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We consider the computation of the Euclidean (or L2) norm of an n -dimensional vector in floating-point arithmetic. We review the classical solutions used to avoid spurious overflow or underflow and/or to obtain very accurate results. We modify a recently published algorithm (that uses double-word arithmetic) to allow for a very accurate solution, free of spurious overflows and underflows. To that purpose, we use a double-word square-root algorithm of which we provide a tight error analysis. The returned L2 norm will be within very slightly more than 0.5 ulp from the exact result, which means that we will almost always provide correct rounding.

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We present an experimental study about granular avalanches when external mechanical vibrations are applied. The results of the flow properties highlight the existence of two distinct regimes: (i) a gravity-driven regime at large angles where scaling laws are in agreement with those reported in the literature for non-vibrating granular flows and (ii) a vibration-driven regime at small angles where no flow occurs without applied vibrations. The flow in this regime is well described by a vibrationinduced activated process. We also propose an empirical law to capture the evolution of the thickness of the deposits as a function of the vibration intensity and the inclination angle.

International audience; In this paper, we investigate experimentally the dynamics of particles in dense granular suspensions when both shear and external vibrations are applied. We study in detail how vibrations affect particle reorganization at the local scale and modify the apparent rheology. The nonlocal nature of the rheology when no vibrations are applied is evidenced, in agreement with previous numerical studies from the literature. It is also shown that vibrations induce structural reorganizations, which tend to homogenize the system and cancel the nonlocal properties.

International audience; We consider the flow of thixotropic yield stress fluids between two concentric cylinders. To account for the fluid thixotropy, we use Houška's model [Houška, Ph.D. thesis, Czech Technical University, Prague, 1981] with a single structural parameter driven by a kinetic equation. Because of the yield stress and the geometric inhomogeneity of the stress, only a part of the material in the gap may flow. Depending on the breakdown rate of the structural parameter, the constitutive relation can lead to a nonmonotonic flow curve. This nonmonotonic behavior is known to induce a discontinuity in the slope of the velocity profile within the flowing material, called shear banding. Thus, for fragile structures, a shear-banded flow characterized by a very sharp transition between the flowing and the static regions may be observed. For stronger structures, the discontinuity disappears and a smooth transition between the flowing and the static regions is observed. The consequences of the thixotropy on the linear stability of the azimuthal flow are studied in a large range of parameters. Although the thixotropy allows shear banding in the base flow, it does not modify fundamentally the linear stability of the Couette flow compared to a simple yield stress fluid. The apparent shear-thinning behavior depends on the thixotropic parameters of the fluid and the results about the onset of the Taylor vortices in shear-thinning fluids are retrieved. Nevertheless, the shear banding modifies the stratification of the viscosity in the flowing zone such that the critical conditions are mainly driven by the width of the flowing region.

International audience; We study the accuracy of the classic algorithm for inverting a complex number given by its real and imaginary parts as floating-point numbers. Our analyses are done in binary floating-point arithmetic, with an unbounded exponent range and in precision $p$; we also assume that the basic arithmetic operations ($+$, $-$, $\times$, $/$) are rounded to nearest, so that the roundoff unit is $u = 2^{-p}$. We bound the largest relative error in the computed inverse either in the componentwise or in the normwise sense. We prove the componentwise relative error bound $3u$ for the complex inversion algorithm (assuming $p \ge 4$), and we show that this bound is asymptotically optimal (as $p\to \infty$) when $p$ is even, and sharp when using one of the basic IEEE 754 binary formats with an odd precision ($p=53,113$). This componentwise bound obviously leads to the same bound $3u$ for the normwise relative error. However, we prove that the smaller bound $2.707131u$ holds (assuming $p \ge 24$) for the normwise relative error, and we illustrate the sharpness of this bound for the basic IEEE 754 binary formats ($p=24, 53, 113$) using numerical examples.

In this article, we study granular avalanches when external mechanical vibrations are applied. We identify conditions of flow arrest and compare with the ones classically observed for nonvibrating granular flows down inclines [Phys. Fluids 11, 542 (1999)PHFLE61070-663110.1063/1.869928]. We propose an empirical law to describe the thickness of the deposits with the inclination angle and the vibration intensity. The link between the surface velocity and the depth of the flow highlights a competition between gravity and vibrations induced flows. We identify two distinct regimes: (a) gravity-driven flows at large angles where vibrations do not modify dynamical properties but the deposits (scaling laws in this regime are in agreement with the literature for nonvibrating granular flows) and (b) vibrations-driven flows at small angles where no flow is possible without applied vibrations (in this last regime, the flow behavior can be properly described by a vibration induced activated process). We show, in this study, that granular flows down inclined planes can be finely tuned by external mechanical vibrations.

