisons l'estimateur du maximum de vraisemblance (EMV) de la loi stationnaire et de la variance asymptotique du théorème de la limite centrale (TLC) pour des fonctionnelles additives des chaînes de Markov ergodiques et nous démontrons sa convergence forte et sa normalité asymptotique. Ensuite, nous considérons un modèle semi-markovien non paramétrique. Nous présentons l'EMV exact du noyau semi-markovien qui gouverne l'évolution de la chaîne semi-markovienne (CSM) et démontrons la convergence forte, ainsi que la normalité asymptotique de chaque sous-vecteur fini de cet estimateur en obtenant des formes explicites pour les matrices de covariance asymptotiques. Ceci a été appliqué pour une observation de longue durée d'une seule trajectoire d'une CSM, ainsi que pour une suite des trajectoires i.i.d. d'une CSM censurée à un instant fixe. Nous introduisons un modèle semi-markovien caché (MSMC) général avec dépendance des temps de récurrence en arrière. Nous donnons des propriétés asymptotiques de l'EMV qui correspond à ce modèle. Nous déduisons également des expressions explicites pour les matrices de covariance asymptotiques qui apparaissent dans le TLC pour l'EMV des principales caractéristiques des CSM. Enfin, nous proposons une version améliorée de l'algorithme EM (Estimation-Maximisation) et une version stochastique de cet algorithme (SAEM) afin de trouver l'EMV pour les MSMC non paramétriques. Des exemples numériques sont présentés pour ces deux algorithmes.

ano.nymous@ccsd.cnrs.fr.invalid (Samis Trevezas), Samis Trevezas

The present work is concerned with the shape reconstruction problem of isotropic elastic inclusions from far-field data obtained by the scattering of a finite number of time-harmonic incident plane waves. This paper aims at completing the theoretical framework which is necessary for the application of geometric optimization tools to the inverse transmission problem in elastodynamics. The forward problem is reduced to systems of boundary integral equations following the direct and indirect methods initially developed for solving acoustic transmission problems. We establish the Fréchet differentiability of the boundary to far-field operator and give a characterization of the first Fréchet derivative and its adjoint operator. Using these results we propose an inverse scattering algorithm based on the iteratively regularized Gauß Newton method and show numerical experiments in the special case of star-shaped obstacles.

ano.nymous@ccsd.cnrs.fr.invalid (Frédérique Le Louër), Frédérique Le Louër

In this paper, we present a network decomposition method using Binary Decision Diagram (BDD), a state-of-the-art data structure to encode and manipulate boolean functions, for computing the reliability of networks such as computer, communication or power networks. We consider the \textit{so-called} $K$-terminal reliability measure $R_K$ which is defined as the probability that a subset $K$ of nodes can communicate to each other, taking into account the possible failures of the network components (nodes and links). We present an exact algorithm for computing the $K$-terminal reliability of graph $G=(V,E)$ in $O(|E|.F_{max}.2^{F_{max}}.B_{F_{max}})$ where $B_{F_{max}}$ is the Bell number of the maximum boundary set $F_{max}$. Other reliability measures are also discussed. Several examples and experiments show the effectiveness of this approach \footnote{This research was supported by the \emph{Conseil Regional de Picardie}.}.

ano.nymous@ccsd.cnrs.fr.invalid (Gary Hardy), Gary Hardy

L’auteur s’intéresse au problème de l’analyse en composantes indépendantes multidimensionnelles (ACIM) qui est la généralisation naturelle du problème ordinaire de l’analyse en composantes indépendantes (ACI). Tout d’abord, afin de faciliter l’utilisation des cumulants des ordres supérieurs, nous présentons de nou- velles formules pour le calcul matriciel des matrices de cumulants d’un vecteur aléatoire réel à partir de ses matrices de moments. Outre les opérations matricielles usuelles, ces formules utilisent uniquement le produit de Kronecker, l’opérateur vec et des matrices de commutation. Nous pouvons immédiatement à partir de ces formules examiner de plus près les structures particulières des matrices de cumulants et ainsi donner des résultats sur les rangs de ces matrices qui caractérisent la dépendance entre les variables aléatoires constituant le vecteur aléatoire. L’intérêt pratique principal de nos formules matricielles réside certainement dans une évaluation des cumulants beaucoup plus aisée et rapide qu’avec la méthode usuelle basée sur une utilisation répétée des formules de Leonov et Shiryaev. Dans la deuxième partie de cette thèse, nous montrons que sous les hypothèses usuelles de l’analyse en composantes indépendantes mul- tidimensionnelles, les matrices de cumulants contractées à un ordre statistique quelconque sont toutes bloc-diagonalisables dans la même base. Nous en déduisons des algorithmes de résolution d’ACIM par bloc-diagonalisation conjointe et comparons les résultats obtenus aux ordres 3 à 6, entre eux et avec d’autres méthodes, sur quelques signaux synthétiques. Des exemples simples ont élaborés afin de justifier la nécessité de combiner des ordres différents pour garantir la meilleure séparation. Nous prouvons aussi que le cas le plus simple à traiter est celui de mélanges de sources qui ont différentes dimensions. Dans la dernière partie de cette thèse nous proposons une famille de méthodes qui exploitent uniquement les sta- tistiques d’ordres supérieurs à deux. Sous certaines hypothèses supplémentaires, ces méthodes permettent après un blanchiment d’ordre quatre des observations de résoudre complètement le problème ACIM bruité en bloc diagonalisant conjointement un ensemble de matrices de cumulants issues des statistiques d’ordres supérieurs strictement à quatre. Une comparaison avec les méthodes ACIM à blanchiment d’ordre deux pour la séparation des activités électriques foetale et maternelle (mesurées via trois électrodes placées sur l’abdomen de la mère) montre que cette nouvelle famille est mieux adaptée à cette application : elles permettent une séparation quasi parfaite de ces deux contributions.

ano.nymous@ccsd.cnrs.fr.invalid (Hanany Ould-Baba), Hanany Ould-Baba

We consider the question of giving an upper bound for the first nontrivial eigenvalue of the Wentzell-Laplace operator of a domain $\Omega$, involving only geometrical informations. We provide such an upper bound, by generalizing Brock's inequality concerning Steklov eigenvalues, and we conjecture that balls maximize the Wentzell eigenvalue, in a suitable class of domains, which would improve our bound. To support this conjecture, we prove that balls are critical domains for the Wentzell eigenvalue, in any dimension, and that they are local maximizers in dimension 2 and 3, using an order two sensitivity analysis. We also provide some numerical evidence.

ano.nymous@ccsd.cnrs.fr.invalid (Marc Dambrine), Marc Dambrine

We aim to reconstruct an inclusion ω immersed in a perfect fluid flowing in a larger bounded domain Ω via boundary measurements on ∂Ω. The obstacle ω is assumed to have a thin layer and is then modeled using generalized boundary conditions (precisely Ventcel boundary conditions). We first obtain an identifiability result (i.e. the uniqueness of the solution of the inverse problem) for annular configurations through explicit computations. Then, this inverse problem of reconstructing ω is studied thanks to the tools of shape optimization by minimizing a least squares type cost functional. We prove the existence of the shape derivatives with respect to the domain ω and characterize the gradient of this cost functional in order to make a numerical resolution. We also characterize the shape Hessian and prove that this inverse obstacle problem is unstable in the following sense: the functional is degenerated for highly oscillating perturbations. Finally, we present some numerical simulations in order to confirm and extend our theoretical results.

ano.nymous@ccsd.cnrs.fr.invalid (Fabien Caubet), Fabien Caubet

Observability Gramians of diffusion equations have been recently connected to infinite Pick and Cauchy matrices. In fact, inverse or observability inequalities can be obtained after estimating the extreme eigenvalues of these structured matrices, with respect to the diffusion semi-group matrix. The purpose is hence to conduct a spectral study of a subclass of symmetric Cauchy matrices and present an algebraic way to show the desired observability results. We revisit observability inequalities for three different observation problems of the diffusion equation and show how they can be (re)stated through simple proofs.

ano.nymous@ccsd.cnrs.fr.invalid (Faker Ben Belgacem), Faker Ben Belgacem

We study the stability of some critical (or equilibrium) shapes in the minimization problem of the energy dissipated by a fluid (i.e. the drag minimization problem) governed by the Stokes equations. We first compute the shape derivative up to the second order, then provide a sufficient condition for the shape Hessian of the energy functional to be coercive at a critical shape. Under this condition, the existence of such a local strict minimum is then proved using a precise upper bound for the variations of the second order shape derivative of the functional with respect to the coercivity and differentiability norms. Finally, for smooth domains, a lower bound of the variations of the drag is obtained in terms of the measure of the symmetric difference of domains.

ano.nymous@ccsd.cnrs.fr.invalid (Fabien Caubet), Fabien Caubet

The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a weak material approximation, a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic error committed by using the weak material approximation and, on a model case, explain that they amplifies instabilities by a second order analysis of the objective function.

ano.nymous@ccsd.cnrs.fr.invalid (Marc Dambrine), Marc Dambrine

Karhunen-Loève's decompositions (KLD) or the proper orthogonal decompositions (POD) of bivariate functions are revisited in this work. We investigate the truncation error first for regular functions and try to improve and sharpen bounds found in the literature. However it happens that (KL)-series expansions are in fact more sensitive to the liability of fields to approximate to be well represented by a small sum of products of separated variables functions. We consider this very issue for some interesting fields solutions of partial differential equations such as the transient heat problem and Poisson's equation. The main tool to state approximation bounds is linear algebra. We show how the singular value decomposition underlying the (KL)-expansion is connected to the spectrum of some Gram matrices. Deriving estimates on the truncation error is thus strongly tied to the spectral properties of these Gram matrices which are structured matrices with low displacement ranks.

