HAL-Ecole des Ponts ParisTech
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A bound-preserving scheme for the Allen-Cahn equation
No full textInternational audienceWe propose and analyze a bound-preserving scheme for the Allen-Cahn equation. We derive an error estimate that is optimal in the -seminorm and has only a polynomial dependence on . Numerical experiments are conducted to compare the performance of our scheme with an operator-splitting scheme
On the dynamics and interactions of coherent magnetic dipolar structures in a magnetohydrodynamic rotating shallow water model
No full textInternational audienceIn this study, we explore the evolution of instabilities in magneto-quasi-geostrophic (MQG) modons on the -plane using a magnetohydrodynamic rotating shallow water model. The numerical experiments have been conducted using a recently proposed second-order flux-globalisation-based path-conservative central-upwind scheme. Our focus is on the evolution and interactions of three key configurations: singular, regular and hollow MQG modons, which represent cases where the magnetic field is confined within the separatrix, evenly distributed inside and outside the separatrix and localised outside the separatrix, respectively. The singular MQG modon emerges as the most stable configuration, demonstrating the greatest resilience to destabilising forces. A notable observation is its transition from a quadrupolar to a tripolar magnetic field structure before reverting to a quadrupole adjusted magnetic modon, accompanied by a clockwise rotation of the system. In terms of stability, singular modons are the most stable ones, while hollow modons are the least stable. As instabilities develop, southward or northward displacements become significantly more pronounced than eastward or westward movements, primarily due to the Coriolis force. Among the configurations, the hollow (singular) modons experience the biggest (smallest) displacements. Additionally, we investigate modon collisions and highlight three scenarios: interactions between cyclonic and anticyclonic components that form a composite modon with meridional bifurcation; collisions of cyclonic vortices that produce a tripolar structure with counterclockwise rotation; and collisions between anticyclonic components that result in a stable, quasi-stationary tripolar configuration. The resulting magnetic poles exhibit a checkered pattern, with their amplitude decreasing with increasing distance from the central vortex
LEARNING CHAOS IN A LINEAR WAY
No full textInternational audienceLearning long-term behaviors in chaotic dynamical systems, such as turbulent flows and climate modelling, is challenging due to their inherent instability and unpredictability. These systems exhibit positive Lyapunov exponents, which significantly hinder accurate long-term forecasting. As a result, understanding long-term statistical behavior is far more valuable than focusing on short-term accuracy. While autoregressive deep sequence models have been applied to capture long-term behavior, they often lead to exponentially increasing errors in learned dynamics. To address this, we shift the focus from simple prediction errors to preserving an invariant measure in dissipative chaotic systems. These systems have attractors, where trajectories settle, and the invariant measure is the probability distribution on attractors that remains unchanged under dynamics. Existing methods generate long trajectories of dissipative chaotic systems by aligning invariant measures, but it is not always possible to obtain invariant measures for arbitrary datasets. We propose the Poincare Flow Neural Network (PFNN), a novel operator learning framework designed to capture behaviors of chaotic systems without any explicit knowledge of the invariant measure. PFNN employs an auto-encoder to map the chaotic system to a finite-dimensional feature space, effectively linearizing the chaotic evolution. It then learns the linear evolution operators to match the physical dynamics by addressing two critical properties in dissipative chaotic systems: (1) contraction, the system's convergence toward its attractors, and (2) measure invariance, trajectories on the attractors following a probability distribution invariant to the dynamics. Our experiments on a variety of chaotic systems demonstrate that PFNN has more accurate predictions and physical statistics compared to competitive baselines
Investigating of the physico-chemistry dhiolated dextran derivatives
No full textInternational audienceThe study aimed to create redox-responsive dextran carriers for controlled hydrophobic molecule release using glutathione, a natural cellular reducing agent, by modifying dextran with a thiol derivative. Investigating the impact of different hydrophobic length on the molecular self-organization of polysaccharide derivatives into nanoparticles helped to understand their roles in this process. The study demonstrated that thiolated dextran particles can be used as emulsifier and can effectively encapsulated hydrophobic molecules like Nile red dye, with the disulfide linkage being cleaved by glutathione under physiological conditions for rapid release. Additionally, the dextran-based particles were found to be non-toxic to living cells
Decoding the geometry of growth: unveiled urban complexity, fractality and spatial dynamics in Île-de-France
No full textInternational audienceThe Île-de-France region faces significant challenges in achieving sustainable urban development amid increasing demands for urbanization. This study conducts a comprehensive analysis of the spatial dynamics of urban areas in Île-de-France (IDF) up to the years 2050 and 2100. The region’s complex urban nature makes it an ideal case for examining various aspects of urbanization, characterized by dense development, modern infrastructure, and a complex coexistence between urban and natural spaces. Employing fractality, cluster, and hotspot analyses, the research integrates land-use/land-cover data with socioeconomic, infrastructural, topographic, and environmental data, utilizing machine-learning models to forecast future land-use configurations. The findings indicate a slight increase in the complexity and densification of urban areas, emphasizing a growth-pattern that aims to enhance connectivity and compactness. The study underscores the importance of proactive planning and management strategies, such as Zones-d’Aménagement-Concerté (ZAC) and Schéma-Directeur-de-la-Région-Île-de-France (SDRIF), to address urban densification and sprawl. The research’s originality lies in the integration of multiple spatial-analysis techniques, offering a valuable tool applicable beyond Île-de-France. Future research directions include examining socioeconomic factors influencing urban growth at finer multi-agent spatial-scales, investigating the impacts of urban growth on transportation and infrastructure, and exploring the spatial relationship between employment and housing opportunities in high-density urban hotspots
Between Authentification and Pedagogy: Language, Central Part of Notarial Work
No full textInternational audienc
A Scalable Digital Twin Architecture for Monitoring & Optimization of Electric Roads: The eRoadMontBlanc Case Study
No full textInternational audienceThis poster presents a scalable digital twin (DT) architecture for electric roads, illustrated through the eRoadMontBlanc project. The goal is to optimize the deployment and real-time management of Electric Road Systems (ERS), which allow EVs to charge while driving. Current DTs are insufficient due to lack of interoperability, scalability, and adaptability. The proposed solution leverages NGSI-LD (ETSI standard) for semantic data modeling and integrates heterogeneous data. The DT will be validated using real or simulated data, focusing on scalability, accuracy, interoperability, and latency
Les déplacements domicile-travail entre villes, un impensé de la mobilité
No full textTravailler dans une ville différente de celle de sa résidence est une pratique de plus en plus courante en France. Un atlas qui vient de paraître se penche sur la géographie de ces flux très majoritairement automobiles, et la façon dont une partie d’entre eux pourrait être remplacée par des transports collectifs