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Preconditioners based on Voronoi quantizers of random variable coefficients for stochastic elliptic partial differential equations
No full textA preconditioning strategy is proposed for the iterative solve of large numbers of linear systems with variable matrix and right-hand side which arise during the computation of solution statistics of stochastic elliptic partial differential equations with random variable coefficients sampled by Monte Carlo. Building on the assumption that a truncated Karhunen-Lo\`{e}ve expansion of a known transform of the random variable coefficient is known, we introduce a compact representation of the random coefficient in the form of a Voronoi quantizer. The number of Voronoi cells, each of which is represented by a centroidal variable coefficient, is set to the prescribed number of preconditioners. Upon sampling the random variable coefficient, the linear system assembled with a given realization of the coefficient is solved with the preconditioner whose centroidal variable coefficient is the closest to the realization. We consider different ways to define and obtain the centroidal variable coefficients, and we investigate the properties of the induced preconditioning strategies in terms of average number of solver iterations for sequential simulations, and of load balancing for parallel simulations. Another approach, which is based on deterministic grids on the system of stochastic coordinates of the truncated representation of the random variable coefficient, is proposed with a stochastic dimension which increases with the number of preconditioners. This approach allows to bypass the need for preliminary computations in order to determine the optimal stochastic dimension of the truncated approximation of the random variable coefficient for a given number of preconditioners
Stress-based topological shape optimization for thick shells using the level set method and trimmed non-conforming multi-patch isogeometric analysis
No full textInternational audienceThis paper introduces a novel method for optimal shape design of thick shells. We consider shells based on the Reissner-Mindlin theory, with the assumption of linear elastic material behavior. The goal is to find the optimal material distribution within the shell's mid-surface. This is achieved using a cost function that minimizes the volume while considering stressbased constraints, with the material distribution represented by a level set function. The evolution of the shape is driven by the gradient of the cost function within the framework of a Hamilton-Jacobi equation. Both the level set and the displacement fields are described using computer aided design compatible tools, within the framework of isogeometric analysis. This allows for precise definition of the optimal shape and straightforward export of the resulting design to commercial software for manufacturing. Furthermore, the proposed method handles complex, non-conforming multi-patch geometries thanks to an augmented Lagrangian formulation. The latter guarantees strong compatibility with real-world engineering applications. The effectiveness of the method is demonstrated through its application to various three-dimensional multi-patch geometries under different loading conditions
Gallium nitride deposition via magnetron sputtering: Linking plasma-surface interactions and thin film crystalline features
No full textInternational audienceGa-atoms dynamic in an Ar/N2 magnetron sputtering discharge for GaN deposition is explored employing plasma diagnostic techniques such as optical emission spectroscopy and microwave interferometry. Through the assessment of gas temperature, electron temperature and density measured from the abovementioned diagnostics, we estimated both the flux and average energy of Ga-atoms impinging on the substrate. Emphasizing the working pressure as a pivotal factor, this study uncovers a correlation between the Ga-atoms flux, their average energy, and the growth rate and crystallinity of the GaN films extracted from ex-situ characterizations. Notably, the pressure value (6.6 Pa) at which both the growth rate and crystalline fraction are the greatest is also the condition at which both the flux and energy of Ga-atoms impinging on the target are maximal. The findings pave the way for improving the understanding and control of the complex interplay between plasma conditions and resulting film properties in the sputtering process
Global Compression of the Plasma Sheet and Magnetotail During Intense Storms From THEMIS Observations
No full textInternational audienceAbstract We estimate the global impact of storms on the global structure and dynamics of the night side plasma sheet from observations by the NASA mission Time History of Events and Macroscale Interactions during Substorms (THEMIS). We focus on an intense storm occurring in December 2015 triggered by interplanetary coronal mass ejections (ICMEs). It starts with a storm sudden commencement (SSC) phase (SYM‐H +50 nT) followed by a growth phase (SYM‐H −188 nT at the minimum) and then a long recovery phase lasting several days. We investigate THEMIS observations when the spacecraft were located in the midnight sector of the plasma sheet at distances typically between 8 and 13 Earth's radii. It is found that the plasma sheet has been globally compressed up to a value of about 4 nPa during the SSC and main phases, that is, 8 times larger than its value during the quiet phase before the event. This compression occurs during periods of high dynamic pressure in the ICME (20 nPa) about one order of magnitude larger than its value in the pristine solar wind. We infer a global increase of the lobe magnetic field from 30 to 100 nT, confirmed by THEMIS data just outside the plasma sheet. During the SSC and main phases, the plasma sheet is found thinner by a factor of 2 relative to its thickness at quiet times, while the Tsyganenko T96 magnetic field model shows very stretched magnetic field lines from inner magnetospheric regions toward the night side. During the recovery phase, whereas the interplanetary pressure has dropped off, the plasma sheet tends to gradually recover its quiet phase characteristics (pressure, thickness, magnetic configuration, etc.) during a long recovery phase of several days
Aspirations and Limits of an Ecological Science in Zola's La joie de vivre
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Doped SnO 2 thin films fabricated at low temperature by atomic layer deposition with a precise incorporation of niobium atoms
