Publications

2002

• Uniqueness and stability in an inverse problem for the Schrödinger equation
  
  • Baudouin Lucie
  • Puel Jean-Pierre
  Inverse Problems, IOP Publishing, 2002, 18 (6), pp.1537-1554.. We study a Schrödinger equation, with time dependant potential, set in a bounded domain with Dirichlet boundary data and real valued initial condition We consider the inverse problem of determining the potential when the normal derivative is given on a part of the boundary. The main tool to prove uniqueness and stability of this inverse problem is an appropriate global Carleman estimate.
• Bandelettes et représentation géométrique des images
  
  • Le Pennec Erwan
  , 2002. Cette thèse introduit une nouvelle représentation des images capturant leur régularité géométrique: la représentation en bandelettes. Elle présente leur construction, leurs propriétés en terme de vitesse d'approxmation ainsi que des applications en compression et en débruitage
• Billard a géométrie variable (de courbures négatives à une courbure positive) avec une particule accélérée
  
  • Colonna Jean-François
  , 2002. Time-dependent billiard (from negative curvatures to positive curvature) with one accelerated particle (Billard a geometrie variable (de courbures negatives a une courbure positive) avec une particule acceleree)
• Diffusions infini-dimensionnelles et champs de Gibbs sur l'espace des trajectoires continues
  
  • Dereudre David
  , 2002. Nous analysons la structure gibbsienne de la loi de diffusions infini-dimensionnelles de type gradient, modélisant des systèmes continus de particules browniennes en interaction. En représentant les solutions de tels systèmes par des mesures ponctuelles sur l'espace des trajectoires, nous démontrons l'équivalence entre être la loi d'une solution d'un système de type gradient et être un champ de Gibbs sur l'espace des trajectoires continues associé à un hamiltonien local dynamique spécifique. Plus généralement, nous montrons que tout champ de Gibbs, suffisamment régulier, se représente comme une diffusion infini-dimensionnelle dont nous calculons la dérive. Nous donnons également diverses applications de ces résultats ; nous exhibons notamment une formule de retournement du temps pour les systèmes de type gradient et en étudions ainsi la réversibilité et la stationnarité.
• On the Convergence of the Monte Carlo Maximum Likelihood Method for Latent Variable Models
  
  • Cappe Olivier
  • Douc Randal
  • Moulines Eric
  • Robert Christian
  Scandinavian Journal of Statistics, Wiley, 2002, 29 (4), pp.615-635. (10.1111/1467-9469.00309)
  DOI : 10.1111/1467-9469.00309
• Montagnes au lever du Soleil
  
  • Colonna Jean-François
  , 2002. Mountains at sunrise (Montagnes au lever du Soleil)
• Montagnes au lever du Soleil
  
  • Colonna Jean-François
  , 2002. Mountains at sunrise (Montagnes au lever du Soleil)
• Bilans d'entropie discrets dans l'approximation numerique des chocs non classiques. Application aux equations de Navier-Stokes multi-pression 2D et a quelques systemes visco-capillaires
  
  • Chalons Christophe
  , 2002. La presente recherche doctorale en analyse numerique (et calcul scientifique) aborde le probleme du controle de la dissipation d'entropie numerique associee a une discretisation donnee. Cette problematique constitue un veritable challenge numerique non encore completement resolu a ce jour. Le travail se decompose en deux parties principales dont les caracteristiques sont reellement differentes. La premiere partie concerne l'approximation numerique des solutions (instationnaires en 1D et stationnaires en 2D) du systeme des equations de Navier-Stokes a plusieurs pressions independantes. Ce systeme est hyperbolique et possede des champs vraiment non lineaires sous des hypotheses classiques, mais s'ecrit naturellement sous forme non conservative. La deuxieme partie est dediee a l'approximation numerique des solutions instationnaires en 1D de quelques systemes de lois de conservation de type soit hyperbolique mais dont les champs possedent un defaut de vraiment non linearite, ou soit mixte hyperbolique-elliptique. Dans toutes ces situations motivees par des applications physiques concretes, le controle de la dissipation d'entropie joue un role déterminant dans la caracterisation des solutions recherchees. Les schemas numeriques proposes dans ce manuscrit sont obtenus par une analyse fine des bilans d'entropie associes.
• Bifurcation problems for Ginzburg-Landau equations and applications to Bose Einstein condensates
  
