Publications

2026

• A note on the discrete Unmapped Tent Pitching for the heterogeneous wave equation
  
  • Bonazzoli Marcella
  • Ciaramella Gabriele
  • Mazzieri Ilario
  , 2026. The Unmapped Tent Pitching (UTP) algorithm is a space-time domain decomposition method for the parallel solution of wave-type problems. We have recently extended UTP to heterogeneous settings and compared, at the continuous level, the computational cost of different space-time decompositions. In this note, we report discrete-level observations showing that the optimal decomposition strategy may differ from the one predicted by the continuous analysis.
• A doubly reduced approximation for the solution to PDE's based on a domain truncation and a reduced basis method: Application to Navier-Stokes equations
  
  • Grosjean Elise
  • Maday Yvon
  , 2023. This paper focuses on the non-intrusive reduced basis (NIRB) method called the \textit{two grids method}. It is used for the simulation of parametric partial differential equations to reduce the associated computational costs of a High-Fidelity code when such problems must be solved for a large number of parameter values or provide a solution in “real time”. As other reduced basis approaches, the “offline step” relies on the High-Fidelity method with a fine enough grid. On the contrary, the non-intrusiveness of the original \textit{two grids method} is based on the use, in the “online step”, of the same method with a much coarser grid, which considerably reduces the cost of this step. We extend here this idea by further reducing the “online step” and further simplify the High-Fidelity method. As an example of application we consider a classical fluid problem, the 2D Backward Facing Step (BFS). We simplify the model by i) truncating the outflow part of the channel at extreme and ii) using a coarse uniform mesh instead of refining it at the re-entrant corner, both choices that contradict what is required to get a high fidelity representation of the flow. To accomplish this, we create two reduced bases and a deterministic process that allows us to pass from one to the other. Several numerical simulations illustrate the ability of this new approach.
• Comprehensive dataset of continuously monitored hydrodynamic and physico-chemical parameters in various karst systems, France
  
  • Cinkus Guillaume
  • Bondu Raphaël
  • Aliouache Mohammed
  • Jourde Hervé
  • Mazzilli Naomi
  • Arfib Bruno
  • Bailly-Comte Vincent
  • Batiot-Guilhe Christelle
  • Celle Hélène
  • Delbart Célestine
  • Fournier Matthieu
  • Labat David
  • Peyraube Nicolas
  • Steinmann Marc
  • Valdès-Lao Danièle
  • Baudement Cécile
  • Béranger Sandra
  • Binet Stéphane
  • Boetsch Anne
  • Brunet Pascal
  • Carrière Simon Damien
  • Chalikakis Konstantinos
  • Charlier Jean-Baptiste
  • Cousquer Yohann
  • Défarge Christian
  • Ducasse Joshua
  • Emblanch Christophe
  • Fabre Juliette
  • Fleury Perrine
  • Garin Thibaut
  • Huon Julien
  • Jardani Abderrahim
  • Johannet Anne
  • Jouves Johan
  • Jozja Nevila
  • Justy Lucile
  • Ladouche Bernard
  • Lamarque Thierry
  • Lastennet Roland
  • Léonardi Véronique
  • Lobry Olivier
  • Lorette Guillaume
  • Loup Christophe
  • Marchand Pierre
  • Manière Louis
  • Maréchal Jean-Christophe
  • Martin Lucie
  • Muller Rémi
  • Massei Nicolas
  • Naessens Fabien
  • Ollivier Chloé
  • Probst Anne
  • Seidel Jean-Luc
  • Serene Leïla
  • Sivelle Vianney
  • Zappelli Alexandre
  Scientific Data, Nature Publishing Group, 2026. Karst aquifers are a crucial source of water, supplying approximately 10% of the global population and often serving as the sole water resource in certain regions. These aquifers are characterized by highly heterogeneous flow dynamics and exhibit significant temporal variability in both hydrodynamic and physico-chemical conditions. Continuous monitoring of these parameters is essential for advancing our understanding of karst aquifer functioning; however, comprehensive, high-frequency datasets remain limited. We present a comprehensive dataset covering 13 karst springs monitored across nine observatories of the French Karst National Observatory Service (SNO KARST), spanning various hydroclimatic regions (oceanic, mountainous, Mediterranean). The SNO KARST aims to strengthen knowledge-sharing and to promote cross-disciplinary research on karst systems at the national scale. The dataset includes: (1) hydrodynamic data (water level, discharge), and (2) physico-chemical data (water temperature, electric conductivity, pH, dissolved oxygen, turbidity, Total Organic Carbon (TOC), Dissolved Organic Carbon (DOC), nitrate, and organic matter fluorescence). Spanning over a decade of continuous monitoring, such a dataset is required for the analysis of the hydrological and physico-chemical dynamics of karst aquifers, the assessment of their vulnerability to pollution and climate change, and the modeling of hydrodynamic and hydrochemical variables, ultimately aiming to improve the management and preservation of these critical water resources in contrasted contexts. (10.1038/s41597-026-07561-0)
  DOI : 10.1038/s41597-026-07561-0
• Numerical analysis of an optimal control approach to solve a tsunami inverse problem
  
