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International audience; Abstract. In this study, an extension on the previously reported status of the COllaborative Carbon Column Observing Network's (COCCON) calibration procedures incorporating refined methods is presented. COCCON is a global network of portable Bruker EM27/SUN FTIR spectrometers for deriving column-averaged atmospheric abundances of greenhouse gases. The original laboratory open-path lamp measurements for deriving the instrumental line shape (ILS) of the spectrometer from water vapour lines have been refined and extended to the secondary detector channel incorporated in the EM27/SUN spectrometer for detection of carbon monoxide (CO). The refinements encompass improved spectroscopic line lists for the relevant water lines and a revision of the laboratory pressure measurements used for the analysis of the spectra. The new results are found to be in good agreement with those reported by Frey et al. (2019) and discussed in detail. In addition, a new calibration cell for ILS measurements was designed, constructed and put into service. Spectrometers calibrated since January 2020 were tested using both methods for ILS characterization, open-path (OP) and cell measurements. We demonstrate that both methods can detect the small variations in ILS characteristics between different spectrometers, but the results of the cell method indicate a systematic bias of the OP method. Finally, a revision and extension of the COCCON network instrument-to-instrument calibration factors for XCO2, XCO and XCH4 is presented, incorporating 47 new spectrometers (of 83 in total by now). This calibration is based on the reference EM27/SUN spectrometer operated by the Karlsruhe Institute of Technology (KIT) and spectra collected by the collocated TCCON station Karlsruhe. Variations in the instrumental characteristics of the reference EM27/SUN from 2014 to 2017 were detected, probably arising from realignment and the dual-channel upgrade performed in early 2018. These variations are considered in the evaluation of the instrument-specific calibration factors in order to keep all tabulated calibration results consistent.

International audience

International audience; BACKGROUND: The aim of this study was to research and compare the effect of Crossfit® (CF), LesMills® (LM) and traditional resistance (TRAD) training program on short performances. METHODS: Participants were assigned randomly into 3 groups and followed the training sessions allocated at the rate of 5 sessions/week for 16 weeks. A battery of tests including anthropometric and performance measures were carried out over three sessions: before training (T0), after eight weeks (T1) and sixteen weeks of training (T2). RESULTS: Findings indicated that strength tests demonstrated a significant time effect (p

In this paper we make an overview of results relating the recent "discoveries" in differential geometry, such as higher structures and differential graded manifolds with some natural problems coming from mechanics. We explain that a lot of classical differential geometric constructions in the context can be conveniently described using the language of Q-structures, and thus Q-structure preserving integrators are potentially of great use in mechanics. We give some hints how the latter can be constructed, and formulate some open problems. Since the text is intended both to mathematics and mechanics communities, we tried to make it accessible to non-geometers as well., Comment: 20 pages, 2 figures

International audience

International audience; Ramadan is characterized by daily abstinence from food and fluid intake from dawn to sunset. The understanding of the Ramadan effects on the diurnal variations of athletic performance is crucial for practitioners, coach and researchers to prepare sport events and optimize performance. The aim of the present study was to reveal the effect of Ramadan on the performance aspect, heart rate and rating of perceived exertion during a karate match. In a randomized counterbalanced, 2 x 2 cross-over order, 22 male and female amateur karate athletes (age = 16.8 years, body mass = 59.1 kg, height = 168.3 cm) participated in simulated karate match at 8-10 a.m. and 5-7 p.m. on three different occasions 1 week before Ramadan, the second week of Ramadan (during Ramadan), and 2 weeks after Ramadan. Performance aspects were analyzed, and heart rate and rating of perceived exertion were assessed before and immediately after the match at each visit. Our results demonstrated that Ramadan adversely affected time-motion variables (fighting time and preparatory time) and heart rate during simulated karate match (p < 0.05, all). However, heart rate pic response to karate match was higher during Ramadan when compared with before Ramadan and after Ramadan. However, rating of perceived exertion results did not show any variation during Ramadan phases. Concerning the interaction of Ramadan and time of day, fighting time and stoppage time were higher in the evening and in the morning before Ramadan and the inverse during Ramadan, respectively (p < 0.05). In conclusion, Ramadan altered the diurnal variation of performance aspect, in terms of fighting time and stoppage time, during simulated karate match.

