Publications

2025

• A two spaces extension of Cauchy-Lipschitz Theorem
  
  • Bertucci Charles
  • Lions Pierre-Louis
  Journal of Differential Equations, Elsevier, 2025, 421, pp.524-530. We adapt the classical theory of local well-posedness of evolution problems to cases in which the nonlinearity can be accurately quantified by two different norms. For ordinary differential equations, we consider ẋ = f (x, x) for a function f : V × E → E where E is a Banach space and V → E a normed vector space. This structure allows us to distinguish between the two dependencies of f in x and allows to generalize classical results. We also prove a similar results for partial differential equations. (10.1016/j.jde.2024.12.031)
  DOI : 10.1016/j.jde.2024.12.031
• Open Problem: Two Riddles in Heavy-Ball Dynamics
  
  • Goujaud Baptiste
  • Taylor Adrien
  • Dieuleveut Aymeric
  , 2025. This short paper presents two open problems on the widely used Polyak's Heavy-Ball algorithm. The first problem is the method's ability to exactly \textit{accelerate} in dimension one exactly. The second question regards the behavior of the method for parameters for which it seems that neither a Lyapunov nor a cycle exists. For both problems, we provide a detailed description of the problem and elements of an answer.
• CoHiRF: A Scalable and Interpretable Clustering Framework for High-Dimensional Data
  
  • Belucci Bruno
  • Lounici Karim
  • Meziani Katia
  , 2025. Clustering high-dimensional data poses significant challenges due to the curse of dimensionality, scalability issues, and the presence of noisy and irrelevant features. We propose Consensus Hierarchical Random Feature (CoHiRF), a novel clustering method designed to address these challenges effectively. CoHiRF leverages random feature selection to mitigate noise and dimensionality effects, repeatedly applies K-Means clustering in reduced feature spaces, and combines results through a unanimous consensus criterion. This iterative approach constructs a cluster assignment matrix, where each row records the cluster assignments of a sample across repetitions, enabling the identification of stable clusters by comparing identical rows. Clusters are organized hierarchically, enabling the interpretation of the hierarchy to gain insights into the dataset. CoHiRF is computationally efficient with a running time comparable to K-Means, scalable to massive datasets, and exhibits robust performance against state-of-the-art methods such as SC-SRGF, HDBSCAN, and OPTICS. Experimental results on synthetic and real-world datasets confirm the method's ability to reveal meaningful patterns while maintaining scalability, making it a powerful tool for high-dimensional data analysis.
• An inverse problem in cell dynamics: Recovering an initial distribution of telomere lengths from measurements of senescence times
  
  • Olayé Jules
  , 2025. Telomeres are repetitive sequences situated at both ends of the chromosomes of eukaryotic cells. At each cell division, they are eroded until they reach a critical length that triggers a state in which the cell stops to divide: the senescent state. In this work, we are interested in the link between the initial distribution of telomere lengths and the distribution of senescence times. We propose a method to retrieve the initial distribution of telomere lengths, using only measurements of senescence times. Our approach relies on approximating our models with transport equations, which provide natural estimators for the initial telomere lengths distribution. We investigate this method from a theoretical point of view by providing bounds on the errors of our estimators, pointwise and in all Lebesgue spaces. We also illustrate it with estimations on simulations, and discuss its limitations related to the curse of dimensionality.
• Stochastic Tangential Pareto Dynamics Provably Samples the Whole Pareto Set
  
  • Jones Zachary
  • Congedo Pietro Marco
  • Le Maitre Olivier
  , 2025. The framework of stochastic multi-objective programming allows for the inclusion of uncertainties in multi-objective optimization problems at the cost of transforming the set of objectives into a set of expectations of random quantities. The stochastic multigradient descent algorithm (SMGDA) gives a solution to these types of problems using only noisy gradient information. However, a bias in the algorithm causes it to converge to only a subset of the whole Pareto front, limiting its use. We analyze the source of this bias and prove the convergence of SMGDA to a stationary point in the nonconvex L-lipschitz smooth case. First, based on this analysis, we propose to reduce the bias of the stochastic multi-gradient calculation using an exponential smoothing technique. We then propose a novel approach to exploring the whole Pareto set by combining the debiased stochastic multigradient with an additive non-vanishing noise that guides the dynamics of the iterates tangential to the Pareto set. We finish by proving that our algorithm, Stochastic Tangential Pareto Dynamics (STPD), generates samples concentrated on the whole Pareto set.
• The N-link model for slender rods in a viscous fluid: well-posedness and convergence to classical elastohydrodynamics equations
  