  • Bourgeois Laurent
  • Moireau Philippe
  • Terrine Raphaël
  , 2026. This paper concerns the reconstruction of an abrupt bottom displacement of the ocean from the measurement of the induced perturbation of the free surface, which is a severely ill-posed inverse problem. This problem is solved by using an optimal control approach, the physics being governed by a time evolution system based on a simple oceanography model. We firstly recast the problem in an abstract framework, secondly propose an implicit Euler scheme for the time discretization combined with a Finite Element method for the space discretization. The main result is an error estimate between the solution to the discrete control optimal problem and the solution to the continuous optimal problem, which is obtained by considering the discrete and continuous weak mixed formulations that characterize the optimality for these two problems. Some numerical experiments illustrate the efficiency of our approach and the consistency of our error estimate.
• No-regret optimization of time-varying bilevel problems
  
  • Mauduit Eliabelle
  • Berthier Eloïse
  • Simonetto Andrea
  , 2026. Bilevel optimization problems arise in many applications where decisions must account for the optimal response of another system, such as in game-theoretic settings. However, these problems are notoriously challenging, as even linear bilevel programs are strongly NP-hard. In this work, we consider bilevel optimization with a known upper-level objective and an unknown, potentially time-varying lower-level response, accessible only through noisy zeroth-order observations. We propose W-SparQ-BL, a Bayesian optimization framework that models the lower-level mapping using multi-output Gaussian processes and enables efficient optimization under uncertainty. Our approach leverages a sparse, observation-based approximation to control the effect of noise and temporal variability, while requiring only limited access to additional information over time. We establish regularity results linking the lower-level response to standard RKHS assumptions for common kernels, including Matérn and squared exponential. We prove that W-SparQ-BL achieves sublinear dynamic regret in both stationary and time-varying settings. Experiments on representative time-varying game-theoretic problems demonstrate the effectiveness of our approach.
• An inverse tsunami problem in the time domain: a well-posedness analysis of the forward problem and an inversion strategy based on a mixed formulation of the Tikhonov regularization
  
  • Bourgeois Laurent
  • Moireau Philippe
  • Terrine Raphaël
  , 2026. This contribution concerns an inverse problem related to a tsunami in the ocean, the tsunami being caused by a submarine earthquake. Considering the very beginning of the phenomenon, a simple linear model incorporating both gravity and acoustic waves is proposed. The main objective is to develop a strategy to solve the inverse problem of retrieving the bottom displacement from the induced free surface perturbation. Such strategy is based on a mixed formulation of the Tikhonov regularization in the space/time domain, the regularization parameter being determined by using the Morozov principle by means of duality in optimization. Some numerical experiments in 2D, which rely on a tensorized finite element method, show that our strategy is effective. A secondary objective is to prove existence and uniqueness of both strong and variational solutions to the forward problem.
• Influence of aerodynamic-acoustic trade-off on weighted-sum optimization of an open rotor and mulitpoint optimization using a discrete adjoint framework
  
