Publications

2020

• Optimisation des parcours patients pour lutter contre l'errance de diagnostic des patients atteints de maladies rares
  
  • Logé Frédéric
  • Besson Rémi
  • Allassonnière Stéphanie
  , 2020. Un patient atteint d'une maladie rare en France doit en moyenne attendre deux ans avant d'être diagnostiqué. Cette errance médicale est fortement préjudiciable tant pour le système de santé que pour les patients dont la pathologie peut s'aggraver. Il existe pourtant un réseau performant de centres de référence maladies rares (CRMR), mais les patients ne sont orientés que trop tardivement vers ces structures. Nous considérons une modélisation probabiliste du parcours patient afin de créer un simulateur permettant d'entraîner un système d'alerte détectant les patients en errance et les orientant vers un CRMR tout en considérant les potentiels surcoûts associés à ces décisions. Les premiers résultats obtenus sur données simulées apparaissent prometteurs. Un important travail de mise en relation des données expertes disponibles avec les données de parcours patients reste à faire ainsi que des ajustements sur la modélisation proposée.
• Coupled optimization of macroscopic structures and lattice infill
  
  • Geoffroy‐donders Perle
  • Allaire Grégoire
  • Michailidis Georgios
  • Pantz Olivier
  International Journal for Numerical Methods in Engineering, Wiley, 2020, 123 (13), pp.2963-2985.. This article is concerned with the coupled optimization of the external boundary of a structure and its infill made of some graded lattice material. The lattice material is made of a periodic cell, macroscopically modulated and oriented. The external boundary may be coated by a layer of pure material with a fixed prescribed thickness. The infill is optimized by the homogenization method while the macroscopic shape is geometrically optimized by the Hadamard method of shape sensitivity. A first original feature of the proposed approach is that the infill material follows the displacement on the exterior boundary during the geometric optimization step. A second key feature is the dehomogenization or projection step which build a smoothly varying lattice infill from the optimal homogenized properties. Several numerical examples illustrate the effectiveness of our approach in 2-d, which is especially convenient when considering design-dependent loads. (10.1002/nme.6392)
  DOI : 10.1002/nme.6392
• Efficient Estimation of Extreme Quantiles using Adaptive Kriging and Importance Sampling
  
  • Razaaly Nassim
  • Crommelin Daan
  • Congedo Pietro Marco
  International Journal for Numerical Methods in Engineering, Wiley, 2020, 121 (9), pp.2086-2105. This study considers an efficient method for the estimation of quantiles associated to very small levels of probability (up to O(10−9)), where the scalar performance function J is complex (eg, output of an expensive‐to‐run finite element model), under a probability measure that can be recast as a multivariate standard Gaussian law using an isoprobabilistic transformation. A surrogate‐based approach (Gaussian Processes) combined with adaptive experimental designs allows to iteratively increase the accuracy of the surrogate while keeping the overall number of J evaluations low. Direct use of Monte‐Carlo simulation even on the surrogate model being too expensive, the key idea consists in using an importance sampling method based on an isotropic‐centered Gaussian with large standard deviation permitting a cheap estimation of small quantiles based on the surrogate model. Similar to AK‐MCS as presented in the work of Schöbi et al., (2016), the surrogate is adaptively refined using a parallel infill criterion of an algorithm suitable for very small failure probability estimation. Additionally, a multi‐quantile selection approach is developed, allowing to further exploit high‐performance computing architectures. We illustrate the performances of the proposed method on several two to eight‐dimensional cases. Accurate results are obtained with less than 100 evaluations of J on the considered benchmark cases. (10.1002/nme.6300)
  DOI : 10.1002/nme.6300
• Robust Lasso-Zero for sparse corruption and model selection with missing covariates
  
  • Descloux Pascaline
  • Boyer Claire
  • Josse Julie
  • Sportisse Aude
  • Sardy Sylvain
  , 2020. We propose Robust Lasso-Zero, an extension of the Lasso-Zero methodology [Descloux and Sardy, 2018], initially introduced for sparse linear models, to the sparse corruptions problem. We give theoretical guarantees on the sign recovery of the parameters for a slightly simplified version of the estimator, called Thresholded Justice Pursuit. The use of Robust Lasso-Zero is showcased for variable selection with missing values in the covariates. In addition to not requiring the specification of a model for the covariates, nor estimating their covariance matrix or the noise variance, the method has the great advantage of handling missing not-at random values without specifying a parametric model. Numerical experiments and a medical application underline the relevance of Robust Lasso-Zero in such a context with few available competitors. The method is easy to use and implemented in the R library lass0.
• Multiscale Analysis of Spectral Broadening of Acoustic Waves by a Turbulent Shear Layer
  
