HAL-Ecole des Ponts ParisTech
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A canonical tree decomposition for order types, and some applications
No full textInternational audienceWe introduce and study a notion of decomposition of planar point sets (or rather of their chirotopes) as trees decorated by smaller chirotopes. This decomposition is based on the concept of mutually avoiding sets (which we rephrase as \emph{modules}), and adapts in some sense the modular decomposition of graphs in the world of chirotopes. The associated tree always exists and is unique up to some appropriate constraints. We also show how to compute the number of triangulations of a chirotope efficiently, starting from its tree and the (weighted) numbers of triangulations of its parts
How to construct decay rates for kinetic Fokker--Planck equations?
No full textInternational audienceWe study time averages for the norm of the solution to kinetic Fokker--Planck equations associated with general Hamiltonians. We provide explicit and constructive decay estimates, allowing fat-tail, sub-exponential and (super-)exponential local equilibria, which also include the classic Maxwellian case. The evolution is subject to a transport operator induced by an external space-confining force. The key step in our estimates is a modified Poincaré inequality, obtained via a Lions-Poincaré inequality and an averaging lemma
Optimizing the diffusion coefficient of overdamped Langevin dynamics
No full textInternational audienceOverdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian inference. By varying the diffusion coefficient, there are in fact infinitely many overdamped Langevin dynamics which are reversible with respect to the target probability measure at hand. This suggests to optimize the diffusion coefficient in order to increase the convergence rate of the dynamics, as measured by the spectral gap of the generator associated with the stochastic differential equation. We analytically study this problem here, obtaining in particular necessary conditions on the optimal diffusion coefficient. We also derive an explicit expression of the optimal diffusion in some appropriate homogenized limit. Numerical results, both relying on discretizations of the spectral gap problem and Monte Carlo simulations of the stochastic dynamics, demonstrate the increased quality of the sampling arising from an appropriate choice of the diffusion coefficient
Global climate modelling of Saturn’s atmosphere, Part V: Large-scale vortices
No full textInternational audienceThis paper presents an analysis of large-scale vortices in the atmospheres of gas giants, focusing on a detailed study conducted using the Saturn-DYNAMICO global climate model (GCM). Large-scale vortices, a prominent feature of gas giant atmospheres, play a critical role in their atmospheric dynamics. By employing three distinct methods-manual detection, machine learning via artificial neural networks (ANN), and dynamical detection using the Automated Eddy-Detection Algorithm (AMEDA)-we characterize the spatial, temporal, and dynamical properties of these vortices within the Saturn-DYNAMICO GCM. Our findings reveal a consistent production of vortices due to well-resolved eddy-to-mean flow interactions, exhibiting size and intensity distributions broadly in agreement with observational data. However, notable differences in vortex location, size, and concentration highlight the model's limitations and suggest areas for further refinement. The analysis underscores the</div
Systèmes à diffusion croisée couplés via une interface mobile
No full textInternational audienceWe propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor deposition of thin films. In our model, cross-diffusion of the various chemical species can be respectively modelled by a size-exclusion system for the solid phase and the Stefan-Maxwell system for the gaseous phase. The coupling between the two phases is modelled by linear phase transition laws of Butler-Volmer type, resulting in an interface evolution. The continuous properties of the model are investigated, in particular its entropy variational structure and stationary states. We introduce a two-point flux approximation finite volume scheme. The moving interface is addressed with a moving-mesh approach, where the mesh is locally deformed around the interface. The resulting discrete nonlinear system is shown to admit a solution that preserves the main properties of the continuous system, namely: mass conservation, nonnegativity, volume-filling constraints, decay of the free energy and asymptotics. In particular, the moving-mesh approach is compatible with the entropy structure of the continuous model. Numerical results illustrate these properties and the dynamics of the model
Les maraîchers et leurs sols : savoirs sensibles et modes de composition dans le maraîchage biologique en Seine-et-Marne
No full textNational audienc
From Teacher Quality to Teaching Quality: Instructional Productivity and Teaching Practices