  • Mohammedi Yacine
  • Daroukh Majd
  • Buszyk Martin
  • Hajczak Antoine
  • Bonnet Marc
  • Salah El-Din Itham
  , 2026, Session: Advances in Open Fan Aeroacoustic Research I, pp.AIAA 2026-3353. Weighted-sum aeroacoustic optimizations are conducted on an isolated open rotor under cruise and take-off conditions to investigate the influence of aerodynamic-acoustic trade-off within the objective function. The composite objective function combines torque and acoustic power level at the Blade Passing Frequency (BPF), while thrust is imposed as a constraint. To this end, a discrete adjoint framework is employed to calculate and provide gradients of the objective function and constraints. A mesh deformation tool modifies the geometry based on updated values of design parameters provided by the optimizer. The acoustic metric is evaluated using a simplified expression of the off-body frequency-domain Ffowcs-Williams and Hawkings (FW-H) equation derived for far-field observers, following the model of Hanson and Parzych (1993) originally written for on-body surfaces. Aerodynamic performance is quantified through axial and tangential forces. The sensitivities of the aerodynamic and acoustic metrics are obtained by analytically differentiating their expressions. Then, the discrete adjoint of a Reynolds-averaged Navier-Stokes solver supplies gradients of the objective and constraint functions relative to blade shape parameters. These values and their gradients are then used by a gradient-based optimizer to guide the aeroacoustic design optimization process. Analysis of the resulting optimal geometries reveals that scenarios accounting for combined contributions of torque and acoustic power at the BPF provide the most favorable trade-offs, with reduced shock intensity associated with dihedral effects at cruise, and delayed flow detachment linked to sweepback effects at take-off, thereby maintaining favorable aerodynamic loading distributions across operating conditions. (10.2514/6.2026-3353)
  DOI : 10.2514/6.2026-3353
• Theoretical Study of Turbulence Ingestion Noise for Propellers in Nonuniform Flows
  
  • Lavanant Romain
  • Cotté Benjamin
  • Serre Gilles
  • Mercier Jean-François
  , 2026. This paper presents an analytical model for predicting the broadband noise radiated by a propeller ingesting a spatially nonuniform turbulent flow. The formulation, derived from Goldstein's acoustic analogy, expresses the far-field power spectral density through azimuthal Fourier decompositions of the incident heterogeneous turbulence spectrum, thereby retaining inter-strip and blade-to-blade correlations along the blade span. The spatially varying turbulence parameters (integral length scale and turbulence intensity) that serve as inputs to the spectrum models are derived analytically from Prandtl's mixing-length shear-production approach. Two turbulence spectrum formulations are considered: a heterogeneous isotropic von Kármán spectrum and a heterogeneous anisotropic Kerschen-Gliebe spectrum. A comparison with experimental data for a rotor ingesting a turbulent boundary layer highlights the respective roles of anisotropy and heterogeneity. On the one hand, an isotropic turbulence description fails to reproduce the measured spectral humps (haystacks) at blade passing frequency harmonics; anisotropy with a stretched streamwise length scale is required. On the other hand, the heterogeneous model captures the progressive attenuation of higher-order haystacks through destructive interference between contributions of varying eddy sizes across the propeller disk, an effect that homogeneous models systematically overpredict. (10.2514/6.2026-3517)
  DOI : 10.2514/6.2026-3517
• Eigenvalue falls in thin broken quantum strips
  
  • Chesnel Lucas
  • Nazarov Sergei A.
  , 2025. We are interested in the spectrum of the Dirichlet Laplacian in thin broken strips with angle $\alpha$. Playing with symmetries, this leads us to investigate spectral problems for the Laplace operator with mixed boundary conditions in trapezoids of thickness $\varepsilon>0$ small. We give an asymptotic expansion of the first eigenvalues and corresponding eigenfunctions as $\varepsilon$ tends to zero. The new point in this work is to study the dependence with respect to $\alpha$. We highlight a curious phenomenon of diving eigenvalues: when the strip is more and more broken, at certain critical angles, that we characterize, an eigenvalue moves down very rapidly below the pack of other eigenvalues. We prove that this occurs more gently at $\alpha=0$ than at positive critical angles.
• Réduction de modèles pour les interactions fluide-structure : exploitation des fonctions de Green adaptées
  
