Data Assimilation for hyperbolic conservation laws. A Luenberger observer approach based on a kinetic description

Developing robust data assimilation methods for hyperbolic conservation laws is a challenging subject. Those PDEs indeed show no dissipation effects and the input of additional information in the model equations may introduce errors that propagate and create shocks. We propose a new approach based on the kinetic description of the conservation law. A kinetic equation is a first order partial differential equation in which the advection velocity is a free variable. In certain cases, it is possible to prove that the nonlinear conservation law is equivalent to a linear kinetic equation. Hence, data assimilation is carried out at the kinetic level, using a Luenberger observer also known as the nudging strategy in data assimilation. Assimilation then resumes to the handling of a BGK type equation. The advantage of this framework is that we deal with a single "linear" equation instead of a nonlinear system and it is easy to recover the macroscopic variables. The study is divided into several steps and essentially based on functional analysis techniques. First we prove the convergence of the model towards the data in case of complete observations in space and time. Second, we analyze the case of partial and noisy observations. To conclude, we validate our method with numerical results on Burgers equation and emphasize the advantages of this method with the more complex Saint-Venant system

A 2D model for hydrodynamics and biology coupling applied to algae growth simulations

Cultivating oleaginous microalgae in specific culturing devices such as raceways is seen as a future way to produce biofuel. The complexity of this process coupling non linear biological activity to hydrodynamics makes the optimization problem very delicate. The large amount of parameters to be taken into account paves the way for a useful mathematical modeling. Due to the heterogeneity of raceways along the depth dimension regarding temperature, light intensity or nutrients availability, we adopt a multilayer approach for hydrodynamics and biology. For free surface hydrodynamics, we use a multilayer Saint-Venant model that allows mass exchanges, forced by a simplified representation of the paddlewheel. Then, starting from an improved Droop model that includes light effect on algae growth, we derive a similar multilayer system for the biological part. A kinetic interpretation of the whole system results in an efficient numerical scheme. We show through numerical simulations in two dimensions that our approach is capable of discriminating between situations of mixed water or calm and heterogeneous pond. Moreover, we exhibit that a posteriori treatment of our velocity fields can provide lagrangian trajectories which are of great interest to assess the actual light pattern perceived by the algal cells and therefore understand its impact on the photosynthesis process.Comment: 27 pages, 11 figure

Accuracy metrics for judging time scale algorithms

Time scales have been constructed in different ways to meet the many demands placed upon them for time accuracy, frequency accuracy, long-term stability, and robustness. Usually, no single time scale is optimum for all purposes. In the context of the impending availability of high-accuracy intermittently-operated cesium fountains, we reconsider the question of evaluating the accuracy of time scales which use an algorithm to span interruptions of the primary standard. We consider a broad class of calibration algorithms that can be evaluated and compared quantitatively for their accuracy in the presence of frequency drift and a full noise model (a mixture of white PM, flicker PM, white FM, flicker FM, and random walk FM noise). We present the analytic techniques for computing the standard uncertainty for the full noise model and this class of calibration algorithms. The simplest algorithm is evaluated to find the average-frequency uncertainty arising from the noise of the cesium fountain's local oscillator and from the noise of a hydrogen maser transfer-standard. This algorithm and known noise sources are shown to permit interlaboratory frequency transfer with a standard uncertainty of less than 10(exp -15) for periods of 30-100 days

Développement d’une méthode de dosage automatisé du méthotrexate dans le plasma humain par couplage direct à la chromatographie liquide de l’extraction sur phase solide à empreintes moléculaires

Peer reviewe

Analytical solutions for the free surface hydrostatic Euler equations

International audienceIn this paper we propose a large set of analytical solutions (FRESH-ASSESS) for the hydrostatic incompressible Euler system in 2d and 3d. These solutions mainly concern free surface flows but partially free surface flows are also considered. These analytical solutions can be especially useful for the validation of numerical schemes

Plant Carbohydrate Scavenging through TonB-Dependent Receptors: A Feature Shared by Phytopathogenic and Aquatic Bacteria

TonB-dependent receptors (TBDRs) are outer membrane proteins mainly known for the active transport of iron siderophore complexes in Gram-negative bacteria. Analysis of the genome of the phytopathogenic bacterium Xanthomonas campestris pv. campestris (Xcc), predicts 72 TBDRs. Such an overrepresentation is common in Xanthomonas species but is limited to only a small number of bacteria. Here, we show that one Xcc TBDR transports sucrose with a very high affinity, suggesting that it might be a sucrose scavenger. This TBDR acts with an inner membrane transporter, an amylosucrase and a regulator to utilize sucrose, thus defining a new type of carbohydrate utilization locus, named CUT locus, involving a TBDR for the transport of substrate across the outer membrane. This sucrose CUT locus is required for full pathogenicity on Arabidopsis, showing its importance for the adaptation to host plants. A systematic analysis of Xcc TBDR genes and a genome context survey suggested that several Xcc TBDRs belong to other CUT loci involved in the utilization of various plant carbohydrates. Interestingly, several Xcc TBDRs and CUT loci are conserved in aquatic bacteria such as Caulobacter crescentus, Colwellia psychrerythraea, Saccharophagus degradans, Shewanella spp., Sphingomonas spp. or Pseudoalteromonas spp., which share the ability to degrade a wide variety of complex carbohydrates and display TBDR overrepresentation. We therefore propose that TBDR overrepresentation and the presence of CUT loci designate the ability to scavenge carbohydrates. Thus CUT loci, which seem to participate to the adaptation of phytopathogenic bacteria to their host plants, might also play a very important role in the biogeochemical cycling of plant-derived nutrients in marine environments. Moreover, the TBDRs and CUT loci identified in this study are clearly different from those characterized in the human gut symbiont Bacteroides thetaiotaomicron, which allow glycan foraging, suggesting a convergent evolution of TBDRs in Proteobacteria and Bacteroidetes