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A general implementation is presented for constructing a wavelet method for solving the nonlinear equation of Schr¨odinger. An explicit formula is derived which yields a stability in of the numerical solution. A simulation is elaborated to show the general behavior of the distribution function. Numerical results and comparison with classical algorithms are provided. This approach prove an attractive scheme for solving such equation.

In this paper, we suggest and analyze a new approximation schemes (3) to solve the extended general variational inequalities (2), which were introduced by Muhammad Aslam Noor (see[7, 9]). Using the projection operator technique, we establish the equivalence between the extended general variational inequalities and the fixed-point problem. This equivalent formulation is used to discuss the existence of a solution of the extended general variational inequalities. Several special cases are also discussed.

In this paper, we propose a large-update primal-dual interior point algorithm for linear optimization. The method is based on a new class of kernel functions which differs from the existing kernel functions in which it has a double barrier term. The investigation according to it yields the best known iteration bound O n log ( n ) log ( n ∈ ) \sqrt n \log (n)\log \left( {{n \over \in }} \right) for large-update algorithm with the special choice of its parameter m and thus improves the iteration bound obtained in Bai et al. [2] for large-update algorithm.

COVID-19-associated mold infections have been increasingly reported, and the main entity is COVID-19-associated aspergillosis (CAPA). Similarly, COVID-19-associated mucormycosis has been reported in hematology, and its prevalence is high and has been increasing in the diabetic population in India during the third COVID-19 pandemic wave. Simultaneous infection with Mucorales and Aspergillus is rare and even rarer during COVID-19. Here, we report the case of a previously immunocompetent patient with severe SARS-CoV-2 infection complicated with probable CAPA and mucormycosis co-infection. Specific diagnostic tools for mucormycosis are lacking, and this case highlights the advantages of analyzing blood and respiratory samples using the quantitative polymerase chain reaction to detect these fungi. We further reviewed the literature on mixed Aspergillus/Mucorales invasive fungal diseases to provide an overview of patients presenting with both fungi and to identify characteristics of this rare infection.

Duca and Lupsa [6] show that the results obtained in Youness [2] concerning the characterization of an E-convex function f in terms of its E-epigraph are incorrect. In this paper we introduce the correct form of this Theorem wich will be used in our study.

We construct in the present paper the effective growth response of trabecular bone, based on micromechanical analyses at the scale of a representative volume element consisting of individual trabeculae defining the representative unit cell (RUC). From a fundamental perspective, we adopt the physically and micromechanically motivated point of view that growth (resp. resorption) occurs as the surface remodeling of the individual trabeculae, the averaging of which leads to a net growth at the mesoscopic scale of the RUC. The effective model for the growing unit cell relies on an average kinematics which has been formulated in terms of the effective growth velocity gradient and effective elastic rate of deformation tensor, both functions of the rate of the effective density and stress applied over the RUC. The evaluation of the relation between the average rate of growth tensor and elastic growth rate versus the external stress applied to the RUC is obtained from a split of the average rate of growth tensor into its spherical and deviatoric parts, each of which being related to the corresponding applied stress quantities. The effective growth model is written for three different loading conditions as a polynomial relation between the components of the rate of growth tensor and similar components of the stress tensor under planar conditions, with a nonlinear function of the effective density as a weighting factor. The developed methodology is quite general and is applicable to any choice of the RUC morphology representative of the internal bone architecture.

The aim of this paper is to study regional gradient observability in a boundary subregion of evolution domain of hyperbolic system. We establish necessary conditions for the sensor structure in order to obtain regional boundary gradient observability. A reconstruction method based on extension of the Hilbert uniqueness method [7] is also developed and leads to a numerical approach successfully illustrated with numerical examples and simulations.

This paper presents a method to deal with an extension of regional gradient observability developed for parabolic system [1,2] to hyperbolic one. This concerns the reconstruction of the state gradient only on a subregion of the system domain. Then necessary conditions for sensors structure are established in order to obtain regional gradient observability. An approach is developed which allows the reconstruction of the system state gradient on a given subregion. The obtained results are illustrated by numerical examples and simulations.