ano.nymous@ccsd.cnrs.fr.invalid (Mejdi Azaïez), Mejdi Azaïez

L'utilisation des méthodes intégrales dans le milieu pétrolier est récente et reste limitée à des problèmes 2D, le puits étant modélisé comme un terme source. Dans ce travail, nous proposons une nouvelle méthode intégrale pour évaluer la performance des puits dans un réservoir stratifié à géométrie quelconque en 3D. Ici, l'écoulement dans le puits est pris en compte par deux types de conditions aux limites, la première linéaire, la seconde non-linéaire et non-locale. Nous avons démontré que chacun des deux modèles (linéaire et non-linéaire) est bien posé. Du point de vue numérique, nous avons développé une nouvelle formulation intégrale, équivalente au modèle linéaire. Les équations intégrales ont été discrétisées par une méthode de Galerkin. D'autre part, nous avons pu tirer profit du problème d'échelle pour faire une approximation filaire du puits. Les tests numériques montrent que cette nouvelle méthode intégrale permet de calculer l'indice de productivité du puits à 1% près.

ano.nymous@ccsd.cnrs.fr.invalid (Valérie Moumas), Valérie Moumas

We are interested in an inverse problem of recovering the position of a pollutant or contaminant source in a stream water. Advection, dispersive transport and the reaction of the solute is commonly modeled by a linear or non-linear parabolic equation. In former works, it is established that a point-wise source is fully identifiable from measurements recorded by a couple of sensors placed, one up-stream and the other down-stream of the pollution source. The observability question we try to solve here is related to the redundancy of sensors when additional information is available on the point-wise source. It may occur, in hydrological engineering, that the intensity of the pollutant is known in advance. In this case, we pursue an identifiability result of a moving source location using a single observation. The chief mathematical tools to prove identifiability are the unique continuation theorem together with an appropriate maximum principle for the parabolic equation under investigation.

ano.nymous@ccsd.cnrs.fr.invalid (Faker Ben Belgacem), Faker Ben Belgacem

Les antennes lentilles sont des dispositifs ayant pour support les ondes électromagnétiques et sont constituées d'une source primaire et d'un système focalisant diélectrique. La montée en importance récente d'applications en ondes millimétriques (exemple : radars d'assistance et d'aide à la conduite), nécessite la construction d'antennes lentilles de quelques centimètres qui répondent à des cahiers des charges spécifiques à chaque cas. L'une des problématiques à résoudre consiste à déterminer la forme optimale de la lentille étant données : (i) les caractéristiques de la source primaire, (ii) les caractéristiques en rayonnement fixées. Ce projet de thèse vise à développer de nouveaux outils pour l'optimisation de forme en utilisant une formulation intégrale du problème. Cette thèse s'articule en deux parties. Dans la première nous avons construit plusieurs formulations intégrales pour le problème de diffraction diélectrique en utilisant une approche par équation intégrale surfacique. Dans la seconde nous avons étudié les dérivées de forme des opérateurs intégraux standard en électromagnétisme dans le but de les incorporer dans un algorithme d'optimisation de forme.

ano.nymous@ccsd.cnrs.fr.invalid (Frédérique Le Louër), Frédérique Le Louër

In this paper, we investigate the existence and characterizations of the Fréchet derivative of solutions to time-harmonic elastic scattering problems with respect to the boundary of the obstacle. Our analysis is based on a technique - the factorization of the difference of the far-field pattern for two different scatterers - introduced by Kress and Päivärinta to establish Fréchet differentiability in acoustic scattering. For the Dirichlet boundary condition an alternative proof of a differentiability result due to Charalambopoulos is provided and new results are proven for the Neumann and impedance exterior boundary value problems.

ano.nymous@ccsd.cnrs.fr.invalid (Frédérique Le Louër), Frédérique Le Louër

Avant d'estimer les paramètres intervenant dans des systèmes dynamiques, linéaires ou non-linéaires, contrôlés ou non contrôlés, il est important d'effectuer une étude d'identifiabilité, c'est à dire si, à partir des données expérimentales, les paramètres étudiés sont uniques ou non. Plusieurs méthodes ont été développées ces dernières années, en particulier une qui est basée sur l'algèbre différentielle. Celle-ci a conduit à un algorithme utilisant le package Diffalg implémenté sous Maple et permettant de tester l'identifiabilité de systèmes d'équations différentielles. Les résultats obtenus à partir de cette étude permettent de mettre en place des méthodes numériques pour obtenir une première estimation des paramètres, ceci sans aucune connaissance à priori de leur valeur. Cette première estimation peut alors être utilisée comme point de départ d'algorithmes itératifs spécialisés dans l'étude des problèmes mal posés : la régularisation de Tikhonov. Dans cette thèse, deux modèles non linéaires en pharmacocinétique de type Michaelis-Menten ont tout d'abord été étudiés. Ensuite, nous nous sommes intéressés à un modèle de pollution décrit par une équation aux dérivées partielles parabolique. Le terme source à identifier était modélisé par le produit de la fonction débit avec la masse de Dirac, de support la position de la source polluante. Le but du travail était de fournir une première estimation de la source polluante. Après avoir obtenu l'identifiabilité du problème continu, nous avons étudié l'identifiabilité d'un problème approché en nous appuyant sur les méthodes d'algèbre différentielle. Celui-ci a été obtenu en approchant la masse de Dirac par une fonction gaussienne et en discrétisant ensuite le système en espace. Les résultats d'identifiabilité ont été obtenus quel que soit le nombre de points de discrétisation en espace. De cette étude théorique, nous en avons déduit des algorithmes numériques donnant une première estimation des paramètres à identifier.

ano.nymous@ccsd.cnrs.fr.invalid (Nathalie Verdière), Nathalie Verdière

This paper deals with parameter and state estimation in a bounded-error context for uncertain dynamical aerospace models when the input is considered optimized or not. In a bounded-error context, perturbations are assumed bounded but otherwise unknown. The parameters to be estimated are also considered bounded. The tools of the presented work are based on a guaranteed numerical set integration solver of ordinary differential equations combined with adapted set inversion computation. The main contribution of this work consists in developing procedures for parameter estimation whose performance is highly related with the input of system. In this paper, a comparison with a classical non-optimized input is proposed.

ano.nymous@ccsd.cnrs.fr.invalid (Qiaochu Li), Qiaochu Li

In this communication, we perform the sensitivity analysis of a building energy model. The aim is to assess the impact of the weather data on the performance of a model of a passive house, in order to better control it. The weather data are uncertain dynamic inputs to the model. To evaluate their impact, the problem of generating coherent weather data arises. To solve it, we carry out the Karhunen-Loève decomposition of the uncertain dynamic inputs. We then propose an approach for the sensitivity analysis of this kind of models. The originality for sensitivity analysis purpose is to separate the random variable of the dynamic inputs, propagated to the model response, from the deterministic spatio/temporal function. This analysis highlights the role of the solar gain on a high-insulated passive building, during winter time.

ano.nymous@ccsd.cnrs.fr.invalid (Floriane Anstett-Collin), Floriane Anstett-Collin

In this paper, we address the issue of performing sensitivity analysis of complex models presenting uncertain static and dynamic inputs. The dynamic inputs are viewed as random processes which can be represented by a linear combination of the deterministic functions depending on time whose coefficients are uncorrelated random variables. To achieve this, the Karhunen-Loève decomposition of the dynamic inputs is performed. For sensitivity analysis purposes, the influence of the dynamic inputs onto the model response is then given by the one of the uncorrelated random coefficients of the Karhunen-Loève decomposition, which is the originality here. The approach is applied to a building energy model, in order to assess the impact of the uncertainties of the material properties and the weather data on the energy performance of a real low energy consumption house.

ano.nymous@ccsd.cnrs.fr.invalid (Floriane Anstett-Collin), Floriane Anstett-Collin

Uncertainty Analysis and Sensitivity Analysis of complex models: Coping with dynamic and static inputs

ano.nymous@ccsd.cnrs.fr.invalid (Floriane Anstett-Collin), Floriane Anstett-Collin

The magnetohydrodynamics laws govern the motion of a conducting fluid, such as blood, in an externally applied static magnetic field B 0. When an artery is exposed to a magnetic field, the blood charged particles are deviated by the Lorentz force thus inducing electrical currents and voltages along the vessel walls and in the neighboring tissues. Such a situation may occur in several bio-medical applications: magnetic resonance imaging (MRI), magnetic drug transport and targeting, tissue engineering… In this paper, we consider the steady unidirectional blood flow in a straight circular rigid vessel with non-conducting walls, in the presence of an exterior static magnetic field. The exact solution of Gold (1962) (with the induced fields not neglected) is revisited. It is shown that the integration over a cross section of the vessel of the longitudinal projection of the Lorentz force is zero, and that this result is related to the existence of current return paths, whose contributions compensate each other over the section. It is also demonstrated that the classical definition of the shear stresses cannot apply in this situation of magnetohydrodynamic flow, because, due to the existence of the Lorentz force, the axisymmetry is broken.

ano.nymous@ccsd.cnrs.fr.invalid (Agnès Drochon), Agnès Drochon

Blood flow in high static magnetic fields induces elevated voltages that contaminate the ECG signal which is recorded simultaneously during MRI scans for synchronization purposes. This is known as the magnetohydrodynamic (MHD) effect, it increases the amplitude of the T wave, thus hindering correct R peak detection. In this paper, we inspect the MHD induced alterations of human ECG signals recorded in a 1.5 Tesla steady magnetic field and establish a primary characterization of the induced changes using time and frequency domain analysis. We also reexamine our previously developed real time algorithm for MRI cardiac gating and determine that, with a minor modification, this algorithm is capable of achieving perfect detection even in the presence of strong MHD artifacts.

