Publications

2011

• Optimal structure of gas transmission trunklines
  
  • Bonnans J. Frederic
  • André Jean
  Optimization and Engineering, Springer Verlag, 2011, 12 (1), pp.175-198. In this paper, we consider the optimal design of a straight pipeline system. Suppose a gas pipeline is to be designed to transport a specified flowrate from the entry point to the gas demand point. Physical and contractual requirements at supply and delivery nodes are known as well as the costs to buy and lay a pipeline or build a compressor station. In order to minimize the overall cost of creation of this mainline, the following design variables need to be determined: the number of compressor stations, the lengths of pipeline segments between compressor stations, the diameters of the pipeline segments, the suction and discharge pressures at each compressor station. To facilitate the calculation of the design of a pipeline, gas engineers proposed, in several handbooks, to base their cost-assessments on some optimal properties from previous experiences and usual engineering practices: the distance between compressors is constant, all diameters are equal, and all inlet (resp. outlet) pressures are equal. The goals of this paper are (1) to state on which assumptions we can consider that the optimal properties are valid and (2) to propose a rigorous proof of the optimal properties (based on nonlinear programming optimality conditions) within a more general framework than before.
• On a heated incompressible magnetic fluid model
  
  • Amirat Youcef
  • Hamdache Kamel
  Communications on Pure and Applied Mathematics, Wiley, 2011, 11 (2), pp.675 - 696. In this paper we study the equations describing the dynamics of heat transfer in an incompressible magnetic fluid under the action of an applied magnetic field. The system consists of the Navier-Stokes equations, the magnetostatic equations and the temperature equation. We prove global-in-time existence of weak solutions to the system posed in a bounded domain of R-3 and equipped with initial and boundary conditions. The main difficulty comes from the singularity of the term representing the Kelvin force due to magnetization. (10.3934/cpaa.2012.11.675)
  DOI : 10.3934/cpaa.2012.11.675
• An introduction to direct and inverse scattering theory
  
  • Dorfler Willy
  • Lechleiter Armin
  • Plum Michael
  • Schneider Guido
  • Wieners Christian
  , 2011, 42, pp.79-126. (10.1007/978-3-0348-0113-3_4)
  DOI : 10.1007/978-3-0348-0113-3_4
• A frictionless contact algorithm for deformable bodies
  
  • Pantz Olivier
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2011, 45 (2), pp.235--254. (10.1051/m2an/2010041)
  DOI : 10.1051/m2an/2010041
• Homogenization of the linearized ionic transport equations in rigid periodic porous media
  
  • Allaire Grégoire
  • Mikelic Andro
  • Piatnitski Andrey
  Journal of Mathematical Physics, American Institute of Physics (AIP), 2011, 52 (6), pp.063701. (10.1063/1.3521555)
  DOI : 10.1063/1.3521555
• Weak Dynamic Programming Principle for Viscosity Solutions
  
  • Bouchard Bruno
  • Touzi Nizar
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2011, 49 (3), pp.948-962. We prove a weak version of the dynamic programming principle for standard stochastic control problems and mixed control-stopping problems, which avoids the technical difficulties related to the measurable selection argument. In the Markov case, our result is tailor-maid for the derivation of the dynamic programming equation in the sense of viscosity solutions.
• PecS is an important player in the regulatory network governing the coordinated expression of virulence genes during the interaction between [i]Dickeya dadantii[/i] 3937 and plants
  
  • Mhedbi-Hajri Nadia
  • Malfatti Pierrette
  • Pedron Jacques
  • Gaubert Stephane
  • Reverchon Sylvie
  • van Gijsegem Frederique
  Environmental Microbiology, Society for Applied Microbiology and Wiley-Blackwell, 2011, 13 (11), pp.2901 - 2914. Successful infection of a pathogen relies on the coordinated expression of numerous virulence factor-encoding genes. In plantbacteria interactions, this control is very often achieved through the integration of several regulatory circuits controlling cellcell communication or sensing environmental conditions. Dickeya dadantii (formerly Erwinia chrysanthemi), the causal agent of soft rot on many crops and ornamentals, provokes maceration of infected plants mainly by producing and secreting a battery of plant cell wall-degrading enzymes. However, several other virulence factors have also been characterized. During Arabidopsis infection, most D. dadantii virulence gene transcripts accumulated in a coordinated manner during infection. This activation requires a functional GacAGacS two-component regulatory system but the Gac system is not involved in the growth phase dependence of virulence gene expression. Here we show that, contrary to Pectobacterium, the AHL-mediated ExpIR quorum-sensing system does not play a major role in the growth phase-dependent control of D. dadantii virulence genes. On the other hand, the global regulator PecS participates in this coordinated expression since, in a pecS mutant, an early activation of virulence genes is observed both in vitro and in planta. This correlated with the known hypervirulence phenotype of the pecS mutant. Analysis of the relationship between the regulatory circuits governed by the PecS and GacA global regulators indicates that these two regulators act independently. PecS prevents a premature expression of virulence genes in the first stages of colonization whereas GacA, presumably in conjunction with other regulators, is required for the activation of virulence genes at the onset of symptom occurrence. (10.1111/j.1462-2920.2011.02566.x)
  DOI : 10.1111/j.1462-2920.2011.02566.x
• Minimal Time Problems with Moving Targets and Obstacles
  