  • Chaillat Stéphanie
  • Pacaut Louise
  • Mercier Jean-François
  • Serre Gilles
  • Trafny Nicolas
  , 2026. Nous considérons un problème d’interaction fluide-structure sur une géométrie complexe, pour lequel nous souhaitons calculer la réponse à des excitations variables. Pour réduire considérable- ment le coût de calcul de cette étude paramétrique sans sacrifier la précision, nous proposons une ap- proche de réduction de modèle séparant les effets de la géométrie et de la source. La méthode repose sur le calcul d’une fonction de Green adaptée au couplage fluide-structure et à la géométrie complexe. Pour rendre le coût de la phase offline acceptable, nous exploitons des méthodes d’éléments de frontière rapides.
• Méthode d'éléments finis discontinus hybridisée pour la résolution itérative accélérée de problèmes d'ondes en fréquence
  
  • Modave Axel
  • Greffe Roland
  • Geuzaine Christophe
  • Rappaport Ari
  • Chabib Ahmed
  , 2026. La discrétisation de problèmes de propagation d’ondes en régime harmonique par éléments finis conduit à des systèmes linéaires coûteux à résoudre. Nous considérons une méthode d’éléments finis discontinus hybridisée en utilisant des variables de transmission aux interfaces entre les mailles. Cette approche permet d’accélérer la convergence des schémas itératifs et possède une structure algo- rithmique adaptée au calcul parallèle, notamment sur cartes graphiques. Nous présentons et étudions des implémentations de cette méthode au moyen de résultats 3D obtenus avec un code C++ dédié.
• A non-local singular non-linear Fokker-Planck PDE
  
  • Bondi Luca
  • Issoglio Elena
  • Russo Francesco
  , 2026. The focus of this paper is a non-local singular non-linear Fokker-Planck partial differential equation (PDE). The peculiarity of this PDE feature is in its divergence coefficient, which presents a product between a Besov distribution and a non-linearity. The latter involves the convolution between an integrable kernel K and the solution of the PDE, which leads to a non-locality of the first order term in the PDE. We prove existence and uniqueness of a solution to the PDE as well as continuity results on its coefficients. Previous analytical results are then applied to the study of well-posedness in law for a non-local singular McKean stochastic differential equation. As byproduct of that probabilistic representation, we establish mass conservation and positivity preserving for the PDE.
• Poisson-type problems with transmission conditions at boundaries of infinite metric trees
  
  • Kachanovska Maryna
  • Naderi Kiyan
  • Pankrashkin Konstantin
  Journal of Mathematical Analysis and Applications, Elsevier, 2026, 557 (1), pp.130261. The paper introduces a Poisson-type problem on a mixed-dimensional structure combining a Euclidean domain and a lower-dimensional self-similar component touching along a compact surface (interface). The lower-dimensional piece is a so-called infinite metric tree (one-dimensional branching structure), and the key ingredient of the study is a rigorous definition of the gluing conditions between the two components. These constructions are based on the recent concept of embedded trace maps and some abstract machineries derived from a suitable Green-type formula. The problem is then reduced to the study of Fredholm properties of a linear combination of Dirichlet-to-Neumann maps for the tree and the Euclidean domain, which yields desired existence and uniqueness results. One also shows that large finite sections of the tree can be used for an efficient approximation of solutions (10.1016/j.jmaa.2025.130261)
  DOI : 10.1016/j.jmaa.2025.130261
• Fault Volume Digital Twin to Reproduce the Full Slip Spectrum, Scaling, and Statistical Laws
  
