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Backstepping for partial differential equations: A survey
No full textInternational audienceSystems modeled by partial differential equations (PDEs) are at least as ubiquitous as those by nature finite-dimensional and modeled by ordinary differential equations (ODEs). And yet, systematic and readily usable methodologies, for such a significant portion of real systems, have been historically scarce. Around the year 2000, the backstepping approach to PDE control began to offer not only a less abstract alternative to PDE control techniques replicating optimal and spectrum assignment techniques of the 1960s, but also enabled the methodologies of adaptive and nonlinear control, matured in the 1980s and 1990s, to be extended from ODEs to PDEs, allowing feedback synthesis for systems that are uncertain, nonlinear, and infinite-dimensional. The PDE backstepping literature has since grown to hundreds of papers and nearly a dozen books. This survey aims to facilitate the entry into this thriving area of overwhelming size and topical diversity. Designs of controllers and observers, for parabolic, hyperbolic, and other classes of PDEs, in one or more dimensions, with nonlinear, adaptive, sampled-data, and event-triggered extensions, are covered in the survey. The lifeblood of control are technology and physics. The survey places a particular emphasis on applications that have motivated the development of the theory and which have benefited from the theory and designs: flows, flexible structures, materials, thermal and chemically reacting dynamics, energy (from oil drilling to batteries and magnetic confinement fusion), and vehicles
An equation for the kinetic energy balance in homogeneous turbulence
No full textInternational audienceWe derive a two-equation model for the energy balance in statistically homogeneous turbulence. The present formulation is expressed in terms of the energy flux, unlike the classical approach, where the dissipation rate appears in the kinetic energy equation. This enables a unified description of both forced and decaying turbulence with a single set of model constants. The model also captures the time lag between the evolution of the kinetic energy and the dissipation rate. Reformulating the system as an equation for the dissipation rate further clarifies how non-equilibrium effects can be incorporated into existing turbulence models
An intense peak of paraglacial dismantlement of mountain slopes: Insights from dating and volume quantification of rock-slope failure deposits in the Icelandic Westfjords (Dýrafjörður and Önundarfjörður)
No full textInternational audienceParaglacial rock slope failures (RSFs) are prominent processes of landscape evolution in deglaciated terrains, such as the Westfjords of Iceland. This study aims to provide chronological and volumetric data on RSF deposits in the Dýrafjörður and Önundarfjörður fjords, in order to document the magnitude, duration, and geomorphic impact of the intense peak of Early and Middle Holocene paraglacial denudation. By refining the timing of a paraglacial signal, this work contributes to a better understanding of sedimentary production and landscape evolution during the Holocene.A total of 17 RSFs was studied, described and mapped using the Schmidt-hammer exposure-age dating method, calibrated with radiocarbon dating. Surficial block morphometry and volumetric estimates of RSF deposits were derived from field measurements, orthophotography, and high-resolution digital elevation models.RSF ages are concentrated in the Early to Middle Holocene. The vast majority of this activity occurred between 12 and 6 cal. ka BP. During this 6000-year interval, ~83 million m3 of debris were deposited, which accounts for approximately 90% of the total volume (~92.5 M m3) from all 17 RSF sites. This indicates a primary paraglacial adjustment phase characterized by high sediment delivery efficiency. Slope reactivations occurred over periods up to 3400 years, with superimpositions of deposits: these are multi-phased RSFs.Finally, a significant lag of approximately 3000 years is observed between the deglaciation (~10.2 cal. ka BP) and the peak in rock-slope failure activity (8–6 cal. ka BP), which coincides with the Holocene Thermal Maximum climax in Iceland (8.6–5.2 cal. ka BP). The subsequent cessation of major RSFs activity after ~4 cal. ka BP marks the transition to a stable, non-glacial equilibrium
Reimagining Urban River Bathing in Europe: A Multisectoral and Interdisciplinary Dive Into Lyon's Rivers (France)