  • Bokanowski Olivier
  • Zidani Hasnaa
  , 2011, 18, Part 1, pp.2589-2593. We consider minimal time problems governed by nonlinear systems under general time dependant state constraints and in the two-player games setting. In general, it is known that the characterization of the minimal time function, as well as the study of its regularity properties, is a difficult task in particular when no controlability assumption is made. In addition to these difficulties, we are interested here to the case when the target, the state constraints and the dynamics are allowed to be time-dependent. We introduce a particular "reachability" control problem, which has a supremum cost function but is free of state constraints. This auxiliary control problem allows to characterize easily the backward reachable sets, and then, the minimal time function, without assuming any controllability assumption. These techniques are linked to the well known level-set approachs. Partial results of the study have been published recently by the authors in SICON. Here, we generalize the method to more complex problems of moving target and obstacle problems. Our results can be used to deal with motion planning problems with obstacle avoidance. (10.3182/20110828-6-IT-1002.02261)
  DOI : 10.3182/20110828-6-IT-1002.02261
• Branching Feller diffusion for cell division with parasite infection
  
  • Bansaye Vincent
  • Tran Viet Chi
  ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada (Rio de Janeiro, Brasil) [2006-....], 2011, 8, pp.95-127. We describe the evolution of the quantity of parasites in a population of cells which divide in continuous-time. The quantity of parasites in a cell follows a Feller diffusion, which is splitted randomly between the two daughter cells when a division occurs. The cell division rate may depend on the quantity of parasites inside the cell and we are interested in the cases of constant or monotone division rate. We first determine the asymptotic behavior of the quantity of parasites in a cell line, which follows a Feller diffusion with multiplicative jumps. We then consider the evolution of the infection of the cell population and give criteria to determine whether the proportion of infected cells goes to zero (recovery) or if a positive proportion of cells becomes largely infected (proliferation of parasites inside the cells).
• Adaptive High-Gain observers with an application to wastewater treatment plants
  
  • Methnani Salowa
  • Damak Tarak
  • Toumi Ahmed
  • Lafont Frédéric
  • Gauthier Jean-Paul
  , 2011. no abstract
• Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh
  
  • Allaire Grégoire
  • Dapogny Charles
  • Frey Pascal
  Comptes Rendus. Mathématique, Académie des sciences (Paris), 2011, 349 (17-18), pp.999--1003. We propose a method for structural optimization that relies on two alternative descriptions of shapes: on the one hand, they are exactly meshed so that mechanical evaluations by finite elements are accurate; on the other hand, we resort to a level-set characterization to describe their deformation along the shape gradient. The key ingredient is a meshing algorithm for building a mesh, suitable for numerical computations, out of a piecewise linear level-set function on an unstructured mesh. Therefore, our approach is at the same time a geometric optimization method (since shapes are exactly meshed) and a topology optimization method (since the topology of successive shapes can change thanks to the power of the level-set method).
• Deterministic state constrained optimal control problems without controllability assumptions
  
  • Bokanowski Olivier
  • Forcadel Nicolas
  • Zidani Hasnaa
  ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2011, 17 (4), pp.pp. 995-1015. In the present paper, we consider nonlinear optimal control problems with constraints on the state of the system. We are interested in the characterization of the value function without any controllability assumption. In the unconstrained case, it is possible to derive a characterization of the value function by means of a Hamilton-Jacobi-Bellman (HJB) equation. This equation expresses the behavior of the value function along the trajectories arriving or starting from any position $x$. In the constrained case, when no controllability assumption is made, the HJB equation may have several solutions. Our first result aims to give the precise information that should be added to the HJB equation in order to obtain a characterization of the value function. This result is very general and holds even when the dynamics is not continuous and the state constraints set is not smooth. On the other hand we study also some stability results for relaxed or penalized control problems. (10.1051/cocv/2010030)
  DOI : 10.1051/cocv/2010030
• Electromagnetic Wave Scattering from Rough Penetrable Layers
  
