Publications

2025

• Some mathematical models for flagellar activation mechanisms
  
  • Alouges François
  • Anello Irene
  • Desimone Antonio
  • Lefebvre-Lepot Aline
  • Levillain Jessie
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2025, 35 (11), pp.2395-2424. This paper focuses on studying a model for molecular motors responsible for the bending of the axoneme in the flagella of microorganisms. The model is a coupled system of partial differential equations inspired by Jülicher et al. or Camalet, incorporating two rows of molecular motors between microtubules filaments. Existence and uniqueness of a solution is proved, together with the presence of a supercritical Hopf bifurcation. Additionally, numerical simulations are provided to illustrate the theoretical results. A brief study on the generalization to N-rows is also included. (10.1142/S0218202525500423)
  DOI : 10.1142/S0218202525500423
• Effects of a mutation on the fitness of a bacterium : theoretical estimation and numerical implementation
  
  • Garnier Guillaume
  , 2025. This thesis presents a mathematical study of genetic mutations and their effects on the fitness of individuals, a central concept in evolutionary biology. A mutation is a spontaneous or induced alteration of DNA, which can be deleterious, neutral, or beneficial. These mutations affect the fitness of individuals, i.e., their ability to survive and reproduce. The main question addressed is the estimation of the Density of Fitness Effects (DFE), which describes the distribution of the effects of mutations on fitness. Understanding the shape of the DFE is essential for predicting population evolution, genetic diversity, and the consequences of conservation programs. The starting point of this work is an experimental protocol developed by Lydia Robert et al. (2018), which allows real-time observation of mutation events in E. coli. These new data open up opportunities for improved estimation of the DFE, but also raise statistical challenges due to experimental noise .In the first part of this manuscript, we consider a stochastic model from [77] that describes the evolution of a bacterial population under mutation pressure. We develop a nonparametric estimation method based on Fourier estimators to recover the DFE, and establish convergence results for our estimator. The second part introduces two deterministic models for the evolution of fitness in a population structured by growth rate. These models allow us to study the asymptotic behavior of the population and provide mathematical insight into the dynamics of mutation accumulation observed in experiments. Finally, the third part applies various statistical methods to the experimental data, aiming to reconstruct the DFE from its empirical moments and to assess whether it is unimodal or multimodal. This work builds a bridge between experimental biology and the mathematical modeling of mutation effects.
• Robust calibration of an air-carbon ablation model employing Plasmatron and molecular beam data
  
  • Piro Vittorio
  • Capriati Michele
  • Bariselli Federico
  • Congedo Pietro Marco
  • Magin Thierry E.
  , 2025. Understanding and accurately predicting gas-surface interaction phenomena during a vehicle's re-entry phase is critical for the design of thermal protection materials. In this work, we aim to improve the robustness of an air-carbon ablation model by calibrating its reaction rates using both low-pressure molecular beam data and high-pressure Plasmatron data, as well as numerical models, following a Bayesian approach. Firstly, the subset of nitrogen chemical reactions is inferred, resulting in a finite-rate nitrogen model successfully calibrated and validated at both low-and highpressure. A surrogate-based Bayesian framework is employed, comparing artificial neural network and Kriging approaches to mimic the nitrogen model predictions at high-pressure and accelerate posterior sampling. Then, for the first time, atomic oxygen reaction rates are also included in the calibration, along with low-pressure oxygen observations. Since the experimental data used for calibration do not include high-pressure conditions, the oxygen reaction rates for accuracy at high pressure could not be fully characterised. Nevertheless, the resulting models demonstrated superior performance compared to the state-of-the-art model under low-pressure conditions.
• Bayesian model updating of rotating wind turbines
  
  • Delette Nina
  • Pfister Jean-Lou
  • Denimal Goy Enora
  • El Amri Mohamed Reda
  • Mevel Laurent
  , 2025, pp.1-3.
• A sequential variational Bayesian approach to Gaussian process quantile regression for optimization
  
