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Mechanical Properties of a Biocomposite Based on Carbon Nanotube and Graphene Nanoplatelet Reinforced Polymers :: Analytical and Numerical Study
No full textInternational audienceBiocomposites based on thermoplastic polymers and natural fibers have recently been used in wind turbine blades, to replace non-biodegradable materials. In addition, carbon nanofillers, including carbon nanotubes (CNTs) and graphene nanoplatelets (GNPs), are being implemented to enhance the mechanical performance of composites. In this work, the Mori–Tanaka approach is used for homogenization of a polymer matrix reinforced by CNT and GNP nanofillers for the first homogenization, and then, for the second homogenization, the effective matrix was used with alfa and E-glass isotropic fibers. The objective is to study the influence of the volume fraction Vf and aspect ratio AR of nanofillers on the elastic properties of the composite. The inclusions are considered in a unidirectional and random orientation by using a computational method by Digimat-MF/FE and analytical approaches by Chamis, Hashin–Rosen and Halpin–Tsai. The results show that CNT- and GNP-reinforced nanocomposites have better performance than those without reinforcement. Additionally, by increasing the volume fraction and aspect ratio of nanofillers, Young’s modulus E increases and Poisson’s ratio ν decreases. In addition, the composites have enhanced mechanical characteristics in the longitudinal orientation for CNT- reinforced polymer and in the transversal orientation for GNP-reinforced polymer
Sub-laser-cycle control of relativistic plasma mirrors
No full textWe present measurements of high-order harmonics and relativistic electrons emitted into the vacuum from a plasma mirror driven by temporally-shaped ultra-intense laser waveforms, produced by collinearly combining the main laser field with its second harmonic. We experimentally show how these observables are influenced by the phase delay between these two frequencies at the attosecond timescale, and relate these observations to the underlying physics through an advanced analysis of 1D/2D Particle-In-Cell simulations. These results demonstrate that sub-cycle shaping of the driving laser field provides fine control on the properties of the relativistic electron bunches responsible for harmonic and particle emission from plasma mirrors
Model-based adaptive filtering of dielectric elastomer loudspeakers
No full textInternational audienceDielectric elastomers are soft actuators that can reach deformations by more than 500% when a high voltage is applied. They have been considered for use as loudspeakers because of their quick response. One of their limitations is an inhomogeneous frequency response, due to the modal behavior of the membrane. In this study, we set up a sensor-free adaptive filtering strategy that relies on a finite element model of the loudspeaker, to improve the frequency response
A fully backward representation of semilinear PDEs applied to the control of thermostatic loads in power systems
No full textInternational audienceWe propose a fully backward representation of semilinear PDEs with application to stochastic control. Based on this, we develop a fully backward Monte-Carlo scheme allowing to generate the regression grid, backwardly in time, as the value function is computed. This offers two key advantages in terms of computational efficiency and memory. First, the grid is generated adaptively in the areas of interest and second, there is no need to store the entire grid. The performances of this technique are compared in simulations to the traditional Monte-Carlo forward-backward approach on a control problem of thermostatic loads
Novel Techniques for a Verified Simulation of Fractional-Order Differential Equations
No full textInternational audienceVerified simulation techniques have been investigated intensively by researchers who are dealing with ordinary and partial differential equations. Tasks that have been considered in this context are the solution to initial value problems and boundary value problems, parameter identification, as well as the solution of optimal control problems in cases in which bounded uncertainty in parameters and initial conditions are present. In contrast to system models with integer-order derivatives, fractional-order models have not yet gained the same attention if verified solution techniques are desired. In general, verified simulation techniques rely on interval methods, zonotopes, or Taylor model arithmetic and allow for computing guaranteed outer enclosures of the sets of solutions. As such, not only the influence of uncertain but bounded parameters can be accounted for in a guaranteed way. In addition, also round-off and (temporal) truncation errors that inevitably occur in numerical software implementations can be considered in a rigorous manner. This paper presents novel iterative and series-based solution approaches for the case of initial value problems to fractional-order system models, which will form the basic building block for implementing state estimation schemes in continuous-discrete settings, where the system dynamics is assumed as being continuous but measurements are only available at specific discrete sampling instants
Impact of a shock wave on a heterogeneous foam film