  • Aftalion Amandine
  , 2002, pp.51.
• Un automate cellulaire binaire monodimensionnel elementaire -110- avec 1 point de depart blanc -en bas et a droite
  
  • Colonna Jean-François
  , 2002. An elementary monodimensional binary cellular automaton -110- with 1 white starting point -bottom right- (Un automate cellulaire binaire monodimensionnel elementaire -110- avec 1 point de depart blanc -en bas et a droite-)
• Un automate cellulaire binaire monodimensionnel elementaire -110- avec 1 point de depart blanc -en bas et a droite
  
  • Colonna Jean-François
  , 2002. An elementary monodimensional binary cellular automaton -110- with 1 white starting point -bottom right- (Un automate cellulaire binaire monodimensionnel elementaire -110- avec 1 point de depart blanc -en bas et a droite-)
• Un automate cellulaire binaire monodimensionnel elementaire -110- avec 49 points de depart blancs -sur la ligne du bas
  
  • Colonna Jean-François
  , 2002. An elementary monodimensional binary cellular automaton -110- with 49 white starting points -on the bottom line- (Un automate cellulaire binaire monodimensionnel elementaire -110- avec 49 points de depart blancs -sur la ligne du bas-)
• A new method for investigating boundary vorticity
  
  • Abboud Toufic
  • Dubois François
  • Salaün Michel
  • Salmon Stéphanie
  Journal of Turbulence, Taylor & Francis, 2002, 3,Number 44, pp.Special Issue: 4th International Workshop on Vortex Flows and Related Numerical Methods. (10.1088/1468-5248/3/1/044)
  DOI : 10.1088/1468-5248/3/1/044
• Stationary measures and phase transition for a class of probabilistic cellular automata
  
  • Dai Pra Paolo
  • Louis Pierre-Yves
  • Roelly Sylvie
  ESAIM: Probability and Statistics, EDP Sciences, 2002, 6, pp.89-104. We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models. (10.1051/ps:2002004)
  DOI : 10.1051/ps:2002004
• Résolution des équations intégrales pour la diffraction d'ondes acoustiques et électromagnétiques - Stabilisation d'algorithmes itératifs et aspects de l'analyse numérique
  
  • Christiansen Snorre H.
  , 2002. Cette thèse porte sur la résolution numérique, par la méthode des équations intégrales de frontière de problèmes de diffraction d'ondes acoustiques et électromagnétiques, en régime fréquentiel. La méthode de Galerkin avec des éléments finis (scalaires ou vectoriels) de surface conduit à des systèmes matriciels mal conditionnés. Dans une première partie, pour accélérer la convergence d'algorithmes itératifs, on propose et étudie théoriquement et numériquement des préconditionneurs basés sur les relations de Calderon qui lient les opérateurs intégraux apparaissant dans les équations. En électromagnétisme on utilise de plus des analogues discrets de la décomposition de Helmholtz des champs tangents. Dans une deuxième partie on utilise des estimations sur ces décompositions pour effectuer une nouvelle analyse numérique de l'équation intégrale de champ électrique. Cette analyse est étendue au cas de la diffraction par les surfaces ouvertes (écrans), modélisant les conducteurs parfaits minces.
• Continuous-Time Dynkin Games with Mixed Strategies
  
