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The work describes the wave propagation in a periodic structure formed by a linear spring-mass chain with local Duffing non-linear resonators. The wave propagation is studied using the Floquet-Bloch theorem combined with a perturbation approach to identify the dispersion relations in the nonlinear periodic structure. The theoretical model is benchmarked by a numerical model that considers an analogous finite resonant spring-mass system. The numerical nonlinear model provides an apparent dispersion relation of the structure obtained from an inverse identification method, the latter based on imposing a wave number as an initial condition, and then obtaining the corresponding frequency from the analysis of the chain amplitude in the time domain. The perturbation and the numerical methods are compared to discuss the behaviour of the wave propagation in the nonlinear resonators periodic chain. The perturbation is then compared with the Harmonic Balance Method previously used in the literature. Keywords: Periodic structures, Resonators, Non-linearities

International audience; In aviation, safety has always been a key issue to reduce the number of incidents and accidents. Nowadays, it is even more important since the air traffic increases every year, and is predicted to reach 7.8 billion passengers worldwide in 2036. Flight safety offices aim at enhancing safety, analyzing past events, and preventing potential critical occurrences. This paper presents TAPAS, a post-operational aircraft approach analysis tool. The software offers an interactive analysis of aircraft approach energy management. The software uses and validates an existing atypical approach detection algorithm on flight data record and flight safety office events from airlines. Various correlations and analysis are conducted to illustrate the potential benefits of this methodology.

International audience; At supercritical conditions, thermodynamics may become strongly nonlinear which is reflected by large thermodynamic Jacobian values. This means that small variations in density, momentum or energy can result in large pressure perturbations. Because of such nonlinearities, simulations of high-pressure flows are subject to stability issues when the conservative form of the Navier-Stokes system is employed. In high-Reynolds number simulations, transported quantities are altered by numerical scheme errors, stabilization methods and filtering procedures. These alterations affect density and energy independently and may lead to significant pressure oscillations due to the nonlinear behavior of the equation of state. The objective of the present work is to compare three methods based on different sets of transport equations, to measure their impact on pressure and mixing temperature. A classical fully-conservative approach based on the transport of internal energy is compared to two quasi-conservative methods: a pressure-based and an enthalpy-based formulation. A suite of test cases of increasing complexity is employed to expose the main differences between these approaches, at conditions relevant for engineering applications. The analysis first confirmed that the energy-based formulation is prone to artificial pressure fluctuations caused by the interaction between thermodynamic nonlinearities and the numerical dissipation introduced by the stabilization scheme. It is also demonstrated that despite the stability properties of the pressure-based formulation, the mixing temperature is not properly captured since the pressure equation is not used in its conservative form. The enthalpy-based approach however, offers an improved representation of the mixing thermodynamic state while avoiding non-physical pressure variations.

International audience; The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. There is a considerable body of mathematical proofs on on-line optimization programs which can be leveraged to assist in the development and verification of their implementation. In this paper, we demonstrate how theoretical proofs of real-time optimization algorithms can be used to describe functional properties at the level of the code, thereby making it accessible for the formal methods community. The running example used in this paper is a generic semi-definite programming (SDP) solver. Semi-definite programs can encode a wide variety of optimization problems and can be solved in polynomial time at a given accuracy. We describe a top-to-down approach that transforms a high-level analysis of the algorithm into useful code annotations. We formulate some general remarks about how such a task can be incorporated into a convex programming autocoder. We then take a first step towards the automatic verification of the optimization program by identifying key issues to be adressed in future work.

International audience; The computational burden of Large-eddy Simulation for reactive flows is exacerbated in the presence of uncertainty in flow conditions or kinetic variables. A comprehensive statistical analysis, with a sufficiently large number of samples, remains elusive. Statistical learning is an approach that allows for extracting more information using fewer samples. Such procedures, if successful, would greatly enhance the predictability of models in the sense of improving exploration and characterization of uncertainty due to model error and input dependencies, all while being constrained by the size of the associated statistical samples. In this paper, we show how a recently developed procedure for probabilistic learning on manifolds can serve to improve the predictability in a probabilistic framework of a scramjet simulation. The estimates of the probability density functions of the quantities of interest are improved together with estimates of the statistics of their maxima. We also demonstrate how the improved statistical model adds critical insight to the performance of the model.