  • Nicolas Hugo
  • Le Maître Olivier
  • Congedo Pietro Marco
  , 2025. Quantile regression [1] extends the classical least-squares regression to the estimation of the conditional quantiles of a random variable. In the frequentist approach, one casts the quantile regression into the problem of minimizing a loss function, possibly completed with regularization terms. The Bayesian counterpart, first proposed in [2], formulates the problem as a posterior inference over a function space. Bayesian inference can rely on Markov chain Monte Carlo (MCMC) methods to sample the posterior distribution. Variation Bayesian inference techniques alleviate some of the computational burdens of MCMC by introducing latent variables and providing an analytical approximation of their posterior distribution.
• On measure-valued solutions for a structured population model with transfers
  
  • Magal Pierre
  • Raoul Gaël
  , 2025, pp.76. We consider a transfer operator where two interacting cells carrying non-negative traits transfer a random fraction of their trait to each other. These transfers can lead to population having singular distributions in trait. We extend the definition of the transfer operator to non-negative measures with a finite second moment, and we discuss the regularity of the fixed distributions of that transfer operator. Finally, we consider a dynamic transfer model where an initial population distribution is affected by a transfer operator: we prove the existence and uniqueness of mild measure-valued solutions for that Cauchy problem.
• Long-time behaviors of dynamics with mean field interactions
  
  • Wang Songbo
  , 2025. This thesis is devoted to the study of the long-time behaviors of dynamics with mean field interactions and their associated particle systems. For most cases treated in the thesis, the structural condition for the long-time behaviors is the flat convexity of the mean field energy functional, which is different from the displacement convexity studied in the classical works of optimal transport and gradient flow. The thesis is comprised of three parts. In the first part, we study the overdamped and underdamped mean field Langevin dynamics, which are gradient dynamics associated to a mean field free energy functional, and show their time-uniform propagation of chaos properties by exploiting their gradient structures and a uniform logarithmic Sobolev inequality. In the second part, we first develop some technical results on logarithmic Sobolev inequalities and apply them to get the time-uniform propagation of chaos for various McKean-Vlasov diffusions. Specifically, for the 2D viscous vortex model, we develop strong regularity bounds on its mean field limit on the whole space and show its propagation of chaos by the Jabin-Wang method; we also study its size of chaos problem using the entropy approach of Lacker and obtain time-uniform sharp bounds in the high viscosity regime. In the last part of the thesis, we explore alternative mean field dynamics that originate from convex optimization problems. For the entropy-regularized optimization, we study a fictitious self-play dynamics and a self-interacting diffusion and show their long-time convergences to the solution of the optimization problem. We also consider a non-linear Schrödinger semigroup, which is a gradient flow for the optimization problem regularized by Fisher information, and show its exponential convergence under a uniform spectral gap condition.
• Open-Canopy: Towards Very High Resolution Forest Monitoring
  
  • Fogel Fajwel
  • Perron Yohann
  • Besic Nikola
  • Saint-André Laurent
  • Pellissier-Tanon Agnès
  • Schwartz Martin
  • Boudras Thomas
  • Fayad Ibrahim
  • d'Aspremont Alexandre
  • Landrieu Loic
  • Ciais Philippe
  , 2025. Estimating canopy height and its changes at meter resolution from satellite imagery remains a challenging computer vision task with critical environmental applications. However, the lack of open-access datasets at this resolution hinders the reproducibility and evaluation of models. We introduce Open-Canopy, the first open-access, country-scale benchmark for very high-resolution (1.5 m) canopy height estimation, covering over 87,000 km² across France with 1.5 m panchromatic resolution satellite imagery and aerial LiDAR data. Additionally, we present Open-Canopy-$\Delta$, a benchmark for canopy height reduction detection between images from different years at tree level---a difficult task for current computer vision models. We evaluate state-of-the-art architectures on these benchmarks, highlighting significant challenges and opportunities for improvement. Our datasets and code are publicly available at \url{https://github.com/fajwel/Open-Canopy}. (10.1109/CVPR52734.2025.00138)
  DOI : 10.1109/CVPR52734.2025.00138
• Wave turbulence, thermalization and multimode locking in optical fibers
  
