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Simulating generalised fluids via interacting wave packets evolution
No full textInternational audienceOne-dimensional integrable and quasi-integrable systems display, on macroscopic scales, a universal form of transport known as Generalized Hydrodynamics (GHD). In its standard Euler-scale formulation, GHD mirrors the equations of a two-dimensional compressible fluid but ignores fluctuations and becomes numerically unwieldy as soon as integrability-breaking perturbations are introduced. We show that GHD can be efficiently simulated as a gas of semiclassical wave packets-a natural generalisation of hard-rod particles-whose trajectories are efficiently mapped onto those of point particles. This representation (i) provides a transparent route to incorporate integrabilitybreaking terms, and (ii) automatically embeds the exact fluctuating-hydrodynamics extension of GHD. The resulting framework enables fast, large-scale simulations of quasi-integrable systems even in the presence of complicated integrability-breaking perturbations. It also manifest the pivotal role of two-point correlations in systems confined by external potentials: we demonstrate that situations where local one-point observables appear thermalised can nevertheless sustain long-lived, far-fromequilibrium long-range correlations for arbitrarily long times, signaling that, differently from what previously stated, true thermalisation is not reached at diffusive time-scales
Euclid Quick Data Release (Q1). Active galactic nuclei identification using diffusion-based inpainting of Euclid VIS images
No full textInternational audienceLight emission from galaxies exhibit diverse brightness profiles, influenced by factors such as galaxy type, structural features and interactions with other galaxies. Elliptical galaxies feature more uniform light distributions, while spiral and irregular galaxies have complex, varied light profiles due to their structural heterogeneity and star-forming activity. In addition, galaxies with an active galactic nucleus (AGN) feature intense, concentrated emission from gas accretion around supermassive black holes, superimposed on regular galactic light, while quasi-stellar objects (QSO) are the extreme case of the AGN emission dominating the galaxy. The challenge of identifying AGN and QSO has been discussed many times in the literature, often requiring multi-wavelength observations. This paper introduces a novel approach to identify AGN and QSO from a single image. Diffusion models have been recently developed in the machine-learning literature to generate realistic-looking images of everyday objects. Utilising the spatial resolving power of the Euclid VIS images, we created a diffusion model trained on one million sources, without using any source pre-selection or labels. The model learns to reconstruct light distributions of normal galaxies, since the population is dominated by them. We condition the prediction of the central light distribution by masking the central few pixels of each source and reconstruct the light according to the diffusion model. We further use this prediction to identify sources that deviate from this profile by examining the reconstruction error of the few central pixels regenerated in each source's core. Our approach, solely using VIS imaging, features high completeness compared to traditional methods of AGN and QSO selection, including optical, near-infrared, mid-infrared, and X-rays
Proof assistants for undergraduate mathematics education: elements of an a priori analysis
No full textInternational audienceThis paper presents an a priori analysis of the use of six different interactive proof assistants for education, based on the resolution of a typical undergraduate exercise on abstract functions. It proposes to analyze these tools according to three main categories of aspects: language and interaction mode, automation and user assistance, and proof structure and visualization. We argue that this analysis may help formulate and clarify further research questions on the possible impact of such tools on the development of reasoning and proving skills
The effects of the spin and quadrupole moment of SgrA* on the orbits of S stars
No full textInternational audienceMeasuring the astrometric and spectroscopic data of stars orbiting the central black hole in our galaxy (Sgr A*) offers a promising way to measure relativistic effects. In principle, the "no-hair" theorem can be tested at the Galactic Center by monitoring the orbital precession of S-stars due to the angular momentum (spin) and quadrupole moment of Sgr A*. Closer-in stars, more strongly affected by the black hole's rotation, may be required. GRAVITY+ could detect such stars that are currently too faint for GRAVITY. We aim to analytically and numerically characterize orbital reorientations induced by spin-related effects of Sgr A* up to the second post-Newtonian (2PN) order. We use the two-timescale method to derive the 2PN analytical expressions of the secular evolution of the orbital parameters that are related to the observer. To study the interaction between the orbital and spin orientations, we introduce observer-independent quantities that offer insight into the Kerr geometry. We also use the post-Newtonian code OOGRE to simulate hypothetical stars orbiting closer to Sgr A*, where spin and quadrupole effects are stronger. This enables comparison with our analytical predictions. We exhibit three orbital-timescale precession rates that encode the in-plane pericenter shift and the out-of-plane redirection of the osculating ellipse. We provide the 2PN expressions of these precession rates and express the orbit-integrated associated angular shifts of the pericenter and of the ellipse axes. We relate these orbital-timescale precession rates to the secular-timescale precession of the orbital angular momentum around the black hole spin axis. We consider that the theoretical insight we provide in this article will be useful in constraining the spin effect of Sgr A* with GRAVITY+ observations
Linking metamorphic transformations and the brittle–ductile transition: Insights from numerical modeling of the granulite-to-eclogite transformation