ano.nymous@ccsd.cnrs.fr.invalid (Dima Abi Abdallah), Dima Abi Abdallah

Blood flow in a steady magnetic field has been of great interest over the past years.Many researchers have examined the effects of magnetic fields on velocity profiles and arterial pressure, and major studies focused on steady or sinusoidal flows. In this paper we present a solution for pulsed magnetohydrodynamic blood flow with a somewhat realistic physiological pressure wave obtained using a windkessel lumped model. A pressure gradient is derived along a rigid vessel placed at the output of a compliant module which receives the ventricle outflow. Then, velocity profile and flow rate expressions are derived in the rigid vessel in the presence of a steady transverse magnetic field. As expected, results showed flow retardation and flattening. The adaptability of our solution approach allowed a comparison with previously addressed flow cases and calculations presented a good coherence with those well established solutions.

ano.nymous@ccsd.cnrs.fr.invalid (Dima Abi Abdallah), Dima Abi Abdallah

This paper investigates the influence of static magnetic field exposure on blood flow. We mainly focus on steady flows in a rigid vessel and review the existing theoretical solutions, each based on some simplifying hypothesis. The results are developed, examined and compared, showing how the magnetohy-drodynamic interactions reduce the flow rate and generate electric voltages across the vessel walls. These effects are found to be moderate for magnetic fields such as those used in magnetic resonance imaging. In this case, a very simplified solution, formulated by neglecting the walls conductivity as well as the induced magnetic fields, is proven suitable.

ano.nymous@ccsd.cnrs.fr.invalid (Dima Abi Abdallah), Dima Abi Abdallah

Cardiac Magnetic Resonance Imaging (MRI) requires synchronization to overcome motion related artifacts caused by the heart’s contractions and the chest wall movements during respiration. Achieving good image quality necessitates combining cardiac and respiratory gating to produce, in real time, a trigger signal that sets off the consecutive image acquisitions. This guarantees that the data collection always starts at the same point of the cardiac cycle during the exhalation phase. In this paper, we present a real time algorithm for extracting a cardiac-respiratory trigger signal using only one, adequately placed, ECG sensor. First, an off-line calculation phase, based on wavelet decomposition, is run to compute an optimal QRS filter. This filter is used, afterwards, to accomplish R peak detection, while a low pass filtering process allows the retrieval of the respiration cycle. The algorithm’s synchronization capabilities were assessed during mice cardiac MRI sessions employing three different imaging sequences, and three specific wavelet functions. The prominent image enhancement gave a good proof of correct triggering. QRS detection was almost flawless for all signals. As for the respiration cycle retrieval it was evaluated on contaminated simulated signals, which were artificially modulated to imitate respiration. The results were quite satisfactory.

ano.nymous@ccsd.cnrs.fr.invalid (Dima Abi-Abdallah), Dima Abi-Abdallah

Blood flow in high static magnetic fields induces elevated voltages that disrupt the ECG signal recorded simultaneously during MRI scans for synchronization purposes. This is known as the magnetohydrodynamic (MHD) effect, it increases the amplitude of the T wave, thus hindering correct R peak detection. In this paper, we present an algorithm for extracting an efficient reference signal from an ECG contaminated by the Nuclear Magnetic Resonance (NMR) environment, that performs a good separation of the R-wave and the MHD artifacts. The proposed signal processing method is based on sub-band decomposition using the wavelet transform, and has been tested on human and small rodents ECG signals acquired during MRI scans in various magnetic field intensities. The results showed an almost flawless trigger generation in fields up to 4.7 Tesla during the three tested imaging sequences (GE, FSE and IRSE)

ano.nymous@ccsd.cnrs.fr.invalid (D Abi-Abdallah), D Abi-Abdallah

A real time algorithm for cardiac and respiratory gating, which only requires an ECG sensor, is proposed here. Three ECG electrodes are placed in such a manner that the modulation of the recorded ECG by the respiratory signal would be maximal; hence, given only one signal we can achieve both cardiac and respiratory MRI gating. First, an off-line learning phase based on wavelet decomposition is run to compute an optimal QRS filter. Afterwards, on one hand the QRS filter is used to accomplish R peak detection, and on the other, a low pass filtering process allows the retrieval of the respiration cycle so that the image acquisition sequences would be triggered by the R peaks only during the expiration phase.

ano.nymous@ccsd.cnrs.fr.invalid (D Abi-Abdallah), D Abi-Abdallah

Nous considérons une ́equation qui modélise la diffusion de la température dans une mousse de graphite contenant des capsules de sel. Les conditions de transition de la température entre le graphite et le sel doivent être traitées correctement. Nous effectuons l'analyse de ce modèle et prouvons qu'il est bien posé. Puis nous en proposons une discrétisation par éléments finis et effectuons l'analyse a priori du problème discret. Quelques expériences numériques confirment l'intérêt de cette approche.

ano.nymous@ccsd.cnrs.fr.invalid (Faker Ben Belgacem), Faker Ben Belgacem

We are concerned with fast methods for the numerical implementation of the direct and inverse scattering problems for a perfectly conducting obstacle. The scattering problem is usually reduced to a single uniquely solvable modified combined-field integral equation (M-CFIE). For the numerical solution of the M-CFIE we propose a new high-order spectral algorithm by transporting this equation on the unit sphere via the Piola transform. The inverse problem is formulated as a nonlinear least squares problem for which the iteratively regularized Gauss-Newton method is applied to recover an approximate solution. Numerical experiments are presented in the special case of star-shaped obstacles.

ano.nymous@ccsd.cnrs.fr.invalid (Frédérique Le Louër), Frédérique Le Louër

A new theorem is provided to test the identifiability of discrete-time systems with polynomial nonlinearities. That extends to discrete-time systems the local state isomorphism approach for continuous-time systems. Two examples are provided to illustrate the approach.

ano.nymous@ccsd.cnrs.fr.invalid (Floriane Anstett), Floriane Anstett

This paper is devoted to the analysis of a second order method for recovering the \emph{a priori} unknown shape of an inclusion $\omega$ inside a body $\Omega$ from boundary measurement. This inverse problem - known as electrical impedance tomography - has many important practical applications and hence has focussed much attention during the last years. However, to our best knowledge, no work has yet considered a second order approach for this problem. This paper aims to fill that void: we investigate the existence of second order derivative of the state $u$ with respect to perturbations of the shape of the interface $\partial\omega$, then we choose a cost function in order to recover the geometry of $\partial \omega$ and derive the expression of the derivatives needed to implement the corresponding Newton method. We then investigate the stability of the process and explain why this inverse problem is severely ill-posed by proving the compactness of the Hessian at the global minimizer.

ano.nymous@ccsd.cnrs.fr.invalid (Lekbir Afraites), Lekbir Afraites

We consider the inverse conductivity problem with one measurement for the equation $div((\sigma_1+(\sigma_2-\sigma_1)\chi_D)\nabla{u})=0$ determining the unknown inclusion $D$ included in $\Omega$. We suppose that $\Omega$ is the unit disk of $\mathbb{R}^2$. With the tools of the conformal mappings, of elementary Fourier analysis and also the action of some quasi-conformal mapping on the Sobolev space $\sH^{1/2}(S^1)$, we show how to approximate the Dirichlet-to-Neumann map when the original inclusion $D$ is a $\varepsilon-$ approximation of a disk. This enables us to give some uniqueness and stability results.

ano.nymous@ccsd.cnrs.fr.invalid (Marc Dambrine), Marc Dambrine

In this paper we describe a high order spectral algorithm for solving the time-harmonic Navier equations in the exterior of a bounded obstacle in three space dimensions, with Dirichlet or Neumann boundary conditions. Our approach is based on combined-field boundary integral equation (CFIE) reformulations of the Navier equations. We extend the spectral method developped by Ganesh and Hawkins - for solving second kind boundary integral equations in electromagnetism - to linear elasticity for solving CFIEs that commonly involve integral operators with a strongly singular or hypersingular kernel. The numerical scheme applies to boundaries which are globally parameterised by spherical coordinates. The algorithm has the interesting feature that it leads to solve linear systems with substantially fewer unknowns than with other existing fast methods. The computational performances of the proposed spectral algorithm are demonstrated on numerical examples for a variety of three-dimensional convex and non-convex smooth obstacles.

ano.nymous@ccsd.cnrs.fr.invalid (Frédérique Le Louër), Frédérique Le Louër

Using a preconditioned Richardson iterative method as a regularization to the data completion problem is the aim of the contribution. The problem is known to be exponentially ill posed that makes its numerical treatment a hard task. The approach we present relies on the Steklov-Poincaré variational framework introduced in [Inverse Problems, vol. 21, 2005]. The resulting algorithm turns out to be equivalent to the Kozlov-Maz’ya-Fomin method in [Comp. Math. Phys., vol. 31, 1991]. We conduct a comprehensive analysis on the suitable stopping rules that provides some optimal estimates under the General Source Condition on the exact solution. Some numerical examples are finally discussed to highlight the performances of the method.