  • Ferraro M.
  • Baudin K.
  • Gervaziev M.
  • Fusaro A.
  • Picozzi Antonio
  • Garnier J.
  • Millot G.
  • Kharenko D.
  • Podivilov E.
  • Babin S.
  • Mangini F.
  • Wabnitz S.
  Physica D: Nonlinear Phenomena, Elsevier, 2025, 481, pp.134758. We present a comprehensive overview of recent advances in theory and experiments on complex light propagation phenomena in nonlinear multimode fibers. On the basis of the wave turbulence theory, we derive kinetic equations describing the out-of-equilibrium process of optical thermalization toward the Rayleigh-Jeans (RJ) equilibrium distribution. Our theory is applied to explain the effect of beam self-cleaning (BSC) in graded-index (GRIN) fibers, whereby a speckled beam transforms into a bell-shaped beam at the fiber output as the input peak power grows larger. Although the output beam is typically dominated by the fundamental mode of the fiber, higher-order modes (HOMs) cannot be fully depleted, as described by the turbulence cascades associated to the conserved quantities. We theoretically explore the role of random refractive index fluctuations along the fiber core, and show how these imperfections may turn out to assist the observation of BSC in a practical experimental setting. This conclusion is supported by the derivation of wave turbulence kinetic equations that account for the presence of a time-dependent disorder (random mode coupling). The kinetic theory reveals that a weak disorder accelerates the rate of RJ thermalization and beam cleaning condensation. On the other hand, although strong disorder is expected to suppress wave condensation, the kinetic equation reveals that an out-of-equilibrium process of condensation and RJ thermalization can occur in a regime where disorder predominates over nonlinearity. In general, the kinetic equations are validated by numerical simulations of the generalized nonlinear Schrodinger equation. We outline a series of recent experiments, which permit to confirm the statistical mechanics approach for describing beam propagation and thermalization. For example, we highlight the demonstration of entropy growth, and point out that there are inherent limits to peak-power scaling in multimode fiber lasers. We conclude by pointing out the experimental observation that BSC is accompanied by an effect of modal phase-locking. From the one hand this explains the observed preservation of the spatial coherence of the beam, but also it points to the need of extending current descriptions in future research.
• Mesh Adaptation Strategies for CFD Simulations Over a Set of Operating Conditions
  
  • Dornier Hugo
  • Le Maître Olivier P
  • Congedo Pietro Marco
  • Salah El Din Itham
  • Bourasseau Sébastien
  • Marty Julien
  , 2025. In computational fluid dynamics, evaluating accurately quantities of interest (global or local) requires capturing complex local phenomena and interactions, such as shocks and flow separations, while controlling the global error. The latter depends highly on the discretization of the computational domain, hence the mesh. In general, the location of the flow structures within the domain is sensitive to boundary and flow conditions. Proposing an a priori mesh with a discretization effort that concentrates on the demanding parts of the domain is thus usually impossible. Adaptive Mesh Refinement (AMR, [1,2,3,4]) is a method developed to iteratively adjust the local mesh resolution to the computed flow structures and construct meshes that achieve a prescribed accuracy for limited discretization and computational cost. This work concerns the problem of mesh adaptation when the operating conditions are variable and follow a prescribed continuous distribution. For instance, variability of the flow conditions appears in uncertainty quantification, operating domain analysis, and robust optimization. These analyses typically require many simulations for different conditions, making the cost-accuracy trade-off even more crucial for these problems. Several mesh adaption methods have been proposed for variable conditions ([5,6,7,8]), but they typically focus primarily on error control without simultaneously optimizing for cost. In this context, we propose two original methodologies. The first one, called Mean Mesh adaptation (MMA, [9,10]), builds a unique adapted mesh to minimize the average error over the continuous operating conditions for a given discretization effort. A key ingredient of MMA is using a small sample set of conditions to estimate the local average error at each iteration of the AMR process. The second method, Error-based Mesh Selection (EMS), tackles the optimal element selection within a library of adapted meshes to achieve the smallest possible error for any given flow conditions. The library consists of meshes independently adapted for different conditions in an offline stage, for cost efficiency, the selection uses a priori error estimations requiring no additional simulation. We used analytical and full CFD supersonic simulations [11,12] to analyze the proposed methods. We show that MMA is robust and accurately approximates the optimal mesh minimizing the average error for a limited construction cost (see figures 1 and 2). Similarly, EMS provides a robust approximation of the optimal selection with limited cost overheads (see figure 3). The EMS method is suitable to be extended for progressive library enrichment and a-posteriori correction of the error estimates.
• Weak solutions of stochastic volterra equations in convex domains with general kernels
  