Prostaglandin E2 (PGE2 ) plays a critical role in intestinal mucosal tolerance and barrier integrity. Cyclooxygenase-2 (COX-2)-dependent PGE2 production involves mobilisation of arachidonic acid. Lactobacillus rhamnosus GG (LbGG) is one of the most widely used probiotics reported to colonise the colonic mucosa. LbGG contributes to the protection of the small intestine against radiation injury through the repositioning of mucosal COX-2 expressing cells. However, it is unknown if LbGG modulates PGE2 production in the colonic mucosa under homeostasis and the major cellular elements involved in these processes. Colonic epithelial and CD90+ mesenchymal stromal cells, also known as (myo) fibroblasts (CMFs), are abundant innate immune cells in normal colonic mucosa able to produce PGE2 . Herein, we tested the hypothesis that under colonic mucosal homeostasis, LbGG modulates the eicosanoid pathway resulting in increased PGE2 production in both epithelial and stromal cells. Among the five tested human colonic epithelial cell lines, only exposure of Caco-2 to LbGG for 24 hr led to the mobilisation of arachidonic acid with concomitant increase in the components within the leukotriene and COX-2-dependent PGE2 pathways. By contrast, CMFs isolated from the normal human colonic mucosa responded to LbGG with increased expression of COX-2 and PGE2 in the prostaglandin pathway, but not 5-LO in the leukotriene pathway. Oral gavage of C57BL/6 mice for 5 days with LbGG (5 × 108 Colony-Forming Unit (CFU)/dose) increased COX-2 expression in the colonic mucosa. The majority of cells upregulating COX-2 protein expression were located in the colonic lamina propria and colocalised with α-SMA+ cells corresponding to the CMF phenotype. This process was myeloid differentiation factor-88-dependent, because silencing of myeloid differentiation factor-88 expression in CMFs abrogated LbGG-induced upregulation of COX-2 in culture and in vivo. Taken together, our data suggest that LbGG increases release of COX-2-mediated PGE2 , contributing to the maintenance of mucosal homeostasis in the colon and CMFs are among the major contributors to this process.

In a context of heightened safety requirements for safety-critical embedded systems and ever-increasing costs of verification and validation, we describe a fully automated, credible autocoding chain for control systems. This chain generates code, along with guarantees of high level functional properties, which cans be independently verified. The platform relies on domain specific knowledge and formal analysis methods to bridge the semantic gap between domain experts and code verification experts. First, a graphical dataflow language is extended with annotation symbols, enabling the control engineer to express high level properties of its control law within the framework of a familiar block-diagram language. A public-domain autocoder is enhanced not only to generate the code implementing the initial design, but also to carry high level properties down to annotations at the level of the code. Finally, using customized code analysis tools, certificates are generated, which guarantee the correctness of the annotations with respect to the code, and can be verified using existing static analysis tools. For now, we limit the conclusions to the bounded-input bounded-output characteristic of linear controllers, however the approach appears readily extendable to a broader array of properties and systems.

International audience; In this paper we derive a new dynamic friction force model for the longitudinal road/tire interaction for wheeled ground vehicles. The model is based on a dynamic friction model developed previously for contact-point friction problems, called the LuGre model. By assuming a contact patch between the tire and the ground we develop a partial differential equation for the distribution of the friction force along the patch. An ordinary differential equation (the lumped model) for the friction force is developed, based on the patch boundary conditions and the normal force distribution along the contact patch. This lumped model is derived to approximate closely the distributed friction model. Contrary to common static friction/slip maps, it is shown that this new dynamic friction model is able to capture accurately the transient behaviour of the friction force observed during transitions between braking and acceleration. A velocity-dependent, steady-state expression of the friction force versus the slip coefficient is also developed that allows easy tuning of the model parameters by comparison with steady-state experimental data. Experimental results validate the accuracy of the new tire friction model in predicting the friction force during transient vehicle motion. It is expected that this new model will be very helpful for tire friction modeling as well as for anti-lock braking (ABS) and traction control design.

Be it snow, volcanic ash or strikes, crisis events impose high costs on the air transport system and society. Airlines have progressively learned to mitigate the irregular operations arising from such events through procedures such as Collaborative Decision Making (CDM) for traffic flow and airport departure management; however the passenger's door-to-door journey during difficult times often remains unpleasant. Meta-CDM (Multimodal, Efficient Transportation in Airports and Collaborative Decision Making), aims at taking a passenger-centric approach when examining how airside and landside CDM can be interlinked with other transport modes to minimize the impact of severe disruptions. In this paper, we provide a preliminary analysis of past successes and failures of passenger-centric operations, by documenting the state of the art in airport CDM, by investigating representative disruptive events and by studying the conditions of development of airport intermodality. In addition, as the success or failure of any new concept depends on which metrics it is being evaluated against, we also discuss the need of relevant KPIs to measure the success of an extended CDM concept.