International audience; We study droplet formation in granular suspensions by systematically varying the volume fractions (ϕ) and particle diameters (d). For suspensions with water as the suspending liquid, we find three different regimes. For dilute suspensions (ϕ ≤ 45%), drop formation follows the predictions for inertial breakup and exhibits identical dynamics to that of pure water. The breakup is strongly asymmetrical in this case. Only for more concentrated suspensions (ϕ > 45%) does the presence of particles change the dynamics and two other regimes, a symmetrical inertial regime and a Bagnoldian regime, are uncovered. We construct and discuss a phase diagram that allows us to understand and predict the breakup behavior in granular suspensions.

International audience; We provide a detailed analysis of Kahan's algorithm for the accurate computation of the determinant of a $2 \times 2$ matrix. This algorithm requires the availability of a fused multiply-add instruction. Assuming radix-$\beta$, precision-$p$ floating-point arithmetic with $\beta$ even, $p \geq 2$, and barring overflow or underflow we show that the absolute error of Kahan's algorithm is bounded by $(\beta+1)/2$ ulps of the exact result and that the relative error is bounded by $2u$ with $u=\frac{1}{2}\beta^{1-p}$ the unit roundoff. Furthermore, we provide input values showing that i) when $\beta/2$ is odd---which holds for $2$ and $10$, the two radices that matter in practice---, the absolute error bound is optimal; ii) the relative error bound is asymptotically optimal, that is, for such input the ratio (relative error)/$2u$ has the form $1-O(\beta^{-p})$. We also give relative error bounds parametrized by the relative order of magnitude of the two products in the determinant, and we investigate whether the error bounds can be improved when adding constraints: When the products in the determinant have opposite signs, which covers the computation of a sum of squares, or when Kahan's algorithm is used for computing the discriminant of a quadratic equation.

This work reports on an experimental study of elastic turbulence in a semi-dilute wormlike micelle system made of a highly elastic betaine surfactant solution. The temporal evolution of both rheological quantities and local flow properties is monitored by combining global rheology, optical visualization, and ultrasonic velocimetry. Even at the smallest applied shear rates or shear stresses, we find that the micellar sample develops large Weissenberg (Wi) numbers, leading the flow to undergo a transition to elastic turbulence. Three-dimensional flows are indeed observed all along the flow curve, which therefore cannot be interpreted in the framework of classical shear banding. Strong fluctuations are also recorded in the rheological quantities, in the reflected light intensity, and in velocity profiles. We show that the power spectral densities (PSDs) of these fluctuations display power law behaviours with exponents ranging from −1 to −3 depending on the applied shear stress or shear rate. The exponents inferred from local velocity measurements are found to be spatially dependent, pointing to inhomogeneous turbulence. The nature of the instability and of the transition to elastic turbulence is further discussed in light of recent experimental and theoretical works on wormlike micelles and polymers.

International audience

International audience; We investigate the behavior of coarse particles confined in foam channels during drainage. Results are reported for particle velocities measured at both microscopic (single foam channel) and macroscopic (foam) scales, as a function of the average velocity of the liquid flow and of the confinement parameter that is the ratio of particle diameter to the maximal particle diameter within channel cross-section. Thanks to numerical simulations, we show that velocities measured for small values of the confinement parameter cannot be understood with the commonly assumed theory for liquid flow in foam channels. Instead, better agreement is obtained by taking into account the characteristics of the flow in the films/ channel transitional areas. Finally, values for longitudinal dispersion coefficients are reported, emphasizing effects of buoyancy on particles motions.

International audience; We investigate the capture of particles in soft porous media. Liquid foam constitutes a model system for such a study, allowing the radii of passage in the pore space to be tuned over several orders of magnitude by adjusting the liquid volume fraction. We show how particle capture is determined by the coupling of interstitial liquid flow and network deformation, and present a simple model of the capture process that shows good agreement with our experimental data.

