Steady state solutions for a lubrication two-fluid flow

International audienceIn this paper, we describe possible solutions for a stationary flow of two superposed fluids between two close surfaces in relative motion. Physically, this study is within the lubrication framework, in which it is of interest to predict the relative positions of the lubricant and the air in the device. Mathematically, we observe that this problem corresponds to finding the interface between the two fluids, and we prove that it is equivalent to solve some polynomial equation. We solve this equation using an original method of polynomial resolution. First, we check that our results are consistent with previous work. Next, we use this solution to answer some physically relevant questions related to the lubrication setting. For instance, we obtain theoretical and numerical results enabling to predict the apparition of a full film with respect to physical parameters (fluxes, shear velocity, . . . ). In particular, we present a figure giving the number of stationary solutions depending on the physical parameters. Moreover, in the last part, we give some indications for a better understanding of the multi-fluid case

The Maxwell-Stefan diffusion limit for a kinetic model of mixtures

International audienceWe consider the non-reactive fully elastic Boltzmann equation for mixtures. We deduce that, under the standard diffusive scaling, its limit for vanishing Mach and Knudsen numbers is the Maxwell-Stefan model for a multicomponent gaseous mixture

Diffusion models for mixtures using a stiff dissipative hyperbolic formalism

International audienceIn this article, we are interested in a system of fluid equations for mixtures with a stiff relaxation term of Maxwell-Stefan diffusion type. We use the formalism developed by Chen, Levermore, Liu in [4] to obtain a limit system of Fick type where the species velocities tend to align to a bulk velocity when the relaxation parameter remains small

Viscoelastic fluids in thin domains: a mathematical proof

The present paper deals with non Newtonian viscoelastic flows of Oldroyd-B tye in thin domains. Such geometries arise for example in the context of lubrication. More precisely, we justify rigorously the asymptotic model obtained heuristically by proving the mathematical convergence of the Navier-Stokes/Oldroyd-B sytem towards the asymptotic model

Multivariate Generalized Gaussian Distribution: Convexity and Graphical Models

We consider covariance estimation in the multivariate generalized Gaussian distribution (MGGD) and elliptically symmetric (ES) distribution. The maximum likelihood optimization associated with this problem is non-convex, yet it has been proved that its global solution can be often computed via simple fixed point iterations. Our first contribution is a new analysis of this likelihood based on geodesic convexity that requires weaker assumptions. Our second contribution is a generalized framework for structured covariance estimation under sparsity constraints. We show that the optimizations can be formulated as convex minimization as long the MGGD shape parameter is larger than half and the sparsity pattern is chordal. These include, for example, maximum likelihood estimation of banded inverse covariances in multivariate Laplace distributions, which are associated with time varying autoregressive processes

Mycotoxins in cereals of 2013 harvest in Croatia

Žitarice na polju i tijekom skladištenja izložene su različitim vrstama plijesni, što za posljedicu može imati kontaminaciju mikotoksinima. Najčešća je kontaminacija hrane i krmiva aflatoksinima, deoksinivalenolom, fumonizinima, ohratoksinom A i zearalenonom u različitim koncentracijama ovisno o okolišnim uvjetima na polju i u skladištu. Cilj ovog rada bio je odrediti pojavnost mikotoksina u hrvatskim žitaricama žetve 2013. U tu svrhu prikupljena su 24 reprezentativna uzorka žitarica (pšenice, ječma i zobi) namijenjena ljudskoj prehrani. Za određivanje mikotoksina korištena je multimikotoksinska metoda tekućinske kromatografije – tandemske masene spektrometrije (LC-MS/MS). Rezultati su utvrdili prisutnost Fusarium mikotoksina, a u manjim koncentracijama detektirani su i mikotoksini rodova Alternaria, Penicillium, Aspergillus, ergot alkaloidi te mikotoksini drugih rodova plijesni. Relativno niske prosječne razine kontaminacije dobivene u ovom radu bi se mogle objasniti toplim i suhim vremenom u periodu cvatnje i žetve žitarica.Cereals are naturally exposed to different species of fungi both in the field and during storage, which may result in mycotoxin contamination of cereal grains. Most commonly, food and feeds are contaminated with aflatoxins, deoksynivalenol, fumonisins, ochratoxin A, and zearalenone in a wide range of concentrations, dependent on environmental and storage conditions. The aim of this study was to determine the occurrence of mycotoxins in cereals from 2013 harvest in Croatia. Twenty-four representative samples of cereals (wheat, barley and oats) for human consumption were collected for this purpose. The mycotoxins were determined using a multimycotoxin method by liquid chromatography tandem mass spectrometry (LC-MS/MS). The results indicated the presence of Fusarium mycotoxins although lower concentrations of Alternaria, Penicillium, Aspergillus, ergot alkaloids and other fungal metabolites were detected as well. Relatively low average contamination levels observed in this study could be associated with a warm and dry weather during flowering and harvest periods

Venus wind map at cloud top level with the MTR/THEMIS visible spectrometer. I. Instrumental performance and first results

Solar light gets scattered at cloud top level in Venus' atmosphere, in the visible range, which corresponds to the altitude of 67 km. We present Doppler velocity measurements performed with the high resolution spectrometer MTR of the Solar telescope THEMIS (Teide Observatory, Canary Island) on the sodium D2 solar line (5890 \AA). Observations lasted only 49 min because of cloudy weather. However, we could assess the instrumental velocity sensitivity, 31 m/s per pixel of 1 arcsec, and give a value of the amplitude of zonal wind at equator at 151 +/- 16 m/s.Comment: 17 pages, 12 figure

Energy method for the Boltzmann equation of monatomic gaseous mixtures

In this paper, we present an energy method for the system of Boltzmann equations in the multicomponent mixture case, based on a micro-macro decomposition. More precisely, the perturbation of a solution to the Bolzmann equation around a global equilibrium is decomposed into the sum of a macroscopic and a microscopic part, for which we obtain a priori estimates at both lower and higher orders. These estimates are obtained under a suitable smallness assumption. The assumption can be justified a posteriori in the higher-order case, leading to the closure of the corresponding estimate

Study of a low Mach nuclear core model for two-phase flows with phase transition I: stiffened gas law

International audienceIn this paper, we are interested in modelling the flow of the coolant (water) in a nuclear reactor core. To this end, we use a monodimensional low Mach number model coupled to the stiffened gas law. We take into account potential phase transitions by a single equation of state which describes both pure and mixture phases. In some particular cases, we give analytical steady and/or unsteady solutions which provide qualitative information about the flow. In the second part of the paper, we introduce two variants of a numerical scheme based on the method of characteristics to simulate this model. We study and verify numerically the properties of these schemes. We finally present numerical simulations of a loss of flow accident (LOFA) induced by a coolant pump trip event