No full textThis paper estimates the causal effects of math instructional time on student achievement using within-student variation across math topics in the TIMSS 2011 data. Based on the assessment’s detailed measurement of math skills, it shows that each weekly hour of math instruction increases student test scores by 4.3% of a SD. However, the productivity of instructional time varies significantly based on the implementation of teaching practices that prioritize student active participation: teachers emphasizing these practices are more than twice as productive as other teachers. This result holds true regardless of student gender, social origin, and is observed internationally in 42 countries
Evidence for the role of thermal and cloud merging in mesoscale convective organization
No full textInternational audienceObservations from airborne field campaigns are used to study the interplay between boundary-layer thermals and clouds in the trades. The size distributions of thermal and cloud-base chords inferred from turbulence and horizontal lidar-radar measurements are robustly described by the sum of two exponentials. Analytical calculations and statistical simulations demonstrate that the two exponentials result from objects merging, respectively representing the populations of merged- and unmerged-object chords. They also show how circulations induced by convective objects facilitate the merging process. The observed day-to-day variability of these populations at cloud base can thus be tied to the variability of thermal merging across the depth of the subcloud layer. Clouds rooted in unmerged thermals are small and shallow while those rooted in merged thermals are wider and deeper. An intricate interplay between thermal- and cloud-merging arises: when thermal merging is weak, thermal number density is high and cloud bases merge easily, leading to strong mesoscale mass fluxes and "Gravel" shallow mesoscale organizations. In contrast, when thermal merging is strong, clouds are fed by sparser but wider thermals, leading to longer cloud lifetimes but weaker cloud merging, weaker mesoscale mass fluxes, and "Flower" mesoscale organizations. This interplay between thermal- and cloud-merging imposes an upper bound on cloud coverage and suggests a negative feedback on the growth of mesoscale circulations. Thermal merging also controls observed size distributions of thermals in deep convective regimes. The merging process thus appears to be a fundamental player in the mesoscale organization of convection
Power in plurality voting games
No full textInternational audienceSimple games in partition function form are used to model voting situations where a coalition being winning or losing might depend on the way players outside that coalition organize themselves. Such a game is called a plurality voting game if in every partition there is at least one winning coalition. In the present paper, we introduce an equal impact power index for this class of voting games and provide an axiomatic characterization. This power index is based on equal weight for every partition, equal weight for every winning coalition in a partition, and equal weight for each player in a winning coalition. Since some of the axioms we develop are conditioned on the power impact of losing coalitions becoming winning in a partition, our characterization heavily depends on a new result showing the existence of such elementary transitions between plurality voting games in terms of single embedded winning coalitions. The axioms restrict then the impact of such elementary transitions on the power of different types of players
Rôle de la pluie dans les échanges de CO2 à l’interface océan-atmosphère
No full textThe ocean plays an important role in the global carbon cycle by absorbing about a quarter of the carbon emitted by human activities every year. Exchanges between the ocean and the atmosphere are governed by various chemicophysical and biological processes. Among these processes, rain has been overlooked in past studies due to its intermittence. However, it alters the physical and biogeochemical properties of the ocean surface, and thus promotes the exchange of carbon dioxide (CO2) at the air-sea interface. Rain impacts this carbon exchange in three different ways. First, as it falls on the ocean surface, it generates turbulence that facilitates the renewal of water masses in contact with the atmosphere. Secondly, it dilutes the seawater at the surface, altering the chemical equilibrium within the oceanic carbon cycle and enabling seawater to absorb greater quantities of CO2. Finally, raindrops directly inject CO2 absorbed during their fall into the ocean through wet deposition. The objective of this thesis is to quantify the impact of rain on the oceanic CO2 sink at different spatiotemporal scales. A first global estimation of the resultant of these three effects on the global ocean uptake has been done using