  • Almakari Michelle
  • Kheirdast Navid
  • Villafuerte Carlos
  • Thomas M.
  • Dubernet Pierpaolo
  • Cheng Jinhui
  • Gupta Ankit
  • Romanet P.
  • Chaillat S.
  • Bhat H.
  Journal of Geophysical Research : Solid Earth, American Geophysical Union, 2026, 131 (5), pp.e2025JB032915. Seismological and geodetic observations of fault zones reveal diverse slip dynamics, scaling, and statistical laws. Existing mechanisms explain some but not all of these behaviors. 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 rate‐and‐state friction with parameters enabling slip instabilities. We do not introduce spatial heterogeneities in frictional properties. Using quasi‐dynamic boundary integral simulations accelerated by hierarchical matrices, we simulate slip dynamics and analyze events produced both on and off the main fault. Despite spatially uniform frictional properties, we observe a natural continuum from slow to fast ruptures, as seen in nature. Our simulations reproduce the Omori law, inverse Omori law, Gutenberg‐Richter scaling, and moment‐duration scaling. We observe seismicity localizing toward the main fault before nucleation of main‐fault events. During slow slip events (SSEs), off‐fault seismicity migrates in patterns resembling fluid diffusion fronts, despite the absence of fluids. We show that tremors, very low‐frequency earthquakes, low frequency earthquakes, SSEs, and earthquakes can all emerge naturally within this fault volume framework, making it an ideal digital twin for testing hypotheses, performing ground‐truth inversions, and probing mechanical properties inaccessible with natural observations. (10.1029/2025JB032915)
  DOI : 10.1029/2025JB032915
• A Rellich-type theorem for the Helmholtz equation in a junction of stratified media
  
  • Al Humaikani Sarah
  • Bonnet-Ben Dhia Anne-Sophie
  • Fliss Sonia
  • Hazard Christophe
  , 2026. <div><p>We prove that there are no non-zero square-integrable solutions to a two-dimensional Helmholtz equation in some unbounded inhomogeneous domains which represent junctions of stratified media. More precisely, we consider domains that are unions of three half-planes, where each half-plane is stratified in the direction orthogonal to its boundary. As for the well-known Rellich uniqueness theorem for a homogeneous exterior domain, our result does not require any boundary condition. Our proof is based on half-plane representations of the solution which are derived through a generalization of the Fourier transform adapted to stratified media. A byproduct of our result is the absence of trapped modes at the junction of open waveguides as soon as the angles between branches are greater than π/2.</p></div>
• Stability of time stepping methods for discontinuous Galerkin discretizations of Friedrichs' systems
  
  • Imperiale Sébastien
  • Joly Patrick
  • Rodríguez Jerónimo
  , 2025. In this work we study new various energy-based theoretical results on the stability of s-stages, s-th order explicit Runge-Kutta integrators as well as a modified leap-frog scheme applied to discontinuous Galerkin discretizations of transient linear symmetric hyperbolic Friedrichs' systems. We restrict the present study to conservative systems and Cauchy problems.
• A posteriori error estimates for mixed finite element discretization of the multigroup Neutron Simplified Transport equations with Robin boundary condition
  
  • Ciarlet Patrick
  • Do Minh-Hieu
  • Gervais Mario
  • Madiot François
  , 2026. We analyse a posteriori error estimates for the discretization with mixed finite elements on simplicial or Cartesian meshes of the multigroup neutron simplified transport (SPN ) equations, in the case where a Robin (or Fourier type) boundary condition is imposed on the boundary. This boundary condition is of particular importance in neutronics, since it corresponds to the well-known vacuum boundary condition. We provide guaranteed and locally efficient estimators. In particular, a specific estimator is designed to handle the Robin boundary condition. We also develop the theory in the case of mixed imposed boundary conditions, of Dirichlet, Neumann or Fourier type. The approach is further extended to a Domain Decomposition Method, the so-called DD+L 2 jumps method. In this framework, the adaptive mesh refinement strategy is implemented for a discretization using Cartesian meshes on each subdomain. Numerical experiments illustrate the theory.
• A neural operator framework for solving inverse scattering problems
  
  • Chenu Victor
  • Haddar Houssem
  • Montanelli Hadrien
  , 2026. We present a neural operator framework for solving inverse scattering problems. A neural operator produces a preliminary indicator function for the scatterer, which, after appropriate rescaling, is used as a regularization parameter within the Linear Sampling Method to validate the initial reconstruction. The neural operator is implemented as a DeepONet with a fixed radial-basis-function trunk, while the noise level required for rescaling is estimated using a dedicated neural network. A neural tangent kernel analysis guides the architectural design, reducing the network tuning to a single discretization parameter, adjustable according to the wavelength. Two-dimensional numerical experiments demonstrate the method's effectiveness, with a Python toolbox provided for reproducibility.
• A comparative analysis of different carbon cap policies on the economic lot-sizing problem with remanufacturing
  
