Publications

2009

• Structure fractale tridimensionnelle
  
  • Colonna Jean-François
  , 2009. Tridimensional fractal structure (Structure fractale tridimensionnelle)
• Structure fractale tridimensionnelle
  
  • Colonna Jean-François
  , 2009. Tridimensional fractal structure (Structure fractale tridimensionnelle)
• Réseau
  
  • Colonna Jean-François
  , 2009. Network (Réseau)
• Effet Larsen
  
  • Colonna Jean-François
  , 2009. Larsen effect (Effet Larsen)
• Réseau fractal
  
  • Colonna Jean-François
  , 2009. Fractal network (Réseau fractal)
• Second-order Analysis for Optimal Control Problems with Pure State Constraints and Mixed Control-State Constraints
  
  • Bonnans Joseph Frederic
  • Hermant Audrey
  Annales de l'Institut Henri Poincaré (C), Analyse non linéaire, EMS, 2009, 26 (2), pp.561-598.
• Sensitivity analysis in HMMs with application to likelihood maximization
  
  • Coquelin Pierre-Arnaud
  • Deguest Romain
  • Munos Rémi
  , 2009. This paper considers a sensitivity analysis in Hidden Markov Models with continuous state and observation spaces. We propose an Infinitesimal Perturbation Analysis (IPA) on the filtering distribution with respect to some parameters of the model. We describe a methodology for using any algorithm that estimates the filtering density, such as Sequential Monte Carlo methods, to design an algorithm that estimates its gradient. The resulting IPA estimator is proven to be asymptotically unbiased, consistent and has computational complexity linear in the number of particles. We consider an application of this analysis to the problem of identifying unknown parameters of the model given a sequence of observations. We derive an IPA estimator for the gradient of the log-likelihood, which may be used in a gradient method for the purpose of likelihood maximization. We illustrate the method with several numerical experiments.
• On the existence of transmission eigenvalues in an inhomogeneous medium
  
  • Cakoni Fioralba
  • Haddar Houssem
  Applicable Analysis, Taylor & Francis, 2009, 88 (4), pp.475-493. We prove the existence of transmission eigenvalues corresponding to the inverse scattering problem for isotropic and anisotropic media for both the scalar problem and Maxwell's equations. Considering a generalized abstract eigenvalue problem, we are able to extend the ideas of Päivärinta and Sylvester [Transmission eigenvalues, SIAM J. Math. Anal. 40, (2008) pp. 783-753] to prove the existence of transmission eigenvalues for a larger class of interior transmission problems. Our analysis includes both the case of a medium with positive contrast and of a medium with negative contrast provided that the contrasts are large enough. (10.1080/00036810802713966)
  DOI : 10.1080/00036810802713966
• Continuous limits of discrete perimeters
  
  • Chambolle Antonin
  • Giacomini Alessandro
  • Lussardi Luca
  , 2009. We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula, and study their limit in the continuum.
• Homogenization of fully overdamped Frenkel-Kontorova models
  
  • Forcadel Nicolas
  • Imbert Cyril
  • Monneau Régis
  Journal of Differential Equations, Elsevier, 2009, 246, pp.pp 1057--1097. In this paper, we consider the fully overdamped Frenkel-Kontorova model. This is an infinite system of coupled first order ODEs. Each ODE represents the microscopic evolution of one particle interacting with its neighbors and submitted to a fixed periodic potential. After a proper rescaling, a macroscopic model describing the evolution of densities of particles is obtained. We get this homogenization result for a general class of Frenkel-Kontorova models. The proof is based on the construction of suitable hull functions in the framework of viscosity solutions. (10.1016/j.jde.2008.06.034)
  DOI : 10.1016/j.jde.2008.06.034
• Acoustic response of a rigid-frame porous medium plate with a periodic set of inclusions
  
  • Groby Jean-Philippe
  • Wirgin Armand
  • de Ryck L.
  • Lauriks W.
  • Gilbert R. P.
  • Xu Y. S.
  Journal of the Acoustical Society of America, Acoustical Society of America, 2009, 126 (2), pp.685-693. The acoustic response of a rigid-frame porous plate with a periodic set of inclusions is investigated by a multipole method. The acoustic properties, in particular, the absorption, of such a structure are then derived and studied. Numerical results together with a modal analysis show that the addition of a periodic set of high-contrast inclusions leads to the excitation of the modes of the plate and to a large increase in the acoustic absorption. (10.1121/1.3158936)
  DOI : 10.1121/1.3158936
• Music for extended scatterers as an instance of the factorization method
  
