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A structure and asymptotic preserving scheme for the quasineutral limit of the Vlasov-Poisson system
No full textIn this work, we propose a new numerical method for the Vlasov-Poisson system that is both asymptotically consistent and stable in the quasineutral regime, i.e. when the Debye length is small compared to the characteristic spatial scale of the physical domain. Our approach consists in reformulating the Vlasov-Poisson system as a hyperbolic problem by applying a spectral expansion in the basis of Hermite functions in the velocity space and in designing a structure-preserving scheme for the time and spatial variables. Through this Hermite formulation, we establish a convergence result for the electric field toward its quasineutral limit together with optimal error estimates. Following this path, we then propose a fully discrete numerical method for the Vlasov-Poisson system, inspired by the approach in [6], and rigorously prove that it is uniformly consistent in the quasineutral limit regime. Finally, we present several numerical simulations to illustrate the behavior of the proposed scheme. These results demonstrate the capability of our method to describe quasineutral plasmas and confirm the theoretical findings: stability and asymptotic preservation
A wake-up strategy enabling GNSS-free NB-IoT links to sparse LEO satellite constellations
No full textInternational audienceThe latest release by the 3rd Generation Partnership Project (3GPP) defines how a non-terrestrial NB-IoT link may be set up between User Equipments (UE) on the ground and Low Earth Orbit (LEO) satellites equipped with Evolved Nodes B (eNB). However, a strong assumption is undertaken. Each UE must have Global Navigation Satellite Systems (GNSS) capabilities to properly pre-compensate the Doppler frequency shift and the propagation delay according to the time-varying relative motion of satellites. Additionally, although Release 18 accounts for discontinuous coverage by LEO satellites, the management of next passes over any spot on the Earth is undefined, thus affecting the system scalability. Remarkably, this contribution enables GNSS-free NB-IoT Direct-to-Satellite communications with sparse LEO satellite constellations. To do that, the UE periodically wakes up until it detects a satellite pass in its range. By listening to several NB-IoT beacons, the estimated Doppler curve is used to pre-compensate ongoing communications in frequency and time. Furthermore, the UE uses the standard information sent from the eNB, together with its own estimated location, to guess the next satellite pass without using GNSS. Simulation results reveal that the introduced wake-up strategy allows GNSS-free UEs to save more energy than if equipped with the most power-efficient GNSS chipsets surveyed in 3GPP specifications, promoting the broader deployment of IoT devices in remote and underserved areas.</div
Directional light scattering in Mie-resonant Si particles with ultra-thin plasmonic shells
No full textInternational audienceMetamaterial research has sought to create nanostructures with strong directional optical scattering to control light propagation at the nanoscale. Core-shell architectures comprised of both resonant cores and resonant shells have been suggested as candidate particles in which the spectral overlap of the electric and magnetic dipoles can be controlled to create strong directional scattering. In this study, we present Au-decorated Si core-shell (Si@Au) particles. These were synthesized by first creating Si particles through the thermal disproportionation of hydrogen silsesquioxane (HSQ), which were then decorated with ∼ 4 nm diameter Au nanoparticles. We characterized the resonant behavior of the core-shell particles using electron energy-loss spectroscopy mapping and optical single-particle scatter spectroscopy. These observations were supported by T-matrix simulations and Mie theory calculations of the scattering spectra, which show that compared to Si, Si@Au particles demonstrate a dampened magnetic dipole resonance for smaller Si core diameters (100 -130 nm) and an enhanced magnetic dipole resonance for larger Si core sizes (150 -200 nm). However, we show that to significantly improve forward scattering intensity, continuous plasmonic shells of ~12 nm thickness are needed
Approximation of feedback gains for abstract parabolic systems
No full textInternational audienceWe consider parabolic controlled systems represented by a pair (A, B), where (A, D(A)) is the infinitesimal generator of an analytic semigroup on a Hilbert space Z and B is an unbounded control operator from a control space U into Z. We consider approximate controlled systems (A ε , B ε ), for ε > 0, where (A ε , D(A ε )) is the infinitesimal generator of an analytic semigroup on a Hilbert space Z ε and B ε is an unbounded control operator from the control space U into Z ε . Since Z ε is not included in Z, we are in the case of nonconforming approximations. We assume that both Z and Z ε are Hilbert subspaces of another Hilbert space H, and that there exist projectors P ∈ L(H) and P ε ∈ L(H) such that Z = P H and Z ε = P ε H, and for which (A, B, P ) and (A ε , B ε , P ε ) satisfy suitable approximation assumptions.When the pair (A, B) is exponentially feedback stabilizable in Z, we first prove that the pair (A ε , B ε ) is exponentially feedback stabilizable in Z ε , uniformly with respect to ε ∈ (0, ε 0 ), for some ε 0 > 0. We next prove that Riccati-based feedback laws stabilizing (A, B) in Z can be approximated by feedback laws stabilizing (A ε , B ε ) in Z ε . This type of results has been established in the eighties and the nineties in the case of conforming approximation, that is when Z ε ⊂ Z. To the best of our knowledge nothing is known in the case of nonconforming approximations. We also extend, to the case of nonconforming approximations, convergence rates obtained in the case of conforming approximations. Nonconforming approximations play a central role in fluid mechanics. In [2], we have shown that the results proved in the present paper apply to the Oseen system (the Navier-Stokes equations linearized around a steady state) and its semidiscrete approximation by a Finite Element Method.</div