  • Garnier Josselin
  • Gay Etienne
  • Savin Eric
  Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2020, 18 (2), pp.798-823. We consider the scattering of acoustic waves emitted by an active source above a plane turbulent shear layer. The layer is modeled by a moving random medium with small spatial and temporal fluctuations of its mean velocity, and constant density and speed of sound. We develop a multi-scale perturbative analysis for the acoustic pressure field transmitted by the layer and derive its power spectral density when the correlation function of the velocity fluctuations is known. Our aim is to compare the proposed analytical model with some experimental results obtained for jet flows in open wind tunnels. We start with the Euler equations for an ideal fluid flow and linearize them about an ambient, unsteady inhomogeneous flow. We study the transmitted pressure field without fluctuations of the ambient flow velocity to obtain the Green's function of the unperturbed medium with constant characteristics. Then we use a Lippmann-Schwinger equation to derive an analytical expression of the transmitted pressure field, as a function of the velocity fluctuations within the layer. Its power spectral density is subsequently computed invoking a stationary-phase argument, assuming in addition that the source is time-harmonic and the layer is thin. We finally study the influence of the source tone frequency and ambient flow velocity on the power spectral density of the transmitted pressure field and compare our results with other analytical models and experimental data. (10.1137/19M1276492)
  DOI : 10.1137/19M1276492
• Entropy supplementary conservation law for non-linear systems of PDEs with non-conservative terms: application to the modelling and analysis of complex fluid flows using computer algebra
  
  • Cordesse Pierre
  • Massot Marc
  Communications in Mathematical Sciences, International Press, 2020, 18 (2), pp.515-534. In the present contribution, we investigate first-order nonlinear systems of partial differential equations which are constituted of two parts: a system of conservation laws and non-conservative first order terms. Whereas the theory of first-order systems of conservation laws is well established and the conditions for the existence of supplementary conservation laws, and more specifically of an entropy supplementary conservation law for smooth solutions, well known, there exists so far no general extension to obtain such supplementary conservation laws when non-conservative terms are present. We propose a framework in order to extend the existing theory and show that the presence of non-conservative terms somewhat complexifies the problem since numerous combinations of the conservative and non-conservative terms can lead to a supplementary conservation law. We then identify a restricted framework in order to design and analyze physical models of complex fluid flows by means of computer algebra and thus obtain the entire ensemble of possible combination of conservative and non-conservative terms with the objective of obtaining specifically an entropy supplementary conservation law. The theory as well as developed computer algebra tool are then applied to a Baer-Nunziato two-phase flow model and to a multicomponent plasma fluid model. The first one is a first-order fluid model, with non-conservative terms impacting on the linearly degenerate field and requires a closure since there is no way to derive interfacial quantities from averaging principles and we need guidance in order to close the pressure and velocity of the interface and the thermodynamics of the mixture. The second one involves first order terms for the heavy species coupled to second order terms for the electrons, the non-conservative terms impact the genuinely nonlinear fields and the model can be rigorously derived from kinetic theory. We show how the theory allows to recover the whole spectrum of closures obtained so far in the literature for the two-phase flow system as well as conditions when one aims at extending the thermodynamics and also applies to the plasma case, where we recover the usual entropy supplementary equation, thus assessing the effectiveness and scope of the proposed theory. (10.4310/CMS.2020.v18.n2.a10)
  DOI : 10.4310/CMS.2020.v18.n2.a10
• Exact zero transmission during the Fano resonance phenomenon in non symmetric waveguides
  
  • Chesnel Lucas
  • Nazarov Sergei A
  Zeitschrift für Angewandte Mathematik und Physik = Journal of Applied mathematics and physics = Journal de mathématiques et de physique appliquées, Springer Verlag, 2020. We investigate a time-harmonic wave problem in a waveguide. We work at low frequency so that only one mode can propagate. It is known that the scattering matrix exhibits a rapid variation for real frequencies in a vicinity of a complex resonance located close to the real axis. This is the so-called Fano resonance phenomenon. And when the geometry presents certain properties of symmetry, there are two different real frequencies such that we have either R = 0 or T = 0, where R and T denote the reflection and transmission coefficients. In this work, we prove that without the assumption of symmetry of the geometry, quite surprisingly, there is always one real frequency for which we have T = 0. In this situation, all the energy sent in the waveguide is backscattered. However in general, we do not have R = 0 in the process. We provide numerical results to illustrate our theorems.
• Particle simulation of space–fractional diffusion equations
  
