Publications

2010

• La fonction de Liouville visualisée comme une marche aléatoire bidimensionnelle pour les nombres entiers de 2 a 1001
  
  • Colonna Jean-François
  , 2010. The Liouville function displayed as a bidimensional random walk for the integer numbers from 2 to 1001 (La fonction de Liouville visualisée comme une marche aléatoire bidimensionnelle pour les nombres entiers de 2 a 1001)
• Mouvement brownien tridimensionnel sur un reseau cubique base sur la dynamique de Verhulst -la palette de couleurs (magenta,rouge,jaune,vert,cyan) est une fonction croissante du temps
  
  • Colonna Jean-François
  , 2010. Tridimensional brownian motion on a cubic lattice based on the Verhulst dynamics -the colors used (magenta,red,yellow,gree,cyan) are an increasing function of the time- (Mouvement brownien tridimensionnel sur un reseau cubique base sur la dynamique de Verhulst -la palette de couleurs (magenta,rouge,jaune,vert,cyan) est une fonction croissante du temps-)
• La fonction de Liouville visualisee comme une marche aleatoire bidimensionnelle pour les nombres entiers de 2 a 100001
  
  • Colonna Jean-François
  , 2010. The Liouville function displayed as a bidimensional random walk for the integer numbers from 2 to 100001 (La fonction de Liouville visualisee comme une marche aleatoire bidimensionnelle pour les nombres entiers de 2 a 100001)
• Mouvement brownien bidimensionnel sur un reseau carre base sur la dynamique de Verhulst -la palette de couleurs (magenta,rouge,jaune,vert,cyan) est une fonction croissante du temps
  
  • Colonna Jean-François
  , 2010. Bidimensional brownian motion on a square lattice based on the Verhulst dynamics -the colors used (magenta,red,yellow,gree,cyan) are an increasing function of the time- (Mouvement brownien bidimensionnel sur un reseau carre base sur la dynamique de Verhulst -la palette de couleurs (magenta,rouge,jaune,vert,cyan) est une fonction croissante du temps-)
• La fonction de Liouville visualisée comme une marche aléatoire bidimensionnelle pour les nombres entiers de 2 a 100001
  
  • Colonna Jean-François
  , 2010. The Liouville function displayed as a bidimensional random walk for the integer numbers from 2 to 100001 (La fonction de Liouville visualisee comme une marche aleatoire bidimensionnelle pour les nombres entiers de 2 a 100001)
• Mouvement brownien tridimensionnel sur un réseau cubique base sur un processus aléatoire -la palette de couleurs (magenta,rouge,jaune,vert,cyan) est une fonction croissante du temps
  
  • Colonna Jean-François
  , 2010. Tridimensional brownian motion on a cubic lattice based on a random process -the colors used (magenta,red,yellow,gree,cyan) are an increasing function of the time- (Mouvement brownien tridimensionnel sur un réseau cubique base sur un processus aléatoire -la palette de couleurs (magenta,rouge,jaune,vert,cyan) est une fonction croissante du temps-)
• Mouvement brownien bidimensionnel sur un reseau carre base sur un processus aleatoire -la palette de couleurs (magenta,rouge,jaune,vert,cyan) est une fonction croissante du temps
  
  • Colonna Jean-François
  , 2010. Bidimensional brownian motion on a square lattice based on a random process -the colors used (magenta,red,yellow,gree,cyan) are an increasing function of the time- (Mouvement brownien bidimensionnel sur un reseau carre base sur un processus aleatoire -la palette de couleurs (magenta,rouge,jaune,vert,cyan) est une fonction croissante du temps-)
• La fonction de Liouville visualisée comme une marche aléatoire tridimensionnelle pour les nombres entiers de 2 a 150001
  
  • Colonna Jean-François
  , 2010. The Liouville function displayed as a tridimensional random walk for the integer numbers from 2 to 150001 (La fonction de Liouville visualisee comme une marche aleatoire tridimensionnelle pour les nombres entiers de 2 a 150001)
• The existence of an infinite discrete set of transmission eigenvalues
  
