Publications

2025

• Examples of non-scattering inhomogeneities
  
  • Chesnel Lucas
  • Haddar Houssem
  • Li Hongjie
  • Xiao Jingni
  Inverse Problems and Imaging, AIMS American Institute of Mathematical Sciences, 2025, 19 (5). We consider the scattering of waves by a penetrable inclusion embedded in some reference medium. We exhibit examples of materials and geometries for which non-scattering frequencies exist, i.e. for which at some frequencies there are incident fields which produce null scattered fields outside of the inhomogeneity. We show in particular that certain domains with corners or even cusps can support non-scattering frequencies. We relate the latter, for some inclusions, to resonance frequencies for Dirichlet or Neumann cavities. We also find situations where incident non-scattering fields solve the Helmholtz equation in a neighbourhood of the inhomogeneity and not in the whole space. In relation with invisibility, we give examples of inclusions of anisotropic materials which are non-scattering for all real frequencies. We prove that corresponding material indices must have a special structure on the boundary.
• Time-Varying Gaussian Process Bandit Optimization with Experts: No-Regret in Logarithmically-Many Side Queries
  
  • Mauduit Eliabelle
  • Berthier Eloïse
  • Simonetto Andrea
  , 2025, 16017, pp.164-182. We study a time-varying Bayesian optimization problem with bandit feedback, where the reward function belongs to a Reproducing Kernel Hilbert Space (RKHS). We approach the problem via an upper-confidence bound Gaussian Process algorithm, which has been proven to yield no-regret in the stationary case. The time-varying case is more challenging and no-regret results are out of reach in general in the standard setting. As such, we instead tackle the question of how many additional observations asked to an expert are required to regain a no-regret property. To do so, we formulate the presence of past observation via an uncertainty injection procedure, and we reframe the problem as a heteroscedastic Gaussian Process regression. In addition, to achieve a no-regret result, we discard long outdated observations and replace them with updated (possibly very noisy) ones obtained by asking queries to an external expert. By leveraging and extending sparse inference to the heteroscedastic case, we are able to secure a no-regret result in a challenging time-varying setting with only logarithmically-many side queries per time step. Our method demonstrates that minimal additional information suffices to counteract temporal drift, ensuring efficient optimization despite time variation. (10.1007/978-3-032-06096-9_10)
  DOI : 10.1007/978-3-032-06096-9_10
• Non-Destructive Ultrasonic Evaluation of Asphalt Concrete Waterproofing in Hydraulic Structures: Experimental and Numerical Study
  
  • Maifia Nabil
  • Belmokhtar Mohamed
  • Villain Géraldine
  • Vautrin Denis
  • Taillade Frédéric
  • Cothenet Alexis
  , 2025, 30 (10). Some hydraulic structures use a multi-layer asphalt concrete coating to ensure waterproofing. Over time, defects may appear in this coating due to ageing of the materials or environmental conditions. In order to prevent further degradation phenomena that could eventually compromise the stability of the structure, we aim to develop a non-destructive monitoring system based on mechanical waves propagation for early detection of such defects. A first step of this study consists in characterizing the presence of defects in terms of measurable mechanical parameters. To this end, six coating samples taken from both healthy and degraded areas of a real embankment dam are considered. They are analysed using a ultrasound acquisition system. The initial results are promising, showing a difference in dynamic modulus between healthy and degraded areas. (10.58286/31682)
  DOI : 10.58286/31682
• Sampled-Based Guided Quantum Walk: Non-variational quantum algorithm for combinatorial optimization
  