  • Lucchesi Marco
  • Allouch Samer
  • Le Maitre Olivier
  • Mustapha Kassem
  • Knio Omar
  Computational Particle Mechanics, Springer Verlag, 2020, 7 (3), pp.491-507. This work explores different particle-based approaches for the simulation of space–fractional diffusion equations in unbounded domains. We rely on smooth particle approximations and consider five different methods for estimating the fractional diffusion term. The first method is based on a direct differentiation of the particle representation, following the Riesz definition of the fractional derivative, and results in a non-conservative scheme. Three methods follow the particle strength exchange (PSE) methodology and are by construction conservative, meaning that the total particle strength is time-invariant. The first PSE algorithm estimates the fractional diffusion flux using direct differentiation and uses an integral representation of the divergence operator. The second one relies on the integral representation of the fractional Laplacian to derive a suitable particle strength exchange formula for the diffusion term. The third PSE construction employs the Green’s function of the fractional diffusion equation. A fifth method is developed based on the diffusion velocity approach, where the diffusion term is transformed into a transport term. The performance of all five methods is assessed, for which analytical solutions are known. A detailed analysis is conducted of the various sources of error, namely filtering, quadrature, domain truncation, and time integration. Computational experiments are used to gain insight into the generalization of the present constructions, such as applications in bounded domains or variable diffusivity. (10.1007/s40571-019-00275-8)
  DOI : 10.1007/s40571-019-00275-8
• Global uniqueness in a passive inverse problem of helioseismology
  
  • Agaltsov Alexey
  • Hohage Thorsten
  • Novikov Roman
  Inverse Problems, IOP Publishing, 2020, 36 (5), pp.055004. We consider the inverse problem of recovering the spherically symmetric sound speed, density and attenuation in the Sun from the observations of the acoustic field randomly excited by turbulent convection.We show that observations at two heights above the photosphere and at two frequencies above the acoustic cutoff frequency uniquely determine the solar parameters. We also present numerical simulations which confirm this theoretical result. (10.1088/1361-6420/ab77d9)
  DOI : 10.1088/1361-6420/ab77d9
• Implied Volatility Structure in Turbulent and Long-Memory Markets
  
  • Garnier Josselin
  • Sølna Knut
  Frontiers in Applied Mathematics and Statistics, Frontiers Media S.A, 2020, 6. We consider fractional stochastic volatility models that extend the classic Black–Scholesmodel for asset prices. The models are general and motivatedby recent empirical resultsregarding the behavior of realized volatility. While such models retain the semimartingaleproperty for the asset price the associated European optionpricing problem becomescomplex, with no explicit solution. In a number of canonicalscaling regimes it is possible,however, to derive asymptotic and sparse representations for the option price and theassociated implied volatility, that are parameterized by afew effective parameters andthat involve power law dependencies on time to maturity. These effective parameters maydepend in a complicated way on the volatility model, but theycan be easily estimatedfrom the observation of a few option prices. The effective parameters associated witha particular underlying asset can be calibrated with respect to liquid contracts writtenon this asset and then used for pricing less liquid contractswritten on the sameunderlying asset. Therefore, the effective parameters provide a robust link betweenfinancial products written on a particular underlying asset. (10.3389/fams.2020.00010)
  DOI : 10.3389/fams.2020.00010
• The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem
  
  • Gatheral Jim
  • Jusselin Paul
  • Rosenbaum Mathieu
  , 2020. Fitting SPX and Vix smiles simultaneously is one of the most challenging problems in volatility modelling. A long-standing conjecture is that it may not be possible to jointly calibrate these two quantities using a model with continuous sample paths. Jim Gatheral, Paul Jusselin and Mathieu Rosenbaum present the quadratic rough Heston model as a counterexample to this conjecture. The key idea is the combination of rough volatility with a price-feedback (Zumbach) effect
• Data Completion Method For the Helmholtz Equation Via Surface Potentials for Partial Cauchy Data
  