  • Vallecilla Andrés
  • Dávila-Gálvez Sebastián
  • Quezada Franco
  International Journal of Production Research, Taylor & Francis, 2026. <div><p>This paper investigates the implementation of carbon cap policies within a remanufacturing production system, focusing on a single-item lot-sizing problem aimed at meeting the demand for end-of-life products under four distinct carbon cap policies. Our study, motivated by the operational dynamics of ECOCITEX, a Chilean textile remanufacturing company, explores the balance between operational costs, carbon emissions, and production levels in response to environmental policies. We introduce a mixed-integer linear programming (MILP) formulation to address economic lot-sizing with considerations for both remanufacturing and carbon emissions constraints. Through extensive computational experiments, we assess the impact of various carbon emissions policies on production and emissions levels and their associated costs, finding that global and rolling-horizon policies offer the best tradeoff between emission reductions and production cost increases. This leads to more environmentally friendly production policies for remanufactured products without compromising financial sustainability. The findings underscore the importance of flexibility in environmental policies for remanufacturing operations, suggesting that stringent carbon caps, while beneficial for emission reductions, may pose challenges to demand fulfillment and cost management. For managers, this highlights the critical need for adaptive policy frameworks that support sustainable production objectives without impeding operational efficiency.</p></div>
• State-constrained optimal control on Wasserstein spaces over Riemannian manifolds
  
  • Treumún Ernesto
  • Zidani Hasnaa
  , 2026. We study a state-constrained optimal control problem in Mayer form on the Wasserstein space P 2 (M ) of a complete (possibly non-compact) Riemannian manifold M . The controlled dynamics is given by a nonlocal continuity equation, where the velocity field depends on both the space variable and the evolving probability measure. In the presence of state constraints, the associated value function may fail to be continuous, which prevents a direct characterization through Hamilton-Jacobi-Bellman equations (HJB). Following a level-set approach, we introduce an auxiliary value function defined on an extended space and prove that its zero-sublevel set recovers the epigraph of the original value function. Our main result shows that this auxiliary function is the unique viscosity solution of a suitable HJB equation on P 2 (M ). To prove uniqueness, we develop a comparison principle based on directional differentiability properties of the squared Wasserstein distance. These properties are shown to hold under a geometric assumption on the underlying manifold, satisfied in particular by Cartan-Hadamard manifolds and spaces with sectional curvature bounded from below. This extends previous results obtained in the unconstrained case and in Euclidean or compact settings to the state-constrained framework on general complete Riemannian manifolds.
• Fluid-structure Green's functions via BEM/BEM coupling for flow induced noise in arbitrary elastic geometries
  
  • Pacaut Louise
  • Chaillat Stéphanie
  • Mercier Jean-François
  • Serre Gilles
  , 2026. We address the challenge of efficiently simulating the noise generated by the interaction of a turbulent flow noise with complex elastic structures, a coupled fluid/structure interaction (FSI) problem. Current approaches typically separate vibro-acoustic and hydro-acoustic contributions, limiting the accuracy of hydrodynamic noise predictions. To overcome this limitation, we develop a numerical method for computing a Green's function tailored to the coupled FSI problem, enabling a monolithic prediction of the radiated noise without separating the two components. This approach not only improves the accuracy of hydrodynamic noise simulations but also significantly reduces computational costs. The Green's function is constructed using a novel integral formulation and solved numerically via a coupled fast BEM/ BEM solver.
• Stochastic Optimal Feedforward-Feedback Control for Partially Observable Sensorimotor Systems
  
