Stabilization of a supercritical hydrogen / oxygen flame behind a splitter plate

The numerical simulation of fluid dynamics and combustion in cryogenic rocket engines is addressed in this paper, with the intent to elucidate flame stabilization mechanisms. A model configuration is devised to allow a fully resolved simulation, both for the dynamics and the flame structure: a two-dimensional splitter plate represents the lip of an injector and the operating point is typical of a real engine. The non-reacting flow field is first scrutinized to evaluate the impact of the large density gradients between the fuel (hydrogen) and oxidizer (oxygen) streams. It is found that the turbulence generated by the splitter is very intense and strongly distorts the high-density-gradient front at both small and large scales. Under reacting conditions, the flame stabilizes right at the lip of the injector, which is a common feature of hydrogen / oxygen flames under these conditions. A particularly complex flame structure is evidenced at the anchoring point, with turbulent transport playing an important role

Degree and birationality of multi‐graded rational maps

We give formulas and effective sharp bounds for the degree of multi-graded rational maps and provide some effective and computable criteria for birationality in terms of their algebraic and geometric properties. We also extend the Jacobian dual criterion to the multi-graded setting. Our approach is based on the study of blow-up algebras, including syzygies, of the ideal generated by the defining polynomials of the rational map. A key ingredient is a new algebra that we call thesaturated special fiber ring, which turns out to be a fundamental tool to analyze the degree of a rational map. We also provide a very effective birationality criterion and a complete description of the equations of the associated Rees algebra of a particular class of plane rational maps

Degree and birationality of multi-graded rational maps

We give formulas and effective sharp bounds for the degree of multi-graded rational maps and provide some effective and computable criteria for birationality in terms of their algebraic and geometric properties. We also extend the Jacobian dual criterion to the multi-graded setting. Our approach is based on the study of blow-up algebras, including syzygies, of the ideal generated by the defining polynomials of the rational map. A key ingredient is a new algebra that we call the saturated special fiber ring, which turns out to be a fundamental tool to analyze the degree of a rational map. We also provide a very effective birationality criterion and a complete description of the equations of the associated Rees algebra of a particular class of plane rational maps

Understanding nitrogen transfer dynamics in a small agricultural catchment: Comparison of a distributed (TNT2) and a semi distributed (SWAT) modeling approaches

The coupling of an hydrological and a crop model is an efficient approach to study the impact of the interactions between agricultural practices and catchment physical characteristics on stream water quality. We analyzed the consequences of using different modeling approaches of the processes controlling the nitrogen (N) dynamics in a small agricultural catchment monitored for 15 years. Two agro-hydrological models were applied: the fully distributed model TNT2 and the semi-distributed SWAT model. Using the same input dataset, the calibration process aimed at reproducing the same annual water and N balance in both models, to compare the spatial and temporal variability of the main N processes. The models simulated different seasonal cycles for soil N. The main processes involved were N mineralization and denitrification. TNT2 simulated marked seasonal variations with a net increase of mineralization in autumn, after a transient immobilization phase due to the burying of the straw with low C:N ratio. SWAT predicted a steady humus mineralization with an increase when straws are buried and a decrease afterwards. Denitrification was mainly occuring in autumn in TNT2 because of the dynamics of N availability in soil and of the climatic and hydrological conditions. SWAT predicts denitrification in winter, when mineral N is available in soil layers. The spatial distribution of these two processes was different as well: less denitrification in bottom land and close to ditches in TNT2, as a result of N transfer dynamics. Both models simulate correctly global trend and inter-annual variability of N losses in small agricultural catchment when a sufficient amount data is available for calibration. However, N processes and their spatial interactions are simulated very differently, in particular soil mineralization and denitrification. The use of such tools for prediction must be considered with care, unless a proper calibration and validation of the different N processes is carried out

A simultaneous spatial autoregressive model for compositional data

In an election, the vote shares by party on a given subdivision of a territory form a vector with positive components adding up to 1 called a composition. Using a conventional multiple linear regression model to explain this vector by some factors is not adapted for at least two reasons. The first one is the existence of the constraint on the sum of the components and the second one is the assumption of statistical independence across territorial units which may be questionable due to potential spatial autocorrelation. We develop a simultaneous spatial autoregressive model for compositional data which allows for both spatial correlation and correlations across equations. We propose an estimation method based on two-stage and three-stage least squares. We illustrate the method with simulations and with a data set from the 2015 French departmental election

A simultaneous spatial autoregressive model for compositional data

In an election, the vote shares by party on a given subdivision of a territory form a vector with positive components adding up to 1 called a composition. Using a conventional multiple linear regression model to explain this vector by some factors is not adapted for at least two reasons. The first one is the existence of the constraint on the sum of the components and the second one is the assumption of statistical independence across territorial units which may be questionable due to potential spatial autocorrelation. We develop a simultaneous spatial autoregressive model for compositional data which allows for both spatial correlation and correlations across equations. We propose an estimation method based on two-stage and three-stage least squares. We illustrate the method with simulations and with a data set from the 2015 French departmental election

Les indicateurs de la fertilité azotée des terres en région tropicale semi-aride

Cette synthèse résume les principaux acquis de la recherche agronomique concernant l'identification et l'utilisation des indicateurs de fertilité azotée des sols. Les différentes approches sont décrites et séparées en deux types : les démarches explicatives, c'est-à-dire fondées sur la compréhension et la quantification des mécanismes déterminant le cycle de l'azote dans les agrosystèmes, et corrélatives, fondées sur la recherche des relations statistiques entre la fertilité et des indicateurs variés. Les démarches et leurs résultats sont analysés et discutés. A partir de méthodes de mesure chimiques, physiques, biologiques ou isotopiques, la première s'attache à quantifier l'aptitude à la minéralisation de compartiments fonctionnels de la matière organique. La seconde s'appuie sur les essais agronomiques au champ et met en évidence des relations statistiques avec des valeurs issues d'analyses chimiques du végétal ou du sol. Leur complémentarité doit être exploitée et leur modélisation adaptée aux sols des régions semi-aride