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Many biological networks include cyclic structures. In such cases, Bayesian networks (BNs), which must be acyclic, are not sound models for structure learning. Dynamic BNs can be used but require relatively large time series data. We discuss an alternative model that embeds cyclic structures within acyclic BNs, allowing us to still use the fac-torization property and informative priors on network structure. We present an implementation in the linear Gaussian case, where cyclic structures are treated as multivariate nodes. We use a Markov Chain Monte Carlo algorithm for inference, allowing us to work with posterior distribution on the space of graphs.

ano.nymous@ccsd.cnrs.fr.invalid (Witold Wiecek), Witold Wiecek

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 discretized with conforming finite elements of order $p \geq 1$, yielding a nonlinear algebraic system of variational inequalities. We consider any iterative semismooth 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 at 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, except for a typically small contact term. 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

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

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

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

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 direct electrochemical reduction of UO2 solid pellets was carried out in LiF-CaF2 (+ 2 mass. % Li2O) at 850°C. An inert gold anode was used instead of the usual reactive sacrificial carbon anode. In this case, oxidation of oxide ions present in the melt yields O2 gas evolution on the anode. Electrochemical characterisations of UO2 pellets were performed by linear sweep voltammetry at 10mV/s and reduction waves associated to oxide direct reduction were observed at a potential 150mV more positive in comparison to the solvent reduction. Subsequent, galvanostatic electrolyses runs were carried out and products were characterised by SEM-EDX, EPMA/WDS and XRD. In one of the runs, uranium oxide was partially reduced and three phases were observed: non reduced UO2 in the centre, pure metallic uranium on the external layer and an intermediate phase representing the initial stage of reduction taking place at the grain boundaries. In another run, the UO2 sample was fully reduced. Due to oxygen removal, the U matrix had a typical coral-like structure which is characteristic of the pattern observed after the electroreduction of solid oxides.

ano.nymous@ccsd.cnrs.fr.invalid (Mathieu Gibilaro), Mathieu Gibilaro

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

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

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

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

In this work, we develop an a-posteriori-steered algorithm for a compositional two-phase flow with exchange of components between the phases in porous media. As a model problem, we choose the two-phase liquid-gas flow with appearance and disappearance of the gas phase formulated as a system of nonlinear evolutive partial differential equations with nonlinear complementarity constraints. The discretization of our model is based on the backward Euler scheme in time and the finite volume scheme in space. The resulting nonlinear system is solved via an inexact semismooth Newton method. The key ingredient for the a posteriori analysis are the discretization, linearization, and algebraic flux reconstructions allowing to devise estimators for each error component. These enable to formulate criteria for stopping the iterative algebraic solver and the iterative linearization solver whenever the corresponding error components do not affect significantly the overall error. Numerical experiments are performed using the Newton-min algorithm as well as the Newton-Fischer-Burmeister algorithm in combination with the GMRES iterative linear solver to show the efficiency of the proposed adaptive method.

ano.nymous@ccsd.cnrs.fr.invalid (Ibtihel Ben Gharbia), Ibtihel Ben Gharbia

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

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

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 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

Background and Objective: This paper deals with the improvement of parameter estimation in terms of precision and computational time for dynamical models in a bounded error context. Methods: To improve parameter estimation, an optimal initial state design is proposed combined with a contractor. This contractor is based on a volumetric criterion and an original condition initializing this contractor is given. Based on a sensitivity analysis, our optimal initial state design methodology consists in searching the minimum value of a proposed criterion for the interested parameters. In our framework, the uncertainty (on measurement noise and parameters) is supposed unknown but belongs to known bounded intervals. Thus guaranteed state and sensitivity estimation have been considered. An elementary effect analysis on the number of sampling times is also implemented to achieve the fast and guaranteed parameter estimation. Results: The whole procedure is applied to a pharmacokinetics model and simulation results are given. Conclusions: The good improvement of parameter estimation in terms of computational time and precision for the case study highlights the potential of the proposed methodology.

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

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 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 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

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

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

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

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

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

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 introduce a new algorithm of proper generalized decomposition (PGD) for parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most that dimension which realizes the best approximation---in the mean parametric norm associated to the elliptic operator---of the error between the exact solution and the Galerkin solution calculated on the subspace. This is analogous to the best approximation property of the proper orthogonal decomposition (POD) subspaces, except that in our case the norm is parameter-dependent. We apply a deflation technique to build a series of approximating solutions on finite-dimensional optimal subspaces, directly in the online step, and we prove that the partial sums converge to the continuous solution in the mean parametric elliptic norm. We show that the standard PGD for the considered parametric problem is strongly related to the deflation algorithm introduced in this paper. This opens the possibility of computing the PGD expansion by directly solving the optimization problems that yield the optimal subspaces.