International audience; In this paper, we discuss the possibility of using computer algebra tools in the process of modeling and qualitative analysis of mechanical systems and problems from theoretical physics. We describe some constructions—Courant algebroids and Dirac structures—from the so-called generalized geometry. They prove to be a convenient language for studying the internal structure of the differential equations of port-Hamiltonian and implicit Lagrangian systems, which describe dissipative or coupled mechanical systems and systems with constraints, respectively. For both classes of systems, we formulate some open problems that can be solved using computer algebra tools and methods. We also recall the definitions of graded manifolds and Q‑structures from graded geometry. On particular examples, we explain how classical differential geometry is described in the framework of the graded formalism and what related computational questions can arise. This direction of research is apparently an almost unexplored branch of computer algebra.

This article reviews some integrators particularly suitable for the numerical resolution of differential equations on a large time interval. Symplectic integrators are presented. Their stability on exponentially large time is shown through numerical examples. Next, Dirac integrators for constrained systems are exposed. An application on chaotic dynamics is presented. Lastly, for systems having no exploitable geometric structure, the Borel-Laplace integrator is presented. Numerical experiments on Hamiltonian and non-Hamiltonian systems are carried out, as well as on a partial differential equation. Keywords: Symplectic integrators, Dirac integrators, long-time stability, Borel summation, divergent series., 33 pages, 18 figures

In this contribution we will describe some objects of the so-called generalized geometry that appear naturally in the analysis of mechanical systems. In particular we will discuss the Dirac structures that we will illustrate by the example of systems with constraints. Dirac structures generalize simultaneously symplectic and Poisson structures. They provide a convenient framework to give a gemetric description of the so-called port-Hamiltonian systems. Then, we will present a framework which is even more general-the one of differential graded manifolds (also called Q-manifolds). The ultimate goal of this work is to construct numerical methods that preserve these geometric structures, and thus guarantee good physical behavior of the simulated systems., Dans cette communication on va décrire certains objets de la géométrie dite généralisée, qui appa-raissent naturellement dans l'analyse des systèmes mécaniques. En particulier, on présentera les structures de Dirac, que l'on illustrera sur l'exemple des systèmes avec contraintes. Les structures de Dirac généralisent à la fois les structures symplectiques et celles de Poisson. Elles sont le bon cadre pour décrire géométriquement les systèmes dits Hamiltoniens à ports. Nous présenterons aussi une structure plus générale, qui est celle des variétés différentielles graduées (dites aussi Q-variétés). L'objectif final de ce travail est la construction de schémas numériques qui préservent ces structures géométriques et garantissent ainsi un bon comportement physique dans les simulations.

International audience

This paper deals with the construction of reduced order models (ROMs) for the simulation of the interaction between a fluid and a rigid solid with imposed rotation velocity. The approach is a follows. First, we derive a monolithic description of the fluid/structure interaction by extending the Navier-Stokes equations from the fluid domain to the solid (rotor) domain similarly to the fictitious-domain approach. Second, we build a ROM by a proper orthogonal decomposition (POD) of the resulting multi-phases flow. This method consists in (i) constructing an optimal albeit empirical spatial basis for a very small sub-space of the solution space, and (ii) projecting the governing equations on this reduced basis. Third, we cope with the reconstruction of the high-dimensional velocity field needed to evaluate the imposed velocity constraint by a POD of the solid membership function. Fourth, we use state of the art method to interpolate between available POD bases to build the proposed POD-ROM for a range of parameters values. The proposed method is applied to an academic configuration and proves efficient in the reconstruction of the velocity in both the fluid and solid domains while substantially reducing the computational cost.

This paper deals with the construction of reduced order models (ROMs) for the simulation of the interaction between a fluid and a rigid solid with imposed rotation velocity. The approach is a follows. First, we derive a monolithic description of the fluid/structure interaction by extending the Navier-Stokes equations from the fluid domain to the solid (rotor) domain similarly to the fictitious-domain approach. Second, we build a ROM by a proper orthogonal decomposition (POD) of the resulting multi-phases flow. This method consists in (i) constructing an optimal albeit empirical spatial basis for a very small sub-space of the solution space, and (ii) projecting the governing equations on this reduced basis. Third, we cope with the reconstruction of the high-dimensional velocity field needed to evaluate the imposed velocity constraint by a POD of the solid membership function. Fourth, we use state of the art method to interpolate between available POD bases to build the proposed POD-ROM for a range of parameters values. The proposed method is applied to an academic configuration and proves efficient in the reconstruction of the velocity in both the fluid and solid domains while substantially reducing the computational cost.