Critical Dynamics of the Anderson Transition on Small-World Graphs
No full textThe Anderson transition on random graphs draws interest through its resemblance to the many-body localization (MBL) transition with similarly debated properties. In this Letter, we construct a unitary Anderson model on Small-World graphs to characterize long time and large size wave-packet dynamics across the Anderson transition. We reveal the logarithmically slow non-ergodic dynamics in the critical regime, confirming recent random matrix predictions. Our data clearly indicate two localization times: an average localization time that diverges, while the typical one saturates. In the delocalized regime, the dynamics are initially non-ergodic but cross over to ergodic diffusion at long times and large distances. Finite-time scaling then allows us to characterize the critical dynamical properties: the logarithm of the average localization time diverges algebraically, while the ergodic time diverges exponentially. Our results could be used to clarify the dynamical properties of MBL and could guide future experiments with quantum simulators
Cluster transport induced by a thermal gradient on a crystalline surface
No full textInternational audienceUsing molecular dynamic (MD) simulations, we study the thermomigration of small clusters consisting of 2, 3 or 4 atoms on a crystalline surface. After evidencing the thermomigration by analyzing the cluster trajectories, we generalize the thermodynamic integration method to compute a thermodynamic potential driving the probability of presence of the clusters on a substrate submitted to a thermal gradient. The study of this thermodynamic potential allows to disentangle the thermomigration effective force from the stochastic diffusion. We show that the heat of transport characterizing the effective force responsible for thermomigration is the sum of the free energy of the cluster-substrate and cluster internal energies. Finally, an unidimensional kinetic model for the thermomigration is proposed and its results compared to the MD trajectories
Formal Integration of Derived Foliations
No full textFrobenius' theorem in differential geometry asserts that every involutive subbundle of the tangent bundle of a manifold M integrates to a decomposition of M into smooth leaves. We prove an infinitesimal analogue of this result for locally coherent qcqs schemes X over coherent rings. More precisely, we integrate partition Lie algebroids on X to formal moduli stacks X → S, where S is the formal leaf space and the fibres of X → S are the formal leaves. We deduce that deformations of X-families of algebro-geometric objects are controlled by partition Lie algebroids on X. Combining our integration equivalence with a result of Fu, we deduce that Toën–Vezzosi's infinitesimal derived foliations (under suitable finiteness hypotheses) are formally integrable
Comparison of different feedback controllers on an airfoil benchmark
No full textInternational audienceThe present paper proposes a comparison of three well-established controllers: a robust proportionalintegral-derivative (PID) controller (Conord and Peaucelle, 2021), a model-free control (Fliess and Join, 2013, 2022) and an adaptive sliding-mode control based on the super-twisting algorithm (Shtessel et al., 2023). The benchmark considered is an airfoil section equipped with trailing edge jets, load sensors and a perturbation system. The objective is to track the lift command under external wind perturbations. The outcome of this work is the comparison of performances for three control laws that are suitable when little knowledge is known from the physics. This study quantifies performance not only in terms of load control, but also in the needed implementation effort
Magnetic Dirac operator in strips submitted to strong magnetic fields
No full textInternational audienceWe consider the magnetic Dirac operator on a curved strip whose boundary carries the infinite mass boundary condition. When the magnetic field is large, we provide the reader with accurate estimates of the essential and discrete spectra. In particular, we give sufficient conditions ensuring that the discrete spectrum is non-empty.</div
WEAK UNIQUENESS FOR THE PDE GOVERNING THE JOINT LAW OF A DIFFUSION AND ITS RUNNING SUPREMUM
No full textIn a previous work [8], it was shown that the joint law of a diffusion process and the running supremum of its first component is absolutely continuous, and that its density satisfies a non standard weak partial differential equation (PDE). In this paper, we establish the uniqueness of the solution to this PDE, providing a more complete understanding of the system’s behavior and further validating the approach introduced in [8]