International audience; Since the introduction of the Fused Multiply and Add (FMA) in the IEEE-754-2008 standard [6] for floating-point arithmetic, division based on Newton-Raphson's iterations becomes a viable alternative to SRT-based divisions. The Newton-Raphson iterations were already used in some architecture prior to the revision of the IEEE-754 norm. For example, Itanium architecture already used this kind of iterations [8]. Unfortunately, the proofs of the correctness of binary algorithms do not extend to the case of decimal floating-point arithmetic. In this paper, we present general methods to prove the correct rounding of division algorithms using Newton-Raphson's iterations in software, for radix 2 and radix 10 floating-point arithmetic.

International audience; We propose several algorithms and provide some related results that make it possible to implement decimal floating-point arithmetic on a processor that does not have decimal operators, using the available binary floating-point functions. In this preliminary study, we focus on round-to-nearest mode only. We show that several functions in decimal32 and decimal64 arithmetic can be implemented using binary64 and binary128 floating-point arithmetic, respectively. Specifically, we discuss the decimal square root and some transcendental functions. We also consider radix conversion algorithms.

International audience; Bubble assemblies offer the remarkable property of adjusting their packing fraction over three orders of magnitude, thus providing an interesting system for the study of liquid flows through granular matter. Although significant work has been done in several fields of research, e.g., foams, porous media, and suspensions, a complete set of data over such a wide range of porosity \eps is still lacking. In this paper, we measure the permeability of a bubbly system in the range 0.1-0.8 and we connect these new data with a recently published set obtained for foams corresponding to \eps

International audience; A forced Ostwald ripening experiment is performed on a single foam bubble. The bubble size is followed as the system is wetted with a constant liquid flow rate delivered from one of the bubble Plateau borders. Obtained ripening velocities cannot be described with a model based on a constant film thickness assumption. Within these well-controlled experimental conditions, the film thickness is measured and found to depend on the imposed liquid flow rate. It is shown that the bubble growth rate is well predicted as the films thickness evolution is explicitly introduced in the ripening model. Finally, it is suggested that existing results for the coarsening of draining foams could be understood following the approach validated on the bubble scale.

International audience; Liquid foams were recognized early to be porous materials, as liquid flowed between the gas bubbles. Drainage theories have been established, and foam permeability has been modeled from the microscopic description of the equivalent pores geometry, emphasizing similarities with their solid counterparts. But to what extent can the theoretical work devoted to the permeability of solid porous materials be useful to liquid foams? In this article, the applicability of the Carman-Kozeny model on foam is investigated. We performed measurements of the permeability of foams with nonmobile surfactants, and we show that, in introducing an equivalent specific surface area for the foam, the model accurately describes the experimental data over two orders of magnitude for the foam liquid fraction, without any additional parameters. Finally, it is shown that this model includes the previous permeability models derived for foams in the dry foams limit.

International audience; Although extensively studied in the past, drainage of aqueous foams still offers major unaddressed issues. Among them, the behaviour of foam films during drainage has great significance as the thickness of the films is known to control the Ostwald ripening in foams, which in turn impacts liquid drainage. We propose a model relating the films' behavior to the liquid flow in foam channels. It is assumed that Marangoni driven recirculation counter flows take place in the transitional region between the foam channel and the adjoining films, and the Gibbs elasticity is therefore introduced as a relevant parameter. The velocity of these counter flows is found to be proportional to the liquid velocity in the channel. The resulting channel permeability is determined and it is shown that Marangoni stresses do not contribute to rigidify the channel's surfaces, in strong contrast with the drainage of horizontal thin liquid films. New experimental data are provided and support the proposed model.

We introduce several algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. For bounded, yet very large values of the exponent, we aim at obtaining correctly rounded results in round-to-nearest mode, that is, our algorithms return the floating-point number that is nearest the exact value.

International audience; This paper deals with the drainage of liquid foams. The liquid velocity is known to be related to viscous dissipation occurring within the elements of the liquid network, i.e. the channels and the nodes. When compared together, available values for the hydrodynamic resistance of a foam node appear to span over more than one order of magnitude. To clarify this point, we propose an alternative experimental method to estimate the value of this parameter. In contrast to previous experimental work performed on the foam scale, the node resistance is not treated as a fitting parameter, but instead it is measured directly on the microscopic scale. The results allow a consistent range of values to emerge for this parameter.