  • Nzongani Ugo
  • Mermoud Dylan Laplace
  • Di Molfetta Giuseppe
  • Simonetto Andrea
  , 2025. We introduce SamBa-GQW, a novel quantum algorithm for solving binary combinatorial optimization problems of arbitrary degree with no use of any classical optimizer. The algorithm is based on a continuous-time quantum walk on the solution space represented as a graph. The walker explores the solution space to find its way to vertices that minimize the cost function of the optimization problem. The key novelty of our algorithm is an offline classical sampling protocol that gives information about the spectrum of the problem Hamiltonian. Then, the extracted information is used to guide the walker to high quality solutions via a quantum walk with a time-dependent hopping rate. We investigate the performance of SamBa-GQW on several quadratic problems, namely MaxCut, maximum independent set, portfolio optimization, and higher-order polynomial problems such as LABS, MAX-$k$-SAT and a quartic reformulation of the travelling salesperson problem. We empirically demonstrate that SamBa-GQW finds high quality approximate solutions on problems up to a size of $n=20$ qubits by only sampling $n^2$ states among $2^n$ possible decisions. SamBa-GQW compares very well also to other guided quantum walks and QAOA. (10.48550/arXiv.2509.15138)
  DOI : 10.48550/arXiv.2509.15138
• Approaches and limitations of Non-Destructive Testing for evaluating bituminous concrete using wave propagation: A review from the laboratory test to in situ case study
  
  • Belmokhtar Mohamed
  • Maifia Nabil
  • Villain Géraldine
  • Vautrin Denis
  • Cothenet Alexis
  , 2025, 30 (10). This work addresses the challenges of using non-destructive testing (NDT) methods based on mechanical wave propagation as alternatives to conventional destructive tests for evaluating the mechanical behavior of bituminous concrete materials and structures. Given the viscoelastic nature of these materials, the paper first outlines the fundamental principles of their mechanical behavior and the key parameters to be identified. The study then focuses on two categories of NDT techniques involving wave propagation: laboratory methods, such as impact resonance testing and ultrasonic excitation; and in-situ methods, referring to geophysical techniques. Finally, the paper presents a comprehensive literature review of these NDT applied to bituminous concrete and discusses their respective advantages and limitations. (10.58286/31648)
  DOI : 10.58286/31648
• On the application of the T-coercivity method for the Helmholtz problem with sign-changing coefficients
  
  • Chaaban Farah
  , 2025. To solve transmission problems with sign-changing coefficients, one can apply the T-coercivity method, which imposes specific mesh conditions near the interface to ensure optimal convergence rates for the finite element approximation. This method was initially proposed and analyzed for the quasi-static case. The aim in this work is to extend it and prove its convergence for the case of non-zero frequency. Additionally, we check its convergence for a general compact perturbation and outline key ideas for a 3D polyhedral interface. Our theoretical results are validated through a numerical test.
• A Newton-type method for non-smooth under-determined systems of equations
  
  • Pinta Titus
  Numerical Algorithms, Springer Verlag, 2025. <div><p>We study a variant of Newton's algorithm applied to under-determined systems of non-smooth equations. The notion of regularity employed in our work is based on Newton differentiability, which generalizes semismoothness. The classic notion of Newton differentiability does not suffice for our purpose, due to the existence of multiple zeros and as such we extend it to uniform Newton differentiability. In this context, we can show that the distance between the iterates and the set of zeros of the system decreases super-linearly. For the special case of smooth equations, the assumptions of our algorithm are simplified. Finally, we provide some numerical examples to showcase the behavior of our proposed method. The key example is a toy model of complementarity constraint problems, showing that our method has great application potential across engineering fields.</p></div> (10.1007/s11075-025-02212-8)
  DOI : 10.1007/s11075-025-02212-8
• Spectrum of slip dynamics, scaling and statistical laws emerge from simplified model of fault and damage zone architecture
  