Purpose: To assess cardiac function by means of a novel free-breathing cardiac magnetic resonance imaging (MRI) strategy. Materials and Methods: A stack of ungated 2D steady-state free precession (SSFP) slices was acquired during free breathing and reconstructed as cardiac cine imaging based on the generalized reconstruction by inversion of coupled systems (GRICS). A motion-compensated sliding window approach allows reconstructing cine movies with most motion artifacts cancelled. The proposed reconstruction uses prior knowledge from respiratory belts and electrocardiogram recordings and features a piecewise linear model that relates the electrocardiogram signal to cardiac displacements. The free-breathing protocol was validated in six subjects against a standard breath-held protocol. Results: Image sharpness, as assessed by the image gradient entropy, was comparable to that of breath-held images and significantly better than in uncorrected images. Volumetric parameters of cardiac function in the left ventricle (LV) and right ventricle (RV) were similar, including end-systolic volumes, end-diastolic volumes and mass, stroke volumes, and ejection fractions (with differences of 3% ± 2.4 in the LV and 2.9% ± 4.4 in the RV). The duration of the free-breathing protocol was nearly the same as the breath-held protocol. Conclusion: Free-breathing cine-GRICS enables accurate assessment of volumetric parameters of cardiac function with efficient correction of motion. J. Magn. Reson. Imaging 2012;340-351. © 2011 Wiley Periodicals, Inc.

Colloque avec actes et comité de lecture. Internationale.; International audience; Nous présentons une contribution numérique à l'étude de l'écoulement du sang, considéré comme un fluide non-newtonien à seuil de contrainte, dans une artère sténosée. L'écoulement est supposé axisymétrique, laminaire, et la conduite comporte une sténose. Les effets de seuil sont pris en compte dans les simulations. A partir de données expérimentales de la littérature, le fluide est représenté par le modèle de Herschel-Bulkley, régularisé pour considérer le comportement aux faibles gradients de vitesse. Les résultats mettent en évidence l'influence du seuil sur les caractéristiques d'écoulement et l'apparition des zones rigides, en fonction des nombres de Reynolds et d'Oldroyd.

Resume Pour les fluides newtoniens dans des configurations simples, la definition du nombre de Reynolds ne presente aucune difficulte, par contre dans le cas d'ecoulement de fluides non newtoniens dans des conduites de formes quelconques, la variation de la viscosite avec la vitesse de cisaillement necessite une generalisation de ce nombre adimensionnel. Malheureusement plusieurs definitions differentes ont ete proposees dans la litterature. Ce travail propose une methode generale valable pour une large classe de fluides non newtoniens et pour toutes les formes de conduite. Une application est developpee pour un fluide viscoelastique s'ecoulant dans une conduite de forme rectangulaire. Les resultats obtenus par cette etude sont en bon accord avec les correlations connues. For Newtonian fluids in simple configurations, the definition of the Reynolds number is quite a standard problem, but for non-Newtonian fluid flows in ducts with arbitrary shape of cross section, the dependence of the viscosity with the shear rate requires a generalization of this dimensionless number, unfortunately several different definitions have been proposed in the literature. This work proposes a general method valid for a large class of non-Newtonian fluids and for all duct shapes. Application is developed for a viscoelastic flow through a rectangular duct. Results obtained in the present investigation are in a good agreement with available correlations.

Malgre les connaissances geologiques accumulees sur plus de 800 puits carottes en continu au cours des quarante dernieres annees, le forage de la phase 8''1/2 du champ petrolifere de Hassi- Messaoud (Algerie) reste a ce jour delicat en raison notamment de problemes de cavage et de pertes de boue. L'objectif de ce travail etait d'etudier les problemes de pertes de boues en utilisant une approche sedimentologique et de localiser les niveaux producteurs sous-jacents du Cambrien. Pour cela, les zones a avancement rapide et lent des forages des series sedimentaires du Trias ont ete reperees afin d'en etablir des cartes de repartition. Ainsi, il a ete mis en evidence : - que les zones a avancement rapide correspondent aux secteurs sans pertes de boue (facies argileux de la plaine d'inondation), alors que les zones a avancement lent correspondent aux secteurs a pertes importantes (facies greseux des barres fluviatiles) ; - que sous les zones a avancement rapide dans les series du Trias, se trouvent des reservoirs d'hydrocarbures potentiels.

The aim of this paper is the introduction of a new concept that concerned the analysis of a large class of distributed parabolic systems. It is the general concept of gradient remediability. More precisely, we study with respect to the gradient observation, the existence of an input operator (gradient efficient actuators) ensuring the compensation of known or unknown disturbances acting on the considered system. Then, we introduce and we characterize the notions of exact and weak gradient remediability and their relationship with the notions of exact and weak gradient controllability. Main properties concerning the notion of gradient efficient actuators are considered. The minimum energy problem is studies, and we show how to find the optimal control, which compensates the disturbance of the system. Approximations and numerical simulations are also presented.Keywords: actuators efficient; disturbance; gradient; parabolic systems; remediability; sensors