  • Aussal Matthieu
  • Boukari Yosra
  • Haddar Houssem
  Inverse Problems, IOP Publishing, 2020, 36 (5), pp.055012. We propose and study a data completion algorithm for recovering missing data from the knowledge of Cauchy data on parts of the same boundary. The algorithm is based on surface representation of the solution and is presented for the Helmholtz equation. This work is an extension of the data completion algorithm proposed by the two last authors where the case of data available of a closed boundary was studied. The proposed method is a direct inversion method robust with respect to noisy incompatible data. Classical regularization methods with discrepancy selection principles can be employed and automatically lead to a convergent schemes as the noise level goes to zero. We conduct 3D numerical investigations to validate our method on various synthetic examples. (10.1088/1361-6420/ab730c)
  DOI : 10.1088/1361-6420/ab730c
• Travelling wave mathematical analysis and efficient numerical resolution for a one-dimensional model of solid propellant combustion
  
  • François Laurent
  • Dupays Joël
  • Davidenko Dmitry
  • Massot Marc
  Combustion Theory and Modelling, Taylor & Francis, 2020, 24 (5), pp.775-809. We investigate a model of solid propellant combustion involving surface pyrolysis coupled to finite activation energy gas phase combustion. Existence and uniqueness of a travelling wave solution are established by extending dynamical system tools classically used for premixed flames, dealing with the additional difficulty arising from the surface regression and pyrolysis. An efficient shooting method allows to solve the problem in phase space without resorting to space discretisation nor fixed-point Newton iterations. The results are compared to solutions from a CFD code developed at ONERA, assessing the efficiency and potential of the method, and the impact of the modelling assumptions is evaluated through parametric studies. (10.1080/13647830.2020.1752943)
  DOI : 10.1080/13647830.2020.1752943
• Browser Fingerprinting: A Survey
  
  • Laperdrix Pierre
  • Bielova Nataliia
  • Baudry Benoit
  • Avoine Gildas
  ACM Transactions on the Web, http://tweb.acm.org/, 2020, 14 (2), pp.1-33. With this article, we survey the research performed in the domain of browser fingerprinting, while providing an accessible entry point to newcomers in the field. We explain how this technique works and where it stems from. We analyze the related work in detail to understand the composition of modern fingerprints and see how this technique is currently used online. We systematize existing defense solutions into different categories and detail the current challenges yet to overcome. (10.1145/3386040)
  DOI : 10.1145/3386040
• Diffusion MRI simulation of realistic neurons with SpinDoctor and the Neuron Module, ISMRM poster
  
  • Nguyen Van-Dang
  • Fang Chengran
  • Wassermann Demian
  • Li Jing-Rebecca
  , 2020. The simulation of diffusion MRI arising from realistic neuron models can help investigate the cellular microstructure. However, ensuring correct connectivity between the distinct compartments comprising the system while minimizing the computational burden is one of the main challenges in our community. The design of accurate and efficient simulation algorithm and the construction of high quality neurons meshes are two difficulties in addressing this problem.The Neuron Module can perform HARDI simulation of realistic neurons at various b-values and diffusion sequences with high accuracy.The computational time per gradient direction is around 30 seconds which is much faster than some Monte-Carlo simulators. The linear relationship between the diffusion direction averaged signal and one over square root of b for tubular structures is validated by our simulations. We believe our work can add substantially to the understanding of the imaging of neuronal microstructure.
• Mean Field Game Approach to Bitcoin Mining
  
  • Bertucci Charles
  • Bertucci Louis
  • Lasry Jean-Michel
  • Lions Pierre-Louis
  , 2020. We present an analysis of the Proof-of-Work consensus algorithm, used on the Bitcoin blockchain, using a Mean Field Game framework. Using a master equation, we provide an equilibrium characterization of the total computational power devoted to mining the blockchain (hashrate). From a simple setting we show how the master equation approach allows us to enrich the model by relaxing most of the simplifying assumptions. The essential structure of the game is preserved across all the enrichments. In deterministic settings, the hashrate ultimately reaches a steady state in which it increases at the rate of technological progress. In stochastic settings, there exists a target for the hashrate for every possible random state. As a consequence, we show that in equilibrium the security of the underlying blockchain is either $i)$ constant, or $ii)$ increases with the demand for the underlying cryptocurrency. (10.48550/arXiv.2004.08167)
  DOI : 10.48550/arXiv.2004.08167
• Peer-to-Peer Electricity Market Analysis: From Variational to Generalized Nash Equilibrium
  