No full textInternational audienceUrban river bathing is re‐emerging across Europe, driven by social demand and climate change impacts. The Urban Bathing Consortium, an interdisciplinary and intersectoral consortium initiated at the University of Lyon (France), is at the forefront of studying the challenges and opportunities of creating and managing healthy, safe, and accessible river bathing spaces. Through interdisciplinary collaboration among researchers and stakeholders, the consortium proposed an analytical framework, identifying seven critical dimensions for urban river bathing: the history and revival of city‐river relationships, legal and regulatory frameworks, bathing water quality, river drowning risks, river ecosystems, social perspectives, and urban planning. By examining these dimensions with state‐of‐the‐art approaches and drawing on Lyon's experiences, the study provides scientific insights and practical recommendations for future sustainable urban river bathing development. These include revitalizing historical city‐river connections, aligning local regulations with EU guidance, advancing holistic microbial water quality control, enhancing safety measures, incorporating ecological considerations, balancing competing river uses in urban planning, and addressing social needs for inclusive river governance
Convergence analysis of semi-smooth Newton method for mixed FEM approximations of dynamic two-body contact and crack problems
No full textInternational audienceA class of elastodynamic problems describing contact between two deformable bodies as well as non-penetrating cracks in a single body is considered in the framework of FEM approximation. For time discretization, the Hilber-Hughes-Taylor (HHT-alpha) method extending Newmark schemes is incorporated. Using mixed variational formulation of the fully discrete contact problem, a semi-smooth Newton method of solution is provided with the locally super-linear convergence. An equivalent primal-dual active set algorithm validates monotone properties of global convergence for the Newton iterates provided by M-matrix property. Numerical solution of the Signorini contact with rigid obstacle is presented for isotropic body in 2D using benchmark and moving load experiment
History-Aware Sequence Modeling for Authentic Learner Profiling in the Age of Generative AI
No full textGenerative AI tools (e.g., ChatGPT, DeepSeek, Copilot) enable students to delegate learning tasks, obscuring authentic learning behaviors and the critical transition from declarative to procedural knowledge. Current learning analytics and AI detectors focus on coarse-grained outputs, failing to capture the nuanced dynamics of learning processes in generative AI-integrated contexts. However, identifying patterns beyond memorization such as using ChatGPT for initial hints or scaffolding remains challenging when learners orchestrate interactions between reasoning, AI assistants, and digital environments. We introduce Auth-LP (Authentic Learner Profiling), a history-aware sequence modeling framework that profiles authentic learning by analyzing timestamped event sequences (e.g., Prompted, AskGenAI, HelpSeeking, HintRequest) in educational contexts integrating generative AI. The framework bridges task-level learner-AI assistant interactions by identifying behavioral states such as Engaged, Struggling, AI-Dependent, and Gaming the System. Auth-LP integrates visual analytics (e.g., heatmaps, radar charts) to gracefully monitor profile transitions as students' behavioral states evolve throughout the learning process. It enables educators to distinguish genuine skill development and learning agency from AI-assisted outputs, informing learning analytics design and enhancing personalized guidance. Our findings, based on a proof of concept conducted within the écri+ project, demonstrate that history-aware sequence modeling supports authentic learner profiling and trustworthy assessment, fostering Human-AI synergy for augmented learning in AI-augmented education.</div
Étude de la microstructure et des propriétés émissives des membranes ultrafines MoSiN nanocomposites autoportantes
No full textThe growing demand for compact, energy-efficient, and robust mid-infrared (mid-IR) light sources is driving the development of advanced thermal emitters for next-generation hightemperature gas sensing technologies. Mid-IR gas sensors, in particular, benefit from this spectral range due to the strong and selective molecular absorption features of most gases. However, their development remains constrained by the lack of efficient, low-power, and thermally stable emitter materials capable of reaching the high temperature (600-1000°C) needed for strong emission across the mid-IR broadband range. Conventional microheaterbased emitters suffer from high power consumption, slow thermal response, and material degradation during repeated heating cycles. Addressing these limitations requires materials that combine high emissivity, thermal stability, and mechanical resilience at nanoscale thicknesses. Reducing the membrane thickness lowers thermal mass, minimizing power consumption and enabling faster heating and cooling for enhanced thermal