  • Arens Tilo
  • Lechleiter Armin
  • Luke D. Russell
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2009, 70 (4), pp.1283--1304. (10.1137/080737836)
  DOI : 10.1137/080737836
• Dynamics of red blood cells in 2D
  
  • Bui Cuc
  • Lleras Vanessa
  • Pantz Olivier
  , 2009, 28, pp.182--194. (10.1051/proc/2009046)
  DOI : 10.1051/proc/2009046
• Homogenization of a conductive and radiative heat transfer problem
  
  • Allaire Grégoire
  • El Ganaoui K.
  Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2009, 7 (3), pp.1148-1170. This paper is devoted to the homogenization of a heat conductionproblem in a periodically perforated domain with a nonlinear andnonlocal boundary condition modeling radiative heat transfer inthe perforations. Because of the critical scaling considered it isessential to use a method of two-scale asymptotic expansionsinside the variational formulation of the problem. We obtain anonlinear homogenized problem of heat conduction with effectivecoefficients which are computed via a cell problem featuring aradiative heat transfer boundary condition. We rigorously justifythis homogenization process for the linearized problem by usingtwo-scale convergence. We perform numerical simulations in twodimensions: we reconstruct an approximate temperature field byadding to the homogenized temperature a corrector term. Thecomputed numerical errors agree with the theoretical predictederrors and prove the effectiveness of our method for multiscalesimulation of conductive and radiative heat transfer problems inperiodically perforated domains. (10.1137/080714737)
  DOI : 10.1137/080714737
• Control problems with mixed constraints and application to an optimal investment problem
  
  • Bonnans J. Frederic
  • Tiba Dan
  Mathematical Reports, Romanian Academy of Sciences, 2009, 4, pp.293-306.
• Comparison principle for a Generalized Fast Marching Method
  
  • Forcadel Nicolas
  SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2009, 47 (3), pp.pp. 1923-1951. In \cite{CFFM06}, the authors have proposed a generalization of the classical Fast Marching Method of Sethian for the eikonal equation in the case where the normal velocity depends on space and time and can change sign. The goal of this paper is to propose a modified version of the Generalized Fast Marching Method proposed in \cite{CFFM06} for which we state a general comparison principle. We also prove the convergence of the new algorithm.
• Numerical study of optimal trajectories with singular arcs for an Ariane 5 launcher
  
  • Martinon Pierre
  • Bonnans J. Frederic
  • Laurent-Varin Julien
  • Trélat Emmanuel
  Journal of Guidance, Control, and Dynamics, American Institute of Aeronautics and Astronautics, 2009, 32 (1), pp.51--55. We consider a flight mission to the geostationary transfer orbit (GTO) for an Ariane 5 launcher, while maximizing the payload or, as a variant, minimizing the fuel consumption. We first solve the complete flight sequence up to the final orbit, assuming a maximal thrust for all propulsion systems. Then we focus on the tmospheric ascent phase, which has been studied for instance in [1, 2, 3]. We are more specifically interested in optimal tra jectories with singular arcs (flight phases with a non maximal thrust) for the boosters. Due to the presence of tabulated data in the physical model, the exact expression of the singular control cannot be obtained from the time derivatives of the switching function. An alternate way to compute the singular control is provided, and numerical experiments are carried out for for several launcher variants.
• Generalized Impedance Boundary Conditions for Thin Dielectric Coatings with Variable Thickness
  
  • Aslanyurek Birol
  • Haddar Houssem
  • Sahinturk Hulya
  , 2009. We derive so-called Generalized Impedance Boundary Conditions (GIBC) that model thin dielectric coatings with variable width. We treat the 2-D electromagnetic problem for both TM and TE polarizations. The expressions of the GIBCs are explicited up to the third order (with respect to the coating width). The order of convergence is numerically validated through various numerical examples. A particular attention is given to the cases where the inner boundary has corner singularities.
• On iterative reconstruction in the nonlinearized polarization tomography
  
  • Novikov Roman
  Inverse Problems, IOP Publishing, 2009, 25 (11), pp.115010 (18pp). We give uniqueness theorem and reconstruction algorithm for the nonlinearized problem of finding the dielectric anisotropy f of the medium from non-overdetermined polarization tomography data. We assume that the medium has uniform background parameters and that the anisotropic (dielectric permeability) perturbation is described by symmetric and sufficiently small matrix-function f . On a pure mathematical level this article contributes to the theory of non-abelian Radon transforms and to iterative methods of inverse scattering.
• Forgetting of the initial distribution for Hidden Markov Models
  