  • Alouges François
  • Lefebvre-Lepot Aline
  • Levillain Jessie
  • Moreau Clément
  , 2025. Flexible fibers at the microscopic scale, such as flagella and cilia, play essential roles in biological and synthetic systems. The dynamics of these slender filaments in viscous flows involve intricate interactions between their mechanical properties and hydrodynamic drag. In this paper, considering a 1D, planar, inextensible Euler-Bernoulli rod in a viscous fluid modeled by Resistive Force Theory, we establish the existence and uniqueness of solutions for the $N$-link model, a mechanical model, designed to approximate the continuous filament with rigid segments. Then, we prove the convergence of the $N$-link model's solutions towards the solutions to classical elastohydrodynamics equations of a flexible slender rod. This provides an existence result for the limit model, comparable to those by Mori and Ohm [Nonlinearity, 2023], in a different functional context and with different methods. Due to its mechanical foundation, the discrete system satisfies an energy dissipation law, which serves as one of the main ingredients in our proofs. Our results provide mathematical validation for the discretization strategy that consists in approximating a continuous filament by the mechanical $N$-link model, which does not correspond to a classical approximation of the underlying PDE.
• The 2024 ACM SIGEVO Outstanding Contribution Awardees
  
  • Auger Anne
  • Rothlauf Franz
  ACM SIGEVOlution, Association for Computing Machinery (ACM), 2025, 17, pp.1-8. The SIGEVO Outstanding Contribution Award recognizes remarkable contributions to Evolutionary Computation (EC) when evaluated over a sustained period of at least 15 years. These contributions can include technical innovations, publications, leadership, teaching, mentoring, and service to the EC community. (10.1145/3717452.3717453)
  DOI : 10.1145/3717452.3717453
• A Surrogate Modelling Approach Based on Anti-Resonance Properties for FRF Prediction of Uncertain Dynamical Systems
  
  • Denimal Goy Enora
  , 2025, pp.81 - 92. Quantifying uncertainties of dynamical responses is crucial for the design of robust mechanical structures. Computing the Frequency Response Function (FRF) is a classical tool in this context. So far, basic approaches to propagateuncertainties have led to poor prediction accuracy due to convergence issues around the peaks. Some previous works proposed numerical strategies to deal with this limitations for small systems and in specific cases. The present work proposed a new approach based on resonance and antiresonance properties to split the FRF in different sections, a surrogate can then be constructed on each section leading to better performances than classical strategies. The methodology is illustrated on a 2 dof academic system. (10.13052/97887-438-0148-1)
  DOI : 10.13052/97887-438-0148-1
• Topology Optimization of Isolated Response Curves in 3D Geometrically-nonlinear Beam
  
  • Denimal Goy Enora
  • Shen Yichang
  • Fruchard Samuel
  • Mélot Adrien
  • Renson Ludovic
  , 2025, pp.81 - 92. Topology optimisation is a powerful tool for designing efficient and light structures. However, classical topology optimisation methods (SIMP, LSF), which are gradient-based, are not adapted to deal with nonlinear vibrations in the context of geometrical nonlinearities as the simulation of such systems is computationally expensive, and the strong nonlinearbehaviour makes the objective function non-convex with many local minima. The present work investigates the potential of using global optimisation methods to topology optimise those structures. To provide more robust nonlinear features in the optimisation, the bifurcations are directly tracked and optimised. The strategy is applied to a 3D finite element model of a beam (10.13052/97887-438-0146-7)
  DOI : 10.13052/97887-438-0146-7
• Classical JAK2V617F+ Myeloproliferative Neoplasms emergence and development based on real life incidence and mathematical modeling
  