An adaptation of the Inverse Distance Weighting (IDW) method to the Grassmann manifold is carried out for interpolation of parametric POD bases. Our approach does not depend on the choice of a reference point on the Grassmann manifold to perform the interpolation, moreover our results are more accurate than those obtained in [ 7 ]. In return, our approach is not direct but iterative and its relevance depends on the choice of the weighting functions which are inversely proportional to the distance to the parameter. More judicious choices of such weighting functions can be carried out via kriging technics [ 23 ], this is the subject of a work in progress.

International audience; In this contribution we will describe some objects of the generalized geometry that appear naturally in the qualitative analysis of mechanical systems. In particular we will discuss the Dirac structures within the framework of the systems with constraints as well as of the port-Hamiltonian systems. From the mathematical point of view, Dirac structures generalize simultaneously symplectic and Poisson structures. As for mechanics, the idea is to design numerical methods that preserve these structures and thus guarantee good physical behaviour in the simulation. Then, we will present a framework which is even more general-the one of differential graded manifolds (also called Q-manifolds), and discuss some possible ways of using them for the "structure preserving integrators" in mechanics. For all of the mentioned constructions we will explain the problems that arise in generic situations-most of them are open, but we think they are suitable for handling with various computer algebra approaches.

International audience; Some of the most important geometric integrators for both ordinary and partial differential equations are reviewed and illustrated with examples in mechanics. The class of Hamiltonian differential systems is recalled and its symplectic structure is highlighted. The associated natural geometric integrators, known as symplectic integrators, are then presented. In particular, their ability to numerically reproduce first integrals with a bounded error over a long time interval is shown. The extension to partial differential Hamiltonian systems and to multisymplectic inte-grators is presented afterwards. Next, the class of Lagrangian systems is described. It is highlighted that the variational structure carries both the dynamics (Euler-Lagrange equations) and the conservation laws (Noether's theorem). Integrators preserving the variational structure are constructed by mimicking the calculus of variation at the discrete level. We show that this approach leads to numerical schemes which preserve exactly the energy of the system. After that, the Lie group of local symmetries of partial differential equations is recalled. A construction of Lie-symmetry-preserving numerical scheme is then exposed. This is done via the moving frame method. Applications to Burgers equation are shown. The last part is devoted to the Discrete Exterior Calculus, which is a structure-preserving integrator based on differential geometry and exterior calculus. The efficiency of the approach is demonstrated on fluid flow problems with a passive scalar advection.

International audience

International audience

Colloque avec actes et comité de lecture. Internationale.; International audience; For many decades, researchers agree that designing physics-conserving numerical solvers should be done through the preservation over time of the geometrical structure of the equations at the discrete scale. It is in this spirit that the most popular geometry-based integrators were developped. They include, for instance, symplectic integrators, variational integrators and Lie-symmetry invariant schemes which preserve, respectively, the symplectic two-form, the Lagrangian structure, and the Lie symmetry group of the equations numerically. In this communication, we present the discrete exterior calculus (DEC) which is a more general geometry-based integrator. DEC aims to be a discrete theory of differential geometry, and especially exterior calculus, which preserves exactly the cohomology structure provided by the exterior derivative operator d. One of the advantage of this approach is the naturally consistent discretisations of the tensorial derivation operators such as divergence, gradient and curl. DEC also guarantees that Stoke's theorem holds at discrete scale. The introduction of DEC in mechanics is new, but has already been used, for example, to build a solver for Euler's equations which respects Kelvin's theorem on the preservation of circulation. In this communication, other applications to Navier-Stokes equations with temperature and passive scalars will be presented.

Geometric integrators are numerical schemes which preserve, at the discrete scale, the geometric structure of the equations. The present communication overviews some of the most important ones, which are symplectic integrators, variational integrators, invariant schemes and discreti- zations based on exterior calculus, Les intégrateurs géométriques sont des schémas numériques préservant, au niveau discret, la structure géométrique des équations. Dans cette communication, on passe en revue quelques intégrateurs géométriques parmi les plus importants en mécanique qui sont les intégrateurs symplectiques, les intégrateurs invariants, les schémas invariants par groupe de symétrie de Lie et les schémas basés sur le calcul extérieur discret

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International audience; La formulation en calcul extérieur des équations de Navier-Stokes anisothermes est présentée. Ces équations sont ensuites discrétisées par la méthode de calcul extérieur discret (DEC). Les résultats numériques par cette méthodes sont comparé aux solutions connues (analytiques ou numériques) Abstract : The intrinsic exterior calculus formulation of the anisothermal Navier-Stokes equations is presented. The equations are then discretized with the Discrete Exterior Calculus method(DEC). The numerical results are compared to known (analytical or numerical) solutions.