  • Almakari Michelle
  • Kheirdast N.
  • Villafuerte C.
  • Thomas Marion Y.
  • Dubernet P.
  • Cheng J.
  • Gupta A.
  • Romanet P.
  • Chaillat S.
  • Bhat Harsha S.
  Journal of Geophysical Research : Solid Earth, American Geophysical Union, 2025. <div><p>Seismological and geodetic observations of a fault zone reveal a wide range of slip dynamics, scaling, and statistical laws. However, the underlying physical mechanisms remain unclear. In this study, we show that incorporating an off-fault damage zone-characterized by distributed fractures surrounding a main fault-can reproduce many key features observed in seismic and geodetic data. We model a 2D shear fault zone in which off-fault cracks follow power-law size and density distributions, and are oriented either optimally or parallel to the main fault. All fractures follow the rate-and-state friction law with parameters chosen such that each can host slip instabilities. We do not introduce spatial heterogeneities in the frictional properties of the fault. Using quasi-dynamic boundary integral simulations accelerated by hierarchical matrices, we simulate slip dynamics of this system and analyze the events produced both on and off the main fault. Despite the spatially uniform frictional properties, we observe a natural continuum from slow to fast ruptures, as observed in nature. Our simulations reproduce the Omori law, the inverse Omori law, the Gutenberg-Richter scaling, and the moment-duration scaling. We also observe seismicity localizing toward the main fault when an event is about to nucleate on the main fault. During slow slip events, off-fault seismicity migrates in a pattern resembling a fluid diffusion front, despite the absence of fluids in the model. We also show that tremors, Very Low Frequency Earthquakes (VLFEs), Low Frequency Earthquakes (LFEs), Slow Slip Events (SSEs), and earthquakes (EQs) can all emerge naturally in the ‘digital twin’ framework.</p></div>
• A global-in-time domain decomposition approach for transient acoustic-elastic interaction
  
  • Bonnet Marc
  • Chaillat Stéphanie
  • Nassor Alice
  , 2025. This work develops a global-in-time iterative domain decomposition approach for transient fluid-structure interaction problems involving acoustic scattering by elastic obstacles. The proposed method, inspired by optimized Schwarz waveform relaxation algorithms, proceeds by iteratively exchanging Robin boundary conditions, enabling the non-intrusive coupling of distinct fluid and structure solvers, and works for arbitrary transient incident acoustic fields. We prove the convergence of the proposed coupling iterations in continuous form. A BEM-FEM coupling implementation of the method is then validated against a reference analytical solution, and its efficiency, accuracy and robustness demonstrated through numerical experiments on configurations representative of potential industrial applications.
• Portage GPU d'un solveur éléments finis discontinus hybridisé pour les problèmes d'ondes en fréquence
  
  • Chabib Ahmed
  • Greffe Roland
  • Geuzaine Christophe
  • Modave Axel
  , 2025. Dans ce travail, nous nous intéressons à la résolution par éléments finis de problèmes de propagation d'ondes en régime harmonique de très grande taille. L'utilisation de cartes graphiques (GPU) permet d'accélérer les calculs, mais il est difficile d'en exploiter pleinement la puissance. Nous considérons une méthode d'éléments finis discontinus de type Galerkin (DG) avec des flux amonts, hybridisée utilisant des variables de transmission définies aux faces des éléments. L'élimination des variables physiques conduit à un système linéaire adapté pour une résolution itérative et une implémentation parallèle efficace sur GPU. Après une description de la méthode, appelée CHDG, nous présentons quelques stratégies de mise en oeuvre sur GPU et nous comparons et discutons leurs performances.
• Accelerating non-local exchange in generalized optimized Schwarz methods
  
  • Claeys Xavier
  • Delville Atchekzai Roxane
  SMAI Journal of Computational Mathematics, Société de Mathématiques Appliquées et Industrielles (SMAI), 2025, 11, pp.517-532. The generalized optimised Schwarz method proposed in [Claeys &amp; Parolin, 2022] is a variant of the Després algorithm for solving harmonic wave problems where transmission condition are enforced by means of a non-local exchange operator. We introduce and analyse an acceleration technique that significantly reduces the cost of applying this exchange operator without deteriorating the precision and convergence speed of the overall domain decomposition algorithm. (10.5802/smai-jcm.133)
  DOI : 10.5802/smai-jcm.133
• User-centered decentralized P2P energy trading model for managing line congestion in Energy Communities
  
