Laboratoire de Mathématiques et de leurs Applications

umerical simulation in fluid mechanics (or CFD) has become one of the basic tools used by engineers. In this course, we will study the methods often used in industrial codes and we will give the most active research strategies which will be the future standards. This course does not aim at teaching the practical use of a CFD code, rather at providing the key knowledge to understand what the codes contain and how to use them in a wise manner. Prerequisites: For this course, it is necessary to have attended a course of introduction to turbulence Content: - Introduction to CFD (Computational Fluid Dynamics) - Standard method used in industrial projects: RANS modelling (Reynolds-averaged Navier-Stokes modelling) - Heat transfer modelling

A refined approach to residual-based error control in finite element (FE) discretizations is presented. The conventional strategies for adaptive mesh refinement in FE methods are mostly based on a posteriori error estimates in the global energy or L"2-norm involving local residuals of the computed solution. The mesh refinement process then aims at equilibrating these local error indicators. Such estimates reflect the approximation properties of the finite element space by local interpolation constants while the stability properties of the continuous model enter through a global stability constant, which may be known explicitly in simple cases. Meshes generated on the basis of such global error estimates may not be appropriate in cases of strongly varying coefficients and for the computation of local quantities as, for example, point values or contour integrals. More detailed information about the mechanism of error propagation can be obtained by employing duality arguments specially adapted to the quantity of interest. This results in a posteriori error estimates in which the local information derived from the dual solution is used in the form of weights multiplied by local residuals. On the basis such estimates, a feed-back process in which the weights are numerically computed with increasing accuracy leads to almost optimal meshes for various kinds of error functionals. This approach is developed here for a simple model problem, namely the Poisson equation in two dimensions, in order to emphasize its basic features. However, the underlying concept is rather universal and has, on a heuristic basis, already been successfully applied to much more complex problems in structural and fluid mechanics as well as in astrophysics. (orig.)

In this paper, we analyse a family of stationary nonlinear equations with $p\& q$- Laplacian $-\Delta_p u -\Delta_q u=\lambda c(x,u)$ which have a wide spectrum of applications in many areas of science. We introduce a new type of variational principles corresponding to this family of equations. Using this formalism, we exhibit intervals for the scalar parameter $\lambda$ where there exist positive solutions of the considered problems. Furthermore, we prove, in another interval, the nonexistence of nontrivial solutions. These results are different from those of existence and nonexistence for stationary equations with single Laplacian.

International audience

Glycoproteomics is a powerful yet analytically challenging research tool. Software packages aiding the interpretation of complex glycopeptide tandem mass spectra have appeared, but their relative performance remains untested. Conducted through the HUPO Human Glycoproteomics Initiative, this community study, comprising both developers and users of glycoproteomics software, evaluates solutions for system-wide glycopeptide analysis. The same mass spectrometrybased glycoproteomics datasets from human serum were shared with participants and the relative team performance for N- and O-glycopeptide data analysis was comprehensively established by orthogonal performance tests. Although the results were variable, several high-performance glycoproteomics informatics strategies were identified. Deep analysis of the data revealed key performance-associated search parameters and led to recommendations for improved 'high-coverage' and 'high-accuracy' glycoproteomics search solutions. This study concludes that diverse software packages for comprehensive glycopeptide data analysis exist, points to several high-performance search strategies and specifies key variables that will guide future software developments and assist informatics decision-making in glycoproteomics.

Abstract The impacts of enhanced nitrogen (N) deposition on the global forest carbon (C) sink and other ecosystem services may depend on whether N is deposited in reduced (mainly as ammonium) or oxidized forms (mainly as nitrate) and the subsequent fate of each. However, the fates of the two key reactive N forms and their contributions to forest C sinks are unclear. Here, we analyze results from 13 ecosystem-scale paired 15 N-labelling experiments in temperate, subtropical, and tropical forests. Results show that total ecosystem N retention is similar for ammonium and nitrate, but plants take up more labelled nitrate ( $${20}_{15}^{25}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mn>20</mml:mn></mml:mrow><mml:mrow><mml:mn>15</mml:mn></mml:mrow><mml:mrow><mml:mn>25</mml:mn></mml:mrow></mml:msubsup></mml:math> %) ( $${{{{{{\rm{mean}}}}}}}_{{{{{{\rm{minimum}}}}}}}^{{{{{{\rm{maximum}}}}}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>mean</mml:mi></mml:mrow><mml:mrow><mml:mi>minimum</mml:mi></mml:mrow><mml:mrow><mml:mi>maximum</mml:mi></mml:mrow></mml:msubsup></mml:math> ) than ammonium ( $${12}_{8}^{16}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mn>12</mml:mn></mml:mrow><mml:mrow><mml:mn>8</mml:mn></mml:mrow><mml:mrow><mml:mn>16</mml:mn></mml:mrow></mml:msubsup></mml:math> %) while soils retain more ammonium ( $${57}_{49}^{65}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mn>57</mml:mn></mml:mrow><mml:mrow><mml:mn>49</mml:mn></mml:mrow><mml:mrow><mml:mn>65</mml:mn></mml:mrow></mml:msubsup></mml:math> %) than nitrate ( $${46}_{32}^{59}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mn>46</mml:mn></mml:mrow><mml:mrow><mml:mn>32</mml:mn></mml:mrow><mml:mrow><mml:mn>59</mml:mn></mml:mrow></mml:msubsup></mml:math> %). We estimate that the N deposition-induced C sink in forests in the 2010s is $${0.72}_{0.49}^{0.96}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mn>0.72</mml:mn></mml:mrow><mml:mrow><mml:mn>0.49</mml:mn></mml:mrow><mml:mrow><mml:mn>0.96</mml:mn></mml:mrow></mml:msubsup></mml:math> Pg C yr −1 , higher than previous estimates because of a larger role for oxidized N and greater rates of global N deposition.