On considere la convection dans une cavite cylindrique, de rapport de forme A (A=hauteur/diametre), chauffee par le bas (Rayleigh-Benard) et soumise a un champ magnetique horizontal, uniforme et constant. Les equations tridimensionnelles de Navier-Stokes, discretisees a l'aide de la methode des elements spectraux isoparametriques, sont resolues par integration temporelle ou methode de Newton. L'utilisation d'une technique de continuation nous permet de tracer des diagrammes de stabilite donnant les seuils d'apparition de la convection et des diagrammes de bifurcation donnant son evolution au dela de ces seuils. Outre des informations sur la stabilisation par champ magnetique, cette etude nous donne un exemple de systeme dynamique interessant par ses proprietes de symetrie et par la selection et l'evolution des modes convectifs

The convective flow occuring in a fluid layer, due to a horizontal temperature gra­ dient and controled by a vertical magnetic field, is studied. The fluid, enclosed in a rectangular cavity, is a conductive liquid metal with a Prandtl number assumed to be small. Velocity, temperature and electric potential are calculated analytically. With these solutions, the effect of lateral confinement and magnetic field intensity on li­

Three-dimensional Rayleigh–Bénard instabilities in binary fluids with Soret effect are studied by linear biglobal stability analysis. The fluid is confined transversally in a duct and a longitudinal throughflow may exist or not. A negative separation factor $\psi = \ensuremath{-} 0. 01$, giving rise to oscillatory transitions, has been considered. The numerical dispersion relation associated with this stability problem is obtained with a two-dimensional Chebyshev collocation method. Symmetry considerations are used in the analysis of the results, which allow the classification of the perturbation modes as ${S}_{l} $ modes (those which keep the left–right symmetry) or ${R}_{x} $ modes (those which keep the symmetry of rotation of $\lrm{\pi} $ about the longitudinal mid-axis). Without throughflow, four dominant pairs of travelling transverse modes with finite wavenumbers $k$ have been found. Each pair corresponds to two symmetry degenerate left and right travelling modes which have the same critical Rayleigh number ${\mathit{Ra}}_{c} $. With the increase of the duct aspect ratio $A$, the critical Rayleigh numbers for these four pairs of modes decrease and closely approach the critical value ${\mathit{Ra}}_{c} = 1743. 894$ obtained in a two-dimensional situation, one of the mode (a ${S}_{l} $ mode called mode A) always remaining the dominant mode. Oscillatory longitudinal instabilities ($k\approx 0$) corresponding to either ${S}_{l} $ or ${R}_{x} $ modes have also been found. Their critical curves, globally decreasing, present oscillatory variations when the duct aspect ratio $A$ is increased, associated with an increasing number of longitudinal rolls. When a throughflow is applied, the symmetry degeneracy of the pairs of travelling transverse modes is broken, giving distinct upstream and downstream modes. For small and moderate aspect ratios $A$, the overall critical Rayleigh number in the small Reynolds number range studied is only determined by the upstream transverse mode A. In contrast, for larger aspect ratios as $A= 7$, different modes are successively dominant as the Reynolds number is increased, involving both upstream and downstream transverse modes A and even the longitudinal mode.

The Marangoni flows are studied by numerical simulation in a liquid layer with an undeformable free upper surface heated by a constant flux and with a rigid bottom at constant temperature. Multirolls structures with different symmetry properties are exhibited in the case of a one-component fluid. More insight is given to the situation with an aspect ratio A = 4 with the determination of bifurcations up to a time dependent flow. The focus of the study is on the influence of the Soret effect on the flow structure when the fluid is a non-reactive binary mixture. Stationary results are compared to the expected behaviour given by previous linear stability analyses. Situations where time dependent flows occur as first bifurcation are also computed : an interesting behaviour corresponding to the successive apparition of new rolls in the middle and on the sides of the cavity is obtained, for which a physical interpretation is proposed.

National audience; Cet article présente l'étude d'un écoulement d'acoustic streaming, c'est-à-dire d'un écoulement quasi-permanent généré par la propagation d'une onde acoustique. Le travail consiste à confronter une étude expérimentale et sa modélisation numérique. Les ultrasons sont émis à 2MHz par un transducteur piézo-électrique de 29 mm de diamètre. Ce dernier est plongé dans une cuve d'eau équipée d'une paroi absorbante à l'extrémité opposée de la source. On ne s'intéresse pour l'instant qu'au champ lointain. Les mesures sont de deux types : champ de pression acoustique (hydrophone) et champ de vitesse (PIV-LDA). En parallèle, on effectue des simulations numériques directes avec le logiciel StarCCM+™. Il s'agit de résoudre les équations de Navier-Stokes en fluide incompressible complétées d'un terme source de force acoustique. L'expression de ce dernier est obtenue par séparation des échelles de temps, ce qui consiste à négliger à l'échelle de temps acoustique les variations temporelles, lentes, de l'écoulement généré. La démarche est ensuite analogue à celle utilisée en turbulence pour le calcul des tensions de Reynolds. On obtient finalement un bon accord entre les résultats expérimentaux et ceux de la modélisation numérique.

