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Injection of acoustic waves via volumetric sources on a control surface for computational aeroacoustics
No full textInternational audienceA formulation to introduce acoustic waves from a control surface using volumetric source terms is proposed for numerical simulations. A general expression of the source terms is derived from the non-linear Euler equations. The method is validated through three academic configurations: the injection of oblique plane waves and the radiation of a monopole source in two and three dimensions, in uniform flow. The governing equations are solved in a Cartesian grid using a low-dispersion and low-dissipation high order finite-difference numerical scheme. However, the control surface has an arbitrary shape, as demonstrated here with the use of a cylindrical surface. Numerical results show good agreement with analytical solutions in both phase and amplitude. The method is then applied to an open-fan aircraft engine configuration. The source terms are computed from a cylindrical control surface enclosing the rotor, based on data extracted from a previous fluid mechanics simulation. The radiated acoustic field is compared with the one obtained using the Ffowcs Williams–Hawkings integral formulation. The two solutions are again found in good agreement for this more realistic configuration
Inégalités de Sobolev Logarithmique généralisées par le schéma JKO
No full textUsing a discrete Bakry-Émery method based on the JKO scheme, relying on the dissipation of entropy and Fisher information along a discrete flow, we establish new generalized logarithmic Sobolev inequality for log-concave measures of the form under strict convexity assumptions on . We then show how this method recovers some well-known inequalities. This approach can be viewed as interpolating between the Bakry-Émery method and optimal transport techniques based on geodesic convexity.En utilisant une version discrète de la méthode de Bakry–Émery basée sur le schéma JKO, reposant sur la dissipation de l’entropie et de l’information de Fisher le long d’un flot discret, nous établissons une nouvelle inégalité de Sobolev logarithmique généralisée pour des mesures log-concaves de la forme , sous des hypothèses de stricte convexité sur . Nous montrons ensuite comment cette méthode permet de retrouver certaines inégalités bien connues. Cette approche peut être vue comme une interpolation entre la méthode de Bakry–Émery et les techniques de transport optimal fondées sur la convexité géodésique
Existence of a solution of the TV Wasserstein gradient flow
No full textOn the flat torus in any dimension we prove existence of a solution to the TV Wasserstein gradient flow equation, only assuming that the initial density is bounded from below and above by strictly positive constants. This solution preserves upper and lower bounds of the densities, and shows a certain decay of the BV norm (of the order of for -- if , otherwise the BV norm is of course bounded -- and of the order of as ). This generalizes a previous result by Carlier and Poon, who only gave a full proof in one dimension of space and did not consider the case .The main tool consists in considering an approximated TV-JKO scheme which artificially imposes a lower bound on the density and allows to find a continuous-in-time solution regular enough to prove that the lower bounds of the initial datum propagates in time, and study on this approximated equation the decay of the BV norm
HARMONY: A Holistic Auto-Scaling Resilient Model for Multi-Objective Adaptation in Microservices Using HPPNs—A Case Study on E-Business Platforms
No full textInternational audienc
Existence and Regularity of Minimizers for a Plateau Approximation Problem
No full textIn this paper, we study the functional introduced by the author in collaboration with Bonnivard, Bretin, and Lemenant, which is designed to approximate Plateau’s problem. We establish the existence of a minimizer and prove its Hölder regularity. Our results may be viewed as a generalization to higher-dimensional surfaces of the one-dimensional work of Bonnivard, Lemenant, and Millot on the approximation of the Steiner problem
A purity theorem for Mahler equations
No full textInternational audienceThe principal aim of this paper is to establish a purity theorem for Mahler functions that is reminiscent of famous purity theorems for G-functions by D. and G. Chudnovsky and for E-functions (and, more generally, for holonomic arithmetic Gevrey series) by Y. André. Our approach is based on a preliminary study of independent interest of the nature of the solutions of Mahler equations. Roughly speaking, we prove a reduction result for Mahler systems, implying that any Mahler equation admits a complete basis of solutions formed of what we call generalized Mahler series. These are sums involving Puiseux series, Hahn series of a very special type and solutions of inhomogeneous equations of order 1 with constant coefficients. In the light of B. Adamczewski, J. P. Bell and D. Smertnig's recent height gap theorem, we introduce a natural filtration on the set of generalized Mahler series according to the arithmetic growth of the coefficients of the Puiseux series involved in their decomposition. This filtration has five pieces. Our purity theorem states that the membership of a generalized Mahler series to one of the three largest pieces of this filtration propagates to any other generalized Mahler series solution of its minimal Mahler equation. We also show that this statement does not extend to the smallest two pieces.</div
3D simulation of residual stresses induced by ElectroMagnetic pulse Peening process
No full textInternational audienceCompression techniques such as shot peening, laser shock peening, and water jet peening are commonly employed to induce residual compressive stresses in mechanical components. These residual stresses play a crucial role in preventing the initiation and propagation of cracks. An innovative method known as the ElectroMagnetic pulse Peening (EMP) process utilizes magnetic forces to introduce residual compressive stresses in mechanical components. The EMP process shares similarities with the ElectroMagnetic Forming (EMF) process, which has been extensively studied through numerical and experimental investigations. Existing numerical studies predominantly feature axisymmetric 2D simulations, with limited availability of 3D simulations due to numerical constraints regarding computing time and resources. Since the EMP process shares similarities with EMF, similar challenges arise with respect to computational resources and time. This paper presents an innovative approach for the 3D simulation of residual stresses induced by the EMP process, based on efficient 2D axisymmetric calculations of the electromagnetic fields. The main objective of this approach is to simulate the mechanical impact of electromagnetic pulses applied by sweeping a surface, in order to analyze the stress distribution in the overlapping regions. First, the 2D model used to simulate electromagnetic phenomena is presented, and the 2D-to-3D transfer technique developed is detailed for computing residual stresses in 3D. Subsequently, the validity of this approach is established through a comparative study between 2D and 3D mechanical results for a single electromagnetic pulse. Finally, a multiple-pulse simulation is conducted to investigate the effect of overlapping treatment regions on an AA6061 aluminum alloy. The outcomes of this study are discussed in terms of the residual stresses at the subsurface
EVALUATING SEGMENTATION USING β1 TOPOLOGICAL METRIC: APPLICATION TO NASAL CAVITIES IN THE CONTEXT OF AIRFLOW SIMULATION
No full textNational audienc
Towards adaptive sustainable scheduling within lithium-ion battery production
No full textInternational audienceThis study studies the increasing complexity of modern manufacturing scheduling, where efficiency, quality, and sustainability must be jointly optimized under flexible machine and operator constraints. Integrating real-time feedback from digital twins into optimization frameworks has emerged as a powerful approach, enabling adaptive and data-informed decision-making. By combining exact methods and metaheuristics, such frameworks can navigate the multi-objective landscape of contemporary production systems effectively. Looking forward, the adoption of surrogate models offers a promising alternative to further enhance performance. By approximating expensive simulations or high-fidelity digital twin responses, surrogate models can significantly reduce computational costs while maintaining solution accuracy