  • San Martín Sebastián
  • García-Muñoz Fernando
  • Quezada Franco
  • Dávila Sebastián
  Sustainable Energy, Grids and Networks, Elsevier, 2025. <div><p>This paper presents a user-centered, fully decentralized framework to allow an energy community (EC) to self-manage line congestion issues through peer-to-peer (P2P) energy trading and a flexibility market using the users' distributed energy resources (DERs) assets to take an energy seller (buyer) role when they have a surplus (deficit). A three-stage optimization-based model is introduced to consider the users' preferences and identify line congestion issues using the Distflow model to evaluate the distribution network (DN) limitations.</p><p>In this regard, users maximize their benefits in the first optimization stage by optimizing their DER operation.</p><p>In the second stage, the distribution system operator (DSO) solves an optimal power flow model to identify potential congestion given the users' preferences. If congestion occurs, the third stage activates a P2P energy and flexibility market designed to resolve the issue by minimizing deviations from the users' initial preferences. To achieve full decentralization, a two-step alternating direction method of multipliers (ADMM) algorithm is employed: the first step addresses optimal power flow, while the second manages the P2P and flexibility market. Tests were conducted on a 33-bus DN for different DER penetration levels, showing that the methodology efficiently meets energy requirements while respecting the network's physical constraints and improving information security.</p></div>
• Eigenvalue falls in thin broken quantum strips
  
  • Chesnel Lucas
  • Nazarov Sergei A.
  , 2025. We are interesting in the spectrum of the Dirichlet Laplacian in thin broken strips with angle α. Playing with symmetries, this leads us to investigate spectral problems for the Laplace operator with mixed boundary conditions in thin trapezoids characterized by a parameter ε small. We give an asymptotic expansion of the first eigenvalues and corresponding eigenfunctions as ε tends to zero. The new point in this work is to study the dependence with respect to α. We show that for a small fixed ε&gt;;0, at certain particular angles α_k , k = 0, 1, . . . , that we characterize, an eigenvalue dives, i.e. moves down rapidly, below the normalized threshold π^2 /ε^2 as α&gt;0 increases. We describe the way the eigenvalue dives below π^2 /ε^2 and prove that the phenomenon is milder at α_0 = 0 than at α_k for k ≥ 1.
• Optimal Control Problem Under Signal Temporal Logic Constraints: A Robust Reformulation using Augmented Dynamics
  
  • Lai En
  • Bonalli Riccardo
  • Girard Antoine
  • Jean Frédéric
  , 2025. This work presents a novel approach for solving optimal control problems under Signal Temporal Logic (STL) constraints. The proposed method reformulates the original problem as a classical continuous-time optimal control problem by augmenting the system dynamics with auxiliary variables that encode STL satisfaction through their evolution and boundary conditions. Introducing a robustness parameter, we also establish the convergence of the reformulated problem to the original one as this parameter tends to zero. Numerical simulations are realized to demonstrate the feasibility of our method, highlighting its potential for practical applications.
• McKean-Vlasov equations with singular coefficients - a review of recent results
  
  • Bondi Luca
  • Issoglio Elena
  • Russo Francesco
  , 2025. This paper focuses on recent works on McKean-Vlasov stochastic differential equations (SDEs) involving singular coefficients. After recalling the classical framework, we review existing recent literature depending on the type of singularities of the coefficients: on the one hand they satisfy some integrability and measurability conditions only, while on the other hand the drift is allowed to be a generalised function. Different types of dependencies on the law of the unknown and different noises will also be considered. McKean-Vlasov SDEs are closely related to non-linear Fokker-Planck equations that are satisfied by the law (or its density) of the unknown. These connections are often established also in this singular setting and will be reviewed here. Important tools for dealing with singular coefficients are also included in the paper, such as Figalli-Trevisan superposition principle, Zvonkin transformation, Markov marginal uniqueness, and stochastic sewing lemma.
• Isolated Rotor Blade Shape Sensitivity for Aeroacoustic Optimization Using a Discrete Adjoint Framework
  