A time integration method of a dynamical system, based on a (possibly divergent) time series decomposition of the solution, followed by a Borel summation using an inverse factorial series, is examined. The stress is put on the robustness of inverse factorial series algorithm, compared to the Borel-Pade one, to compute the Borel sum of the solution.

Monte-Carlo simulation is used to study the surface recombination effects on the electron beam induced current technique. The current is collected by a nanoscale electrode. We choose three values for the surface recombination velocity reflecting the sample surface states; zero, infinite value and an intermediate one. From a probabilistic point of view, each of the three surface velocities is described by a collection probability related to the surface effects and to the electrode size. Even if probabilities corresponding to zero and intermediate velocity are chosen to be close one to the other, the results are different. For intermediate velocity the collection efficiency profile is similar to that corresponding to the infinite velocity. Both profiles narrow with diminution of their maximum. At electron beam energies higher than 4 keV the profiles are superimposed because of the large penetration depth, and the smallness of the electrode and its depletion zone.

This paper presents numerical study of an oval-sail, a bluff-body equipped with a grid all along the span. Suction based flow control is applied to this body that is developed for wind assisted ship propulsion. First, a choice of numerical turbulence model is discussed through results of an oval-sail without suction. Three turbulence models are applied: the Ri j SSG, the Ri j EBRSM and the v2 f model. Then, computations are performed for the oval-sail fitted with suction grid. These last simu- lations are carried out with the low-Reynolds-number Ri j EBRSM turbulence model. The influence of the grid geometry on the oval-sail aerodynamic performances is highlighted. All simulations are carried out for the sail set at zero incidence. The Reynolds number based on the free stream velocity and the profile chord is Re = 5105. Results are compared to available experimental data.

In this manuscript, we present optimal sensitivity results of eigenvalues and eigenspaces with respect to self-adjoint compact operators. We show that while eigenvalues depend in a Lipschitzian way in compact operators, the eigenspaces are only locally Lipschitz. Our results generalize to arbitrary dimension eigenspaces the results obtained in [19] for one-dimensional eigenspaces sensitivity and thus simplify the celebrate results by Davis and Kahan [6] developed for general Hermitian operator perturbations. Moreover, Proper Orthogonal Decomposition bases sensitivity is carried out in the case of time-interval perturbations, spatial perturbations (Gappy-POD) or parameter perturbations.

The title compound, C5H4Cl2N2, is essentially planar with an r.m.s. deviation for all non-H atoms of 0.009 Å. The largest deviation from the mean plane is 0.016 (4) Å for an N atom. In the crystal, molecules are linked by pairs of C—H...N hydrogen bonds, forming inversion dimers, enclosing anR22(6) ring motif.

In the title molecule, C16H12Cl2O2Se, the C—Se—C angle is 100.05 (14)°, with the dihedral angle between the planes of the benzene rings being 69.92 (17)°. The average endocyclic angles (Se—Car—Car; ar = aromatic) facing the Se atom are 120.0 (3) and 119.4 (3)°. The Se atom is essentially coplanar with the benzene rings, with Se—Car—Car—Cartorsion angles of −179.2 (3) and −179.7 (3)°. In the crystal, molecules are linkedviaC—H...O hydrogen bonds forming chains propagating along thea-axis direction. The chains are linkedviaC—H...π interactions, forming a three-dimensional network.

This paper proposes an advanced energy management strategy for a stand-alone hybrid energy system. The considered hybrid system includes a photovoltaic panel, a fuel cell, an electrolyzer, a battery bank and a supercapacitor. The proposed power management system aims to control the energy flow within the system and decides the amount of the load power shared with each power source. The system control is implemented in two parts: a central power flow controller that provides overall control of the power system and a local loads controller, which controls the different loads according to the energy balance of the system. The hybrid power system has been tested by simulation using models implemented in Matlab/Simulink software. The simulation is performed over a short and a long period of time in order to evaluate the performance of the dynamic controllers and the effectiveness of the management strategy. For a long simulation period, a house located in the province of Batna ( 35 ° 33 ′ N 6 ° 10 ′ E) has been taken as a case study with a deep study on real load profile for an average house with all required weather data with respect to the location. The simulation results confirm the efficiency of the proposed control strategy, as it increases the reliability of the system and improves its energy balance.