No full textInternational audienceLiquid foams are, amongst other applications, used to mitigate shock waves. This aspect has received considerable attention at the macroscopic scale. However, the interaction between foam films and shock waves is still poorly understood and may be an important missing local information to build mitigation models. In this paper, we experimentally identify a new process leading to the foam film rupture, which dominates when the film thickness is sufficiently heterogeneous. Using a two-thickness film with a sharp and localised thickness gradient, we record the deformation of the interface between the thick and the thin parts. We observe the growth of an excess liquid area in the thin part and establish an analytical model and scaling laws which account for this phenomenon. Our results in this ideal configuration are consistent with actual rupture processes at stake in heterogeneous foam films
Meta Automatic Curriculum Learning
No full textA major challenge in the Deep RL (DRL) community is to train agents able to generalize their control policy over situations never seen in training. Training on diverse tasks has been identified as a key ingredient for good generalization,which pushed researchers towards using rich procedural task generation systems controlled through complex continuous parameter spaces. In such complex taskspaces, it is essential to rely on some form of Automatic Curriculum Learning(ACL) to adapt the task sampling distribution to a given learning agent, instead of randomly sampling tasks, as many could end up being either trivial or unfeasible.Since it is hard to get prior knowledge on such task spaces, many ACL algorithms explore the task space to detect progress niches over time, a costly tabula-rasa process that needs to be performed for each new learning agents, although they might have similarities in their capabilities profiles. To address this limitation, we introduce the concept of Meta-ACL, and formalize it in the context of black-box RL learners, i.e. algorithms seeking to generalize curriculum generation toan (unknown) distribution of learners. In this work, we present AGAIN, a first in-stantiation of Meta-ACL, and showcase its benefits for curriculum generation overclassical ACL in multiple simulated environments including procedurally generated parkour environments with learners of varying morphologies
Gamma-convergence results for nematic elastomer bilayers: relaxation and actuation
No full text38 pages, 2 figuresWe compute effective energies of thin bilayer structures composed by soft nematic elastic-liquid crystals in various geometrical regimes and functional configurations. Our focus is on order-strain interaction in elastic foundations composed of an isotropic layer attached to a nematic substrate. We compute Gamma-limits as the layers thickness vanishes in two main scaling regimes exhibiting spontaneous stress relaxation and shape-morphing, allowing in both cases out-of-plane displacements. This extends the plane strain modelling of [*], showing the asymptotic emergence of fully coupled macroscopic active-nematic foundations. Subsequently, we focus on actuation and compute asymptotic configurations of an active plate on nematic foundation interacting with an applied electric field. From the analytical standpoint, the presence of an electric field and its associated electrostatic work turns the total energy into a non-convex and non-coercive functional. We show that equilibrium solutions are min-max points of the system, that min-maximising sequences pass to the limit and, that the limit system can exert mechanical work under applied electric fields. [*]: P. Cesana and A. A. Le\'on Baldelli. "Variational modelling of nematic elastomer foundations". In: Mathematical Models and Methods in Applied Sciences 14 (2018
Variational modelling of nematic elastomer foundations
No full textWe compute the -limit of energy functionals describing mechanical systems composed of a thin nematic liquid crystal elastomer sustaining a homogeneous and isotropic elastic membrane. We work in the regime of infinitesimal displacements and model the orientation of the liquid crystal according to the order tensor theories of both Frank and De Gennes. We describe the asymptotic regime by analysing a family of functionals parametrised by the thickness of the membranes and the relative ratio of the elastic constants, establishing that, in the limit, the system is represented by a two-dimensional integral functional interpreted as a linear membrane on top of a nematic active foundation involving an effective De Gennes optic tensor which allows for low order states. The latter can suppress shear energy by formation of microstructure as well as act as a pre-strain transmitted by the foundation to the overlying film
On a surprising instability result of Perfectly Matched Layers for Maxwell's equations in 3D media with diagonal anisotropy
No full textInternational audienceThe analysis of Cartesian Perfectly Matched Layers (PMLs) in the context of time-domain electromagnetic wave propagation in a 3D unbounded anisotropic homogeneous medium modelled by a diagonal dielectric tensor is presented. Contrary to the 3D scalar wave equation or 2D Maxwell's equations some diagonal anisotropies lead to the existence of backward waves giving rise to instabilities of the PMLs. Numerical experiments confirm the presented result.Dans cette note nous nous intéressons à l’analyse de stabilité de la méthode de couches absorbantesparfaitement adaptées (PMLs) pour la propagation d’ondes électromagnétiques en régime transitoiredans un milieu anisotrope décrit par un tenseur diélectrique diagonal. Contrairement aux cas de l’équationd’ondes scalaire 3D et des équations de Maxwell 2D, certaines anisotropies diagonales mènent à l’existenced’ondes inverses qui provoquent des instabilités de la méthode PML. Ce résultat est illustré par des simulationsnumériques