ano.nymous@ccsd.cnrs.fr.invalid (Duc Thang Du), Duc Thang Du

We are concerned with the inverse problem of detecting sources in a coupled diffusion-reaction system. This problem arises from the Biochemical Oxygen Demand-Dissolved Oxygen model(\footnote{The acronym BOD-DO model is currently used.}) governing the interaction between organic pollutants and the oxygen available in stream waters. The sources we consider are point-wise and simulate stationary or moving pollution sources. The ultimate objective is to obtain their discharge location and recover their output rate from accessible measurements of DO when BOD measurements are difficult and time consuming to obtain. It is, as a matter of fact, the most realistic configuration. The subject to address here is the identifiability of these sources, in other words to determine if the observations uniquely determine the sources. The key tool is the study of coupled parabolic systems derived after restricting the global model to regions at the exterior of the observations. The absence of any prescribed condition on the BOD density is compensated by data recorded on the DO which provide over-determined Cauchy boundary conditions. Now, the first step toward the identifiability of the sources is precisely to recover the BOD at the observation points (of DO). This may be achieved by handling and solving the coupled systems. Unsurprisingly, they turn out to be ill-posed. That issue is investigated first. Then, we state a uniqueness result owing to a suitable saddle-point variational framework and to Pazy's uniqueness Theorem. This uniqueness complemented by former identifiability results proved in [2011, Inverse problems] for scalar reaction-diffusion equations yields the desired identifiability for the global model.

ano.nymous@ccsd.cnrs.fr.invalid (Faker Ben Belgacem), Faker Ben Belgacem

In the present work, we consider the inverse conductivity problem of recovering inclusion with one measurement. First, we use conformal mapping techniques for determining the location of the anomaly and estimating its size. We then get a good initial guess for quasi-Newton type method. The inverse problem is treated from the shape optimization point of view. We give a rigorous proof for the existence of the shape derivative of the state function and of shape functionals. We consider both Least Squares fitting and Kohn and Vogelius functionals. For the numerical implementation, we use a parametrization of shapes coupled with a boundary element method. Several numerical exemples indicate the superiority of the Kohn and Vogelius functional over Least Squares fitting.

ano.nymous@ccsd.cnrs.fr.invalid (Lekbir Afraites), Lekbir Afraites

This paper is concerned by the analysis of nonlinear controlled or uncontrolled dynamical model identifiability. The proposed approach is based on the construction of an input-output ideal. The aim is to develop an algorithm which gives identifiability results from this approach. Differential algebra theory allows realization of such a project. In order to state the algorithm, new results of differential algebra must be proved. Then the implementation is done in a symbolic computing language

ano.nymous@ccsd.cnrs.fr.invalid (Lilianne Denis-Vidal), Lilianne Denis-Vidal

Nous décrivons le niveau de dégradation caractéristique d'une structure à l'aide d'un processus stochastique appelé processus de dégradation. La dynamique de ce processus est modélisée par un système différentiel à environnement markovien. Nous étudions la fiabilité du système en considérant la défaillance de la structure lorsque le processus de dégradation dépasse un seuil fixe. Nous obtenons la fiabilité théorique à l'aide de la théorie du renouvellement markovien. Puis, nous proposons une procédure d'estimation des paramètres des processus aléatoires du système différentiel. Les méthodes d'estimation et les résultats théoriques de la fiabilité, ainsi que les algorithmes de calcul associés, sont validés sur des données simulés. Notre méthode est appliquée à la modélisation d'un mécanisme réel de dégradation, la propagation des fissures, pour lequel nous disposons d'un jeu de données expérimental.

ano.nymous@ccsd.cnrs.fr.invalid (Julien Chiquet), Julien Chiquet

Ce travail porte sur un problème inverse de sources dipolaires et son application à l'identification des sources de l'activité cérébrale telle qu'elle peut être mesurée par l'Electro-Encéphalo-Graphie (EEG). Des résultats d'identifiabilité et de stabilité ont été établis. Par ailleurs, une étude du problème de Cauchy en 3D, motivée par l'application de la méthode d'identification dite "algébrique", a été faite à l'aide de la méthode itérative introduite par Kozlov, Maz'ya et Fomin et au moyen des équations intégrales de frontières. En outre, une autre méthode basée sur une fonctionnelle coût de type Kohn et Vogelius a été considérée pour l'identification des sources et dont les résultats numériques sont avérés plus performants que ceux donnés par la méthode des moindres carrés.

ano.nymous@ccsd.cnrs.fr.invalid (Maha Farah), Maha Farah

This article concerns the variance estimation in the central limit theorem for finite recurrent Markov chains. The associated variance is calculated in terms of the transition matrix of the Markov chain. We prove the equivalence of different matrix forms representing this variance. The maximum likelihood estimator for this variance is constructed and it is proved that it is strongly consistent and asymptotically normal. The main part of our analysis consists in presenting closed matrix forms for this new variance. Additionally, we prove the asymptotic equivalence between the empirical and the MLE estimator for the stationary distribution.

ano.nymous@ccsd.cnrs.fr.invalid (Samis Trevezas), Samis Trevezas

La première partie concerne l'estimation séquentielle du paramètre de régression pour le modèle de Cox pour des données censurées à droite. Il est ainsi possible de définir des règles d'arrêt garantissant une bonne estimation. Celles-ci conduisent alors à des estimateurs dépendant de tailles d'échantillons aléatoires pour lesquels le comportement asymptotique est le même que celui des estimateurs non séquentiels. Les propriétés démontrées sont étendues au cadre multidimensionnel et illustrées par des simulations. Cette première partie s'achève par l'étude théorique du comportement de la variable d'arrêt dans le cadre d'intervalles de confiance séquentiels. La règle d'arrêt normalisée est alors asymptotiquement normale. La seconde partie porte sur la construction de tests d'homogénéité dans le cadre d'un modèle de durées de vie non paramétrique incluant des covariables ainsi que la censure à droite. Une statistique de test est proposée et son comportement asymptotique est établi.

ano.nymous@ccsd.cnrs.fr.invalid (Christelle Breuils), Christelle Breuils

Ventcel boundary conditions are second order di erential conditions that appear in asymptotic models. Like Robin boundary conditions, they lead to well-posed variational problems under a sign condition of the coe cient. This is achieved when physical situations are considered. Nevertheless, situations where this condition is violated appeared in several recent works where absorbing boundary conditions or equivalent boundary conditions on rough surface are sought for numerical purposes. The well-posedness of such problems was recently investigated : up to a countable set of parameters, existence and uniqueness of the solution for the Ventcel boundary value problem holds without the sign condition. However, the values to be avoided depend on the domain where the boundary value problem is set. In this work, we address the question of the persistency of the solvability of the boundary value problem under domain deformation.

ano.nymous@ccsd.cnrs.fr.invalid (Marc Dambrine), Marc Dambrine

This paper is concerned with the shape sensitivity analysis of the solution to the Helmholtz transmission problem for three dimensional sound-soft or sound-hard obstacles coated by a thin layer. This problem can be asymptotically approached by exterior problems with an improved condition on the exterior boundary of the coated obstacle, called Generalised Impedance Boundary Condition (GIBC). Using a series expansion of the Laplacian operator in the neighborhood of the exterior boundary, we retrieve the first order GIBCs characterizing the presence of an interior thin layer with either a constant or a variable thickness. The first shape derivative of the solution to the original Helmholtz transmission problem solves a new thin layer transmission problem with non vanishing jumps across the exterior and the interior boundary of the thin layer. In the special case of thin layers with a constant thickness, we show that we can interchange the first order differentiation with respect to the shape of the exterior boundary and the asymptotic approximation of the solution. Numerical experiments are presented to highlights the various theoretical results.

ano.nymous@ccsd.cnrs.fr.invalid (Djalil Kateb), Djalil Kateb

It has been proven that the knowledge of an accurate approximation of the Dirichlet-to-Neumann (DtN) map is useful for a large range of applications in wave scattering problems. We are concerned in this paper with the construction of an approximate local DtN operator for time-harmonic elastic waves. The main contributions are the following. First, we derive exact operators using Fourier analysis in the case of an elastic half-space. These results are then extended to a general three-dimensional smooth closed surface by using a local tangent plane approximation. Next, a regularization step improves the accuracy of the approximate DtN operators and a localization process is proposed. Finally, a first application is presented in the context of the On-Surface Radiation Conditions method. The efficiency of the approach is investigated for various obstacle geometries at high frequencies.

ano.nymous@ccsd.cnrs.fr.invalid (Stéphanie Chaillat), Stéphanie Chaillat

In order to optimize the performance of a diesel engine subject to legislative constraints on pollutant emissions, it is necessary to improve their design, and to identify how design parameters a ect engine behaviours. One speci city of this work is that it does not exist a physical model of engine behaviour under all possible operational conditions. A powerful strategy for engine modeling is to build a fast emulator based on carefully chosen observations, made according to an experimental design. In this paper, two Kriging models are considered. One is based on a geostatistical approach and the other corresponds to a Gaussian process metamodel approach. Our aim is to show that the use of each of these methods does not lead to the same results, particularly when "atypical" points are present in our database. In a more precise way, the statistical approach allows us to obtain a good quality modeling even if atypical data are present, while this situation leads to a bad quality of the modeling by the geostatistical approach. This behaviour takes a fundamental importance for the problem of the pollutant emissions, because the analysis of these atypical data, which are rarely erroneous data, can supply precious information for the engine tuning in the design stage.

ano.nymous@ccsd.cnrs.fr.invalid (Sébastien Castric), Sébastien Castric

The aim of this article is to explore the possibility of using a family of fixed finite element shape functions that does not match the domain to solve a boundary value problem with Dirichlet boundary condition. The domain is embedded in a bounding box and the finite element approximation is associated to a regular structured mesh of the box. The shape of the domain is independent of the discretization mesh. In these conditions, a meshing tool is never required. This may be especially useful in the case of evolving domains, for example shape optimization or moving interfaces. Nitsche method has been intensively applied. However, Nitsche is weighted with the mesh size h and therefore is a purely discrete point of view with no interpretation in terms of a continuous variational approach associated with a boundary value problem. In this paper, we introduce an alternative to Nitsche method which is associated with a continuous bilinear form. This extension has strong restrictions: it needs more regularity on the data than the usual method. We prove the well-posedness of our formulation and error estimates. We provide numerical comparisons with Nitsche method.