  • Touzi Nizar
  • Vieille Nicolas
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2002, 41 (4), pp.1073-1088. Let $(X,Y,Z)$ be a triple of payoff processes defining a Dynkin game $$\tilde R(\sigma,\tau) =E\left[ X_\sigma \mathbf{1}_{\{\tau > \sigma\}} +Y_\tau \mathbf{1}_{\{\tau < \sigma\}} +Z_\tau \mathbf{1}_{\{\tau=\sigma\}}\right]$$ where $\sigma$ and $\tau$ are stopping times valued in $[0,T]$. In the case $Z=Y$, it is well known that the condition $X\leq Y$ is needed in order to establish the existence of value for the game, i.e., $\inf_{\tau}\sup_{\sigma}\tilde R(\sigma,\tau)=\sup_{\sigma}\inf_{\tau}\tilde R(\sigma,\tau)$. In order to remove the condition $X\leq Y$, we introduce an extension of the Dynkin game by allowing for an extended set of strategies, namely, the set of mixed strategies. The main result of the paper is that the extended Dynkin game has a value when $Z\leq Y$, and the processes $X$ and $Y$ are restricted to be semimartingales continuous at the terminal time $T$. (10.1137/S0363012900369812)
  DOI : 10.1137/S0363012900369812
• Application of a Multi-Objective Evolutionary Algorithm to Topological Optimum Design
  
  • Hamda Hatem
  • Roudenko Olga
  • Schoenauer Marc
  , 2002, pp.121-132. The paper deals with multi-objective Topological Optimum Design (TOD) problems. Considered optimization criteria are the minimization of both the mass of the structure and its maximal displacement under a prescribed loading. Multi-objective evolutionary algorithm using Voronoi representation are applied on the cantilever plate, the popular benchmark problems of TOD. The results are discussed in the light of the single objective approaches used in previous works: whereas the quality of the result is very similar, the number of Finite Element Analyzes needed to obtain a full set of trade-off structures by the multi-objective method is more or less the same that needed to obtain only one solution using a single-objective algorithm with a limit on the maximal displacement: This makes multi-objective approach extremely interesting for solving real life TOD problems where the evaluation cost is usually quite high while the possibility of making of a well justified choice of definitive design is very important.
• The linear sampling method for anisotropic media
  
  • Cakoni Fioralba
  • Colton David
  • Haddar Houssem
  Journal of Computational and Applied Mathematics, Elsevier, 2002, 146 (2), pp.285--299. (10.1016/S0377-0427(02)00361-8)
  DOI : 10.1016/S0377-0427(02)00361-8
• The skewed multifractal random walk with applications to option smiles
  
  • Pochart B.
  • Bouchaud J. -P.
  , 2002. We generalize the construction of the multifractal random walk (MRW) due to Bacry, Delour and Muzy to take into account the asymmetric character of the financial returns. We show how one can include in this class of models the observed correlation between past returns and future volatilities, in such a way that the scale invariance properties of the MRW are preserved. We compute the leading behaviour of q-moments of the process, that behave as power-laws of the time lag with an exponent zeta_q=p-2p(p-1) lambda^2 for even q=2p, as in the symmetric MRW, and as zeta_q=p(1-2p lambda^2)+1-alpha (q=2p+1), where lambda and alpha are parameters. We show that this extended model reproduces the `HARCH' effect or `causal cascade' reported by some authors. We illustrate the usefulness of this skewed MRW by computing the resulting shape of the volatility smiles generated by such a process, that we compare to approximate cumulant expansions formulas for the implied volatility. A large variety of smile surfaces can be reproduced.
• Closure laws for a two-fluid two-pressure model
  
  • Coquel Frédéric
  • Gallouët Thierry
  • Hérard Jean-Marc
  • Seguin Nicolas
  Comptes Rendus. Mathématique, Académie des sciences (Paris), 2002, 334 (10), pp.927-932. Closure laws for interfacial pressure and interfacial velocity are proposed within the frame work of two-pressure two-phase flow models. These enable us to ensure positivity of void fractions, mass fractions and internal energies when investigating field by field waves in the Riemann problem. (10.1016/S1631-073X(02)02366-X)
  DOI : 10.1016/S1631-073X(02)02366-X
• The linear sampling method for solving the electromagnetic inverse medium problem
  