  • Baranda Ana Fernández
  • Bansaye Vincent
  • Lauret Evelyne
  • Mounier Morgane
  • Ugo Valérie
  • Méléard Sylvie
  • Giraudier Stéphane
  , 2024. Mathematical modeling allows us to better understand myeloproliferative neoplasms (MPN) emergence and development. We tested different mathematical models on an initial cohort to determine the emergence and evolution times before diagnosis of JAK2V617F classical MPN (Polycythemia Vera (PV) and Essential Thrombocythemia (ET)). We considered the time before diagnosis as the sum of two independent periods: the time (from embryonic development) for the JAK2V617F mutation to occur, not disappear and enter proliferation, and a second time corresponding to the expansion of the clonal population until diagnosis. We demonstrate using progressively complexified models that the rate of active mutation occurrence cannot be constant, but rather increases exponentially with age following the Gompertz model. We found that the first tumorous cell takes an average time of 63.1 ± 13 years to appear and start proliferation. On the other hand, the expansion time is constant: 8.8 years once the mutation has emerged. These results were validated in an external cohort. Using this model, we analyzed JAK2V167F ET versus PV, and obtained that the time of active mutation occurrence for PV takes approximately 1.5 years more than for ET to develop, while the expansion time was similar. In conclusion, our multi-step approach and the ultimate age-dependent model for the emergence and development of MPN demonstrates that the emergence of a JAKV617F mutation should be linked to an aging mechanism, and indicates a 8 − 9 years period of time to develop a full MPN. (10.48550/arXiv.2406.06765)
  DOI : 10.48550/arXiv.2406.06765
• Convergence of a discrete selection-mutation model with exponentially decaying mutation kernel to a Hamilton-Jacobi equation
  
  • Jeddi Anouar
  , 2024. In this paper we derive a Hamilton-Jacobi equation with obstacle from a discrete linear integro-differential model in population dynamics, with exponentially decaying mutation kernel. The fact that the kernel has exponential decay leads to a modification of the classical Hamilton-Jacobi equation obtained previously from continuous models in \cite{BMP}. We consider a population parameterized by a scaling parameter $K$ and composed of individuals characterized by a quantitative trait, subject to selection and mutation. In the regime of large population $K\rightarrow +\infty,$ small mutations and large time we prove that the WKB transformation of the density converges to the unique viscosity solution of a Hamilton-Jacobi equation with obstacle. (10.48550/arXiv.2412.06657)
  DOI : 10.48550/arXiv.2412.06657
• Constrained non-linear estimation and links with stochastic filtering
  
  • Chaintron Louis-Pierre
  • Mertz Laurent
  • Moireau Philippe
  • Zidani Hasnaa
  , 2025. This article studies the problem of estimating the state variable of non-smooth subdifferential dynamics constrained in a bounded convex domain given some real-time observation. On the one hand, we show that the value function of the estimation problem is a viscosity solution of a Hamilton Jacobi Bellman equation whose sub and super solutions have different Neumann type boundary conditions. This intricacy arises from the non-reversibility in time of the non-smooth dynamics, and hinders the derivation of a comparison principle and the uniqueness of the solution in general. Nonetheless, we identify conditions on the drift (including zero drift) coefficient in the non-smooth dynamics that make such a derivation possible. On the other hand, we show in a general situation that the value function appears in the small noise limit of the corresponding stochastic filtering problem by establishing a large deviation result. We also give quantitative approximation results when replacing the non-smooth dynamics with a smooth penalised one.
• Learning extreme Expected Shortfall and Conditional Tail Moments with neural networks. Application to cryptocurrency data
  
  • Allouche Michaël
  • Girard Stéphane
  • Gobet Emmanuel
  Neural Networks, Elsevier, 2025, 182, pp.106903. We propose a neural networks method to estimate extreme Expected Shortfall, and even more generally, extreme conditional tail moments as functions of confidence levels, in heavy-tailed settings. The convergence rate of the uniform error between the log-conditional tail moment and its neural network approximation is established leveraging extreme-value theory (in particular the high-order condition on the distribution tails) and using critically two activation functions (eLU and ReLU) for neural networks. The finite sample performance of the neural network estimator is compared to bias-reduced extreme-value competitors using synthetic heavy-tailed data. The experiments reveal that our method largely outperforms others. In addition, the selection of the anchor point appears to be much easier and stabler than for other methods. Finally, the neural network estimator is tested on real data related to extreme loss returns in cryptocurrencies: here again, the accuracy obtained by cross-validation is excellent, and is much better compared with competitors. (10.1016/j.neunet.2024.106903)
  DOI : 10.1016/j.neunet.2024.106903
• Uniform minorization condition and convergence bounds for discretizations of kinetic Langevin dynamics
  