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

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

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

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

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

L'analyse par microsonde électronique (EPMA) permet de quantifier, avec une grande précision, les concentrations élémentaires d'échantillons de compositions inconnues. Elle permet, par exemple, de quantifier les actinides présents dans les combustibles nucléaires neufs ou irradiés, d'aider à la gestion des déchets nucléaires ou encore de dater certaines roches. Malheureusement, ces analyses quantitatives ne sont pas toujours réalisables dû à l'indisponibilité des étalons de référence pour certains actinides. Afin de pallier cette difficulté, une méthode d'analyse dite « sans standard » peut-être employée au moyen d'étalons virtuels. Ces derniers sont obtenus à partir de formules empiriques ou à partir de calculs basés sur des modèles théoriques. Toutefois, ces calculs requièrent la connaissance de paramètres physiques généralement mal connus, comme c'est le cas pour les sections efficaces de production de rayons X. La connaissance précise de ces sections efficaces est requise dans de nombreuses applications telles que dans les codes de transport de particules et dans les simulations Monte-Carlo. Ces codes de calculs sont très utilisés en médecine et particulièrement en imagerie médicale et dans les traitements par faisceau d'électrons. Dans le domaine de l'astronomie, ces données sont utilisées pour effectuer des simulations servant à prédire les compositions des étoiles et des nuages galactiques ainsi que la formation des systèmes planétaires.Au cours de ce travail, les sections efficaces de production des raies L et M du plomb, du thorium et de l'uranium ont été mesurées par impact d'électrons sur des cibles minces autosupportées d'épaisseur variant de 0,2 à 8 nm. Les résultats expérimentaux ont été comparés avec les prédictions théoriques de sections efficaces d'ionisation calculées grâce à l'approximation de Born en ondes distordues (DWBA) et avec les prédictions de formules analytiques utilisées dans les applications pratiques. Les sections efficaces d'ionisation ont été converties en sections efficaces de productions de rayons X grâce aux paramètres de relaxation atomique extraits de la littérature. Les résultats théoriques du modèle DWBA sont en excellents accords avec les résultats expérimentaux. Ceci permet de confirmer les prédictions de ce modèle et de valider son utilisation pour le calcul de standards virtuels.Les prédictions de ce modèle ont été intégrées dans le code Monte-Carlo PENELOPE afin de calculer l'intensité de rayons X produite par des standards pur d'actinides. Les calculs ont été réalisés pour les éléments dont le numéro atomique est 89 ≤ Z ≤ 99 et pour des tensions d'accélération variant du seuil d'ionisation jusque 40 kV, par pas de 0,5 kV. Pour une utilisation pratique, les intensités calculées pour les raies L et M les plus intenses ont été regroupées dans une base de données.Les prédictions des standards virtuels ainsi obtenus ont été comparées avec des mesures effectuées sur des échantillons de composition connue (U, UO2, ThO2, ThF4, PuO2…) et avec les données acquises lors de précédentes campagnes de mesures. Le dosage des actinides à l'aide de ces standards virtuels a montré un bon accord avec les résultats attendus. Ceci confirme la fiabilité des standards virtuels développés et démontre que la quantification des actinides par microsonde électronique est réalisable sans standards d'actinides et avec un bon niveau de confiance.

ano.nymous@ccsd.cnrs.fr.invalid (Aurélien Moy), Aurélien Moy

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

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

This paper deals with optimal input design for parameter estimation in a bounded-error context. Uncertain controlled nonlinear dynamical models, when the input can be parametrized by a finite number of parameters, are considered. The main contribution of this paper concerns criteria for obtaining optimal inputs in this context. Two input design criteria are proposed and analysed. They involve sensitivity functions. The first criterion requires the inversion of the Gram matrix of sensitivity functions. The second one does not require this inversion and is then applied for parameter estimation of a model taken from the aeronautical domain. The estimation results obtained using an optimal input are compared with those obtained with an input optimized in a more classical context (Gaussian measurement noise and parameters a priori known to belong to some boxes). These results highlight the potential of optimal input design in a bounded-error context.

ano.nymous@ccsd.cnrs.fr.invalid (Carine Jauberthie), Carine Jauberthie

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

This paper deals with optimal input design for parameter estimation in a bounded-error context. Uncertain controlled nonlinear dynamical models, when the input can be parametrized by a finite number of parameters, are considered. The main contribution of this paper concerns criteria for obtaining optimal inputs in this context. Two input design criteria are proposed and analysed. They involve sensitivity functions. The first criterion requires the inversion of the Gram matrix of sensitivity functions. The second one does not require this inversion and is then applied for parameter estimation of a model taken from the aeronautical domain. The estimation results obtained using an optimal input are compared with those obtained with an input optimized in a more classical context (Gaussian measurement noise and parameters a priori known to belong to some boxes). These results highlight the potential of optimal input design in a bounded-error context.

ano.nymous@ccsd.cnrs.fr.invalid (Carine Jauberthie), Carine Jauberthie

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 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 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

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

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 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

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 Ben Belgacem), F Ben Belgacem

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 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

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 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 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

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

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