Texte intégral disponible sur demande.; The article deals with mobile consumption in urban hubs. From a qualitative enquiry in four francilian sites, investing on the way users experience their entering in urban hubs, it gives a particular explanation of mobile consumption. Along with the results, it appears that consumption in spaces of mobility depends on both travellers' capabilities and locations specificities. Yet there are two obstacles to consumption that hold back the gathering of those two elements. In one hand the exchange spaces can be only understood with a cognitive process based on an abstraction : in order to move on, the traveller first has to make a mental representation of where he is and where he tends to go, locating himself on a webmap where informative symbols are the only situated references. In the other hand, locations are made up in such a way that functionality appears a more important matter than ease.; L'article traite de la consommation ambulante dans les pôles d'échanges. A partir d'une enquête qualitative dans quatre sites franciliens portant sur la manière qu'ont les usagers de s'engager dans un pôle d'échanges, il propose une lecture de la consommation ambulante. Au fil des résultats, il apparaît que la consommation dans les espaces de mobilité dépend à la fois des « capabilités » du voyageur et des attributs des lieux. La rencontre de ces deux types d'attributs butte cependant sur deux obstacles à la consommation. D'une part, les lieux d'échanges ne peuvent être compris que par le biais de processus cognitifs faisant appel à l'abstraction : pour se déplacer, le voyageur sort mentalement du lieu et se déplace dans le plan de réseau dont les symboles signalétiques sont les seuls référents situés. D'autre part, les lieux sont aménagés de façon à ce que la fonctionnalité prime sur l'aisance.

The transport properties of a suspension of motile bacteria under flow are a fundamental scientific issue in order to understand the colonisation of new environments by microorganisms. Numerous studies report the singular behaviour of these active suspensions in flow. Accumulation at the walls, collective motion, modification of the rheological behaviour are all phenomena that reveal the richness of these systems. Nevertheless, many questions remain. In this thesis, we present the effect of a flow on the transport of a suspension of motile Escherichia coli bacteria in confined geometries. Experiments were carried out in a Hele-Shaw cell to understand the influence of flow and confinement Peclet numbers on the transport of the suspension in a Poiseuille flow. The swimming properties of E. coli were characterised in a fluid at rest using two non-intrusive optical techniques: tracking and differential dynamic microscopy. In flow, these properties are strongly dependent on shear. Rheotaxis effect has been pointed out at the vicinity of a surface and favours upstream swimming; upstream migration also found in the bulk. We also show that confinement of the suspension influences the thickness of the boundary layer and, with the intensity of the flow, modifie the distribution of bacteria through the Hele-Shaw cell., Les propriétés de transport d'une suspension de bactéries motiles sous écoulement présentent un enjeu scientifique fondamental dans la compréhension de la colonisation de nouveaux milieux par ces microorganismes. De nombreuses études font part du comportement singulier de ces suspensions actives en écoulement. L'accumulation aux parois, les comportements collectifs, la modification du comportement rhéologique sont d'autant de phénomènes qui révèlent la richesse de ces systèmes. Malgré tout, de nombreuses questions subsistent. Dans ce travail de thèse, nous présentons l'effet d'un écoulement sur le transport d'une suspension de bactéries Escherichia coli motiles en milieu confiné. Des expériences ont été menées en cellule de Hele-Shaw pour comprendre l'influence du Péclet hydrodynamique et du Péclet de confinement sur le transport de la suspension en écoulement de Poiseuille. Les propriétés de nage d'E. coli ont été caractérisées dans un fluide à l'équilibre par deux techniques optiques de mesures non-intrusives : le tracking et la microscopie dynamique différentielle. En écoulement, ces propriétés se voient être fortement modifiées et dépendantes du cisaillement. L'effet de rhéotaxie a été mis en évidence et favorise la migration bactérienne à contre-courant aux parois ; migration retrouvée également loin des surfaces. Nous montrons également que le confinement de la suspension influe sur l'épaisseur de la couche limite qui, couplé à l'intensité de l'écoulement, modifient la distribution en bactéries dans la cellule de Hele-Shaw.

Background: Postpartum haemorrhage (PPH) may be complicated by a coagulopathy reflecting its severity. Our main goal is to study the correlation between TEG® parameters and standard coagulation assays. We also aim at analysing the performance of TEG® to detect a coagulopathy and to predict a severe PPH. Methods: In a single-center retrospective study, we included patients with PPH that were treated with sulprostone. During the first 24h, besides the standard coagulation assays (PT, APTT, fibrinogen according to the Clauss method (FibC), platelets), we performed a Kaolin and Functional Fibrinogen TEG® test. Results : We included 62 patients and performed 90 TEG® tests. There was a moderate to high correlation between the FibC values and FLEV/MRTGG-F/MA-K/MRTGG-F values and between the platelets count and FLEV/MA-K/MRTGG-K values (r=0.5-0.8, p