  • Abi Jaber Eduardo
  • Alfonsi Aurélien
  • Szulda Guillaume
  , 2025. We establish new weak existence results for d-dimensional Stochastic Volterra Equations (SVEs) with continuous coefficients and possibly singular one-dimensional nonconvolution kernels. These results are obtained by introducing an approximation scheme and showing its convergence. A particular emphasis is made on the stochastic invariance of the solution in a closed convex set. To do so, we extend the notion of kernels that preserve nonnegativity introduced in Alfonsi (2025) to non-convolution kernels and show that, under suitable stochastic invariance property of a closed convex set by the corresponding Stochastic Differential Equation, there exists a weak solution of the SVE that stays in this convex set. We present a family of non-convolution kernels that satisfy our assumptions, including a nonconvolution extension of the well-known fractional kernel. We apply our results to SVEs with square-root diffusion coefficients and non-convolution kernels, for which we prove the weak existence and uniqueness of a solution that stays within the nonnegative orthant. We derive a representation of the Laplace transform in terms of a non-convolution Riccati equation, for which we establish an existence result. (10.48550/arXiv.2506.04911)
  DOI : 10.48550/arXiv.2506.04911
• Stochastic Dynamics of Incoherent Branched Flows
  
  • Garnier Josselin
  • Picozzi Antonio
  • Torres Theo
  Physical Review Letters, American Physical Society, 2025, 134 (22), pp.223803. (10.1103/PhysRevLett.134.223803)
  DOI : 10.1103/PhysRevLett.134.223803
• Estimation of extreme risk measures with neural networks
  
  • Girard Stéphane
  • Allouche Michaël
  • Gobet Emmanuel
  , 2025, pp.1-6. We propose new parameterizations for neural networks in order to estimate extreme risk measures, such as conditional tail moments, in heavy-tailed settings. The proposed neural network estimator is able to extrapolate in the distribution tails thanks to an extension of the usual extreme-value second-order condition to an arbitrary order. The convergence rate of the uniform error between the log-conditional tail moment and its neural network approximation is established. The finite sample performance of the neural network estimator is compared to bias-reduced extreme-value competitors on simulated data. It is shown that our method outperforms them in difficult heavy-tailed situations where other estimators almost all fail. Finally, the neural network estimator is tested on real data to investigate the behavior of cryptocurrency extreme loss returns.
• Design of experiments based on a low fidelity model for seismic fragility curves estimation
  
  • Van Biesbroeck Antoine
  • Gauchy Clément
  • Feau Cyril
  • Garnier Josselin
  ESAIM: Proceedings and Surveys, EDP Sciences, 2025, 79, pp.96-109. Seismic fragility curves are key quantities of interest for Seismic Probabilistic Risk Assessment studies. They express the probability of failure of a mechanical structure of interest conditional to a scalar value derived from the ground motion signal coined Intensity Measure. In the literature, Bayesian approaches have emerged to enable their estimation within the difficult context of limited data availability. Yet, the log-normal modeling over which most of them are based requires the use of computationally expensive Markov chain Monte Carlo methods for providing Bayesian estimators. In this work, we propose an efficient modeling for the estimation of fragility curves in the Bayesian context, based on a low fidelity model of the structure's response to the ground motion signal and an objective prior. The analytical expression of our modeling allows fast generation of estimates. Also, the representative bias arisen by the modeling choice is handled with a judicious design of experiments methodology. Finally, our method is evaluated on a real case study, and the results highlight its efficiency and its ability to robustly overcome any bias when coupled with the design of experiments we propose. (10.1051/proc/202579096)
  DOI : 10.1051/proc/202579096
• Automatically generated cardiovascular digital twin in critical care: a proof of concept study
  