  • Cakoni Fioralba
  • Gintides Drossos
  • Haddar Houssem
  SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2010, 42 (1), pp.237-255. (10.1137/090769338)
  DOI : 10.1137/090769338
• Preprocessing the Reciprocity Gap Sampling Method in Buried-Object Imaging Experiments
  
  • Ozdemir Ozgur
  • Haddar Houssem
  IEEE Geoscience and Remote Sensing Letters, IEEE - Institute of Electrical and Electronics Engineers, 2010, 7 (4), pp.756 -760. (10.1109/LGRS.2010.2047003)
  DOI : 10.1109/LGRS.2010.2047003
• Application of a coupled FV/FE multiscale method to cement media
  
  • Abballe Th.
  • Allaire Grégoire
  • Laucoin E.
  • Montarnal Ph.
  Networks and Heterogeneous Media, American Institute of Mathematical Sciences, 2010, 5 (3), pp.603-615. We present here some results provided by a multiscale resolution method using both Finite Volumes and Finite Elements. This method is aimed at solving very large diffusion problems with highly oscillating coefficients. As an illustrative example, we simulate models of cement media, where very strong variations of diffusivity occur. As a by-product of our simulations, we compute the effective diffusivities of these media. After a short introduction, we present a theorical description of our method. Numerical experiments on a two dimensional cement paste are presented subsequently. The third section describes the implementation of our method in the calculus code MPCube and its application to a sample of mortar. Finally, we discuss strengths and weaknesses of our method, and present our future works on this topic. (10.3934/nhm.2010.5.603)
  DOI : 10.3934/nhm.2010.5.603
• Convergence of a non-monotone scheme for Hamilton-Jacobi-Bellman equations with discontinuous data
  
  • Bokanowski Olivier
  • Megdich Nadia
  • Zidani Hasnaa
  Numerische Mathematik, Springer Verlag, 2010, 115 (1), pp.1--44. On étudie un schéma non monotone pour l'équation Hamilton Jacobi Bellman du premier ordre, en dimension 1. Le schéma considèré est lié au schéma anti-diffusif, appellé UltraBee, proposé par Bokanowski-Zidani (publié en 2007 dans J. Sci. Compt.). Ici, on prouve la convergence, en norme $L^1$, à l'ordre 1, pour une condition initiale discontinue. Le caractère anti-diffusif du schéma est illustré par quelques exemples numériques. (10.1007/s00211-009-0271-1)
  DOI : 10.1007/s00211-009-0271-1
• Measurability of optimal transportation and strong coupling of martingale measures
  
  • Fontbona Joaquin
  • Guérin Hélène
  • Méléard Sylvie
  Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2010, 15, pp.124-133. We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability result for this map, with respect to the space variable and to the parameter. The proof needs to establish the measurability of some set-valued mappings, related to the support of the optimal transference plans, which we use to perform a suitable discrete approximation procedure. A motivation is the construction of a strong coupling between orthogonal martingale measures. By this we mean that, given a martingale measure, we construct in the same probability space a second one with specified covariance measure. This is done by pushing forward one martingale measure through a predictable version of the optimal transport map between the covariance measures. This coupling allows us to obtain quantitative estimates in terms of the Wasserstein distance between those covariance measures. (10.1214/ECP.v15-1534)
  DOI : 10.1214/ECP.v15-1534
• Two-scale expansion with drift approach to the Taylor dispersion for reactive transport through porous media
  
  • Allaire Grégoire
  • Brizzi Robert
  • Mikelic Andro
  • Piatnitski Andrey
  Chemical Engineering Science, Elsevier, 2010, 65, pp.2292-2300. In this work we study reactive flows through porous media. We suppose dominant Peclet's number, dominant Damköhler's number and general linear reactions at the pore boundaries. Our goal is to obtain the dispersion tensor and the upscaled model. We introduce the multiple scale expansions with drift for the problem and use this technique to upscale the reactive flow equations. Our result is illustrated with numerical simulations for the dispersion tensor.
• Spectral Volumetric Integral Equation Methods for Acoustic Medium Scattering in a Planar Homogeneous 3D Waveguide
  