  • Berret Bastien
  • Jean Frédéric
  , 2026. Robust control of complex engineered and biological systems hinges on the integration of feedforward and feedback mechanisms. This is exemplified in neural motor control, where feedforward muscle co-contraction complements sensory-driven feedback corrections to ensure stable behaviors. However, deriving a general continuous-time framework to determine such optimal control policies for partially observable, stochastic, nonlinear, and high-dimensional systems remains a formidable computational challenge. Here, we introduce a framework that extends neighboring optimal control by enabling the feedforward plan to explicitly account for feedback uncertainties and latencies. Using statistical linearization, we transform the stochastic problem into an approximately equivalent deterministic optimization within a tractable, augmented state space that retains critical nonlinearities, offering both mechanistic interpretability and theoretical guarantees on approximation fidelity. We apply this framework to human neuromechanics, demonstrating that muscle co-contraction emerges as an optimal adaptation to task demands, given the characteristics of our sensorimotor system. Our results provide a computational foundation for neuromotor control and a generalizable tool for the control of nonlinear stochastic systems.
• Asymptotic models for time-domain scattering by small particles
  
  • Savchuk Adrian
  , 2026. In this manuscript, we address the problem of time-dependent wave scattering by multiple small particles of arbitrary shape. To approximate the solution of the associated boundary-value problem, we derive an asymptotic model that achieves a higher convergence rate compared to existing models. Our method relies on a boundary integral formulation, semi-discretized in space using a Galerkin approach, where the main challenge lies in choosing appropriate basis functions for the Galerkin space. We show that using equilibrium densities as basis functions yields a cubic-convergent asymptotic model that ensures a priori stability in the time domain due to the coercivity properties of the single-layer boundary integral operator. Unlike the case of spheres, where entries can be computed explicitly, the generalized method requires double integration, which becomes computationally expensive as the number of particles increases. To address this, we derive a simplified model that preserves the stability and convergence properties of the original formulation, alongside a lower-order but computationally advantageous Born model, providing a rigorous theoretical error analysis for both. When the distance between obstacles decreases with the small parameter, the cubic convergence of the scattered field can no longer be guaranteed. To overcome this limitation, we derive high-order asymptotic models by enriching the basis functions in the Galerkin space to maintain accuracy even for closely clustered particles. Finally, the proposed framework is applied to more complex interactions between a large obstacle and multiple small particles, and is further extended to time-domain electromagnetic scattering by small spheres. Numerical experiments validate the theoretical stability and performance across all proposed models.
• Metamaterials and Fluid Flows
  
  • Avallone Francesco
  • Bosia Federico
  • Chen Yi
  • Colombo Giada
  • Craster Richard
  • de Ponti Jacopo Maria
  • Fabbiane Nicolò
  • Haberman Michael
  • Hussein Mahmoud
  • Hwang Wontae
  • Iemma Umberto
  • Juhl Abigail
  • Kadic Muamer
  • Kotsonis Marios
  • Laude Vincent
  • Marquet Olivier
  • Mery Fabien
  • Michelis Theodoros
  • Nouh Mostafa
  • Ragni Daniele
  • Touboul Marie
  • Wegener Martin
  • Krushynska Anastasiia
  Nature Communications, Nature Publishing Group, 2026. (10.1038/s41467-026-70163-2)
  DOI : 10.1038/s41467-026-70163-2
• Dominance Properties for Fair Electricity Supply Planning in Collective Self-Consumption
  
  • Jorquera-Bravo Natalia
  • Elloumi Sourour
  • Kedad-Sidhoum Safia
  • Plateau Agnès
  , 2026. <div><p>This study addresses the problem of fair electricity supply planning within collective self-consumption communities, focusing on shared distributed energy sources and a common electricity storage system. The objective is to determine an electricity supply plan that ensures a fair allocation of shared resources. We formulate the electricity supply planning problem as a mixed integer linear programming (MILP) model, subsequently reformulated into a linear programming (LP) model thanks to some dominance properties. We then propose a series of fairness measures for the allocation of green electricity and shared economic benefits, including proportional allocation and max-min fairness. We prove that the dominance properties can be extended in most of these fairness models. We conduct numerical experiments based on a real case study, as well as on a set of generated instances. The results illustrate their impact on the use of green electricity produced, resource allocation, and participant costs. They also underscore the trade-offs between achieving fairness and maintaining operational efficiency, thereby offering insights for the fair management of energy resources in self-consumption communities.</p></div>