National audience

In the title compound, C9H10N2O4, the planes of the nitro groups subtend dihedral angles of 55.04 (15) and 63.23 (15)° with that of the aromatic ring. These tilts are in opposite senses and the molecule possesses approximate mirror symmetry about a plane normal to the molecule. In the crystal, molecules form stacks in the [100] direction with adjacent molecules related by translation, although the centroid–centroid separation of 4.136 (5) Å is probably too long to regard as a significant aromatic π–π stacking interaction. An extremely weak C—H...O interaction is also present.

International audience

A time integration method for the resolution of ordinary and partial dierential equations is proposed. The method consists in computing a formal solution as a (eventually divergent) time series. Next, the Borel resummation method is applied to deduce an (sectorial) analytical solution. The speed and spectral properties of the scheme are analyzed through some examples. Applications to fluid mechanics are presented. ResumOn propose une methode numerique d'integration temporelle d'´ equations di´ erentielles ou aux derivees partielles. Cette methode consiste d'abordcalculer une solution sous forme de serie formelle, dont le rayon de convergence peutnul. Ensuite, la methode de resommation de Borel- Laplace est utilisee pour deduire une solution analytique (dans un secteur) de l'´ equation. La rapidite et les proprietes geometriques du schema sont analyseestravers quelques exemples. Des applications en mecanique des fluides sont presentees.

In what follows, we consider the Proper Orthogonal Decomposition (POD) technique of model order reduction, for a parameterized quasi-nonlinear parabolic equation. A POD basis associated with a set of reference values of the characteristic parameters is considered. From this basis, a parametric reduced order model (ROM) projecting the initial equation is constructed. A mathematical a priori estimate of the parametric squared L2-error induced by this projection is developed. This later estimate is based on both, the parametric behavior of the squared L2-ROM-error thanks to the resolution of a Ricatti differential inequality in the parametric ROM-error, and the convergence rate of the parametric ROM to the full problem, via the augmentation of the basis dimension. Indeed, under restrictive conditions on the solutions regularity of such equations, we are able to precise the slope of the logarithm of the squared L2-norm of the ROM error, as a function of the logarithm of the basis modes number. Numerical experiments of our theoretical estimate, are presented for the 2D Navier-Stokes equations in the case of an unsteady and incompressible fluid flow in a channel around a circular cylinder. A mathematical a priori estimate of the parametric squared L2-error induced by the model reduction by POD is developped for a parameterized quasi-nonlinear parabolic equation. This estimate is obtained thanks to the resolution of a Ricatti differential inequality.

International audience; The development of Gestion et Etude des Informations Spectroscopiques Atmosphériques (GEISA: Management and Study of Spectroscopic Information) was started over three decades at Laboratoire de Météorologie Dynamique (LMD) in France. GEISA is a computer accessible spectroscopic database, designed to facilitate accurate forward radiative transfer calculations using a line-by-line and layer-by-layer approach. More than 350 users have been registered for on-line use of the GEISA facilities. The current 2003 edition of GEISA (GEISA-03) is a system comprising three independent sub-databases devoted respectively to: line transition parameters, infrared and ultraviolet/visible absorption cross-sections, microphysical and optical properties of atmospheric aerosols.Currently, GEISA is involved in activities related to the assessment of the capabilities of IASI (Infrared Atmospheric Sounding Interferometer on board of the METOP European satellite) through the GEISA/IASI database derived from GEISA.The GEISA-03 content is presented, placing emphasis on molecular species of interest for Earth and planetary atmosphere studies, with details on the updated 2008 archive underway. A critical assessment on the needs, in terms of molecular parameters archive, related with recent satellite astrophysical missions is made. Detailed information on free on-line GEISA and GEISA/IASI access is given at http://ara.lmd.polytechnique.fr and http://ether.ipsl.jussieu.fr.