  • Durmus Alain
  • Enfroy Aurélien
  • Moulines Éric
  • Stoltz Gabriel
  Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2025, 61 (1). We study the convergence in total variation and $V$-norm of discretization schemes of the underdamped Langevin dynamics. Such algorithms are very popular and commonly used in molecular dynamics and computational statistics to approximatively sample from a target distribution of interest. We show first that, for a very large class of schemes, a minorization condition uniform in the stepsize holds. This class encompasses popular methods such as the Euler-Maruyama scheme and the schemes based on splitting strategies. Second, we provide mild conditions ensuring that the class of schemes that we consider satisfies a geometric Foster--Lyapunov drift condition, again uniform in the stepsize. This allows us to derive geometric convergence bounds, with a convergence rate scaling linearly with the stepsize. This kind of result is of prime interest to obtain estimates on norms of solutions to Poisson equations associated with a given numerical method. (10.1214/23-AIHP1442)
  DOI : 10.1214/23-AIHP1442
• Annealed limit for a diffusive disordered mean-field model with random jumps
  
  • Erny Xavier
  Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2025, 61 (1), pp.510-532. We study a sequence of $N-$particle mean-field systems, each driven by $N$ simple point processes $Z^{N,i}$ in a random environment. Each $Z^{N,i}$ has the same intensity $(f(X^N_{t-}))_t$ and at every jump time of $Z^{N,i},$ the process $X^N$ does a jump of height $U_i/\sqrt{N}$ where the $U_i$ are disordered centered random variables attached to each particle. We prove the convergence in distribution of $X^N$ to some limit process $\bar X$ that is solution to an SDE with a random environment given by a Gaussian variable, with a convergence speed for the finite-dimensional distributions. This Gaussian variable is created by a CLT as the limit of the patial sums of the $U_i.$ To prove this result, we use a coupling for the classical CLT relying on the result of [Koml\'os, Major and Tusn\'ady (1976)], that allows to compare the conditional distributions of $X^N$ and $\bar X$ given the random environment, with the same Markovian technics as the ones used in [Erny, L\"ocherbach and Loukianova (2022)]. (10.1214/23-AIHP1432)
  DOI : 10.1214/23-AIHP1432
• Uniswap v3: impermanent loss modeling and swap fees asymptotic analysis
  
  • Echenim Mnacho
  • Gobet Emmanuel
  • Maurice Anne-Claire
  , 2023. Automated Market Makers have emerged quite recently, and Uniswap is one of the most widely used platforms (it covers 60% of the total value locked on Ethereum blockchain at the time of writing this article). This protocol is challenging from a quantitative point of view, as it allows participants to choose where they wish to concentrate liquidity. There has been an increasing number of research papers on Uniswap v3 but often, these articles use heuristics or approximations that can be far from reality: for instance, the liquidity in the pool is sometimes assumed to be constant over time, which contradicts the mechanism of the protocol. The ob- jectives of this work are fourfold: first, to revisit Uniswap v3’s principles in detail (starting from the open source code) to build an unambiguous knowledge base. Second, to analyze the Im- permanent Loss of a liquidity provider by detailing its evolution, with no assumption on the swap trades or liquidity events that occur over the time period. Third, we introduce the notion of a liquidity curve. For each curve, we can construct a payoff at a given maturity, net of fees. Conversely, we show how any concave payoff can be synthetized by an initial liquidity curve and some tokens outside the pool; this paves the way for using Uniswap v3 to create options. Fourth, we analyze the asymptotic behavior of collected fees without any simplifying hypoth- esis (like a constant liquidity), under the mild assumption that the pool price coincides with a latent price (general Ito process) every time the latter changes by γ%. The asymptotic analysis is conducted as γ → 0. The value of the collected fees then coincides with an integral of call and put prices. Our derivations are supported by graphical illustrations and experiments.
• On the entropy dissipation of systems of quadratures
  