  • Lechleiter Armin
  • Nguyen Dinh Liem
  , 2010. Scattering of acoustic waves from an inhomogeneous medium can be described by the Lippmann-Schwinger integral equation. For scattering problems in free space, Vainikko proposed a fast spectral solution method that exploits the convolution structure of this equation's integral operator by using the fast Fourier transform. In a planar 3--dimensional waveguide, the integral operator of the Lippmann-Schwinger integral equation fails to be a convolution. In this paper, we show that the separable structure of the kernel nevertheless allows to construct fast spectral collocation methods similar to Vainikko's technique. The numerical analysis of this method requires smooth material parameters; if the material parameters are, say, discontinuous, no theoretical statement on convergence is available. We show how to construct a Galerkin variant of Vainikko's method for which a rigorous convergence analysis is available even for discontinuous materials. For several distant scattering objects inside the 3--dimensional waveguide this discretization technique leads to a computational domain consisting of one large box containing all scatterers, and hence many unnecessary unknowns. However, the integral equation can be reformulated as a coupled system with unknowns defined on the different parts of the scatterer. Discretizing this coupled system by a combined spectral/multipole approach yields an efficient method for waveguide scattering from multiple objects.
• The interior transmission problem for regions with cavities
  
  • Cakoni Fioralba
  • Colton David
  • Haddar Houssem
  SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2010, 42 (1), pp.145-162. (10.1137/090754637)
  DOI : 10.1137/090754637
• Towards a general convergence theory for inexact Newton regularizations
  
  • Lechleiter Armin
  • Rieder Andreas
  Numerische Mathematik, Springer Verlag, 2010, 114 (3), pp.521--548. (10.1007/s00211-009-0256-0)
  DOI : 10.1007/s00211-009-0256-0
• Approximation of Liquid-Vapor Phase Transition for Compressible Fluids with Tabulated EOS
  
  • Faccanoni Gloria
  • Kokh Samuel
  • Allaire Grégoire
  Comptes Rendus de l'Academie des Sciences. Série IV, Physique, Astronomie, Elsevier, 2010, 348 (7-8), pp.473-478. This Note investigates the approximation of phase change in compressible fluids with complex equation of state (EOS). Assuming a local and instantaneous equilibrium with respect to phasic pressures, temperatures and chemical potentials when both phases are present leads to the classical de nition of an equilibrium EOS for the two-phase medium. Unfortunately, there is no explicit expression of the equilibrium EOS in most cases. We propose simple means to approximate the equilibrium EOS when both phases are governed by very general EOS, including tabulated ones. We present a relaxation type numerical algorithm based on this approximation for simulating two-phase flows with phase change. (10.1016/j.crma.2010.01.012)
  DOI : 10.1016/j.crma.2010.01.012
• Homotopy Algorithm for Optimal Control Problems with a Second-order State Constraint
  
  • Hermant Audrey
  Applied Mathematics and Optimization, Springer Verlag (Germany), 2010, 61 (1), pp.85-127. This paper deals with optimal control problems with a regular second-order state constraint and a scalar control, satisfying the strengthened Legendre-Clebsch condition. We study the stability of structure of stationary points. It is shown that under a uniform strict complementarity assumption, boundary arcs are stable under sufficiently smooth perturbations of the data. On the contrary, nonreducible touch points are not stable under perturbations. We show that under some reasonable conditions, either a boundary arc or a second touch point may appear. Those results allow us to design an homotopy algorithm which automatically detects the structure of the trajectory and initializes the shooting parameters associated with boundary arcs and touch points. (10.1007/s00245-009-9076-y)
  DOI : 10.1007/s00245-009-9076-y
• Identification of generalized impedance boundary conditions in inverse scattering problems
  
