Publications

2011

• Energy contracts management by stochastic programming techniques
  
  • Cen Zhihao
  • Bonnans J. Frederic
  • Christel Thibault
  Annals of Operations Research, Springer Verlag, 2011, 200 (1), pp.199-222. We consider the problem of optimal management of energy contracts, with bounds on the local (time step) amounts and global (whole period) amounts to be traded, integer constraint on the decision variables and uncertainty on prices only. After building a finite state Markov chain by using vectorial quantization tree method, we rely on the stochastic dual dynamic programming (SDDP) method to solve the continuous relaxation of this stochastic optimization problem. An heuristic for computing sub optimal solutions to the integer optimization problem, based on the Bellman values of the continuous relaxation, is provided. Combining the previous techniques, we are able to deal with high-dimension state variables problems. Numerical tests applied to realistic energy markets problems have been performed. (10.1007/s10479-011-0973-5)
  DOI : 10.1007/s10479-011-0973-5
• 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.
• Sensor fault reconstruction and observability for unknown inputs, with an application to wastewater treatment plants
  
  • Methnani Salowa
  • Gauthier Jean-Paul
  • Lafont Frédéric
  International Journal of Control, Taylor & Francis, 2011, 84, pp.822-833.
• 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
• Sampling the Fermi statistics and other conditional product measures
  
  • Gaudilliere Alexandre
  • Reygner Julien
  Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2011, 47, pp.790-812. Through a Metropolis-like algorithm with single step computational cost of order one, we build a Markov chain that relaxes to the canonical Fermi statistics for k non-interacting particles among m energy levels. Uniformly over the temperature as well as the energy values and degeneracies of the energy levels we give an explicit upper bound with leading term km(ln k) for the mixing time of the dynamics. We obtain such construction and upper bound as a special case of a general result on (non-homogeneous) products of ultra log-concave measures (like binomial or Poisson laws) with a global constraint. As a consequence of this general result we also obtain a disorder-independent upper bound on the mixing time of a simple exclusion process on the complete graph with site disorder. This general result is based on an elementary coupling argument and extended to (non-homogeneous) products of log-concave measures.
• Optimal Design of Low-contrast Two-phase Structures For the Wave Equation
  
  • Allaire Grégoire
  • Kelly Alex
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2011, 21 (7), pp.1499--1538. This paper is concerned with the following optimal design problem:¯nd the distribution of two phases in a given domain that minimizes an objective function evaluated through the solution of a wave equation. This type of optimization problem is known to be ill-posed in the sense that it generically does not admit a minimizer among classical admissible designs. Its relaxation could be found, in principle, through homogenization theory but, unfortunately, it is not always explicit, in particular for objective functions depending on the solution gradient. To circumvent this di±culty, we make the simplifying assumption that the two phases have a low constrast. Then, a second-order asymptotic expansion with respect to the small amplitude of the phase coe±cients yields a simpli¯ed optimal design problem which is amenable to relaxation by means of H-measures. We prove a general existence theorem in a larger class of composite materials and propose a numerical algorithm to compute minimizers in this context. As in the case of an elliptic state equation, the optimal composites are shown to be rank-one laminates. However, the proof that relaxation and small-amplitude limit commute is more delicate than in the elliptic case. (10.1142/S0218202511005477)
  DOI : 10.1142/S0218202511005477
• On the existence of a limit value in some non expansive optimal control problems
  
  • Quincampoix Marc
  • Renault Jérôme
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2011, 49 (5), pp.2118-2132. We investigate a limit value of an optimal control problem when the horizon converges to infinity. For this aim, we suppose suitable nonexpansive-like assumptions which does not imply that the limit is independent of the initial state as it is usually done in the literature. (10.1137/090756818)
  DOI : 10.1137/090756818
• On the reconstruction of conductivity of bordered two-dimensional surface in R^3 from electrical currents measurements on its boundary
  
  • Henkin Gennadi
  • Novikov Roman
  The Journal of Geometric Analysis, Springer, 2011, 21, pp.543-587. An electrical potential U on bordered surface X (in Euclidien three-dimensional space) with isotropic conductivity function sigma>0 satisfies equation d(sigma d^cU)=0, where d^c is real operator associated with complex (conforme) structure on X induced by Euclidien metric of three-dimensional space. This paper gives exact reconstruction of conductivity function sigma on X from Dirichlet-to-Neumann mapping (for aforementioned conductivity equation) on the boundary of X. This paper extends to the case of the Riemann surfaces the reconstruction schemes of R.Novikov (1988) and of A.Bukhgeim (2008) given for the case of domains in two-dimensional Euclidien space. The paper extends and corrects the statements of Henkin-Michel (2008), where the inverse boundary value problem on the Riemann surfaces was firstly considered.
• Explicit characterization of the support of non-linear inclusions
  
  • Lechleiter Armin
  Inverse Problems and Imaging, AIMS American Institute of Mathematical Sciences, 2011, 5 (3), pp.675--694. (10.3934/ipi.2011.5.675)
  DOI : 10.3934/ipi.2011.5.675
• A nonasymptotic theorem for unnormalized Feynman-Kac particle models
  
  • Cérou Frédéric
  • del Moral Pierre
  • Guyader Arnaud
  Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2011, 47 (3), pp.629-649. We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman-Kac models. We provide an original stochastic analysis-based on Feynman-Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the L(2)-relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first results of this type for this class of unnormalized models. We also illustrate these results in the context of particle absorption models, with a special interest in rare event analysis. (10.1214/10-AIHP358)
  DOI : 10.1214/10-AIHP358
• Control of the bilinear Schrödinger equation for fully coupling potentials
  
  • Caponigro Marco
  • Boscain Ugo
  • Chambrion Thomas
  • Sigalotti Mario
  , 2011, pp.to appear. We present a general result of approximate controllability for the bilinear Schrödinger equation (with wave function varying in the unit sphere of an infinite dimensional Hilbert space), under the hypothesis that the Schrödinger operator has discrete spectrum and that the control potential couples all eigenstates. The control method is based on a tracking procedure for the Galerkin approximations, lifted in SU(n). The method allows to estimate the L 1 norm of the control laws achieving controllability.
• 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
• 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
• 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
• 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.
• 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).
• 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.
• 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
• Spectral theory for a mathematical model of the weak interaction: The decay of the intermediate vector bosons W±, II
  
  • Aschbacher Walter H.
  • Barbaroux Jean-Marie
  • Faupin Jérémy
  • Guillot Jean-Claude
  Annales Henri Poincaré, Springer Verlag, 2011, 12 (8), pp.1539-1570. We do the spectral analysis of the Hamiltonian for the weak leptonic decay of the gauge bosons W+/-. Using Mourre theory, it is shown that the spectrum between the unique ground state and the first threshold is purely absolutely continuous. Neither sharp neutrino high energy cutoff nor infrared regularization are assumed. (10.1007/s00023-011-0114-3)
  DOI : 10.1007/s00023-011-0114-3