ano.nymous@ccsd.cnrs.fr.invalid (Jean-Paul Boufflet), Jean-Paul Boufflet

Dans cet article, nous traitons un problème de Cauchy dans le cadre de la localisation des sources épileptiques en Electro-Encéphalo-Graphie (EEG). Plus particulièrement, il s'agit du problème de construction des données de Cauchy sur la surface du cerveau à partir des données du potentiel mesuré par l'EEG à la surface de la tête. Notre résolution est basée sur un algorithme itératif alternatif initialement proposé par Kozlov, Mazjya et Fomin. Nous présentons dans ce papier l'étude umérique de cette méthode que nous avons implémentée en trois dimensions. Nous donnons également des applications et des résultats numériques.

ano.nymous@ccsd.cnrs.fr.invalid (Abdellatif El-Badia), Abdellatif El-Badia

Dans cet article nous allons estimer la ﬁabilité d'un système binaire et obtenir son intervalle de conﬁance par l'approximation normale asymptotique. Cette méthode peut s'appliquer aux systèmes complexes et de grande taille réduisant la largeur de l'intervalle de conﬁance.

ano.nymous@ccsd.cnrs.fr.invalid (Yunhui Hou), Yunhui Hou

The aim of this article is to explore the possibility of using a family of fixed finite elements shape functions to solve a Dirichlet boundary value problem with an alternative variational formulation. The domain is embedded in a bounding box and the finite element approximation is associated to a regular structured mesh of the box. The shape of the domain is independent of the discretization mesh. In these conditions, a meshing tool is never required. This may be especially useful in the case of evolving domains, for example shape optimization or moving interfaces. This is not a new idea, but we analyze here a special approach. The main difficulty of the approach is that the associated quadratic form is not coercive and an inf-sup condition has to be checked. In dimension one, we prove that this formulation is well posed and we provide error estimates. Nevertheless, our proof relying on explicit computations is limited to that case and we give numerical evidence in dimension two that the formulation does not provide a reliable method. We first add a regularization through a Nitscheterm and we observe that some instabilities still remain. We then introduce and justify a geometrical regularization. A reliable method is obtained using both regularizations.

ano.nymous@ccsd.cnrs.fr.invalid (Gaël Dupire), Gaël Dupire

The invariance principle for M/M/1 and M/M/∞ queues states that when properly renormalized (i.e. rescaled and centered), the Markov processes which describe these systems both converge to a diffusive limit when the driving parameters go to infinity: a killed Brownian motion in the former case and an Ornstein-Uhlenbeck process for the latter. The purpose of this paper is to assess the rate of convergence in these diffusion approximations. To this end, we extend to these contexts, the functional Stein's method introduced for the Brownian approximation of Poisson processes.

ano.nymous@ccsd.cnrs.fr.invalid (Eustache Besançon), Eustache Besançon

Enhancing the safety of high-temperature reactors (HTRs) is based on the quality of the fuel particles, requiring good knowledge of the microstructure of the four-layer particles designed to retain the fission products during irradiation and under accidental conditions. This paper focuses on the intensive research work performed to characterize the micro- and nanostructure of each unirradiated layer (silicon carbide and pyrocarbon coatings). The analytic expertise developed in the 1970s has been recovered and innovative advanced characterization methods have been developed to improve the process parameters and to ensure the production reproducibility of coatings.

ano.nymous@ccsd.cnrs.fr.invalid (D. Helary), D. Helary

A mathematical model for the forward problem in electroencephalographic (EEG) source localization in neonates is proposed. The model is able to take into account the presence and ossification process of fontanels which are characterized by a variable conductivity. A subtraction approach is used to deal with the singularity in the source term, and existence and uniqueness results are proved for the continuous problem. Discretization is performed with 3D Finite Elements of type P1 and error estimates are proved in the energy (H 1-)norm. Numerical simulations for a three-layer spherical model as well as for a realistic neonatal head model have been obtained and corroborate the theoretical results. A mathematical tool related to the concept of Gâteau derivatives is introduced which is able to measure the sensitivity of the electric potential with respect to small variations in the fontanel conductivity. Numerical simulations attest that the presence of fontanels in neonates does have an impact on EEG measurements. The present work is an essential preamble to the numerical analysis of the corresponding EEG source reconstruction.

ano.nymous@ccsd.cnrs.fr.invalid (M Darbas), M Darbas

The purpose is a finite element approximation of the heat diffusion problem in composite media, with non-linear contact resistance at the interfaces. As already explained in [Journal of Scientific Computing, {\bf 63}, 478-501(2015)], hybrid dual formulations are well fitted to complicated composite geometries and provide tractable approaches to variationally express the jumps of the temperature. The finite elements spaces are standard. Interface contributions are added to the variational problem to account for the contact resistance. This is an important advantage for computing codes developers. We undertake the analysis of the non-linear heat problem for a large range of contact resistance and we investigate its discretization by hybrid dual finite element methods. Numerical experiments are presented at the end to support the theoretical results.

ano.nymous@ccsd.cnrs.fr.invalid (F Belgacem), F Belgacem

The nutrient-poor grasslands of Western Europe are of major conservation concern because land use changes threaten their high biodiversity. Studies assessing their characteristics show that their past and ongoing dynamics are strongly related to human activities. Yet, the initial development patterns of this specific ecosystem remain unclear. Here, we examine findings from previous paleoecological investigations performed at local level on European grassland areas ranging from several hundred square meters to several square kilometers. Comparing data from these locally relevant studies at a regional scale, we investigate these grasslands' spatiotemporal patterns of origin and long-term dynamics. The study is based on taxonomic identification and radiocarbon AMS dating of charcoal pieces from soil/soil sediment archives of nutrient-poor grasslands in Mediterranean and temperate Western Europe (La Crau plain, Mont Lozère, Grands Causses, Vosges Mountains, Franconian Alb, and Upper-Normandy region). We address the following questions: (1) What are the key determinants of the establishment of these nutrient-poor grasslands? (2) What temporal synchronicities might there be? and (3) What is the spatial scale of these grasslands' past dynamics? The nutrient-poor grasslands in temperate Western Europe are found to result from the first anthropogenic woodland clearings during the late Neolithic, revealed by fire events in mesophilious mature forests. In contrast, the sites with Mediterranean affinities appear to have developed at earlier plant successional stages (pine forest, matorral), established before the first human impacts in the same period. However, no general pattern of establishment and dynamics of the nutrient-poor grasslands could be identified. Local mechanisms appear to be the key determinants of the dynamics of these ecosystems. Nevertheless, this paleoecological synthesis provides insights into past climate or human impacts on present-day vegetation.

ano.nymous@ccsd.cnrs.fr.invalid (Vincent Robin), Vincent Robin

The invariance principle for M/M/1 and M/M/∞ queues states that when properly renormalized (i.e. rescaled and centered), the Markov processes which describe these systems both converge to a diffusive limit when the driving parameters go to infinity: a killed Brownian motion in the former case and an Ornstein-Uhlenbeck process for the latter. The purpose of this paper is to assess the rate of convergence in these diffusion approximations. To this end, we extend to these contexts, the functional Stein's method introduced for the Brownian approximation of Poisson processes.

ano.nymous@ccsd.cnrs.fr.invalid (Eustache Besançon), Eustache Besançon

We present a first version of a software dedicated to an application of a classical nonlinear control theory problem to the study of compartmental models in biology. The software is being developed over a new free computer algebra library dedicated to differential and algebraic elimination.

ano.nymous@ccsd.cnrs.fr.invalid (François Boulier), François Boulier

This paper considers two different methods in the analysis of nonlinear controlled dynamical system identifiability. The corresponding identifiability definitions are not equivalent. Moreover one is based on the construction of an input-output ideal and the other on the similarity transformation theorem. Our aim is to develop algorithms which give identifiability results from both approaches. Differential algebra theory allows realization of such a project. In order to state these algorithms, new results of differential algebra must be proved. Then the implementation of these algorithms is done in a symbolic computation language.

ano.nymous@ccsd.cnrs.fr.invalid (Lilianne Denis-Vidal), Lilianne Denis-Vidal

In many applications, the estimation of derivatives has to be done from noisy measured signal. In this paper, an original method based on a distribution approach is presented. Its interest is to report the derivatives on infinitely differentiable functions. Thus, the estimation of the derivatives is done only from the signal. Besides, this method gives some explicit formulae leading to fast calculus. For all these reasons, it is an efficient method in the case of noisy signals as it will be confirmed in several examples.

ano.nymous@ccsd.cnrs.fr.invalid (Nathalie Verdière), Nathalie Verdière

[...]

ano.nymous@ccsd.cnrs.fr.invalid (Nathalie Verdière), Nathalie Verdière

In this paper, we study a Chikungunya epidemic transmission model which describes an epidemic disease transmitted by Aedes mosquitoes. This model includes the spatial mobility of humans which is probably a factor that has influenced the re-emergence of several diseases. Assuming that the spatial mobility of humans is random described as Brownian random motion, an original model including a reaction-diffusion system is proposed. Since the displacement of mosquitoes is limited to a few meters, compared with humans, one can ignore mosquitoes mobility. Therefore, the complete model is composed of a reaction-diffusion system coupled with ordinary differential equations (ODEs). In this paper, we prove the existence and uniqueness, the positivity and boundedness of the global solution for the model and give some numerical simulations.