  • Kimmig François
  • Le Gall Arthur
  • Windsor Camille
  • Vallée Fabrice
  • Chapelle Dominique
  • Moireau Philippe
  , 2025. This proof of concept study demonstrates the capabilities of a virtually automatically generated digital twin framework for enhancing hemodynamic monitoring in critical care. By combining a deterministic cardiovascular model with patient-specific data through data assimilation techniques, the digital twin can act as a data denoiser, reconstruct physiological waveforms that are typically unavailable in critical care settings and generate clinically relevant biomarkers. Validation was performed using real data from patients under general anesthesia. The proposed framework efficient calibration and ability to follow the patient's state over time supports the possibility of real-time bedside applications.
• A high-order matrix-free adaptive solver for the shallow water equations with irregular bathymetry
  
  • Arpaia Luca
  • Orlando Giuseppe
  • Ferrarin Christian
  • Bonaventura Luca
  , 2025. We present the first step in the development of an Adaptive Mesh Refinement (AMR) solver for coastal engineering applications, based on a high-order Discontinuous Galerkin (DG) method as implemented in the deal.II library. This environment provides efficient and native parallelization techniques and automatically handles non-conforming meshes to implement both static and dynamic AMR approaches. The proposed method is automatically well-balanced, allows the use of realistic bathymetry data without any regularity assumption, and includes a consistent conservative discretization for transported chemical species. Numerical experiments on idealized benchmarks validate the proposed approach, while results obtained on realistic bathymetries and complex domains show its potential for accurate and efficient adaptive simulations of coastal flows.
• Dynamics of screened particles towards equi-spaced ground states
  
  • de Luca Lucia
  • Goldman Michael
  • Ponsiglione Marcello
  , 2025. This paper deals with the dynamics - driven by the gradient flow of negative fractional seminorms - of empirical measures towards equi-spaced ground states. Specifically, we consider periodic empirical measures $\mu$ on the real line that are screened by the Lebesgue measure, i.e., with $\mu- d x$ having zero average. To each of these measures $\mu$ we associate a (periodic) function $u$ satisfying $u'= d x - \mu$. For $s\in (0,\frac 12)$ we introduce energy functionals $\mathcal E^s(\mu)$ that can be understood as the density of the $s$-Gagliardo seminorm of $u$ per unit length. Since for $s\ge \frac 12$, the $s$-Gagliardo seminorms are infinite on functions with jumps, some regularization procedure is needed: For $s\in[\frac 12,1)$ we define $\mathcal E_\varepsilon^s(\mu):= \mathcal E^s(\mu_\varepsilon)$, where $\mu_\varepsilon$ is obtained by mollifying $\mu$ on scale $\varepsilon$. We prove that the minimizers of $\mathcal E^s$ and $\mathcal E_\varepsilon^s$ are the equi-spaced configurations of particles with lattice spacing equal to one. Then, we prove the exponential convergence of the corresponding gradient flows to the equi-spaced steady states. Finally, although for $s\in[\frac 12 ,1)$ the energy functionals $\mathcal E_\varepsilon^s$ blow up as $\varepsilon\to 0$, their gradients are uniformly bounded (with respect to $\varepsilon$), so that the corresponding trajectories converge, as $\varepsilon\to 0$, to the gradient flow solution of a suitable renormalized energy.
• Numerical strategies for the microscale simulation of Li-ion batteries
  