International audience; The temporal stability of a Carreau fluid flowing down an inclined porous substrate is considered. A reduced model is derived under the assumption of small permeability which decouples the flow in the liquid layer from the filtration flow in the porous medium and incorporates the effect of the porous medium by means of an effective slip condition at the liquid-solid interface. The slip coefficient in the effective slip condition is a function of the structure, permeability of the porous medium and the rheology of the fluid saturating the porous medium. The effects of shear-thinning rheology and permeability of the substrate on the stability of the film flow system are investigated. This problem gives rise to a generalized eigenvalue formulation which is solved through two approaches. The problem is solved analytically for long waves in the limiting cases of weakly and strongly non-Newtonian behaviors (power-law limit). A numerical investigation is carried out in the general case. The results are shown to agree well for the weakly non-Newtonian limit. Further, the power-law model and the Carreau model agree on a wide range of shear-thinning parameter values for a thin film over a rigid substrate. However, when considering a porous medium, this trend is not observed. The Carreau model gives valid results for the entire range of shear-thinning parameter values for a film over a rigid/porous substrate. The novelty of the present investigation lies in the inclusion of both the effects of bottom permeability and shear-thinning rheology. Both permeability and shear-thinning rheology have a destabilizing effect on the film flow system. The numerical results indicate the correlation between the effects due to shear-thinning properties and permeability. An energy balance analysis performed on the perturbation fields shows that destabilization induced by both shear-thinning and permeability is linked to the viscous shear work rate on the free surface.

International audience; Several studies have described cranio-cerebral correlations in accordance with the 10-20 electrode placement system. These studies have made a significant contribution to human brain imaging techniques, such as near-infrared spectroscopy and trans-magnetic stimulation. With the recent development of high resolution EEG, an extension of the 10-20 system has been proposed. This new configuration, namely the 10-10 system, allows the placement of a high number (64-256) of EEG electrodes. Here, we describe the craniocerebral correlations with the 10-10 system. Thanks to the development of a new EEG-MRI sensor and an automated algorithm which enables the projection of electrode positions onto the cortical surface, we studied the cortical projections in 16 healthy subjects using the Talairach stereotactic system and estimated the variability of cortical projections in a statistical way. We found that the cortical projections of the 10-10 system could be estimated with a grand standard deviation of 4.6 mm in x, 7.1 mm in y and 7.8 mm in z. We demonstrated that the variability of projections is greatest in the central region and parietal lobe and least in the frontal and temporal lobes. Knowledge of cranio-cerebral correlations with the 10-10 system should enable to increase the precision of surface brain imaging and should help electrophysiological analyses, such as localization of superficial focal cortical generators.

International audience; Spatial localization of scalp EEG electrodes is a major step for dipole source localization and must be accurate, reproducible and practical. Several methods have been proposed in the last 15 years. The most widely used method is currently electromagnetic digitization. Nevertheless, this method is difficult to use in a clinical environment and has not been validated with a high number of electrodes. In this paper, we introduce a new automatic method for localizing and labeling EEG sensors using MRI. First, we design a new scalp EEG sensor. Secondly, we validate this new technique on a head phantom and then in a clinical environment with volunteers and patients. For this, we compare the reproducibility, accuracy and performance of our method with electromagnetic digitization. We demonstrate that our method provides better reproducibility with a significant difference (p

Colloque avec actes et comité de lecture. Internationale.; International audience; Une étude expérimentale du comportement d'un fluide viscoélastique, dans une contraction brusque, est présentée. Notre travail concerne principalement l'écoulement d'une solution aqueuse viscoélastique (solution de polyacrylamide : Séparan AP-30) à différentes concentrations dans une contraction brusque à symétrie plane de rapport 4 :1. On étudie l'influence de l'inertie et de la propriété élastique du fluide sur les profils de vitesse et les pertes de charge générées. Les mesures des composantes de la vitesse à différents débits volumiques, par Vélocimétrie Laser à effet Doppler (LDV), montrent clairement à forts nombres de Reynolds le caractère élongationnel de l'écoulement à l'aval de la contraction. Une comparaison de la structure de l'écoulement, entre le fluide viscoélastique et un fluide newtonien, montre des comportements complètement différents à l'amont et à l'aval du plan de contraction. Le problème de caractérisation et de modélisation de la solution viscoélastique est également abordé. Mots clés : fluide viscoélastique, contraction brusque, vitesses et pressions