ano.nymous@ccsd.cnrs.fr.invalid (Shousheng Zhu), Shousheng Zhu

In the last years, several epidemics have been reported in particular the chikungunya epidemic on the R eunion Island. For predicting its possible evolution, new models describing the transmission of the chikungunya to the human population have been proposed and studied in the literature. In such models, some parameters are not directely accessible from experiments and for estimating them, iterative algorithms can be used. However, before searching for their values, it is essential to verify the identi ability of models parameters to assess wether the set of unknown parameters can be uniquely determined from the data. Thus, identi ability is particularly important in modeling. Indeed, if the model is not identi able, numerical procedures can fail and in that case, some supplementary data have to be added or the set of admissible data has to be reduced. Thus, this paper proposes to study the identi ability of the proposed models by (Moulay, Aziz-Alaoui & Cadivel 2011).

ano.nymous@ccsd.cnrs.fr.invalid (Djamila Moulay), Djamila Moulay

The aim of this paper is to identify the localization and the flow rate of a pollution source in a river by measuring the concentration of a substrate giving significant information. This concentration is assumed to be measured in two points of the river. The simplest model of such a problem consists in a parabolic partial derivative equation. We propose to discretize this P.D.E. in space, which leads to a system of differential equations in time. Then, the analysis of identifiability is carried out using an approach based on differential algebra. A numerical parameter estimation is inferred from this procedure, which gives a first parameter estimate without a priori knowledge about unknown parameters.

ano.nymous@ccsd.cnrs.fr.invalid (Nathalie Verdiere), Nathalie Verdiere

In different fields of research, modeling has become a major issue for studying and predicting the possible evolution of a system, in particular in epidemiology. Indeed, according to the globalization of our societies and the genetic mutation of certain diseases or transmission vectors, several epidemics have appeared in the last years in regions not yet concerned by such a catastrophe. One can name, for example, the chikungunya epidemic on the Réunion Island in 2005-2006. In this paper, a model describing the propagation of the chikungunya to the human population is taken again from \cite{Moulay2010}. In such models, some parameters are not directly accessible from experiments and have to be estimated numerically from an iterative algorithm. However, before searching for their values, it is essential to verify the identifiability of model parameters to assess whether the set of unknown parameters can be uniquely determined from the data. Indeed, this study insures that numerical procedures can be successful and if the identifiability is not ensured, some supplementary data have to be added or the set of admissible data has to be reduced. A first identifiability study had been done in \cite{Moulay2012} in considering that the number of eggs can be easily counted. However, after discussing with epidemiologist searchers, it appears that it is the number of larvae who can be estimated weeks by weeks. Thus, this paper proposes to do an identifiability study with this assumption and thanks to an integration of one of the model equations, some easier equations linking the inputs, outputs and parameters are obtained permitting a simpler identifiability study.

ano.nymous@ccsd.cnrs.fr.invalid (Zhu Shousheng), Zhu Shousheng

We propose an adaptive inexact version of a class of semismooth Newton methods. As a model problem, we study the system of variational inequalities describing the contact between two membranes. This problem is written using a complementary formulation and discretized with conforming finite elements , yielding a nonlinear, semismooth (non-differentiable) algebraic system. We consider any iterative linearization algorithm like the Newton-min or the Newton Fischer–Burmeister which we complement by any iterative linear algebraic solver. We then derive an a posteriori estimate on the error between the exact solution and the approximate solution which is valid on any step of the linearization and algebraic resolutions. Our estimate is based on flux reconstructions in discrete subspaces of $\mathbf{H}(\mathrm{div}, \Omega)$ and on potential reconstructions in discrete subspaces of $H^1(\Omega)$ satisfying the constraints. It distinguishes the discretization, linearization, and algebraic components of the error. Consequently, we can formulate adaptive stopping criteria for both solvers, giving rise to an adaptive version of the considered inexact semismooth Newton algorithm. Under these criteria, the efficiency of our estimates is also established, meaning that we prove them equivalent with the error up to a generic constant. Numerical experiments for the Newton-min algorithm in combination with the GMRES algebraic solver confirm the efficiency of the developed adaptive method.

ano.nymous@ccsd.cnrs.fr.invalid (Jad Dabaghi), Jad Dabaghi

In this chapter, we present the empirical estimation of some reliability measures, such as the rate of occurrence of failures and the steady-state availability, for a discrete-time semi-Markov system. The probability of first occurred failure is introduced and estimated. A numerical application is given to illustrate the strong consistency of these estimators.

ano.nymous@ccsd.cnrs.fr.invalid (Stylianos Georgiadis), Stylianos Georgiadis

The present paper aims at the introduction of the semi-Markov model in continuous time as a candidate model for the description of seismicity patterns in time domain in the Northern Aegean Sea (Greece). Estimators of the semi-Markov kernels, Markov renewal functions and transition functions are calculated through a nonparametric method. Moreover , the hitting times for spatial occurrence of the strongest earthquakes as well as the confidence intervals of certain important indicators are estimated. Firstly, the classification of model states is based on earthquakes magnitude. The instantaneous earthquake occurrence rate between the states of the model as well as the total earthquake occurrence rate are calculated. In order to increase the consistency between the model and the process of earthquake generation, seismotectonic features have been incorporated as an important component in the model. Therefore, a new classification of states is proposed which combines both magnitude and fault orientation states. This model which takes into account seismotectonic features contributes significantly to the seismic hazard assessment in the region under study. The model is applied to earthquake catalogues for the Northern Aegean Sea, an area that accommodates high seismicity, being a key structure from the seismotec-tonic point of view.

ano.nymous@ccsd.cnrs.fr.invalid (Irene Votsi), Irene Votsi

Nowdays, one of the greatest problems that earth has to face up is pollution, and that is what leads European Union to make stricter laws about pollution constraints. Moreover, the European laws lead to the increase of emission constraints. In order to take into account these constraints, automotive constructors are obliged to create more and more complex systems. The use of model to predict systems behavior in order to make technical choices or to understand its functioning, has become very important during the last decade. This paper presents two stage approaches for the prediction of NOx (nitrogen oxide) emissions, which are based on an ordinary Kriging method. In the first stage, a reduction of data will take place by selecting signals with correlations studies and by using a fast Fourier transformation. In the second stage, the Kriging method is used to solve the problem of the estimation of NOx emissions under given conditions. Numerical results are presented and compared to highlight the effectiveness of the proposed methods

ano.nymous@ccsd.cnrs.fr.invalid (El Hassane Brahmi), El Hassane Brahmi

In this work we introduce a stabilized, numerical method for a multi-dimensional, discrete-fracture model (DFM) for single-phase Darcy flow in fractured porous media. In the model, introduced in an earlier work, flow in the (n − 1)-dimensional fracture domain is coupled with that in the n-dimensional bulk or matrix domain by the use of Lagrange multipliers. Thus the model permits a finite element discretization in which the meshes in the fracture and matrix domains are independent so that irregular meshing and in particular the generation of small elements can be avoided. In this paper we introduce in the numerical formulation, which is a saddle-point problem based on a primal, variational formulation for flow in the matrix domain and in the fracture system, a consistent stabilizing term which penalizes discontinuities in the Lagrange multipliers. For this penalized scheme we show stability and prove convergence. With numerical experiments we analyze the performance of the method for various choices of the penalization parameter and compare with other numerical DFM's.

ano.nymous@ccsd.cnrs.fr.invalid (Markus Köppel), Markus Köppel

The Finite Element Method is a widely-used method to solve numerical problems coming for instance from physics or biology. To obtain the highest confidence on the correction of numerical simulation programs implementing the Finite Element Method, one has to formalize the mathematical notions and results that allow to establish the sound-ness of the method. The Lax–Milgram theorem may be seen as one of those theoretical cornerstones: under some completeness and coercivity assumptions, it states existence and uniqueness of the solution to the weak formulation of some boundary value problems. This article presents the full formal proof of the Lax–Milgram theorem in Coq. It requires many results from linear algebra, geometry, functional analysis , and Hilbert spaces.

ano.nymous@ccsd.cnrs.fr.invalid (Sylvie Boldo), Sylvie Boldo

Résumé du papier "A Coq formal proof of the Lax-Milgram Theorem", CPP 2017.

ano.nymous@ccsd.cnrs.fr.invalid (Sylvie Boldo), Sylvie Boldo

In recent years, many MAC protocols for wireless sensor networks have been proposed and most of them are evaluated using Matlab simulator and/or network simulators (OMNeT++, NS2, etc). However, most of them have a static behavior and few network simulations are available for adaptive protocols. Specially, in OMNeT++/MiXiM, there are few energy efficient MAC protocols for WSNs (B-MAC & L-MAC) and no adaptive ones. To this end, the TAD-MAC (Traffic Aware Dynamic MAC) protocol has been simulated in OMNeT++ with the MiXiM framework and implementation details are given in this paper. The simulation results have been used to evaluate the performance of TAD-MAC through comparisons with B-MAC and L-MAC protocols.

ano.nymous@ccsd.cnrs.fr.invalid (Van-Thiep Nguyen), Van-Thiep Nguyen

This article concerns maximum-likelihood estimation for discrete time homogeneous nonparametric semi-Markov models with finite state space. In particular, we present the exact maximum-likelihood estimator of the semi-Markov kernel which governs the evolution of the semi-Markov chain (SMC). We study its asymptotic properties in the following cases: (i) for one observed trajectory, when the length of the observation tends to infinity, and (ii) for parallel observations of independent copies of an SMC censored at a fixed time, when the number of copies tends to infinity. In both cases, we obtain strong consistency, asymptotic normality, and asymptotic efficiency for every finite dimensional vector of this estimator. Finally, we obtain explicit forms for the covariance matrices of the asymptotic distributions.