  • Bourgeois Laurent
  • Haddar Houssem
  Inverse Problems and Imaging, AIMS American Institute of Mathematical Sciences, 2010, 4 (1), pp.19-38. In the context of scattering problems in the harmonic regime, we consider the problem of identification of some Generalized Impedance Boundary Conditions (GIBC) at the boundary of an object (which is supposed to be known) from far field measurements associated with a single incident plane wave at a fixed frequency. The GIBCs can be seen as approximate models for thin coatings, corrugated surfaces or highly absorbing media. After pointing out that uniqueness does not hold in the general case, we propose some additional assumptions for which uniqueness can be restored. We also consider the question of stability when uniqueness holds. We prove in particular Lipschitz stability when the impedance parameters belong to a compact subset of a finite dimensional space. (10.3934/ipi.2010.4.19)
  DOI : 10.3934/ipi.2010.4.19
• Numerical Algorithms for Perspective Shape from Shading
  
  • Breuss Michael
  • Cristiani Emiliano
  • Durou Jean-Denis
  • Falcone Maurizio
  • Vogel Oliver
  Kybernetika, Institute of Information Theory and Automation, 2010, 46, pp.207--225. The Shape-From-Shading (SFS) problem is a fundamental and classic problem in computer vision. It amounts to compute the 3-D depth of objects in a single given 2-D image.This is done by exploiting information about the illumination and the image brightness.We deal with a recent model for Perspective SFS (PSFS) for Lambertian surfaces. It is defined by a Hamilton–Jacobi equation and complemented by state constraints boundaryconditions. In this paper we investigate and compare three state-of-the-art numerical approaches. We begin with a presentation of the methods. Then we discuss the use of some acceleration techniques, including cascading multigrid, for all the tested algorithms. The main goal of our paper is to analyze and compare recent solvers for the PSFS problem proposed in the literature.
• Homogenization approach to the dispersion theory for reactive transport through porous media
  
  • Allaire Grégoire
  • Mikelic Andro
  • Piatnitski Andrey
  SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2010, 42 (1), pp.125-144.
• Les agriculteurs entre clôtures et passerelles
  
  • Dubuisson-Quellier Sophie
  • Giraud Christophe
  , 2010, pp.111-129. Les mondes agricoles ont été longtemps caractérisés dans les représentations savantes ou communes par une certaine clôture sociale. Le groupe socioprofessionnel des agriculteurs était considéré comme l'un de ceux dont la reproduction s'appuie le plus sur l'héritage (encore aujourd'hui 85% des agriculteurs ont un père agriculteur) et sur l'homogamie (87% des conjointes d'agriculteurs en 1959 avaient une origine agricole). Aujourd'hui, ces mondes agricoles évoluent, sous l'effet d'une porosité plus grande avec d'autres mondes du travail mais aussi d'une plus grande sensibilité aux débats contemporains.
• Modeling and Simulation of Nucleate Boiling
  
  • Faccanoni Gloria
  • Kokh Samuel
  • Allaire Grégoire
  , 2012, pp.49-53. This work investigates the modelization and simulation of liquid-vapor phase change in compressible flows. Each phase is modeled as a compressible fluid equipped with its own Equation of State (EOS). We suppose that inter-phase equilibrium processes in the medium operate at a short timescale compared to the other physical phenomena such as convection or thermal diffusion. This assumption provides an implicit definition of an equilibrium EOS for the two-phase medium. Within this framework, mass transfer is the result of local and instantaneous equilibria between both phases. The overall model is strictly hyperbolic. We examine properties of the equilibrium EOS and we propose a discretization strategy based on a Finite-Volume relaxation method. This method allows to cope with the implicit definition of the equilibrium EOS, even when the model involves complex EOSs for the pure phases, including tabulated ones. We present two-dimensional numerical simulations that shows that the model is able to reproduce mechanism such as nucleation.
• The nonlinear Schrödinger equation with white noise dispersion
  
  • de Bouard Anne
  • Debussche Arnaud
  Journal of Functional Analysis, Elsevier, 2010, 259 (5), pp.1300-1321. Under certain scaling the nonlinear Schrödinger equation with random dispersion converges to the nonlinear Schrödinger equation with white noise dispersion. The aim of this work is to prove that this latter equation is globally well posed in $L^2$ or $H^1$. The main ingredient is the generalization of the classical Strichartz estimates. Additionally, we justify rigorously the formal limit described above. (10.1016/j.jfa.2010.04.002)
  DOI : 10.1016/j.jfa.2010.04.002