  • Asad Ali
  , 2025. In this thesis, we develop and analyze numerical strategies for the simulation of lithium-ion batteries (LIBs) based on their continuum description at the microscale. Our focus is on addressing the computational challenges posed by this inherently multiphysics and multiscale problem, particularly the nonlinearity at the reaction interface and the stiffness of the governing equations.In the first phase of this doctoral work, we tackle the temporal multiscale nature of LIBs by decoupling the domains into subproblems that can be solved independently. Building upon an adaptive high-order coupling strategy, we implement this approach in a Python code. The effectiveness and performance of the method are demonstrated through 1D LIB half-cell simulations. Additionally, we discuss how this promising numerical strategy can be extended to 3D LIB simulations.The multiphysics nature of the LIB model further motivates us to explore adaptive methods in both space and time to reduce computational costs. To extend our study to higher dimensions, we employ a C++ framework with a monolithic solution strategy. Specifically, we implement a multiresolution-based adaptive mesh refinement (AMR) technique using SAMURAI and an adaptive high-order implicit time integrator using PETSc, examining their performance when used together. Using this fully adaptive implementation, we conduct parametric studies to evaluate the impact of interdigitated electrodes on the performance and behavior of 2D LIB half cells.The thesis concludes by synthesizing the two numerical strategies developed to address the computational challenges of LIB microscale simulations. As a natural extension of this work, we propose a unified framework that integrates these approaches, providing a robust foundation for tackling additional complexities that may arise in future microscale LIB model developments.
• Faster Latency Constrained Service Placement in Edge Computing with Deep Reinforcement Learning
  
  • Forghieri Orso
  • Carlinet Yannick
  • Hyon Emmanuel
  • Le Pennec Erwan
  • Perrot Nancy
  , 2025. To enhance the user experience on mobile devices, Mobile Edge Computing (MEC) is a paradigm which integrates computing capabilities directly within access networks. However, designing efficient computation offloading policies in MEC systems remains a challenge. In particular, the decision on whether to process an incoming computation task locally on the mobile device or offload it to the cloud must intelligently adapt to dynamic environmental conditions. This article presents a novel approach that aims to address an edge computing optimization problem, issued from industrial cases, by modeling it as a combinatorial optimization problem combining multicommodity flow and linear latencies constraints. We develop an equivalent linear formulation of the Service Placement Problem, allowing us to use traditional Integer Linear Programming (ILP) methods that turns out to be inefficient in practice. We therefore develop a use-case-based heuristic and a Reinforcement Learning (RL) methodology to model the network configuration under orchestration actions. The latest allows us to transfer learning across pre-training of the agent and shows proof of its efficiency on a dynamic real-world instance, aiming for practical deployment conditions. This comparison reveals that RL is a robust approach that can solve large realistic instances, reaching an optimality gap smaller than 25% on average below a second of runtime for dynamic service placement.
• Optimizing the diffusion coefficient of overdamped Langevin dynamics
  
  • Lelièvre Tony
  • Pavliotis Grigorios A.
  • Robin Geneviève
  • Santet Régis
  • Stoltz Gabriel
  Mathematics of Computation, American Mathematical Society, 2025. Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian inference. By varying the diffusion coefficient, there are in fact infinitely many overdamped Langevin dynamics which are reversible with respect to the target probability measure at hand. This suggests to optimize the diffusion coefficient in order to increase the convergence rate of the dynamics, as measured by the spectral gap of the generator associated with the stochastic differential equation. We analytically study this problem here, obtaining in particular necessary conditions on the optimal diffusion coefficient. We also derive an explicit expression of the optimal diffusion in some appropriate homogenized limit. Numerical results, both relying on discretizations of the spectral gap problem and Monte Carlo simulations of the stochastic dynamics, demonstrate the increased quality of the sampling arising from an appropriate choice of the diffusion coefficient. (10.1090/mcom/4098)
  DOI : 10.1090/mcom/4098
• From energy bounds to dimensional estimates in a branched transport model for type-I superconductors
  
  • De Philippis Guido
  • Goldman Michael
  • Berardo Ruffini
  , 2025. We consider a branched transport type problem which describes the magnetic flux through type-I superconductors in a regime of very weak applied fields. At the boundary of the sample, deviation of the magnetization from being uniform is penalized through a negative Sobolev norm. It was conjectured by S. Conti, F. Otto and S. Serfaty that as a result, the trace of the magnetization on the boundary should be a measure of Hausdorff dimension 8/5. We prove that this conjecture is equivalent to the proof of local energy bounds with an optimal exponent. We then obtain local bounds which are however not optimal. These yield improved lower bounds on the dimension of the irrigated measure but unfortunately does not improve on the trivial upper bound. In order to illustrate the dependence of this dimension on the choice of penalization, we consider in the last part of the paper a toy model where the boundary energy is given by a Wasserstein distance to Lebesgue. In this case minimizers are finite graphs and thus the trace is atomic.
• Asymptotic Analysis of a bi-monomeric nonlinear Becker-Döring system
  
