Publications

2010

• 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-)
• 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 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)
• 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
• 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
• 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
• 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 boundary conditions. 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.
• 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
• An efficient data structure to solve front propagation problems
  
  • Bokanowski Olivier
  • Cristiani Emiliano
  • Zidani Hasnaa
  Journal of Scientific Computing, Springer Verlag, 2010, 42 (2), pp.251--273. In this paper we develop a general efficient sparse storage technique suitable to coding front evolutions in d>= 2 space dimensions. This technique is mainly applied here to deal with deterministic target problems with constraints, and solve the associated minimal time problems. To this end we consider an Hamilton-Jacobi-Bellman equation and use an adapted anti-diffusive Ultra-Bee scheme. We obtain a general method which is faster than a full storage technique. We show that we can compute problems that are out of reach by full storage techniques (because of memory). Numerical experiments are provided in dimension d=2,3,4. (10.1007/s10915-009-9329-6)
  DOI : 10.1007/s10915-009-9329-6
• Uniform estimates for metastable transition times in a coupled bistable system
  
  • Barret Florent
  • Bovier Anton
  • Méléard Sylvie
  Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2010, 15 (12). We consider a coupled bistable N-particle system driven by a Brownian noise, with a strong coupling corresponding to the synchronised regime. Our aim is to obtain sharp estimates on the metastable transition times between the two stable states, both for fixed N and in the limit when N tends to infinity, with error estimates uniform in N. These estimates are a main step towards a rigorous understanding of the metastable behavior of infinite dimensional systems, such as the stochastically perturbed Ginzburg-Landau equation. Our results are based on the potential theoretic approach to metastability.
• 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
• High-order accurate thin layer approximations for time-domain electromagnetics, Part II: transmission layers
  
  • Chun Sun
  • Haddar Houssem
  • Hesthaven Jan S.
  Journal of Computational and Applied Mathematics, Elsevier, 2010, 234 (8), pp.2587--2608. (10.1016/j.cam.2010.03.022)
  DOI : 10.1016/j.cam.2010.03.022
• A variational method for wave scattering from penetrable rough layers
  
  • Lechleiter Armin
  • Ritterbusch Sebastian
  IMA Journal of Applied Mathematics, Oxford University Press (OUP), 2010, 75 (3), pp.366--391. (10.1093/imamat/hxp040)
  DOI : 10.1093/imamat/hxp040
• Construction of minimization sequences for shape optimization
  
  • Trabelsi Karim
  • Pantz Olivier
  , 2010, pp.278 -283. (10.1109/MMAR.2010.5587222)
  DOI : 10.1109/MMAR.2010.5587222
• Progress on the strong Eshelby's conjecture and extremal structures for the elastic moment tensor
  
  • Ammari Habib
  • Capdeboscq Yves
  • Kang Hyeonbae
  • Lee Hyundae
  • Milton Graeme W.
  • Zribi Habib
  Journal de Mathématiques Pures et Appliquées, Elsevier, 2010, 94 (1), pp.93--106. (10.1016/j.matpur.2010.01.003)
  DOI : 10.1016/j.matpur.2010.01.003
• 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.
• COMPETITIVE OR WEAK COOPERATIVE STOCHASTIC LOTKA-VOLTERRA SYSTEMS CONDITIONED TO NON-EXTINCTION
  
  • Cattiaux Patrick
  • Méléard Sylvie
  Journal of Mathematical Biology, Springer, 2010, 60 (6), pp.797-829. We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a stochastic Lotka-Volterra system, obtained as limit of renormalized interacting birth and death processes. The weak cooperation assumption allows the system not to blow up. We study the existence and uniqueness of a quasi-stationary distribution, that is convergence to equilibrium conditioned to non extinction. To this aim we generalize in two-dimensions spectral tools developed for one-dimensional generalized Feller diffusion processes. The existence proof of a quasi-stationary distribution is reduced to the one for a $d$-dimensional Kolmogorov diffusion process under a symmetry assumption. The symmetry we need is satisfied under a local balance condition relying the ecological rates. A novelty is the outlined relation between the uniqueness of the quasi-stationary distribution and the ultracontractivity of the killed semi-group. By a comparison between the killing rates for the populations of each type and the one of the global population, we show that the quasi-stationary distribution can be either supported by individuals of one (the strongest one) type or supported by individuals of the two types. We thus highlight two different long time behaviors depending on the parameters of the model: either the model exhibits an intermediary time scale for which only one type (the dominant trait) is surviving, or there is a positive probability to have coexistence of the two species. (10.1007/s00285-009-0285-4)
  DOI : 10.1007/s00285-009-0285-4
• 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.