  • Douc Randal
  • Fort Gersende
  • Moulines Éric
  • Priouret Pierre
  Stochastic Processes and their Applications, Elsevier, 2009, 119 (4), pp.1235--1256. The forgetting of the initial distribution for discrete Hidden Markov Models (HMM) is addressed: a new set of conditions is proposed, to establish the forgetting property of the filter, at a polynomial and geometric rate. Both a pathwise-type convergence of the total variation distance of the filter started from two different initial distributions, and a convergence in expectation are considered. The results are illustrated using different HMM of interest: the dynamic tobit model, the non-linear state space model and the stochastic volatility model.
• Spectral theory for a mathematical model of the weak interactions: The decay of the intermediate vector bosons W+/-. I
  
  • Barbaroux Jean-Marie
  • Guillot J. -C.
  Advances in Mathematical Physics, Hindawi Publishing Corporation, 2009, 2009, pp.978903. We consider a Hamiltonian with cutoffs describing the weak decay of spin one massive bosons into the full family of leptons. The Hamiltonian is a self-adjoint operator in an appropriate Fock space with a unique ground state. We prove a Mourre estimate and a limiting absorption principle above the ground state energy and below the first threshold for a sufficiently small coupling constant. As a corollary, we prove absence of eigenvalues and absolute continuity of the energy spectrum in the same spectral interval. (10.1155/2009/978903)
  DOI : 10.1155/2009/978903
• TWO ASYMPTOTIC MODELS FOR ARRAYS OF UNDERGROUND WASTE CONTAINERS
  
  • Allaire Grégoire
  • Briane Marc
  • Brizzi Robert
  • Capdeboscq Yves
  Applicable Analysis, Taylor & Francis, 2009, 88 (10-11), pp.1445-1467. We study the homogenization of two models of an underground nuclear waste repository. The nuclear waste cells are periodically stored in the middle of a geological layer and are the only source terms in a parabolic evolution problem. The diffusion constants have a very large contrast between the fuel repository and the soil. It is thus a combined problem of homogenization and singular perturbation. For two different asymptotic contrasts we give the homogenized limit problem which is rigorously justified by using two-scale convergence. Eventually we perform 2-d numerical computations to show the effectiveness of using the limit model instead of the original one. (10.1080/00036810902922590)
  DOI : 10.1080/00036810902922590
• Dynamic Numerical Investigation of Random Packing for Spherical and Nonconvex Particles
  
  • Faure Sylvain
  • Lefebvre-Lepot Aline
  • Semin Benoît
  ESAIM: Proceedings, EDP Sciences, 2009, 28, pp.13-32. We simulate the sedimentation in a parallelepipedic container of spheres and nonconvex particles constituted by two overlapping spheres. We use the self-written code SCoPI. Thanks to an efficient handling of contacts between particles, it allowed us to consider up to 100, 000 spheres and 10, 000 nonconvex particles. The packing fraction (in bulk and close to a wall) as well as the mean value and the distribution of contacts of the final packings are reported. The results obtained for the classical case of spherical particles (packing fraction: 63.7%, mean number of contacts: 6) are in agreement with previous studies and validate the algorithm. The packing fraction for nonconvex particles increases and then decreases with respect to the aspect ratio, which is similar to the ellipsoid (convex) case. The number of contacts is different from the number of neighbours, which is of course never the case for spherical particles (convex particles). The number of contacts is discontinuous when slightly increasing the aspect ratio from the spherical case: it is equal to 6 in the spherical case and to 10 in the nonconvex case. These values correspond to the isocounting values, i.e. the number of contacts is twice the number of degrees of freedom. This contrasts with the ellipsoid case, where it sharply but continuously increases. Concerning the number of neighbours, it continuously increases for small aspect ratio (which is similar to the convex particle case), but decreases for higher aspect ratio. (10.1051/proc/2009037)
  DOI : 10.1051/proc/2009037
• Efficient solution of a wave equation with fractional order dissipative terms
  
  • Haddar Houssem
  • Li Jing-Rebecca
  • Matignon Denis
  Journal of Computational and Applied Mathematics, Elsevier, 2009, 234 (6), pp.2003-2010. (10.1016/j.cam.2009.08.051)
  DOI : 10.1016/j.cam.2009.08.051
• The factorization method is independent of transmission eigenvalues
  
  • Lechleiter Armin
  Inverse Problems and Imaging, AIMS American Institute of Mathematical Sciences, 2009, 3 (1), pp.123--138. (10.3934/ipi.2009.3.123)
  DOI : 10.3934/ipi.2009.3.123