  • Doumic Marie
  • Fellner Klemens
  • Mezache Mathieu
  • Velázquez Juan J L
  Nonlinearity, IOP Publishing, 2025. To provide a mechanistic explanation of sustained then damped oscillations observed in a depolymerisation experiment, a bi-monomeric variant of the seminal Becker-D\"oring system has been proposed in~(Doumic, Fellner, Mezache, Rezaei, J. of Theor. Biol., 2019). When all reaction rates are constant, the equations are the following: \begin{align*} \frac{dv}{dt} & =-vw+v\sum_{j=2}^{\infty}c_{j}, \qquad \frac{dw}{dt} =vw-w\sum_{j=1}^{\infty}c_{j}, \\ \frac{dc_{j}}{dt} & =J_{j-1}-J_{j}\ \ ,\ \ j\geq1\ \ ,\ \ \ J_{j}=wc_{j}-vc_{j+1}\ \ ,\ \ j\geq1\ \ ,\ J_{0}=0, \end{align*} where $v$ and $w$ are two distinct unit species, and $c_i$ represents the concentration of clusters containing $i$ units. We study in detail the mechanisms leading to such oscillations and characterise the different phases of the dynamics, from the initial high-amplitude oscillations to the progressive damping leading to the convergence towards the unique positive stationary solution. We give quantitative approximations for the main quantities of interest: period of the oscillations, size of the damping (corresponding to a loss of energy), number of oscillations characterising each phase. We illustrate these results by numerical simulation, in line with the theoretical results, and provide numerical methods to solve the system. (10.1088/1361-6544/adc3e5)
  DOI : 10.1088/1361-6544/adc3e5
• Model Updating of Rotating Wind Turbines Using Operational Modal Analysis and Floquet Mode Decomposition
  
  • Delette Nina
  • Denimal Goy Enora
  • Pfister Jean-Lou
  • El Amri Reda
  • Mevel Laurent
  , 2025, pp.1-7. The structural complexity of modern wind turbines, combined with numerous uncertain or unknown parameters, presents significant challenges for accurate predictive modeling. Model updating, which refines numerical model parameters using measurement data, offers a means to mitigate these discrepancies. While extensively applied to stationary structures, its extension to rotating wind turbines remains limited, as their time-periodic dynamics violate key assumptions underlying conventional methods. This study develops a numerical framework for model updating of rotating wind turbines based on an equivalent Linear Time-Invariant (LTI) approximation, derived through a Fourier decomposition of the system’s Floquet modes. A simplified 5 Degrees of Freedom (DoF) turbine model is employed to evaluate the effectiveness of a deterministic model updating strategy leveraging this approximation. Synthetic vibration data, generated from the model using a predefined parameter set, serve as reference measurements for assessing parameter recovery accuracy. Modal features extracted via Operational Modal Analysis (OMA) are used to construct the cost function that quantifies discrepancies between predicted and observed modes. The results underscore the potential of equivalent LTI representations in facilitating model updating for rotating systems, as they effectively capture the modal characteristics identified via OMA. This study establishes a foundation for extending this methodology to more complex, industrial-scale wind turbine models, provided that the computational cost of model evaluation remains manageable.
• The equilibrium price of bubble assets
  
  • Bertucci Charles
  • Lasry Jean-Michel
  • Lions Pierre Louis
  , 2025. Considering a simple economy, we derive a new Hamilton-Jacobi equation which is satisfied by the value of a "bubble" asset. We then show, by providing a rigorous mathematical analysis of this equation, that a unique non-zero stable solution exists under certain assumptions. The economic interpretation of this result is that, if the bubble asset can produce more stable returns than fiat money, agents protect themselves from hazardous situations through the bubble asset, thus forming a bubble's consensus value. Our mathematical analysis uses different ideas coming from the study of semi-linear elliptic equations.
• Robust topology optimization accounting for uncertain microstructural changes
  
  • Masson Hugo
  • Peigney Michaël
  • Denimal Goy Enora
  , 2025.