ano.nymous@ccsd.cnrs.fr.invalid (Samis Trevezas), Samis Trevezas

We derive rates of contraction of posterior distributions on non-parametric models resulting from sieve priors. The aim of the study was to provide general conditions to get posterior rates when the parameter space has a general structure, and rate adaptation when the parameter is, for example, a Sobolev class. The conditions employed, although standard in the literature, are combined in a different way. The results are applied to density, regression, nonlinear autoregression and Gaussian white noise models. In the latter we have also considered a loss function which is different from the usual l2 norm, namely the pointwise loss. In this case it is possible to prove that the adaptive Bayesian approach for the l2 loss is strongly suboptimal and we provide a lower bound on the rate.

ano.nymous@ccsd.cnrs.fr.invalid (Julyan Arbel), Julyan Arbel

L’objectif de ce travail est de prendre en compte l’influence de la présence de défauts surfaciques sur le comportement jusqu’à rupture des structures et ce sans description fine de la géométrie des perturbations. L’approche proposée s’appuie principalement sur deux outils : une analyse asymptotique fine des équations de Navier et l’utilisation des modèles à discontinuité forte. Une stratégie de couplage des deux approches permettant l’analyse du comportement de la structure jusqu’à rupture est également présentée.

ano.nymous@ccsd.cnrs.fr.invalid (Delphine Brancherie), Delphine Brancherie

In this paper we study the shape differentiability properties of a class of boundary integral operators and of potentials with weakly singular pseudo-homogeneous kernels acting between classical Sobolev spaces, with respect to smooth deformations of the boundary. We prove that the boundary integral operators are infinitely differentiable without loss of regularity. The potential operators are infinitely shape differentiable away from the boundary, whereas their derivatives lose regularity near the boundary. We study the shape differentiability of surface differential operators. The shape differentiability properties of the usual strongly singular or hypersingular boundary integral operators of interest in acoustic, elastodynamic or electromagnetic potential theory can then be established by expressing them in terms of integral operators with weakly singular kernels and of surface differential operators.

ano.nymous@ccsd.cnrs.fr.invalid (Martin Costabel), Martin Costabel

In this work, we consider singular perturbations of the boundary of a smooth domain. We describe the asymptotic behavior of the solution uε of a second order elliptic equation posed in the perturbed domain with respect to the size parameter ε of the deformation. We are also interested in the variations of the energy functional. We propose a numerical method for the approximation of uε based on a multiscale superposition of the unperturbed solution u0 and a profile defined in a model domain. We conclude with numerical results.

ano.nymous@ccsd.cnrs.fr.invalid (Marc Dambrine), Marc Dambrine

We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic scattering problems, we study the shape differentiability properties of the standard electromagnetic boundary integral operators. The latter are typically bounded on the space of tangential vector fields of mixed regularity $TH\sp{-\frac{1}{2}}(\Div_{\Gamma},\Gamma)$. Using Helmholtz decomposition, we can base their analysis on the study of pseudo-differential integral operators in standard Sobolev spaces, but we then have to study the Gâteaux differentiability of surface differential operators. We prove that the electromagnetic boundary integral operators are infinitely differentiable without loss of regularity. We also give a characterization of the first shape derivative of the solution of the dielectric scattering problem as a solution of a new electromagnetic scattering problem.

ano.nymous@ccsd.cnrs.fr.invalid (Martin Costabel), Martin Costabel

The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the interface Γ. In this paper, following an idea developed by Kleinman and Martin for acoustic scattering problems, we consider methods for solving the dielectric scattering problem using a single integral equation over Γ. for a single unknown density. One knows that such boundary integral formulations of the Maxwell equations are not uniquely solvable when the exterior wave number is an eigenvalue of an associated interior Maxwell boundary value problem. We obtain four different families of integral equations for which we can show that by choosing some parameters in an appropriate way, they become uniquely solvable for all real frequencies. We analyze the well-posedness of the integral equations in the space of finite energy on smooth and non-smooth boundaries.

ano.nymous@ccsd.cnrs.fr.invalid (Martin Costabel), Martin Costabel

We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic scattering problems, we study the shape differentiability properties of the standard electromagnetic boundary integral operators. Using Helmholtz decomposition, we can base their analysis on the study of scalar integral operators in standard Sobolev spaces, but we then have to study the Gâteaux differentiability of surface differential operators. We prove that the electromagnetic boundary integral operators are infinitely differentiable without loss of regularity and that the solutions of the scattering problem are infinitely shape differentiable away from the boundary of the obstacle, whereas their derivatives lose regularity on the boundary. We also give a characterization of the first shape derivative as a solution of a new electromagnetic scattering problem.

ano.nymous@ccsd.cnrs.fr.invalid (Martin Costabel), Martin Costabel

This work is devoted to the numerical simulation of an incompressible fluid through a porous interface, modeled as a macroscopic resistive interface term in the Stokes equations. We improve the results reported in [M2AN, 42(6):961-990, 2008], by showing that the standard Pressure Stabilized Petrov-Galerkin (PSPG) finite element method is stable, and optimally convergent, without the need for controlling the pressure jump across the interface.

ano.nymous@ccsd.cnrs.fr.invalid (Alfonso Caiazzo), Alfonso Caiazzo

We consider a model for fluid flow in a porous medium with a fracture. In this model, the fracture is represented as an interface between subdomains, where specific equations have to be solved. In this article we analyse the discrete problem, assuming that the fracture mesh and the subdomain meshes are completely independent, but that the geometry of the fracture is respected. We show that despite this non-conformity, first order convergence is preserved with the lowest order Raviart-Thomas(-Nedelec) mixed finite elements. Numerical simulations confirm this result.

ano.nymous@ccsd.cnrs.fr.invalid (Najla Frih), Najla Frih

We propose a model for a medical device, called a stent, designed for the treatment of cerebral aneurysms. The stent consists of a grid, immersed in the blood flow and located at the inlet of the aneurysm. It aims at promoting a clot within the aneurysm. The blood flow is modelled by the incompressible Navier-Stokes equations and the stent by a dissipative surface term. We propose a stabilized finite element method for this model and we analyse its convergence in the case of the Stokes equations. We present numerical results for academical test cases, and on a realistic aneurysm obtained from medical imaging.

ano.nymous@ccsd.cnrs.fr.invalid (Miguel Angel Fernández), Miguel Angel Fernández

This paper addresses a complex multi-physical phenomemon involving cardiac electrophysiology and hemodynamics. The purpose is to model and simulate a phenomenon that has been observed in MRI machines: in the presence of a strong magnetic field, the T-wave of the electrocardiogram (ECG) gets bigger, which may perturb ECG-gated imaging. This is due a magnetohydrodynamic (MHD) eff ect occurring in the aorta. We reproduce this experimental observation through computer simulations on a realistic anatomy, and with a three-compartment model: inductionless magnetohydrodynamic equations in the aorta, bidomain equations in the heart and electrical di ffusion in the rest of the body. These compartments are strongly coupled and solved using fi nite elements. Several benchmark tests are proposed to assess the numerical solutions and the validity of some modeling assumptions. Then, ECGs are simulated for a wide range of magnetic field intensities (from 0 to 20 Tesla).

ano.nymous@ccsd.cnrs.fr.invalid (Vincent Martin), Vincent Martin

Nous complétons ici les résultats d'isomorphismes de l'opérateur de Laplace dans des espaces de Sobolev avec poids et nous donnons quelques applications. Parmi celles-ci, nous obtenons des inégalités semblables à celle de Calderon-Zygmund et en particulier des propriétés de continuité des transformées de Riesz dans des espaces avec poids. Nous donnons également des propriétes de potentiels newtoniens de certaines distributions.

ano.nymous@ccsd.cnrs.fr.invalid (Chérif Amrouche), Chérif Amrouche

We consider an inverse problem that arises in the management of water resources and pertains to the analysis of the surface waters pollution by organic matter. Most of physical models used by engineers derive from various additions and corrections to enhance the earlier deoxygenation-reaeration model proposed by Streeter and Phelps in 1925, the unknowns being the biochemical oxygen demand (BOD) and the dissolved oxygen (DO) concentrations. The one we deal with includes Taylor's dispersion to account for the heterogeneity of the contamination in all space directions. The system we obtain is then composed of two reaction-dispersion equations. The particularity is that both Neumann and Dirichlet boundary conditions are available on the DO tracer while the BOD density is free of any condition. In fact, for real-life concerns, measurements on the dissolved oxygen are easy to obtain and to save. In the contrary, collecting data on the biochemical oxygen demand is a sensitive task and turns out to be a long-time process. The global model pursues the reconstruction of the BOD density, and especially of its flux along the boundary. Not only this problem is plainly worth studying for its own interest but it can be also a mandatory step in other applications such as the identification of the pollution sources location. The non-standard boundary conditions generate two difficulties in mathematical and computational grounds. They set up a severe coupling between both equations and they are cause of ill-posedness for the data reconstruction problem. Existence and stability fail. Identifiability is therefore the only positive result one can seek after ; it is the central purpose of the paper. We end by some computational experiences to assess the capability of the mixed finite element capability in the missing data recovery (on the biochemical oxygen demand).

ano.nymous@ccsd.cnrs.fr.invalid (Mejdi Azaïez), Mejdi Azaïez

We consider a mixed reaction diffusion system describing the organic pollution in stream-waters. It may be viewed as the static version of Streeter-Phelps equations relating the Biochemical Oxygen Demand and Dissolved Oxygen to which dispersion terms are added. In this work, we propose a mixed variational formulation and prove its well-posedness. Next, we develop two finite element discretizations of this problem and establish optimal a priori error estimates for the second discrete problem.