  • Haddar Houssem
  • Lechleiter Armin
  SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2011, 43, pp.2418-2443. We consider scattering of time-harmonic electromagnetic waves from an unbounded penetrable dielectric layer mounted on a perfectly conducting infinite plate. This model describes for instance propagation of monochromatic light through dielectric photonic assemblies mounted on a metal plate. We give a variational formulation for the electromagnetic scattering problem in a suitable Sobolev space of functions defined in an unbounded domain containing the dielectric structure. Further, we derive a Rellich identity for a solution to the variational formulation. For simple material configurations and under suitable non-trapping and smoothness conditions, this integral identity allows to prove an a-priori estimate for such a solution. A-priori estimates for solutions to more complicated material configurations are then shown using a perturbation approach. While the estimates derived from the Rellich identity show that the electromagnetic rough surface scattering problem has at most one solution, a limiting absorption argument finally implies existence of a solution to the problem. (10.1137/100783613)
  DOI : 10.1137/100783613
• Weighted Radon transforms for which the Chang approximate inversion formula is precise
  
  • Novikov Roman
  Uspekhi Mat. Nauk, 2011, 66 (2), pp.237-238. We describe all weighted Radon transforms on the plane for which the Chang approximate inversion formula is precise. Some subsequent results, including the Cormack type inversion for these transforms, are also given.
• Absence of exponentially localized solitons for the Novikov-Veselov equation at positive energy
  
  • Novikov Roman
  Physics Letters A, Elsevier, 2011, 375, pp.1233-1235. In this note we show that the Novikov-Veselov equation at positive energy (an analog of KdV in 2+1 dimensions) has no exponentially localized solitons ( in the two-dimensional sense).
• On adaptive stratification
  
  • Etoré Pierre
  • Fort Gersende
  • Jourdain Benjamin
  • Moulines Éric
  Annals of Operations Research, Springer Verlag, 2011, 189 (1), pp.127-154. This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the strata, which should be ideally fitted to thesubsets where the functions to integrate is nearly constant, and on the allocation of the number of samples within each strata. When the dimension is large and the function to integrate is complex, finding such partitions and allocating the sample is a highly non-trivial problem. In this work, we investigate a novel method to improve the efficiency of the estimator "on the fly", by jointly sampling and adapting the strata and the allocation within the strata. The accuracy of estimators when this method is used is examined in detail, in the so-called asymptotic regime (\ie\ when both the number of samples and the number of strata are large). We illustrate the use of the method for the computation of the price of path-dependent options in models with both constant and stochastic volatility. The use of this adaptive technique yields variance reduction by factors sometimes larger than 1000 compared to classical Monte Carlo estimators. (10.1007/s10479-009-0638-9)
  DOI : 10.1007/s10479-009-0638-9
• Differential games and Zubov's method
  
  • Grüne Lars
  • Serea Oana
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2011, 49 (9), pp.2349-2377. In this paper we provide generalizations of Zubov's equation to differential games without Isaacs' condition. We show that both generalizations of Zubov's equation (which we call min-max and max-min Zubov equation, respectively) possess unique viscosity solutions which characterize the respective controllability domains. As a consequence, we show that under the usual Isaacs condition the respective controllability domains as well as the local controllability assumptions coincide. (10.1137/100787829)
  DOI : 10.1137/100787829
• Generalized impedance boundary conditions for thin dielectric coatings with variable thickness
  
  • Aslanyurek Birol
  • Haddar Houssem
  • Shahinturk Hulya
  Wave Motion, Elsevier, 2011, 48 (7), pp.681-700. (10.1016/j.wavemoti.2011.06.002)
  DOI : 10.1016/j.wavemoti.2011.06.002
• Asymptotic behaviour of the number of the Eulerian circuits
  
  • Isaev Mikhail
  The Electronic Journal of Combinatorics, Open Journal Systems, 2011, 18 (1), pp.219. We determine the asymptotic behaviour of the number of the Eulerian circuits in undirected simple graphs with large algebraic connectivity (the second-smallest eigenvalue of the Laplacian matrix). We also prove some new properties of the Laplacian matrix.
• A continuous semigroup of notions of independence between the classical and the free one
  