No full textInternational audienceGeophysical observations combined with detailed petro-structural analyses conducted in the field and in the laboratory indicate that « brittle » deformation occurs within subduction zones in rocks that are otherwise expected to deform in a « ductile » manner under the associated pressure–temperature conditions. These brittle events are most commonly localized in regions where metamorphic transformations are predicted to occur. Because such reactions may induce substantial changes in density and strength, they are frequently invoked as a primary mechanism driving the ductile-to-brittle switch in subducting rocks. However, the physical processes that link metamorphic transformations to changes in deformation style remain incompletely understood.This contribution addresses this issue through the emblematic example of the granulite-to-eclogite transformation exposed at Holsnøy (Bergen Arcs, Norway). We combine field-based structural and petrological observations with numerical modeling developed over the past several years to investigate the mechanical and rheological consequences of this transformation.We specifically examine whether eclogitization necessarily initiates along pre-existing brittle precursors or whether the reaction itself can trigger faulting, how the transformation propagates through the rock, and the extent to which the inherited granulitic foliation influences reaction localization. We further discuss the mechanisms leading to the formation of eclogitic shear zones as opposed to static eclogites (commonly referred to as eclogite fingers). Finally, we assess the relative roles of fluid availability and far field stress in controlling the spatial distribution and mechanical impact of the reaction.By confronting field observations with numerical modeling, this presentation aims to show that the answers to these questions may not be unique, and that much remains to be done to fully understand the impact of metamorphic reactions on the rheological behavior of rocks
L’identité professionnelle des professeurs des écoles en mathématiques et technologies numériques (MAT&N1d) à l’entrée dans la formation: Un outil de lecture fondé sur le cadre DAaT-DP
No full textSchool Teachers' Professional Identity in Mathematics and Digital Technologies (MAT&N1d) at Entry into Training: A DAaT-DP-Based Analytical Framework. This article examines primary school teachers' professional identity in mathematics and digital technologies (MAT&N1d) at the onset of training. It mobilises the DAaT-DP framework (Lin, 2025) in an original way: the capture of initial professional identity IP(t₀) -the actor's state at a given point in time, prior to any formal training. Using the QPRO-PE questionnaire administered in Martinique, it produces a national collective portrait and three individual portraits. Results reveal a configuration of constrained openness and a dominant technician epistemic posture. I3 (organisational support) emerges as a public policy variable.Cet article interroge l’identité professionnelle des professeurs des écoles en mathématiques et technologies numériques (MAT&N1d) à l’entrée dans la formation. Il mobilise le cadre DAaT-DP (Double Approche adaptée aux Technologies pour le Développement Professionnel, Lin, 2025) comme outil de lecture, en en proposant un usage original : la capture de l’identité professionnelle initiale IP(t₀) — état de l’acteur à un instant T, antérieur à toute formation formelle. À partir du questionnaire QPRO-PE — questionnaire d’identité professionnelle des professeurs des écoles — et le QGD-PE — questionnaire sur les savoirs en géométrie dynamique — administrés en Martinique (Lin, 2025a), l’article propose un portrait collectif national et trois portraits individuels. Les résultats mettent en évidence une configuration d’ouverture contrainte — disposition favorable au numérique couplée à un déficit structurel de soutien organisationnel (I3) — et une posture épistémologique dominante technicienne (E-TECH). I3 apparaît comme variable de pilotage public autant que pédagogique
Peptidomimetics Inspired by α-Synuclein or Its Chaperone αB-Crystallin Differentially Modulate α-Synuclein Aggregation
No full textInternational audienceAggregation of the α-Synuclein (αSyn) protein in neurons is responsible for synucleinopathies such as Parkinson's disease. In healthy cells, αSyn is primarily present as monomers. Under pathological conditions, oligomers and fibrils are formed, leading to neuronal toxicity and death. No treatment prevents fatal synucleinopathies. We designed small peptidomimetics based on the structure of αSyn aggregates and on its chaperone protein αB-Crystallin. Interestingly, a relationship between the impact of peptidomimetics on the αSyn aggregation process, their sequences, and secondary conformation has been evidenced. In vitro and in cellular assays demonstrated that one compound based on αB-Crystallin was able to interfere with αSyn folding and aggregation by reducing the formation of oligomers and promoting off-pathway aggregation. The demonstration that physiological chaperone proteins can be mimicked by small peptide derivatives paves the way for new strategies to design inhibitors of amyloid protein aggregation, a hallmark of around 50 neurodegenerative and systemic amyloid diseases.</div
A Riemann-Roch formula for singular reductions by circle actions
No full textWe compute a Riemann-Roch formula for the invariant Riemann-Roch number of a quantizable Hamiltonian S^1-manifold (M,\omega,\mathcal{J}) in terms of the geometry of its symplectic quotient, allowing 0 to be a singular value of the moment map \mathcal{J}:M\to\mathbb{R}. The formula involves a new explicit local invariant of the singularities. Our approach relies on a complete singular stationary phase expansion of the associated Witten integral
Partial Bergman kernels and determinantal point processes on Kähler manifolds
No full textWe compute the full off-diagonal asymptotics of the equivariant and partial Bergman kernels associated with a circle action on a prequantized Kähler manifold with bounded geometry at infinity, then use these results to compute the asymptotics of the linear statistics of the associated determinantal point process as the number of points grows to infinity, showing that its distribution converges to a centered normal variable with variance given by the sum of an -norm squared in the bulk and an -norm squared on the boundary of the associated droplet