We present and analyze a new a posteriori error estimator for lowest order conforming finite elements. It is based on Raviart--Thomas finite elements and can be obtained locally by a postprocessing technique involving for each vertex a local subproblem associated with a dual mesh. Under certain regularity assumptions on the right-hand side, we obtain an error estimator where the constant in the upper bound for the true error tends to one. Replacing the conforming finite element solution by a postprocessed one, the error estimator is asymptotically exact. The local equivalence between our estimator and the standard residual-based error estimator is established. Numerical results illustrate the performance of the error estimator.

International audience

INV

It is often reasonable to assume that the dependence structure of a bivariate continuous distribution belongs to the class of extreme-value copulas. The latter are characterized by their Pickands dependence function. In this paper, a procedure is proposed for testing whether this function belongs to a given parametric family. The test is based on a Cramér–von Mises statistic measuring the distance between an estimate of the parametric Pickands dependence function and either one of two nonparametric estimators thereof studied by Genest and Segers [Ann. Statist. 37 (2009) 2990–3022]. As the limiting distribution of the test statistic depends on unknown parameters, it must be estimated via a parametric bootstrap procedure, the validity of which is established. Monte Carlo simulations are used to assess the power of the test and an extension to dependence structures that are left-tail decreasing in both variables is considered.

Let $A:\mathcal{D}(A)\to\mathcal{X}$ be the generator of an analytic semigroup and $B:\mathcal{V}\to[\mathcal{D}(A^*)]'$ a relatively bounded control operator. In this paper, we consider the stabilization of the system $y'=Ay+Bu$, where u is the linear combination of a family $(v_1,\ldots,v_K)$. Our main result shows that if $(A^*,B^*)$ satisfies a unique continuation property and if K is greater than or equal to the maximum of the geometric multiplicities of the unstable modes of A, then the system is generically stabilizable with respect to the family $(v_1,\ldots,v_K)$. With the same functional framework, we also prove the stabilizability of a class of nonlinear systems when using feedback or dynamical controllers. We apply these results to stabilize the Navier–Stokes equations in two and three dimensions by using boundary controls.

In the present work, structural property of polycrystalline sample Ba_0.97Bi_0.02Ti_0.9Zr_0.05Nb_0.04O₃ (BBTZN) prepared by a molten-salt method were investigated.

France is the first pesticide-consuming country in Europe. Glyphosate is the most used pesticide worldwide and glyphosate is detected in the general population of industrialized countries, with higher levels found in farmers and children. Little data was available concerning exposure in France. Our objective was to determine glyphosate levels in the French general population and to search for an association with seasons, biological features, lifestyle status, dietary habits, and occupational exposure. This study includes 6848 participants recruited between 2018 and 2020. Associated data include age, gender, location, employment status, and dietary information. Glyphosate was quantified by a single laboratory in first-void urine samples using ELISA. Our results support a general contamination of the French population, with glyphosate quantifiable in 99.8% of urine samples with a mean of 1.19 ng/ml + / - 0.84 after adjustment to body mass index (BMI). We confirm higher glyphosate levels in men and children. Our results support glyphosate contamination through food and water intake, as lower glyphosate levels are associated with dominant organic food intake and filtered water. Higher occupational exposure is confirmed in farmers and farmers working in wine-growing environment. Thus, our present results show a general contamination of the French population with glyphosate, and further contribute to the description of a widespread contamination in industrialized countries.

Technological advances in molecular biology over the past decade have given rise to high dimensional and complex datasets offering the possibility to investigate biological associations between a range of genomic features and complex phenotypes. The analysis of this novel type of data generated unprecedented computational challenges which ultimately led to the definition and implementation of computationally efficient statistical models that were able to scale to genome-wide data, including Bayesian variable selection approaches. While extensive methodological work has been carried out in this area, only few methods capable of handling hundreds of thousands of predictors were implemented and distributed. Among these we recently proposed GUESS, a computationally optimised algorithm making use of graphics processing unit capabilities, which can accommodate multiple outcomes. In this paper we propose R2GUESS, an R package wrapping the original C++ source code. In addition to providing a user-friendly interface of the original code automating its parametrisation, and data handling, R2GUESS also incorporates many features to explore the data, to extend statistical inferences from the native algorithm (e.g., effect size estimation, significance assessment), and to visualize outputs from the algorithm. We first detail the model and its parametrisation, and describe in details its optimised implementation. Based on two examples we finally illustrate its statistical performances and flexibility.