International audience; Air traffic management ensures the safety of flight by optimizing flows and maintaining separation between aircraft. After giving some definitions, some typical feature of aircraft trajectories are presented. Trajectories are objects belonging to spaces with infinite dimensions. The naive way to address such problem is to sample trajectories at some regular points and to create a big vector of positions (and or speeds). In order to manipulate such objects with algorithms, one must reduce the dimension of the search space by using more efficient representations. Some dimension reduction tricks are then presented for which advantages and drawbacks are presented. Then, front propagation approaches are introduced with a focus on Fast Marching Algorithms and Ordered upwind algorithms. An example of application of such algorithm to a real instance of air traffic control problem is also given. When aircraft dynamics have to be included in the model, optimal control approaches are really efficient. We present also some application to aircraft trajectory design. Finally, we introduce some path planning techniques via natural language processing and mathematical programming.

Embedded system control often relies on linear systems, which admit quadratic invariants. The parts of the code that host linear system implementations need dedicated analysis tools, since intervals or linear abstract domains will give imprecise results, if any at all, on these systems. Previous work by FERET proposes a specific abstraction for digital filters that addresses this issue on a specific class of controllers.This paper aims at generalizing the idea. It works directly on system representation, relying on existing methods from control theory to automatically generate quadratic invariants for linear time invariant systems, whose stability is provable. This class encompasses n-th order digital filters and, in general, controllers embedded in critical systems.While control theorists only focus on the existence of such invariants, this paper proposes a method to effectively compute tight ones. The method has been implemented and applied to some benchmark systems, giving good results. It also considers floating points issues and validates the soundness of the computed invariants.

International audience; In this paper, we present an application of the Floquet-Bloch theorem in the context of electrodynamics for vibroacoustique power flow optimization by mean of distributed and shunted piezoelectric patches. The main purpose of this work is first to propose a dedicated numerical approach able to compute the multi-modal wave dispersions curves into the whole first Brillouin zone for periodically distributed 2D shunted piezo-mechanicalsystems. By using a specific indicator evaluating the evanescent part Bloch’s waves, we optimize, in a second time, the piezoelectric shunting electrical impedance for controlling energy diffusion into the proposed semi-active distributed set of cells. A 3D modeling of semi-distributed distribution of the optimal smart metamaterial is used for validating the obtained cell design.

International audience; The influence of vortical structures on the transport and mixing of passive scalars is investigated. Initial conditions are taken from a direct numerical simulation database of forced homogeneous isotropic turbulence, with passive scalar fluctuations, driven by a uniform mean gradient, are performed for Taylor microscale Reynolds numbers (R λ) of 140 and 240, and Schmidt numbers 1/8 and 1. For each R λ, after reaching a fully developed turbulent regime, which is statistically steady, the Coherent Vorticity Extraction is applied to the flow. It is shown that the coherent part is able to preserve the vortical structures with only less than 4% of wavelet coefficients while retaining 99.9% of energy. In contrast, the incoherent part is structureless and contains negligible energy. By taking the total, coherent and incoherent velocity fields in turn as initial conditions, new simulations were performed without forcing while the uniform mean scalar gradient is maintained. It is found that the results from simulations with total and coherent velocity fields as initial conditions are very similar. In contrast, the time integration of the incoherent flow exhibits its primarily dissipative nature. The evolutions of passive scalars at Schmidt numbers 1/8 and 1 advected by the total, coherent or incoherent velocity suggest that the vortical structures retained in the coherent part play a dominant role in turbulent transport and mixing. Indeed, the total and coherent flows give almost the same time evolution of the scalar variance, scalar flux and mean scalar dissipation, while the incoherent flow only gives rise to weak scalar diffusion.

International audience; In the context of mid-frequency elastodynamical analysis of periodic structures, the Floquet-Bloch theorem has been recently applied. The latter allows the use of limited-size modeling of a representative cell to characterize waves dispersion properties of the assembled structure. The theorem provides a rigorous and well posed spectral problem representing waves dispersion in viscolelastic media. In particular, the wave-FEM (WFE) method and associated techniques are based on the Floquet-Bloch approach. Most of the current applications are limited either to undamped or to slightly damped systems. Through the mesh of the k-space (k being the wave number vector) inside or at the boundary of the first Brillouin zone is performed. For each wave headings a linear spectral problem is solved in order to obtain the corresponding eigenfrequency and the corresponding Floquet vector. Such process is more easily implemented for undamped structures but face some drawbacks when damping is considered. In this paper, the Floquet-Bloch theorem is used to set up an alternative technique in order to estimate the dispersion characteristics of a periodic structure. The approach is based on the same basic assumption, but the generalized eigenvalue problem which has to be solved differs from the one usually considered in WFE. Instead of discretising the k-space, the harmonic frequency and the wave heading are used to scan the k-space. Then the formulated eigenvalue problem is solved and the dispersion characteristics are obtained, including spatial attenuation terms. Some fundamentals properties of the eigensolutions are discussed, and the methodology is finally applied on a 2D waveguide application which can be found in the literature for an undamped case. The same example is considered with various damping levels, in order to illustrate the performances and specificities the efficiency of proposed approach. The proposed approach finds application in the analysis of wave propagation in the presence of damping materials or shunted piezoelectric patches, as well as in actively controlled systems, where equivalent damping terms are associated with the considered control scheme.