We derive analytical properties for the degeneracy $\nu(N,j)$ occurring in the decomposition $\bigoplus\limits_{j}^\frac{N}{2}\nu(N,j)\mathbb C^{2j+1}$ of the state space $\mathbb C^{2\otimes N}$. We also investigate the dynamics of two qubits coupled via Ising interactions to separate spin baths, and we study the thermodynamic limit., Comment: 14 pages, 6 figures, minor typographical errors fixed

International audience

International audience

International audience

Colloque avec actes et comité de lecture. Internationale.; International audience; Nous nous intéressons à des problèmes d'évolution issus de la mécanique. Si on cherche la solution sous forme d'un développement en série formelle en fonction du temps, souvent, une telle série est divergente, mais tout en étant de type Gevrey (ne diverge pas plus vite que la série de factorielles). A cette solution formelle, on peut associer une procédure de resommation de type Borel-Laplace qui permet de construire une solution asymptotique à la solution du problème recherchée. Une telle technique donne des informations utiles sur la singularité de la solution et leur comportement, mais elle peut aussi être la base pour le développement de nouveaux schémas temporels permettant la simulation numérique de problème d'évolutions sur de grands intervalles de temps. Notre objectif dans cette communication est de présenter ces deux aspects en les illustrant sur des problèmes issus de la mécanique.

Colloque avec actes et comité de lecture. Internationale.; International audience; La méthode POD-multiphasique, développée par E. Liberge et A. Hamdouni (Journal of Fluids and Structures, 26(2) : 292 – 311, 2010), permet de construire des modèles réduits (ROM-POD) pour les problèmes d'interaction fluide-structure valables aussi bien pour des petits déplacements de la structure que pour des grands déplacements. La performance de l'approche a été validée sur des configurations de type vibrations sous écoulements de cylindres seuls ou en réseaux. L'objectif de la communication est de présenter la construction d'un modèle réduit paramétrique permettant l'étude de la stabilité de ce type de configurations en fonction de l'évolution des caractéristiques des solides (par exemple la raideur). Le modèle paramétré sera construit d'une part uniquement à partir d'un modèle réduit unique de référence, d'autre part grâce à une interpolation de modèles réduits construits pour différents paramètres. Cette interpolation sera basée sur la minimisation d'un lagrangien sur une variété bien choisie pour tenir compte du fait que l'ensemble des modèles réduits a une structure de variété différentielle et non d'un espace vectoriel.

Colloque avec actes et comité de lecture. Internationale.; International audience; Dans cet article, on présente quelques résultats de simulation numérique d’un écoulement turbulent autour d’un turbo-voile. Les équations instationnaires de Navier Stokes, formulées pour un écoulement turbulent et incompressible, sont résolues dans un domaine tridimensionnel qui entoure le profil. Ces calculs sont exécutés pour un nombre de Reynolds Re = 105. Le profil retenu ressemble au turbo-voile de l’Alcyone de Cousteau. Plusieurs configurations ont été considérées. Dans un premier cas, le profil est placé sous une incidence nulle puis sous un angle d’attaque de 15°. Ces simulations sont effectuées pour un profil sans grille, en faisant abstraction de la zone fluide à l’intérieur du turbo-voile. Différents modèles de turbulence sont appliqués : le modèle k- / V2-f, formulé pour les bas nombres de Reynolds, le modèle Rij SSG avec une loi de paroi et le modèle LES dynamique. Ensuite, c’est le cas du turbo-voile équipé d’une grille avec aspiration qui est étudié. Pour cette dernière configuration, les calculs sont exécutés avec le modèle Rij SSG formulés pour les hauts nombres de Reynolds. L’influence de quelques paramètres caractéristiques de la grille sur les performances du profil est simulée. Les principaux résultats extraits des calculs sont les coefficients de portance (Cl) et de traînée (Cd) ainsi que les contours des vitesses et pression autour du profil.

International audience; On présente des schémas d'intégration temporelle basés sur la méthode de resommation de séries divergentes pour la résolution numérique d'équations différentielles et d'équations aux dérivées partielles. Les applications sont orientées vers les problèmes de mécanique de fluides. Le cas des équations de Navier-Stokes est abordé.

International audience; Dans cette communication, nous établissons un résultat mathématique sur la sensibilité paramétrique des modèles d'ordre réduit (ROM) obtenus par la méthode de la décomposition orthogonale aux valeurs propres (POD). Nous nous intéressons plus particulièrement aux équations de Navier-Stokes pour un écoulement fluide bidimensionnel et incompressible. Nous présentons aussi une comparaison avec des simulations numériques pour la configuration d'un écoulement instationnaire dans un canal autour d'un cylindre carré.

