Publications

2010

• Un ensemble de Mandelbrot brumeux dans l'ensemble des pseudo-quaternions (un 'MandelBulb')
  
  • Colonna Jean-François
  , 2010. A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') (Un ensemble de Mandelbrot brumeux dans l'ensemble des pseudo-quaternions (un 'MandelBulb'))
• La fonction spéciale de Liouville visualisée comme une marche aléatoire bidimensionnelle pour les nombres entiers de 2 a 100001
  
  • Colonna Jean-François
  , 2010. The special Liouville function displayed as a bidimensional random walk for the integer numbers from 2 to 100001 (La fonction spéciale de Liouville visualisée comme une marche aléatoire bidimensionnelle pour les nombres entiers de 2 a 100001)
• 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 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 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)
• 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-)
• 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)
• 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.
• 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
• Asymptotic models for scattering from unbounded media with high conductivity
  
  • Haddar Houssem
  • Lechleiter Armin
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2010, 44 (6), pp.1295-1317. (10.1051/m2an/2010029)
  DOI : 10.1051/m2an/2010029
• A sampling method for inverse scattering in the time domain
  
  • Chen Qiang
  • Haddar Houssem
  • Lechleiter Armin
  • Monk Peter
  Inverse Problems, IOP Publishing, 2010, 26 (8), pp.085001, 17. (10.1088/0266-5611/26/8/085001)
  DOI : 10.1088/0266-5611/26/8/085001
• On the determination of Dirichlet or transmission eigenvalues from far field data
  
  • Cakoni Fioralba
  • Colton David
  • Haddar Houssem
  Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2010, 348 (7-8), pp.379-383. (10.1016/j.crma.2010.02.003)
  DOI : 10.1016/j.crma.2010.02.003
• Homogenization of nonlinear reaction-diffusion equation with a large reaction term
  
  • Allaire Grégoire
  • Piatnitski Andrey
  Annali dell'Universita di Ferrara, Springer Verlag, 2010, 56, pp.141-161.
• Optimal control of a parabolic equation with time-dependent state constraints
  
  • Bonnans J. Frederic
  • Jaisson Pascal
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2010, 48 (7), pp.4550-4571. In this paper we study the optimal control problem of the heat equation by a distributed control over a subset of the domain, in the presence of a state constraint. The latter is integral over the space and has to be satisfied at each time. Using for the first time the technique of alternative optimality systems in the context of optimal control of partial differential equations, we show that both the control and multiplier are continuous in time. Under some natural geometric hypotheses, we can prove that extended polyhedricity holds, allowing to obtain no-gap second-order optimality conditions, that characterize quadratic growth. An expansion of the value function and of approximate solutions can be computed for a directional perturbation of the r.h.s. of the state equation.
• The step-harmonic potential
  
  • Rizzi Luca
  • Piattella Oliver
  • Cacciatori Sergio
  • Gorini Vittorio
  American Journal of Physics, American Association of Physics Teachers, 2010, pp.19. We analyze the behavior of a quantum system described by a one-dimensional asymmetric potential consisting of a step plus a harmonic barrier. We solve the eigenvalue equation by the integral representation method, which allows us to classify the independent solutions as equivalence classes of homotopic paths in the complex plane. We then consider the propagation of a wave packet reflected by the harmonic barrier and obtain an expression for the interaction time as a function of the peak energy. For high energies we recover the classical half-period limit. (10.1119/1.3379290)
  DOI : 10.1119/1.3379290
• Unique solvability of equations of motion for ferrofluids
  
  • Amirat Youcef
  • Hamdache Kamel
  Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2010, 73, pp.471-494.
• Imaging of periodic dielectrics
  
  • Lechleiter Armin
  BIT Numerical Mathematics, Springer Verlag, 2010, 50 (1), pp.59--83. (10.1007/s10543-010-0255-7)
  DOI : 10.1007/s10543-010-0255-7
• Explicit polyhedral approximation of the Euclidean ball
  
  • Bonnans J. Frederic
  • Lebelle M.
  RAIRO - Operations Research, EDP Sciences, 2010, 44 (1), pp.45-60. We discuss the problem of computing points of IRn whose convex hull contains the Euclidean ball, and is contained in a small multiple of it. Given a polytope containing the Euclidean ball, we introduce its successor obtained by intersection with all tangent spaces to the Euclidean ball, whose normals point towards the vertices of the polytope. Starting from the L-infinity ball, we discuss the computation of the two first successors, and give a complete analysis in the case when n = 6. (10.1051/ro/2010003)
  DOI : 10.1051/ro/2010003
• 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.
• 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.
• 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