ano.nymous@ccsd.cnrs.fr.invalid (Faker Ben Belgacem), Faker Ben Belgacem

Ill-posedness and/or Ill-conditioning are features users have to deal with appropriately in the controllability of diffusion problems for secure and reliable outputs. We investigate those issues in the case of a boundary Dirichlet control, in an attempt to underline the origin of the troubles arising in the numerical computations and to shed some light on the difficulties to obtain good quality simulations. The exact controllability is severely ill-posed while, in spite of its well-posedness, the null-controllability turns out to be very badly ill-conditioned. Theoretical and numerical results are stated on the heat equation in one dimension to illustrate the specific instabilities of each problem. The main tools used here are first a characterization of the subspace where the HUM control lies and the study of the spectrum of some structured matrices, of Pick and Löwner type, obtained from the Fourier calculations on the state and adjoint equations.

ano.nymous@ccsd.cnrs.fr.invalid (Faker Ben Belgacem), Faker Ben Belgacem

Nous considérons une ́equation qui modélise la diffusion de la température dans une mousse de graphite contenant des capsules de sel. Les conditions de transition de la température entre le graphite et le sel doivent être traitées correctement. Nous effectuons l'analyse de ce modèle et prouvons qu'il est bien posé. Puis nous en proposons une discrétisation par éléments finis et effectuons l'analyse a priori du problème discret. Quelques expériences numériques confirment l'intérêt de cette approche.

ano.nymous@ccsd.cnrs.fr.invalid (Faker Ben Belgacem), Faker Ben Belgacem

The mortar spectral element method is a domain decomposition technique that allows for discretizing second- or fourth-order elliptic equations when set in standard Sobolev spaces.he aim of this paper is to extend this method to problems formulated in the space of square-integrable vector fields with square-integrable curl.We consider the problem of computing the vector potential associated with a divergence- free function in dimension 3 and propose a discretization of it. The numerical analysis of the discrete problem is performed and numerical experiments are presented, they turn out to be in good coherency with the theoretical results.

ano.nymous@ccsd.cnrs.fr.invalid (Mjedi Azaïez), Mjedi Azaïez

The inverse problem under investigation consists of the boundary data completion in a deoxygenation-reaeration model in stream-waters. The unidimensional transport model we deal with is based on the one introduced by Streeter and Phelps, augmented by Taylor dispersion terms. The missing boundary condition is the load or/and the flux of the biochemical oxygen demand indicator at the outfall point. The counterpart is the availability of two boundary conditions on the dissolved oxygen tracer at the same point. The major consequences of these non-standard boundary conditions is that dispersive transport equations on both oxygen tracers are strongly coupled and the resulting system becomes ill-posed. The main purpose is a finite element space-discretization of the variational problem put under a non-symmetric mixed form. Combining analytical calculations, numerical computations and theoretical justifications, we try to elucidate the characteristics related to the ill-posedness of this data completion dynamical problem and understand its mathematical structure.

ano.nymous@ccsd.cnrs.fr.invalid (Faker Ben Belgacem), Faker Ben Belgacem

The main purpose of this paper is to investigate the strong approximation of the $p$-fold integrated empirical process, $p$ being a fixed positive integer. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer process. Our arguments are based in part on results of Koml\'os, Major and Tusn\'ady (1975). Applications include the two-sample testing procedures together with the change-point problems. We also consider the strong approximation of integrated empirical processes when the parameters are estimated. Finally, we study the behavior of the self-intersection local time of the partial sum process representation of integrated empirical processes.

ano.nymous@ccsd.cnrs.fr.invalid (Sergio Alvarez-Andrade), Sergio Alvarez-Andrade

A sensitivity analysis of a suspension model has been performed in order to highlight the most influential parameters on the sprung mass displacement. To analyse this dynamical model, a new global and bounded dynamic method is investigated. This method, based on the interval analysis, consists in determining lower and upper bounds including the dynamic sensitivity indices. It requires only the knowledge of the parameter variation ranges and not the joint probability density function of the parameters which is hard to estimate. The advantage of the proposed approach is that it takes into account the recursive behavior of the system dynamics.

ano.nymous@ccsd.cnrs.fr.invalid (Sabra Hamza), Sabra Hamza

Electron back-scattering diffraction (EBSD) can be successfully performed on SiC coatings for HTR fuel particles. EBSD grain maps obtained from thick and thin unirradiated samples are presented, along with pole figures showing textures and a chart showing the distribution of grain aspect ratios. This information is of great interest, and contributes to improving the process parameters and ensuring the reproducibility of coatings

ano.nymous@ccsd.cnrs.fr.invalid (D. Helary), D. Helary

This paper focuses on Generalized Impedance Boundary Conditions (GIBC) with second order derivatives in the context of linear elasticity and general curved interfaces. A condition of the Wentzell type modeling thin layer coatings on some elastic structure is obtained through an asymptotic analysis of order one of the transmission problem at the thin layer interfaces with respect to the thickness parameter. We prove the well-posedness of the approximate problem and the theoretical quadratic accuracy of the boundary conditions. Then we perform a shape sensitivity analysis of the GIBC model in order to study a shape optimization/optimal design problem. We prove the existence and characterize the first shape derivative of this model. A comparison with the asymptotic expansion of the first shape derivative associated to the original thin layer transmission problem shows that we can interchange the asymptotic and shape derivative analysis. Finally we apply these results to the compliance minimization problem. We compute the shape derivative of the compliance in this context and present some numerical simulations.

ano.nymous@ccsd.cnrs.fr.invalid (Fabien Caubet), Fabien Caubet

In this work we present a novel discrete fracture model for single-phase Darcy flow in porous media with fractures of co-dimension one, which introduces an additional unknown at the fracture interface. Inspired by the fictitious domain method this Lagrange multiplier couples fracture and matrix domain and represents a local exchange of the fluid. The multipliers naturally impose the equality of the pressures at the fracture interface. The model is thus appropriate for domains with fractures of permeability higher than that in the surrounding bulk domain. In particular the novel approach allows for independent, regular meshing of fracture and matrix domain and therefore avoids the generation of small elements. We show existence and uniqueness of the weak solution of the continuous primal formulation. Moreover we discuss the discrete inf-sup condition of two different finite element formulations. Several numerical examples verify the accuracy and convergence of proposed method.

ano.nymous@ccsd.cnrs.fr.invalid (Markus Köppel), Markus Köppel

Faults and geological barriers can drastically affect the flow patterns in porous media. Such fractures can be modeled as interfaces that interact with the surrounding matrix. We propose a new technique for the estimation of the location and hydrogeological properties of a small number of large fractures in a porous medium from given distributed pressure or flow data. At each iteration, the algorithm builds a short list of candidates by comparing fracture indicators. These indicators quantify at the first order the decrease of a data misfit function; they are cheap to compute. Then, the best candidate is picked up by minimization of the objective function for each candidate. Optimally driven by the fit to the data, the approach has the great advantage of not requiring remeshing, nor shape derivation. The stability of the algorithm is shown on a series of numerical examples representative of typical situations.

ano.nymous@ccsd.cnrs.fr.invalid (Hend Ben Ameur), Hend Ben Ameur

To obtain the highest confidence on the correction of numerical simulation programs implementing the finite element method, one has to formalize the mathematical notions and results that allow to establish the soundness of the method. The Lax-Milgram theorem may be seen as one of those theoretical cornerstones: under some completeness and coercivity assumptions, it states existence and uniqueness of the solution to the weak formulation of some boundary value problems. The purpose of this document is to provide the formal proof community with a very detailed pen-and-paper proof of the Lax-Milgram theorem.

ano.nymous@ccsd.cnrs.fr.invalid (François Clément), François Clément

Recently several authors considered finite mixture models with semi-/non-parametric component distributions. Identifiability of such model parameters is generally not obvious, and when it occurs, inference methods are rather specific to the mixture model under consideration. In this paper we propose a generalization of the EM algorithm to semiparametric mixture models. Our approach is methodological and can be applied to a wide class of semiparametric mixture models. The behavior of the EM type estimators we propose is studied numerically through several Monte Carlo experiments but also by comparison with alternative methods existing in the literature. In addition to these numerical experiments we provide applications to real data showing that our estimation methods behaves well, that it is fast and easy to be implemented.

ano.nymous@ccsd.cnrs.fr.invalid (Laurent Bordes), Laurent Bordes

The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer process. Our arguments are based in part on the Komlós et al. (1975)'s results. Applications include the two-sample testing procedures together with the change-point problems. We also consider the strong approximation of the integrated empirical process when the parameters are estimated. Finally, we study the behavior of the self-intersection local time of the partial sum process representation of the integrated empirical process. Reference: Koml\'os, J., Major, P. and Tusn\'ady, G. (1975). An approximation of partial sums of independent RV's and the sample DF. I. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 32, 111-131.

ano.nymous@ccsd.cnrs.fr.invalid (Sergio Alvarez-Andrade), Sergio Alvarez-Andrade

Observability Gramians of diffusion equations have been recently connected to infinite Pick and Cauchy matrices. In fact, inverse or observability inequalities can be obtained after estimating the extreme eigenvalues of these structured matrices, with respect to the diffusion semi-group matrix. The purpose is hence to conduct a spectral study of a subclass of symmetric Cauchy matrices and present an algebraic way to show the desired observability results. We revisit observability inequalities for three different observation problems of the diffusion equation and show how they can be (re)stated through simple proofs.

ano.nymous@ccsd.cnrs.fr.invalid (Faker Ben Belgacem), Faker Ben Belgacem