Anomaly detection (AD) in high-volume environmental data requires one to tackle a series of challenges associated with the typical low frequency of anomalous events, the broad-range of possible anomaly types, and local nonstationary environmental conditions, suggesting the need for flexible statistical methods that are able to cope with unbalanced high-volume data problems. Here, we aimed to detect anomalies caused by technical errors in water-quality (turbidity and conductivity) data collected by automated in situ sensors deployed in contrasting riverine and estuarine environments. We first applied a range of artificial neural networks that differed in both learning method and hyperparameter values, then calibrated models using a Bayesian multiobjective optimization procedure, and selected and evaluated the "best" model for each water-quality variable, environment, and anomaly type. We found that semi-supervised classification was better able to detect sudden spikes, sudden shifts, and small sudden spikes, whereas supervised classification had higher accuracy for predicting long-term anomalies associated with drifts and periods of otherwise unexplained high variability.

The development of a three-dimensional viscous incompressible flow generated behind an infinitely long circular cylinder, impulsively started into rectilinear motion and rotationally oscillating, is studied computationally. The numerical scheme, an hybrid vortex method, is used to integrate the velocity–vorticity formulation of the Navier–Stokes equations. The Reynolds number considered is $\Rey\,{=}\,400$ , which is moderate though beyond the critical values $\Rey_2\,{\simeq}\,190$ and $\Rey_2'\,{\simeq}\,260$ for which the flow becomes spontaneously three-dimensional. The numerical method is explained and its main points are developed. This scheme is then applied to solve some two-dimensional problems, both in order to validate the method and to compute a nominal two-dimensional flow, required to measure the impact of three-dimensionality. The three-dimensional flow past a steady cylinder is also compared to benchmark simulations. Once the flow has become fully three-dimensional, beyond the transient regime and saturation of instabilities, the cylinder begins a rotary oscillation around its axis. Two kinds of rotations are considered: constant amplitude and several frequencies, and constant frequency and various amplitudes. When amplitude and frequency are high enough, the whole flow comes back to its two-dimensional state. This result gives a justification for two-dimensional computations in the literature related to rotating cylinders. For the first super-harmonic frequency of the flow, a parametric study is performed in order to find the impact of the amplitude on the topology of the flow. A bifurcation is clearly identified. Finally, the mechanisms involved in the return to a two-dimensional state are explained: the interaction between transverse instabilities and von Kármán streets is quantified by means of a correlation analysis.

International audience

Deciphering the biotic and abiotic factors that control microbial community structure over time and along an environmental gradient is a pivotal question in microbial ecology. Carnoulès mine (France), which is characterized by acid waters and very high concentrations of arsenic, iron, and sulfate, provides an excellent opportunity to study these factors along the pollution gradient of Reigous Creek. To this end, biodiversity and spatiotemporal distribution of bacterial communities were characterized using T-RFLP fingerprinting and high-throughput sequencing. Patterns of spatial and temporal variations in bacterial community composition linked to changes in the physicochemical conditions suggested that species-sorting processes were at work in the acid mine drainage. Arsenic, temperature, and sulfate appeared to be the most important factors that drove the composition of bacterial communities along this continuum. Time series investigation along the pollution gradient also highlighted habitat specialization for some major members of the community (Acidithiobacillus and Thiomonas), dispersal for Acidithiobacillus, and evidence of extinction/re-thriving processes for Gallionella. Finally, pyrosequencing revealed a broader phylogenetic range of taxa than previous clone library-based diversity. Overall, our findings suggest that in addition to environmental filtering processes, additional forces (dispersal, birth/death events) could operate in AMD community.

Abstract Discrete triangular distributions are introduced, in order to serve as kernels in the non-parametric estimation for probability mass function. They are locally symmetric around every point of estimation. Their variances depend on the smoothing bandwidth and establish a bridge between Dirac and discrete uniform distributions. The boundary bias related to the discrete triangular kernel estimator is solved through a modification of the kernel near the boundary. The mean integrated squared errors and then the optimal bandwidth are investigated. We also study the adequate bandwidth for excess zeros. The performance of the discrete triangular kernel estimator is illustrated using simulated count data. An application to count data from football is described and compared with a binomial kernel estimator.

In this paper, we will show that, for elliptic problems in heterogeneous media, there exists a local (generalized) finite element basis (AL basis) consisting of $O\big( \big( \log\frac{1}{H}\big) ^{d+1}\big)$ basis functions per nodal point such that the convergence rates of the classical finite element method for Poisson-type problems are preserved. Here H denotes the mesh width of the finite element mesh and d is the spatial dimension. We provide several numerical examples beyond our theory, where even $O(1)$ basis functions per nodal point are sufficient to preserve the convergence rates.