  • Benaych-Georges Florent
  • Lévy Thierry
  The Annals of Probability, Institute of Mathematical Statistics, 2011, 39 (3), pp.904-938. In this paper, we investigate a continuous family of notions of independence which interpolates between the classical and free ones for non-commutative random variables. These notions are related to the liberation process introduced by D. Voiculescu. To each notion of independence correspond new convolutions of probability measures, for which we establish formulae and of which we compute simple examples. We prove that there exists no reasonable analogue of classical and free cumulants associated to these notions of independence. (10.1214/10-AOP573)
  DOI : 10.1214/10-AOP573
• Exponential instability in the Gel'fand inverse problem on the energy intervals
  
  • Isaev Mikhail
  Journal of Inverse and Ill-posed Problems, De Gruyter, 2011, 19 (3), pp.453-473. We consider the Gel'fand inverse problem and continue studies of [Mandache,2001]. We show that the Mandache-type instability remains valid even in the case of Dirichlet-to-Neumann map given on the energy intervals. These instability results show, in particular, that the logarithmic stability estimates of [Alessandrini,1988], [Novikov,Santacesaria,2010] and especially of [Novikov,2010] are optimal (up to the value of the exponent).
• Polymorphic evolution sequence and evolutionary branching
  
  • Champagnat Nicolas
  • Méléard Sylvie
  Probability Theory and Related Fields, Springer Verlag, 2011, 151 (1-2), pp.45-94. We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large and the mutation rate small. We prove that under a good combination of these two scales, the population process is approximated in the long time scale of mutations by a Markov pure jump process describing the successive trait equilibria of the population. This process, which generalizes the so-called trait substitution sequence, is called polymorphic evolution sequence. Then we introduce a scaling of the size of mutations and we study the polymorphic evolution sequence in the limit of small mutations. From this study in the neighborhood of evolutionary singularities, we obtain a full mathematical justification of a heuristic criterion for the phenomenon of evolutionary branching. To this end we finely analyze the asymptotic behavior of 3-dimensional competitive Lotka-Volterra systems. (10.1007/s00440-010-0292-9)
  DOI : 10.1007/s00440-010-0292-9
• Hedging and Vertical Integration in Electricity Markets
  
  • Aïd René
  • Chemla Gilles
  • Porchet Arnaud
  • Touzi Nizar
  Management Science, INFORMS, 2011, 57 (8). This paper analyzes the interactions between competitive (wholesale) spot, retail, and forward markets and vertical integration in electricity markets. We develop an equilibrium model with producers, retailers, and traders to study and quantify the impact of forward markets and vertical integration on prices, risk premia, and retail market shares. We point out that forward hedging and vertical integration are two separate mechanisms for demand and spot price risk diversification that both reduce the retail price and increase retail market shares. We show that they differ in their impact on prices and firms' utility because of the asymmetry between production and retail segments. Vertical integration restores the symmetry between producers' and retailers' exposure to demand risk, whereas linear forward contracts do not. Vertical integration is superior to forward hedging when retailers are highly risk averse. We illustrate our analysis with data from the French electricity market. (10.1287/mnsc.1110.1357)
  DOI : 10.1287/mnsc.1110.1357
• Optimal Control of the Atmospheric Reentry of a Space Shuttle by an Homotopy Method
  
  • Hermant Audrey
  Optimal Control Applications and Methods, Wiley, 2011, 32 (6), pp.627-646. This paper deals with the optimal control problem of the atmospheric reentry of a space shuttle with a second-order state constraint on the thermal flux. We solve the problem using the shooting algorithm combined with an homotopy method which automatically determines the structure of the optimal trajectory (composed of one boundary arc and one touch point). (10.1002/oca.961)
  DOI : 10.1002/oca.961
• Micro-Macro Modelling of an Array of Spheres Interacting Through Lubrication Forces
  
  • Lefebvre-Lepot Aline
  • Maury Bertrand
  • Lefebvre Aline
  Advances in Mathematical Sciences and Applications, Gakkōtosho Co. Ltd, 2011, 21 (2), pp.535–557. We consider here a discrete system of spheres interacting through a lubrication force. This force is dissipative, and singular near contact: it behaves like the reciprocal of interparticle distance. We propose a macroscopic constitutive equation which is built as the natural continuous counterpart of this microscopic lubrication model. This model, which is of the newtonian type, relies on an elongational viscosity, which is proportional to the reciprocal of the local fluid fraction. We then establish the convergence in a weak sense of solutions to the discrete problem towards the solution to the partial differential equation which we identified as the macroscopic constitutive equation.