Preliminary mission design for planetary satellite orbiters requires a deep knowledge of the long term dynamics that is typically obtained through averaging techniques. The problem is usually formulated in the Hamiltonian setting as a sum of the principal part, which is given through the Kepler problem, plus a small perturbation that depends on the specific features of the mission. It is usually derived from a scaling procedure of the restricted three body problem, since the two main bodies are the Sun and the planet whereas the satellite is considered as a massless particle. Sometimes, instead of the restricted three body problem, the spatial Hill problem is used. In some cases the validity of the averaging is limited to prohibitively small regions, thus, depriving the analysis of significance. We find this paradigm at Enceladus, where the validity of a first order averaging based on the Hill problem lies inside the body. However, this fact does not invalidate the technique as perturbation methods are used to reach higher orders in the averaging process. Proceeding this way, we average the Hill problem up to the sixth order obtaining valuable information on the dynamics close to Enceladus. The averaging is performed through Lie transformations and two different transformations are applied. Firstly, the mean motion is normalized whereas the goal of the second transformation is to remove the appearance of the argument of the node. The resulting Hamiltonian defines a system of one degree of freedom whose dynamics is analyzed. © 2010 Springer Science+Business Media B.V.

A wavelet transform on the negative half real axis is developed using an average-interpolation scheme. This transform is redundant and can be used to perform causal wavelet processing, such as on-line signal denoising, without delay. Nonetheless, in practice some boundary effects occur and thus a small amount of delay is required to reduce them. The effect of this delay is studied using a numerical example of a signal with large noise and sharp transients. It is shown that the delay required to obtain acceptable denoising levels is decreased by using the proposed redundant transform instead of a non-redundant one. We also present results from the experimental implementation of the proposed algorithm for the denoising of a feedback signal during the control of a three-phase permanent-magnet synchronous brushless DC motor. Copyright © 2006 John Wiley & Sons, Ltd.

An extension to the LuGre dynamic friction model from longitudinal to longitudinal/lateral motion is developed in this paper. Application of this model to a tire yields a pair of partial differential equations that model the tire-road contact forces and aligning moment. A comparison of the steady-state behavior of the dynamic model with existing static tire friction models is presented. This comparison allows one to determine realistic values of the parameters for the new dynamic model. By the introduction of a set of mean states we reduce the partial differential equation to a lumped model governed by a set of three ordinary differential equations. Such a lumped form describes the aggregate effect of the friction forces and moments and it can be useful for control design and on-line estimation. A method to incorporate wheel rim rotation is also discussed. The proposed model is evaluated by comparing both its steady-state as well as its dynamic characteristics via a series of numerical simulations. The results of the simulations corroborate steady-state and dynamic/transient tire characteristics found in the literature.

International audience; A wavelet transform on the negative half real axis is developed using an average-interpolation scheme. This transform is redundant and can be used to perform causal wavelet processing, such as signal denoising, without delay. Nonetheless, in practice some boundary effects occur and thus a small amount of delay is required to reduce them. The theory is implemented on a challenging signal with large noise and sharp transients. Results from the experimental implementation of the proposed algorithm for the denoising of a feedback signal for controlling a three-phase permanent-magnet synchronous brushless DC motor are also presented.

International audience; A wavelet transform on the negative half real axis is developed using an average- interpolation scheme. This transform can be used to perform causal wavelet processing, such as signal denoising, with a small delay. The delay required to obtain acceptable denoising levels is decreased by using a redundant transform instead of a non-redundant one. Results from the experimental implementation of the proposed algorithm for the denoising of a feedback signal for controlling a three-phase permanent-magnet synchronous brushless DC motor that drives a reaction wheel system are presented.

International audience; In this paper we derive a dynamic friction force for road/tire interaction for wheeled ground vehicles. The model is based on a similar dynamic friction model for contact developed previously for contact-point friction problems, called the LuGre model. We show that the dynamic LuGre friction model is able to accurately capture velocity and rod/surface dependence of the tire friction force. A comparison between the friction forces predicted by our model and experimental data is also provided.