No full textInternational audienceNb-doped SnO 2 (NTO) thin films were synthesized by atomic layer deposition technique at low temperature (100 °C). For an efficient incorporation of the Nb atoms, i.e. fine control of their amount and distribution, various supercycle ratios and precursor pulse sequences were explored. The thin film growth process studied by in-situ QCM revealed that the Nb incorporation is highly impacted by the surface nature as well as the amount of species available at the surface. This was confirmed by the actual concentration of the Nb atom incorporated inside the thin film as determined by XPS. Highly transparent thin films which transmit more than 95% of the AM1.5 global solar irradiance over a wide spectral range (300–1000 nm) were obtained. In addition, the Nb atoms influenced the optical band gap, conduction band, and valence band levels. While SnO 2 thin film were too resistive, films tuned to conductive nature upon Nb incorporation with controlled concentration. Optimal incorporation level was found to be ⩽1 at.% of Nb, and carrier concentration reached up 2.5 × 10 18 cm −3 for the as-deposited thin films. As a result, the high optical transparency accompanied with tuned electrical property of NTO thin films fabricated by ALD at low temperature paves the way for their integration into temperature-sensitive, nanostructured optoelectrical devices
Techniques d’audit des grands modèles de langage
No full textSi les grands modèles de langages sont déjà présents dans notre quotidien à travers les automates conversationnels (en anglais chatbots), leur transversalité pousse à une intégration dans une grande part du tissu économique. Il devient souhaitable de pouvoir les comparer, et nécessaire de comprendre et d’évaluer les risques posés par leur intégration. Un écosystème d’audit des modèles de langage se développe pour répondre à ces aspirations.S’il est difficile de définir ce qu’est un « bon modèle de langage », l’auditer l’est tout autant. Le nombre d’initiatives politiques (Bletchley, 2023) (EO 14110, 2023), juridiques, commerciales et techniques relevant de l’audit de grands modèles de langage ne cesse d’augmenter. Le choix et la mise en avant de certaines techniques d’audit sont souvent liés à des enjeux commerciaux, si ce n’est politiques. Pour cette raison, les solutions qui ressortent peuvent parfois être simplificatrices, voire trompeuses.Pour appréhender l’état actuel de l’écosystème d’audit des grands modèles de langage, il est donc nécessaire de comprendre de façon indépendante la réalité des techniques mises en jeu. C’est l’objet de cette note d’analyse technique.En particulier, un petit nombre de classements et de « benchmarks » occupent une place importante dans les discussions sur les grands modèles de langage. Leur principe et les détails de leur fonctionnement seront explicités
Can Orbital-Selective N\'eel Transitions Survive Strong Nonlocal Electronic Correlations?
No full textThe authors acknowledge support from IDRIS/GENCI Orsay under project number A0130901393 and the help of theCPHT computer support team.International audienceSpin- or orbital-selective behaviours in correlated electron materials offer rich promise for spintronics or orbitronics phenomena and applications deriving from them. Strong local electronic Coulomb correlations might lead to an orbital-selective Mott state, characterised by the coexistence of localized electrons in some orbitals with itinerant electrons in others. Nonlocal electronic fluctuations are much more entangled in orbital space than the local ones. For this reason, finding orbital-selective phenomena related to nonlocal correlations, such as orbital-selective magnetic transitions, is a challenge. In this work we investigate possibilities to realize an orbital-selective N\'eel transition (OSNT). We illustrate that stabilising this state requires a decoupling of magnetic fluctuations in different orbitals, which can only be realized in the absence of Hund's exchange coupling. On the basis of two-orbital calculations for a Hubbard model with different bandwidths we show that the proposed OSNT can be found all the way from the weak to the strong coupling regime. In the weak coupling regime the transition is governed by a Slater mechanism and thus occurs first for the narrow orbital. At strong coupling a Heisenberg mechanism of the OSNT sets in, and the transition occurs first for the wide orbital. Remarkably, at intermediate values of the interaction we find a non-trivial regime of the OSNT, where the Slater mechanism leads to a N\'eel transition occurring first for the wide orbital. Our work suggests strategies for searching for orbital-selective N\'eel ordering in real materials, in view of possible spin-orbitronics applications
Skewness and kurtosis of solar wind proton distribution functions: The normal inverse-Gaussian model and its implications
No full textInternational audienceContext. In the solar wind (SW), the particle distribution functions are generally not Gaussian. They present nonthermal features that are related to underlying acceleration and heating processes. These processes are critical in the overall dynamics of this expanding astrophysical fluid. Aims. The Proton Alpha Sensor (PAS) on board Solar Orbiter commonly observes skewed proton distributions, with a more populated high-energy side in the magnetic field direction than the Gaussian distribution. Our objectives are: (1) to identify a theoretical statistical function that adequately models the observed distributions and (2) to use its statistical interpretation to constrain the acceleration and heating processes. Methods. We analyzed the 3D velocity distribution functions (VDFs) measured by PAS and compared them to model statistical functions. Results. We show that the normal inverse Gaussian (NIG), a type of hyperbolic statistical distribution, provides excellent fits of skewed and leptokurtic proton distributions. NIG can model both the core distribution and the beam, if present. We propose an interpretation that is inspired by the mathematical formulation of the NIG. It assumes that the acceleration or heating mechanism can be modeled as a drifting diffusion process in velocity space, controlled (or subordinated) by the time of interaction of the particles with “accelerating structures”. The probability function of the interaction time is an inverse Gaussian (IG), obtained by considering a random drift across structures of a given size. The control of the diffusion by interaction times that follow an IG probability function formally defines the NIG distribution. Following this model, we show that skewness and kurtosis can be used to estimate the kinetic and thermal energy gains provided by the interaction with structures. For example, in the case studies presented here, the analyzed populations would have gained kinetic energy representing approximately two to four times their thermal energy, with an increase in velocity – due to acceleration – of from one-tenth to one-third of the observed flow velocity. We also show that the model constrains the initial temperature of the populations. Conclusions. Overall, the NIG model offers excellent fits of the observed proton distributions. Combining the skewness and the kurtosis, it also leads to constraints in the part of acceleration and heating due to the interactions with structures in the formation of the proton populations. We suggest that these effects add to the classical thermal evolution of the bulk velocity and temperature resulting from SW expansion