  • Pichard Teddy
  • Laurent Frédérique
  , 2025. <div>The method of moments in kinetic theory is a popular discretization technique with respect to the kinetic velocity variable. It can be seen as a non-linear Galerkin semi-discretization in velocity. Among these methods, the quadrature-based methods exploiting the theory of orthogonal polynomials are well suited for numerical purposes. However, two important properties of the original kinetic equation are lost during such approximations: the strong hyperbolicity, corresponding to transport phenomena, and the dissipation of entropy, corresponding to the trend of the solution towards an equilibrium. These two properties are closely related through symmetrization techniques. In this work, we aim to clarify the treatment of these two properties in the derivation of quadrature-based moment systems, and to prove H-theorems, namely dissipation of entropy and equilibrium representation, after such derivations. From this study, we develop of quadrature-based closures adapted to specific entropies. These closures are of two types, either with fixed quadrature points (or velocities), namely the discrete velocity methods (DVM), and with varying ones, namely the quadrature-based method of moments (QMOM). To adapt the closures to specific entropies, the number of quadrature points is increased compared to the number of moments, resulting in augmented systems (ADVM or AQMOM) with more unknowns than equations, and the additional parameters are constrained to match the entropy requirements. Similarly, the quadrature-based entropies are of two types, either those based on a symmetrization criterion on the flux vector, which are only intended to have an entropy, or those corresponding to a quadrature formula of the kinetic entropy, which are intended to reproduce the kinetic trend towards the equilibrium. At each step of these developments, based on the considered entropy, we provide definitions for the flux vectors, adapted relaxation operators (with common conservation properties), we compute the associated entropic variables, and highlight the corresponding symmetrization property of the flux and equilibria. Finally, we provide an entropy-dissipative discretization for such moment systems.</div>
• Mathematical model linking telomeres to senescence in Saccharomyces cerevisiae reveals cell lineage versus population dynamics
  
  • Rat Anaïs
  • Martinez Fernandez Veronica
  • Doumic Marie
  • Teixeira Maria Teresa
  • Xu Zhou
  Nature Communications, Nature Publishing Group, 2025, 16 (1), pp.1024. Telomere shortening ultimately causes replicative senescence. However, identifying the mechanisms driving replicative senescence in cell populations is challenging due to the heterogeneity of telomere lengths and the asynchrony of senescence onset. Here, we present a mathematical model of telomere shortening and replicative senescence in Saccharomyces cerevisiae which is quantitatively calibrated and validated using data of telomerase-deficient single cells. Simulations of yeast populations, where cells with varying proliferation capacities compete against each other, show that the distribution of telomere lengths of the initial population shapes population growth, especially through the distribution of cells’ shortest telomere lengths. We also quantified how factors influencing cell viability independently of telomeres can impact senescence rates. Overall, we demonstrate a temporal evolution in the composition of senescent cell populations—from a state directly linked to critically short telomeres to a state where senescence onset becomes stochastic. This population structure may promote genome instability and facilitate senescence escape. (10.1038/s41467-025-56196-z)
  DOI : 10.1038/s41467-025-56196-z
• Individual cell fate and population dynamics revealed by a mathematical model linking telomere length and replicative senescence
  
  • Rat Anaïs
  • Martinez Fernandez Veronica
  • Doumic Marie
  • Teixeira Maria Teresa
  • Xu Zhou
  Nature Communications, Nature Publishing Group, 2025, 16 (1), pp.1024. Progressive shortening of telomeres ultimately causes replicative senescence and is linked with aging and tumor suppression. Studying the intricate link between telomere shortening and senescence at the molecular level and its population-scale effects over time is challenging with current approaches but crucial for understanding behavior at the organ or tissue level. In this study, we developed a mathematical model for telomere shortening and the onset of replicative senescence using data from Saccharomyces cerevisiae without telomerase. Our model tracks individual cell states, their telomere length dynamics, and lifespan over time, revealing selection forces within a population. We discovered that both cell genealogy and global telomere length distribution are key to determine the population proliferation capacity. We also discovered that cell growth defects unrelated to telomeres also affect subsequent proliferation and may act as confounding variables in replicative senescence assays. Overall, while there is a deterministic limit for the shortest telomere length, the stochastic occurrence of non-terminal arrests drive cells into a totally different regime, which may promote genome instability and senescence escape. Our results offer a comprehensive framework for investigating the implications of telomere length on human diseases. (10.1101/2023.11.22.568287)
  DOI : 10.1101/2023.11.22.568287
• Convergence and Error Estimates of A Semi-Lagrangian scheme for the Minimum Time Problem
  
  • Akian Marianne
  • Liu Shanqing
  , 2024. We consider a semi-Lagrangian scheme for solving the minimum time problem, with a given target, and the associated eikonal type equation. We first use a discrete time deterministic optimal control problem interpretation of the time discretization scheme, and show that the discrete time value function is semiconcave under regularity assumptions on the dynamics and the boundary of target set. We establish a convergence rate of order $1$ in terms of time step based on this semiconcavity property. Then, we use a discrete time stochastic optimal control interpretation of the full discretization scheme, and we establish a convergence rate of order $1$ in terms of both time and spatial steps using certain interpolation operators, under further regularity assumptions. We extend our convergence results to problems with particular state constraints. We apply our results to analyze the convergence rate and computational complexity of the fast-marching method. We also consider the multi-level fast-marching method recently introduced by the authors.
• Small-scale interface dynamic modelling based on the geometric method of moments for a two-scale two-phase flow model with a disperse small scale
  