  • Mohammedi Yacine
  • Daroukh Majd
  • Buszyk Martin
  • Hajczak Antoine
  • Salah El Din Itham
  • Bonnet Marc
  , 2025. A discrete adjoint framework is developed to optimize rotor self-noise from steady fluid simulations in the rotating frame. To this end, a simplified expression of the off-body frequency-domain Ffowcs-Williams and Hawkings (FW-H) equation is derived for far-field observers, following the model of Hanson and Parzych (1993) originally written for on-body surfaces. The latter is implemented and compared against the results given by an established time-domain FW-H solver. Far-field acoustic pressure sensitivities are derived analytically and validated by comparison with second-order accurate finite differences. The sensitivities of any objective function expressed in terms of the acoustic pressure can therefore be reconstructed. Then the discrete adjoint of a Reynolds-averaged Navier-Stokes solver provides the objective function gradients with respect to the blade shape parameters. The complete workflow is validated against finite difference evaluations on an isolated open rotor in cruise conditions. (10.2514/6.2025-3367)
  DOI : 10.2514/6.2025-3367
• Convergence rates of curved boundary element methods for the 3D Laplace and Helmholtz equations
  
  • Faria Luiz
  • Marchand Pierre
  • Montanelli Hadrien
  , 2025. We establish improved convergence rates for curved boundary element methods applied to the three-dimensional (3D) Laplace and Helmholtz equations with smooth geometry and data. Our analysis relies on a precise analysis of the consistency errors introduced by the perturbed bilinear and sesquilinear forms. We illustrate our results with numerical experiments in 3D based on basis functions and curved triangular elements up to order four.
• Attraction of the core and the cohesion flow
  
  • Laplace Mermoud Dylan
  Theory and Decision, Springer Verlag, 2025, 99 (1-2), pp.377-392. We adopt a continuous-time dynamical system approach to study the evolution of the state of a game driven by the willingness to reduce the total dissatisfaction of the coalitions about their payment. Inspired by the work of Grabisch and Sudhölter about core stability, we define a vector field on the set of preimputations from which is defined, for any preimputation, a cohesion curve describing the evolution of the state. We prove that for each preimputation, there exists a unique cohesion curve. Subsequently, we show that, for the cohesion flow of a balanced game, the core is the unique minimal attractor of the flow, the realm of which is the whole preimputation set. These results improve our understanding of the ubiquity of the core in the study of cooperative games with transferable utility. (10.1007/s11238-025-10060-0)
  DOI : 10.1007/s11238-025-10060-0
• $C^{ 0,1}$ -Itô chain rules and generalized solutions of parabolic PDEs
  
  • Ciccarella Carlo
  • Russo Francesco
  Stochastics and Dynamics, World Scientific Publishing, 2025, 25 (03n04). In this paper we first establish an It\^o formula for a finite quadratic variation process $X$ expanding $f(t,X_t),$ when $f$ is of class $C^2$ in space and is absolutely continuous in time. Second, via a Fukushima-Dirichlet decomposition we obtain an explicit chain rule for $f(t,X_t)$, when $X$ is a continuous semimartingale and $f$ is a ``quasi-strong solution'' (in the sense of approximation of classical solutions) of a parabolic PDE. (10.1142/S0219493725500194)
  DOI : 10.1142/S0219493725500194
• The algebraic structures of social organizations: the operad of cooperative games
  
  • Laplace Mermoud Dylan
  • Roca I Lucio Victor
  , 2025. <div><p>The main goal of this paper is to settle a conceptual framework for cooperative game theory in which the notion of composition/aggregation of games is the defining structure. This is done via the mathematical theory of algebraic operads: we start by endowing the collection of all cooperative games with any number of players with an operad structure, and we show that it generalises all the previous notions of sums, products and compositions of games considered by Owen, Shapley, von Neumann and Morgenstern, and many others. Furthermore, we explicitly compute this operad in terms of generators and relations, showing that the Möbius transform map induces a canonical isomorphism between the operad of cooperative games and the operad that encodes commutative triassociative algebras. In other words, we prove that any cooperative game is a linear combination of iterated compositions of the 2-player bargaining game and the 2-player dictator games. We show that many interesting classes of games (simple, balanced, capacities a.k.a fuzzy measures and convex functions, totally monotone, etc) are stable under compositions, and thus form suboperads. In the convex case, this gives by the submodularity theorem a new operad structure on the family of all generalized permutahedra. Finally, we focus on how solution concepts in cooperative game theory behave under composition: we study the core of a composite and describe it in terms of the core of its components, and we give explicit formulas for the Shapley value and the Banzhaf index of a compound game.</p></div>
• On the Formation of Steady Coalitions
  