response. For nanoscale membranes where both high emissivity and mechanical strength are critical, integrating these attributes within a composite material offers an effective and promising solution. In this context, this study develops and investigates ultrathin freestanding MoSiN nanocomposite membranes, examining their structural, optical, and thermal properties to assess their suitability as efficient, low-power, and thermally stable mid-IR emitters for compact and reliable gas sensing applications. Freestanding MoSiN membranes, 6-16 nm thick with lateral dimensions of 10 mm × 10 mm supported on silicon frames, were fabricated and characterized. The microstructure and composition of the ultrathin MoSiN membranes were thoroughly studied to elucidate the distribution of intermetallic and dielectric phases. The microstructural analysis reveals that MoSiN possess a complex nanocomposite structure, comprising intermetallic phases (MoSi2 and Mo5Si3) and silicon oxynitride (SiOxNy) dielectric phase. The intermetallic phases facilitate free-carrier absorption in the mid-IR region, while the dielectric phase enhances mechanical integrity and provides strong resistance to oxidation. Membrane exhibits metal-like emissivity (~0.41) and retains thermal and mechanical stability at high temperature (900°C). Repeated laser pulsed-heating experiments confirm rapid thermal response, excellent repeatability, and efficient radiative cooling, validating its potential as a durable microheater emitter material. FTIR spectroscopy shows broadband absorption in the 2-8 µm range, dominated by free-carrier processes, with negligible phonon absorption beyond 8 µm. Emissivity shows a strong thickness dependence due to interference effects, as confirmed by optical modeling using Fresnel equations and the generalized matrix method. Electrical characterization shows resistivity (~10 -4 Ω•cm) with a positive temperature coefficient, indicating metallic conduction. Overall, MoSiN behaves as a semimetal combining metallic absorption and dielectric-induced stability. These results highlight ultrathin freestanding MoSiN membranes as a compelling platform for mid-infrared emitters, offering a synergistic combination of low power, thermal iii efficiency, mechanical durability, and CMOS compatibility for gas sensing applications in harsh environments.To my dearest Daddy, Mummy, and Neethu-Your boundless love, selfless sacrifices, and quiet strength have sustained me in ways words cannot fully captureLa demande croissante en sources lumineuses compactes, écoénergétiques et robustes dans le domaine de l'infrarouge moyen (IR moyen) stimule le développement d'émetteurs thermiques avancés pour les technologies de détection de gaz à haute température de nouvelle génération. Les capteurs de gaz à infrarouge moyen, en particulier, tirent parti de cette gamme spectrale en raison des caractéristiques d'absorption moléculaire fortes et sélectives de la plupart des gaz. Cependant, leur développement reste limité par le manque de matériaux émetteurs efficaces, à faible consommation d'énergie et thermiquement stables, capables d'atteindre la température élevée (~900°C) nécessaire pour une émission forte dans toute la gamme à large bande de l'infrarouge moyen. Les émetteurs conventionnels à micro-réchauffeurs souffrent d'une consommation d'énergie élevée, d'une réponse thermique lente et d'une dégradation des matériaux lors de cycles de chauffage répétés. Pour remédier à ces limitations, il faut des matériaux qui combinent une émissivité élevée, une stabilité thermique et une résilience mécanique à des épaisseurs nanométriques. La réduction de l'épaisseur de la membrane diminue la masse thermique, minimise la consommation d'énergie et permet un chauffage et un refroidissement plus rapides pour une réponse thermique améliorée. Pour les membranes à l'échelle nanométrique où une émissivité élevée et une résistance mécanique sont essentielles, l'intégration de ces propriétés dans un matériau composite offre une solution efficace et prometteuse. Dans ce contexte, cette étude développe et examine des membranes nanocomposites MoSiN ultrafines autonomes, en étudiant leurs propriétés structurelles, optiques et thermiques afin d'évaluer leur adéquation en tant qu'émetteurs infrarouges moyens efficaces, à faible consommation d'énergie et thermiquement stables pour des applications compactes et fiables de détection de gaz. Des membranes MoSiN autonomes, d'une épaisseur de 6 à 16 nm et de dimensions latérales de 10 mm × 10 mm, supportées par des cadres en silicium, ont été fabriquées et caractérisées. La microstructure et la composition des membranes MoSiN ultrafines ont été étudiées de manière approfondie afin d'élucider la distribution des phases intermétalliques et diélectriques. L'analyse microstructurale révèle que le MoSiN possède une structure nanocomposite complexe, comprenant des