  • Le Cadre Hélène
  • Jacquot Paulin
  • Wan Cheng
  • Alasseur Clémence
  European Journal of Operational Research, Elsevier, 2020, 282 (2), pp.753-771. We consider a network of prosumers involved in peer-to-peer energy exchanges, with differentiation price preferences on the trades with their neighbors, and we analyze two market designs: (i) a centralized market, used as a benchmark, where a global market operator optimizes the flows (trades) between the nodes, local demand and exibility activation to maximize the system overall social welfare; (ii) a distributed peer-to-peer market design where prosumers in local energy communities optimize selfishly their trades, demand, and exibility activation. We first characterize the solution of the peer-to-peer market as a Variational Equilibrium and prove that the set of Variational Equilibria coincides with the set of social welfare optimal solutions of market design (i). We give several results that help understanding the structure of the trades at an equilibrium or at the optimum. We characterize the impact of preferences on the network line congestion and renewable energy surplus under both designs. We provide a reduced example for which we give the set of all possible generalized equilibria, which enables to give an approximation of the price of anarchy. We provide a more realistic example which relies on the IEEE 14-bus network, for which we can simulate the trades under dierent preference prices. Our analysis shows in particular that the preferences have a large impact on the structure of the trades, but that one equilibrium (variational) is optimal. Finally, the learning mechanism needed to reach an equilibrium state in the peer-to-peer market design is discussed together with privacy issues. (10.1016/j.ejor.2019.09.035)
  DOI : 10.1016/j.ejor.2019.09.035
• Multilevel Monte-Carlo methods and lower-upper bounds in Initial Margin computations
  
  • Bourgey F
  • de Marco S
  • Gobet Emmanuel
  • Zhou Alexandre
  Monte Carlo Methods and Applications, De Gruyter, 2020, 26 (2). The Multilevel Monte-Carlo (MLMC) method developed by Giles [Gil08] has a natural application to the evaluation of nested expectation of the form E [g(E [f (X, Y)|X])], where f, g are functions and (X, Y) a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of Initial Margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotical optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal/dual algorithms for stochastic control problems. (10.1515/mcma-2020-2062)
  DOI : 10.1515/mcma-2020-2062
• Game on Random Environment, Mean-field Langevin System and Neural Networks
  
  • Conforti Giovanni
  • Kazeykina Anna
  • Ren Zhenjie
  , 2022. In this paper we study a type of games regularized by the relative entropy, where the players' strategies are coupled through a random environment variable. Besides the existence and the uniqueness of equilibria of such games, we prove that the marginal laws of the corresponding mean-field Langevin systems can converge towards the games' equilibria in different settings. As applications, the dynamic games can be treated as games on a random environment when one treats the time horizon as the environment. In practice, our results can be applied to analysing the stochastic gradient descent algorithm for deep neural networks in the context of supervised learning as well as for the generative adversarial networks.
• Forward and backward uncertainty quantification with active subspaces: application to hypersonic flows around a cylinder
  
  • Cortesi Andrea F
  • Constantine Paul G
  • Magin Thierry
  • Congedo Pietro Marco
  Journal of Computational Physics, Elsevier, 2020, 407, pp.109079. We perform a Bayesian calibration of the freestream velocity and density starting from measurements of the pressure and heat flux at the stagnation point of a hypersonic high-enthalpy flow around a cylinder. The objective is to explore the possibility of using stagnation heat flux measurements, together with pressure measurements, to rebuild freestream conditions since such measurements are available for recent space missions but not exploited for freestream characterization. First, we formulate an algorithm of mesh adaptation, enabling accurate numerical solutions in an automatic way for a given set of inputs. Secondly, active subspaces are used to find a lowdimensional dependence structures in the input-to-output map of the forward numerical solver. Then, surrogate models on the active variables are used to accelerate the forward uncertainty propagation by Monte Carlo sampling and the Markov Chain Monte Carlo sampling of the posterior distribution for Bayesian inversion. A preliminary sensitivity analysis with sparse Polynomial Dimensional Decomposition is performed on the chemical model of the air mixture, to determine the most influential uncertain chemical parameters in the forward problem. Then, the forward and backward methodologies are applied to the simulation of a hypersonic flow around a cylinder, in conditions for which experimental data are available, revealing new insights towards the potential exploitation of heat flux data for freestream rebuilding. (10.1016/j.jcp.2019.109079)
  DOI : 10.1016/j.jcp.2019.109079
• Eco-evolutionary dynamics of nested Darwinian populations and the emergence of community-level heredity
  