reanalysis and observational (in-situ and satellite) products over the period 2008 to 2018. This study shows that rain increases the oceanic carbon sink by 140 to 190 million tonnes of carbon per year, representing an increase of 6 to 8 % in the 2.36 billion tonnes absorbed annually by the oceans. The main regions affected by these processes are the tropics, the storm track regions and the Southern Ocean. However, variations in the global estimates are due to large uncertainties on the rain rates themselves and on the associated ocean's surface response. A more detailed study of the sensitivity of the impact of rain to rainfall rates is carried out at regional (using radar measurements) and global scales. An increase of 15 % in the combined effect of rain-induced turbulence and dilution is assessed using satellite-based precipitation estimates instead of reanalysis rain data, the former being characterized by a greater contribution of heavy rainfall to the total rainfall volume. Finally, these fine-scale processes are integrated into the CO2 flux calculations of a global ocean biogeochemistry model (GOBM) forced by atmospheric reanalysis. It allows us to take into account the response of surface biogeochemistry to the rain impact on CO2 exchanges at the air-sea interface. In this framework, the total rain effect leads to an increase of 0.9 % in the global ocean sink over the period 1980 to 2022. This significant attenuation of the adjustment in ocean carbon uptake is linked to the accumulation of CO2 absorbed through these processes in the ocean surface layer. This result is directly linked to the capacity of the ocean general circulation model to transfer CO2 in its interior.L'océan joue un rôle important dans le cycle global du carbone en absorbant chaque année environ 25 % du carbone émis par les activités humaines. Les échanges entre l'océan et l'atmosphère sont gouvernés par différents processus physico-chimiques et biologiques. Parmi ces processus, la pluie a été mise de côté dans les études passées du fait de son importante intermittence. Elle modifie cependant les propriétés physiques et biogéochimiques de la surface de l'océan et donc favorise les échanges de dioxyde de carbone (CO2) à sa surface. La pluie agit de trois façons différentes sur cet échange de carbone. Tout d'abord, en tombant sur la surface de l'océan, elle crée de la turbulence qui favorise le renouvellement des masses d'eaux en contact avec l'atmosphère. Elle dilue l'eau de mer en surface ce qui modifie les équilibres chimiques impliqués dans le cycle océanique du carbone et permet à l'eau de mer d'absorber une plus grande quantité de CO2. Enfin, elle injecte directement dans l'océan le CO2 atmosphérique qui est dissous dans les gouttes de pluie lors de leur chute. Ce travail de thèse a pour objectif de quantifier l'impact de la pluie sur le puits de CO2 océanique à différentes échelles spatio-temporelles. Une première évaluation diagnostic à l'échelle globale de ces trois effets de la pluie a été réalisée à partir de produits de réanalyse et d'observations (in-situ et satellitaire) sur la période de 2008 à 2018. Cette étude montre que la pluie augmente le puits de carbone océanique de 140 à 190 millions de tonnes de carbone par an, représentant un accroissement de 6 à 8 % des 2,36 milliards de tonnes absorbées chaque année par les océans. Les principales régions affectées par ces processus sont les tropiques, les rails de dépression et l'océan Austral. La variation de ces estimations est liée à des incertitudes dans la représentation de la dilution induite par la pluie à l'échelle globale ainsi qu'à des disparités entre les produits de pluie globaux. Une étude plus approfondie de la sensibilité de l'impact de la pluie aux taux de pluie est réalisée à l'échelle régionale (à l'aide de mesures radar) et globale. Une augmentation de 15 % de l'effet combiné de l'accroissement de turbulence et de la dilution induits par la pluie est évalué en substituant un jeu de données de pluie de réanalyse par celui d'un produit satellitaire, ce dernier étant caractérisé par une plus grande contribution des pluies fortes au volume total de pluie. Enfin, ces processus de fine échelle sont intégrés aux calculs de flux de CO2 d'un modèle de biogéochimie océanique global (GOBM) forcé par une réanalyse atmosphérique. Ce cadre d'étude nous permet de prendre en compte la réponse de la biogéochimie de surface à l'impact de la pluie sur les échanges interfaciaux de CO2. L'effet total de la pluie est alors réévalué à un accroissement de 0.9 % du puits océanique global sur la période de 1980 à 2022. Cette importante atténuation de l'ajustement de l'absorption de CO2 par l'océan est liée à l'accumulation du CO2 ajouté par le biais de ces processus dans la couche de surface de l'océan. Ainsi, ce résultat met en avant l'importance de la représentation des mécanismes contrôlant le transfert de CO2 dans l'océan intérieur au sein du modèle de circulation générale océanique