phases intermétalliques (MoSi2 et Mo5Si3) et une phase diélectrique d'oxynitrure de silicium (SiOxNy). Les phases intermétalliques facilitent l'absorption des porteurs libres dans la région de l'infrarouge moyen, tandis que la phase diélectrique améliore l'intégrité mécanique et offre une forte résistance à l'oxydation. La membrane présente une émissivité de type métallique (~0.41) et conserve sa stabilité thermique et mécanique à haute température (900°C). Des expériences répétées de chauffage par impulsions laser confirment une réponse thermique rapide, une excellente répétabilité et un refroidissement radiatif efficace, validant son potentiel en tant que matériau émetteur micro-chauffant durable. La spectroscopie FTIR montre une absorption à large bande dans la gamme 2-8 µm, dominée par des processus de porteurs libres, avec une absorption phononique négligeable au-delà de 8 µm. L'émissivité montre une forte dépendance à l'épaisseur due à des effets d'interférence, comme le confirment la modélisation optique à l'aide des équations de Fresnel et la méthode matricielle généralisée. La caractérisation électrique montre une résistivité (~10-4 Ω·cm) avec un coefficient de température positif, indiquant une conduction métallique. Dans l'ensemble, le MoSiN se comporte comme un semi-métal combinant une absorption métallique et une stabilité induite par diélectrique. Ces résultats mettent en évidence les membranes MoSiN ultrafines autonomes comme une plateforme convaincante pour les émetteurs infrarouges moyens, offrant une combinaison synergique de faible puissance, d'efficacité thermique, de durabilité mécanique et de compatibilité CMOS pour les applications de détection de gaz dans des environnements difficiles
Direct Fluoroformylation of the C3 ‐Position of Indoles with 2,4‐Dinitro(trifluoromethoxy)benzene as Fluorocarbonyl Source
No full textInternational audienceWe herein report the direct fluoroformylation of indoles and other heteroaromatic cycles. Acyl fluorides are very useful moieties in coupling reactions with or without metal. However, they are usually obtained from the corresponding carboxylic acids or from aryl halides in pallado‐catalyzed carbonylation/fluorination reactions. Our method uses fluorophosgene generated in situ from 2,4‐dinitro(trifluoromethoxy)benzene (DNTFB) as a fluoroformylating agent without any metal and from carboxylic acid‐free heteroaromatic rings. Moreover, our method can be telescoped with amidification reactions in a one‐pot process
Weak error estimates of fully-discrete schemes for the stochastic Cahn-Hilliard equation
No full textInternational audienceWe study a class of fully-discrete schemes for the numerical approximation of solutions of stochastic Cahn-Hilliard equations with cubic nonlinearity and driven by additive noise. The spatial (resp. temporal) discretization is performed with a spectral Galerkin method (resp. a tamed exponential Euler method). We consider two situations: space-time white noise in dimension d " 1 and trace-class noise in dimensions d " 1, 2, 3. In both situations, we prove weak error estimates, where the weak order of convergence is twice the strong order of convergence with respect to the spatial and temporal discretization parameters. To prove these results, we show appropriate regularity estimates for solutions of the Kolmogorov equation associated with the stochastic Cahn-Hilliard equation, which have not been established previously and may be of interest in other contexts
A purity theorem for Mahler equations
No full textInternational audienceThe principal aim of this paper is to establish a purity theorem for Mahler functions that is reminiscent of famous purity theorems for G-functions by D. and G. Chudnovsky and for E-functions (and, more generally, for holonomic arithmetic Gevrey series) by Y. André. Our approach is based on a preliminary study of independent interest of the nature of the solutions of Mahler equations. Roughly speaking, we prove a reduction result for Mahler systems, implying that any Mahler equation admits a complete basis of solutions formed of what we call generalized Mahler series. These are sums involving Puiseux series, Hahn series of a very special type and solutions of inhomogeneous equations of order 1 with constant coefficients. In the light of B. Adamczewski, J. P. Bell and D. Smertnig's recent height gap theorem, we introduce a natural filtration on the set of generalized Mahler series according to the arithmetic growth of the coefficients of the Puiseux series involved in their decomposition. This filtration has five pieces. Our purity theorem states that the membership of a generalized Mahler series to one of the three largest pieces of this filtration propagates to any other generalized Mahler series solution of its minimal Mahler equation. We also show that this statement does not extend to the smallest two pieces.</div