  • Doulcier Guilhem
  • Lambert Amaury
  • de Monte Silvia
  • Rainey Paul
  eLife, eLife Sciences Publication, 2020, 9. Interactions among microbial cells can generate new chemistries and functions, but exploitation requires establishment of communities that reliably recapitulate community-level phenotypes. Using mechanistic mathematical models, we show how simple manipulations to population structure can exogenously impose Darwinian-like properties on communities. Such imposition causes communities to participate directly in the process of evolution by natural selection and drives the evolution of cell-level interactions to the point where, despite underlying stochasticity, derived communities give rise to offspring communities that faithfully re-establish parental phenotype. The mechanism (developmental correction) is akin to a developmental process that arises from density dependent interactions among cells. Knowledge of ecological factors affecting evolution of developmental correction has implications for understanding the evolutionary origin of egalitarian transitions in individuality, symbioses, and for top-down engineering of microbial communities. (10.7554/eLife.53433)
  DOI : 10.7554/eLife.53433
• Quantitative approximation of the Burgers and Keller-Segel equations by moderately interacting particles
  
  • Olivera Christian
  • Richard Alexandre
  • Tomasevic Milica
  , 2020. In this work we obtain rates of convergence for two moderately interacting stochastic particle systems with singular kernels associated to the viscous Burgers and Keller-Segel equations. The main novelty of this work is to consider a non-locally integrable kernel. Namely for the viscous Burgers equation in $\mathbb{R}$, we obtain almost sure convergence of the mollified empirical measure to the solution of the PDE in some Bessel space with a rate of convergence of order $N^{-1/8}$, on any time interval. The same holds for the genuine empirical measure in Wasserstein distance. In the case of the Keller-Segel equation on a $d$-dimensional torus, we obtain almost sure convergence of the mollified empirical measure to the solution of the PDE in some $L^q$ space with a rate of order $N^{-\frac{1}{2d+1}}$. The result holds up to the maximal existence time of the PDE, for any value of the chemo-attractant sensitivity $\chi$.
• Surrogate based shape optimization and uncertainty assessment of a ERCOFTAC pump
  
  • Fracassi Alessia
  • de Donno Remo
  • Ghidoni Antonio
  • Congedo Pietro Marco
  Engineering Optimization, Taylor & Francis, 2020, pp.1-18. Centrifugal pumps, being used nowadays for many applications, must be suited for a wide range of pressure ratios and flow rates. To overcome difficulties arising from the design and performance prediction of this class of turbomachinery, many researchers proposed the coupling of CFD codes and optimization algorithms for a fast and effective design procedure. However, uncertainties are present in most engineering applications such as turbomachines, and their influence on turbomachinery performance should be considered. In this work we apply some advanced optimization techniques to the blade optimization of an ERCOFTAC-like pump, and we assess the robustness of the optimal profiles through an uncertainty propagation study. The main source of uncertainty is constituted by the uncertainty of the operating conditions, primarily the rotational speed of the pump shaft that affects also the flow rate. (10.1080/0305215X.2020.1858075)
  DOI : 10.1080/0305215X.2020.1858075
• Numerical treatment of the nonconservative product in a multiscale fluid model for plasmas in thermal nonequilibrium: application to solar physics
  
  • Wargnier Quentin
  • Faure Sylvain
  • Graille Benjamin
  • Magin Thierry E.
  • Massot Marc
  SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2020, 42 (2), pp.B492–B519. This contribution deals with the modeling of collisional multicomponent magnetized plasmas in thermal and chemical nonequilibrium aiming at simulating and predicting magnetic reconnections in the chromosphere of the sun. We focus on the numerical simulation of a simplified fluid model in order to properly investigate the influence on shock solutions of a nonconservative product present in the electron energy equation. Then, we derive jump conditions based on travelling wave solutions and propose an original numerical treatment in order to avoid non-physical shocks for the solution, that remains valid in the case of coarse-resolution simulations. A key element for the numerical scheme proposed is the presence of diffusion in the electron variables, consistent with the physically-sound scaling used in the model developed by Graille et al. following a multiscale Chapman-Enskog expansion method [M3AS, 19 (2009) 527--599]. The numerical strategy is eventually assessed in the framework of a solar physics test case. The computational method is able to capture the travelling wave solutions in both the highly- and coarsely-resolved cases. (10.1137/18M1194225)
  DOI : 10.1137/18M1194225
• Shape Reconstruction of Deposits Inside a Steam Generator Using Eddy Current Measurements
  
  • Audibert Lorenzo
  • Girardon Hugo
  • Haddar Houssem
  , 2020.