1528-7483; A homometallic Zr(IV)-oxalate three-dimensional (3-D) coordination polymer of formula [Zr(OH)2(C2O4)*0.5H2O] is reported. This compound was found to be a microporous solid with reversible sorption abilities. Upon guest release and sorption, the crystalline material undergoes single crystal to single crystal transitions. The crystal structures for three phases have been solved from single crystal diffraction studies. They consist of the guest containing frameworks [Zr(OH)2(C2O4)*0.5H2O], 1, 3, and the guest-free porous phase [Zr(OH)2(C2O4)], 2; all are found with tetragonal space group I4/m. Phase 1 has been obtained by controlled diffusion of the reagents (ZrO(NO3)2 and H2C2O4) in a silica gel medium; the other phases have been formed from 1 by thermal activation (2) and re-adsorption of H2O (3).

International audience

International audience

Colloque avec actes et comité de lecture. Internationale.; International audience; Cette communication a pour objectif principal de donner une contribution mathématique sur la sensibilité paramétrique de la méthode de réduction de modèles par projection connue sous le nom de POD pour Proper Orthogonal Decomposition. Les modèles d'ordre réduit par POD (ROM-POD) sont utilisés pour des problèmes de contrôle, de stabilité, d'optimisation de forme, des problèmes inverses, etc...Il y a aussi les problèmes d'évolution paramétrique, où la POD devient très intéressante: En mécanique des fluides, nous pouvons citer les problèmes de contrôle optimal par variation des paramètres caractéristiques des écoulements fluides; Où il est indispensable de pouvoir prédire le comportement de ces écoulements en temps réel. Une solution appliquée pour ce genre de problèmes consiste à utiliser un modèle ROM-POD de référence construit à une valeur initiale du paramètre caractéristique, pour simuler des écoulements fluides pour d'autres valeurs de ce paramètre. La question qui se pose naturellement est la suivante: Dans quelle mesure le modèle ROM-POD de référence reste adapté au problème complet en fonction de l'évolution paramétrique? D'où le problème de déterminer une région de validité du modèle ROM-POD initial, où il approche le problème complet à une précision fixée au préalable. Il est important aussi de se poser la question de l'augmentation de la dimension du modèle réduit, de manière à élargir la région de confiance sans que la réduction de modèles perde son sens. Nous proposons un premier élément de réponse à ces deux questions fondamentales dans le cadre des équations de Navier-Stokes pour un fluide bidimensionnel et incompressible. Le paramètre de ces équations est le nombre de Reynolds décrit par la variation de la viscosité, pour une vitesse et une hauteur fixes. Plus précisément, nous donnons une estimation a priori du carré de l'erreur entre la solution du modèle réduit et celle du problème semi-discret en espace associé aux équations de Navier-Stokes. Cette estimation dépend de la distance entre deux paramètres distincts et de l'évolution de la dimension du ROM-POD.

Fluid-Structure Interactions are present in a large number of systems of nuclear power plants and nuclear on-board stoke-holds. Particularly in steam generators, where tube bundles are submitted to cross-flow which can lead to structure vibrations. We know that numerical studies of such a complex mechanism is very costly, that is why we propose the use of reduced-order methods in order to reduce calculation times and to make easier parametric studies for such problems. We use the multiphase-POD approach, initially proposed by Liberge (E. Liberge; POD-Galerkin Reduction Models for Fluid-Structure Interaction Problems, PhD Thesis, Universite de La Rochelle, 2008). This method is an adaptation of the classical POD approach to the case of a moving structure in a flow, considering the whole system (fluid and structure) as a multiphase domain. We are interested in the case of large displacements of a structure moving in a fluid, in order to observe the ability of the multiphase-POD technique to give a satisfying solution reconstruction. We obtain very interesting results for the case of a single circular cylinder in cross-flow (lock-in phenomenon). Then we present the application of the method to a case of confined cylinders in large displacements too. Here again, results are encouraging. Finally, we propose to go further presenting a first step in parametric studies with POD-Galerkin approach. We only consider a flowing-fluid around a fixed structure and the Burgers’ equation. A future work will consist in applications to fluid-structure interactions.