  • Haddar Houssem
  • Monk Peter
  Inverse Problems, IOP Publishing, 2002, 18 (3), pp.891--906. (10.1088/0266-5611/18/3/323)
  DOI : 10.1088/0266-5611/18/3/323
• The linear sampling method for solving the electromagnetic inverse scattering problem
  
  • Colton David
  • Haddar Houssem
  • Monk Peter
  SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2002, 24 (3), pp.719--731. (10.1137/S1064827501390467)
  DOI : 10.1137/S1064827501390467
• Compact Unstructured Representations for Evolutionary Design
  
  • Hamda Hatem
  • Jouve François
  • Lutton Evelyne
  • Schoenauer Marc
  • Sebag Michèle
  Applied Intelligence, Springer Verlag, 2002, 16, pp.139-155. This paper proposes a few steps to escape structured extensive representations for objects, in the context of evolutionary Topological Optimum Design (TOD) problems : early results have demonstrated the potential power of Evolutionary methods to find numerical solutions to yet unsolved TOD problems, but those approaches were limited because the complexity of the representation was that of a fixed underlying mesh. Different compact unstructured representations are introduced, the complexity of which is self-adaptive, i.e. is evolved by the algorithm itself. The Voronoi-based representations are variable length lists of alleles that are directly decoded into object shapes, while the IFS representation, based on fractal theory, involves a much more complex morphogenetic process. First results demonstrates that Voronoi-based representations allow one to push further the limits of Evolutionary Topological Optimum Design by actually removing the correlation between the complexity of the representations and that of the discretization. Further comparative results among all these representations on simple test problems seems to indicate that the complex causality in the IFS representation disfavor it compared to the Voronoi-based representations. (10.1023/A:1013666503249)
  DOI : 10.1023/A:1013666503249
• An approximate solution of the Riemann problem for a realisable second-moment turbulent closure
  
  • Berthon Christophe
  • Coquel Frédéric
  • Hérard Jean-Marc
  • Uhlmann Markus
  Shock Waves, Springer Verlag, 2002, 11 (4), pp.245-269. An approximate solution of the Riemann problem associated with a realisable and objective turbulent second-moment closure, which is valid for compressible flows, is examined. The main features of the continuous model are first recalled. An entropy inequality is exhibited, and the structure of waves associated with the non-conservative hyperbolic convective system is briefly described. Using a linear path to connect states through shocks, approximate jump conditions are derived, and the existence and uniqueness of the one-dimensional Riemann problem solution is then proven. This result enables to construct exact or approximate Riemann-type solvers. An approximate Riemann solver, which is based on Gallouët's recent proposal is eventually presented. Some computations of shock tube problems are then discussed. (10.1007/s001930100109)
  DOI : 10.1007/s001930100109
• Homogenization and localization for a 1-D eigenvalue problem in a periodic medium with an interface
  
  • Allaire Grégoire
  • Capdeboscq Yves
  Annali di Matematica Pura ed Applicata, Springer Verlag, 2002, 181 (3), pp.247--282. In one space dimension we address the homogenization of the spectral problem for a singularly perturbed diffusion equation in a periodic medium. Denoting by the period, the diffusion coefficient is scaled as 2. The domain is made of two purely periodic media separated by an interface. Depending on the connection between the two cell spectral equations, three different situations arise when goes to zero. First, there is a global homogenized problem as in the case without an interface. Second, the limit is made of two homogenized problems with a Dirichlet boundary condition on the interface. Third, there is an exponential localization near the interface of the first eigenfunction. (10.1007/s102310100040)
  DOI : 10.1007/s102310100040