  • Laplace Mermoud Dylan
  , 2024. This paper studies the formation of the grand coalition of a cooperative game by investigating its possible internal dynamics. Each coalition is capable of forcing all players to reconsider the current state of the game when it does not provide sufficient payoff. Different coalitions may ask for contradictory evolutions, leading to the impossibility of the grand coalition forming. In this paper, we give a characterization of the impossibility, for a given state, of finding a new state dominating the previous one such that each aggrieved coalition has a satisfactory payoff. To do so, we develop new polyhedral tools related to a new family of polyhedra, appearing in numerous situations in cooperative game theory. (10.48550/arXiv.2410.05087)
  DOI : 10.48550/arXiv.2410.05087
• Projection onto the core: An optimal reallocation to correct market failure
  
  • Laplace Mermoud Dylan
  , 2024. This paper provides formulae and algorithms to compute the projection onto the core of a preimputation outside it. The core of a game is described using an exponential number of linear constraints, and we cannot know beforehand which are redundant or defining the polytope. We apply these new results to market games, a class of games in which every game has a nonempty core. Given an initial state of the game represented by a preimputation, it is not guaranteed that the state of the game evolves toward the core following the dynamics induced by the domination relations. Our results identify and compute the most efficient side payment that acts on a given state of the game and yields its closest core allocation. Using this side payment, we propose a way to evaluate the failure of a market to reach a state of the economy belonging to the core, and we propose a new solution concept consisting of preimputations that minimizes this failure. (10.48550/arXiv.2411.11810)
  DOI : 10.48550/arXiv.2411.11810
• Nonlocal vector calculus on the sphere
  
  • Montanelli Hadrien
  • Slevinsky Richard Mikael
  • Du Qiang
  , 2025. (10.48550/arXiv.2505.12372)
  DOI : 10.48550/arXiv.2505.12372
• Two-phase Trajectory Planning Method for Robust Planetary Landing in a Sensor-equipped Area
  
  • Leparoux Clara
  • Hérissé Bruno
  • Jean Frédéric
  , 2025, pp.1296-1301. This article addresses the planetary landing problem by considering uncertainties and leveraging the presence of a detection area where precise measurements are available. The flight consists of two distinct phases: the first phase, subject to a high level of uncertainties, and the second phase, during which the vehicle is feedback controlled to ensure precise landing. We propose a method to compute the optimal control for the initial phase, aiming to minimize fuel consumption for the entire trajectory while satisfying a probabilistic constraint that ensures the vehicle reaches the detection zone with a specified threshold. (10.23919/ECC65951.2025.11186925)
  DOI : 10.23919/ECC65951.2025.11186925
• Parametric study of turbulence ingestion noise for marine propellers
  
  • Lavanant Romain
  • Cotté Benjamin
  • Serre Gilles
  • Mercier Jean-François
  , 2025, pp.1851-1858. Hydrodynamic noise is an important component of the overall noise radiated by a ship, particularly at low frequencies where propeller noise could be dominant especially at high speed. This study proposes a simplified analytical solution of the phenomenon of spectral humps of propeller noise due to the interaction between a rotating propeller and an incident turbulent flow. The acoustic radiation is described by the Ffowcs-Williams and Hawkings analogy in the compact approximation. The inflow turbulence field is assumed to be homogeneous and isotropic and is modeled using a von Kármán spectrum. Experimental validation and comparison with more costly analytical solutions demonstrate the ability of the developed model to correctly capture the characteristics of the humps related to turbulence ingestion. From the results obtained, a parametric analysis enables us to define a criterion for the emergence and shape of turbulence ingestion humps according to the propeller advance ratio, improving the criterion proposed by Ffowcs-Williams and Hawkings in 1969. (10.61782/fa.2025.0670)
  DOI : 10.61782/fa.2025.0670