  • Loison Arthur
  • Pichard Teddy
  • Kokh Samuel
  • Massot Marc
  Journal of Fluid Mechanics, Cambridge University Press (CUP), 2025, 1003 (A27), pp.1--42. In this contribution, we develop a versatile formalism to derive unified two-phase models describing both the separated and disperse regimes as introduced by Loison et al. (2024). It relies on the stationary action principle and interface geometric variables. This contribution provides a novel method to derive small-scale models for the dynamics of the interface geometry. They are introduced here on a simplified case where all the scales and phases have the same velocity and that does not take into account large-scale capillary forces. The derivation tools yield a proper mathematical framework through hyperbolicity and signed entropy evolution. The formalism encompasses a hierarchy of small-scale reduced-order models based on a statistical description at a mesoscopic kinetic level and is naturally able to include the description of a disperse phase with polydispersity in size. This hierarchy includes both a cloud of spherical droplets and non-spherical droplets experiencing a dynamical behaviour through incompressible oscillations. The associated small-scale variables are moments of a number density function resulting from the geometric method of moments (GeoMOM). This method selects moments as small-scale geometric variables compatible with the structure and dynamics of the interface; they are defined independently of the flow topology and, therefore, this model allows the coupling of the two-scale flow with an inter-scale transfer. It is shown in particular that the resulting dynamics provides partial closures for the interface area density equation obtained from the averaging approach. (10.1017/jfm.2024.1200)
  DOI : 10.1017/jfm.2024.1200
• Brochette first-passage percolation
  
  • Marivain Maxime
  , 2025. We investigate a novel first-passage percolation model, referred to as the Brochette first-passage percolation model, where the passage times associated with edges lying on the same line are equal. First, we establish a point-to-point convergence theorem, identifying the time constant. In particular, we explore the case where the time constant vanishes and demonstrate the existence of a wide range of possible behaviours. Next, we prove a shape theorem, showing that the limiting shape is the $L^1$ diamond. Finally, we extend the analysis by proving a point-to-point convergence theorem in the setting where passage times are allowed to be infinite.
• Kernel density estimation for stationary random fields with values in a finite-dimensional Riemannian manifold
  
  • Nefzi Wiem
  • Yao Anne-Françoise
  • KHARDANI Salah
  , 2025. <div><p>This paper investigates some asymptotic properties of the kernel spatial density estimation for stationary α-mixing process on a finite-dimensional Riemannian manifold without boundary. The results extend beyond the classical independently and identically distributed (i.i.d.) data, focusing on the case where the manifold is known and extending the classical theory to random fields.</p></div>
• Nonparametric Regression on Riemannian manifold under α-Mixing process
  
  • Nefzi Wiem
  • Yao Anne-Françoise
  • KHARDANI Salah
  , 2025. <div><p>The main focus of our paper is to investigate the behavior of the kernel estimator for the regression function between a real-valued random variable Y and a random variable X, where X takes values in a Riemannian submanifold. The estimator is adapted from the article of Pelletier (2006). Additionally, we study data that adheres to the α-mixing condition, which imposes valuable constraints on the dependence structure of the observations. Specifically, we provide the rate of convergence in mean square error, enabling us to assess the precision and efficiency of the estimator.</p></div>
• Derivation of a 4-moment model for electron transport in Hall thrusters from a gyrokinetic model
  
  • Tazakkati Zoubaïr
  • Laguna Alejandro Alvarez
  • Massot Marc
  • Pichard Teddy
  , 2025. <div><p>We model the motion of a population of electrons in a strong electromagnetic field undergoing elastic electron/electron collisions. This regime is derived from a dimensional analysis of the electron confinement in Hall-effect thrusters. The electrons exhibit a very high cyclotron frequency and a E × B-drift, modelled by stiff PDEs at the mesoscopic scale. We obtain a gyrokinetic model in which the fastest oscillations of the system are filtered out by averaging the rotation of the electrons around the magnetic field lines. The model is derived in the strong electromagnetic field limit. Based on this gyrokinetic model, we then develop a 10-moment model. The averaging operation performed at the kinetic scale leads to symmetry properties that allow to reduce the 10-moment model to a 4-moment model.</p></div>