Publications

2004

• Montagnes multifractales sous la neige
  
  • Colonna Jean-François
  , 2004. Snowy multifractal mountains (Montagnes multifractales sous la neige)
• Maximum principle and existence of almost-periodic solutions of second-order differential systems
  
  • Cieutat Philippe
  Differential and integral equations, Khayyam Publishing, 2004, 17 (7-8), pp.921-942. We give sufficient conditions for the existence of almost- periodic solutions of the second-order differential system u′′ =f(t,u,u′), which satisfies the maximum principle. Our hypotheses do not impose the uniqueness of bounded solutions.
• On the Fréchet derivative for obstacle scattering with an impedance boundary condition
  
  • Haddar Houssem
  • Kress Rainer
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2004, 65 (1), pp.194--208 (electronic). (10.1137/S0036139903435413)
  DOI : 10.1137/S0036139903435413
• Radiocarbon behaviour in seawater and the brown algae Fucus serratus in the vicinity of the COGEMA La Hague spent fuel reprocessing plant (Goury)—France
  
  • Douville Eric
  • Fievet Bruno
  • Germain Pierre
  • Fournier Marc
  Journal of Environmental Radioactivity, Elsevier, 2004, 77 (3), pp.355-368. (10.1016/j.jenvrad.2004.04.003)
  DOI : 10.1016/j.jenvrad.2004.04.003
• TEST-CASE NO 19: SHOCK-BUBBLE INTERACTION (PN)
  
  • Kokh Samuel
  • Allaire G.
  Multiphase Science and Technology, Begell House, 2004, 16 (1-3), pp.117-120. (10.1615/multscientechn.v16.i1-3.190)
  DOI : 10.1615/multscientechn.v16.i1-3.190
• Low-Rank Solution of Lyapunov Equations
  
  • Li Jing-Rebecca
  • White Jacob
  SIAM Review, Society for Industrial and Applied Mathematics, 2004, 46 (4), pp.693--713.
• Practical drift conditions for subgeometric rates of convergence
  
  • Douc Randal
  • Fort Gersende
  • Moulines Éric
  • Soulier Philippe
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2004, 14 (3), pp.1353-1377. We present a new drift condition which implies rates of convergence to the stationary distribution of the iterates of a \psi-irreducible aperiodic and positive recurrent transition kernel. This condition, extending a condition introduced by Jarner and Roberts [Ann. Appl. Probab. 12 (2002) 224-247] for polynomial convergence rates, turns out to be very convenient to prove subgeometric rates of convergence. Several applications are presented including nonlinear autoregressive models, stochastic unit root models and multidimensional random walk Hastings-Metropolis algorithms. (10.1214/105051604000000323)
  DOI : 10.1214/105051604000000323
• On the Validity of Chapman-Enskog expansion for shock waves with small strength
  
  • Bedjaoui Nabil
  • Klingenberg Christian
  • LeFloch Philippe G.
  , 2004. We justify a Chapman-Enskog expansion for discontinuous solutions of hyperbolic conservation laws containing shock waves with small strength. Precisely, we establish pointwise uniform estimates for the difference between the traveling waves of a relaxation model and the traveling waves of the corresponding diffusive equations determined by a Chapman-Enskog expansion procedure to first- or second-order.
• On the structure of the set of bounded solutions on an almost periodic Liénard equation
  
  • Cieutat Philippe
  Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2004, 58, pp.885-898. We study some properties of bounded solutions on (0; +∞) of the following almost periodic Lie$nard equation: x′′ + f(x)x′ + g(x) = p(t); where p : R → R is almost periodic function and g : (a; b) → R is strictly decreasing function. Notably, we describe the set of initial conditions of the bounded solutions on (0;+∞) and we state that these solutions are asymptotically almost periodic.
• Structural optimization using sensitivity analysis and a level-set method
  
  • Allaire Grégoire
  • Jouve François
  • Toader Anca-Maria
  Journal of Computational Physics, Elsevier, 2004, 194, pp.363-393. In the context of structural optimization we propose a new numericalmethod based on a combination of the classical shape derivative and ofthe level-set method for front propagation. We implement this methodin two and three space dimensions for a model of linear or nonlinearelasticity. We consider various objective functions with weight andperimeter constraints. The shape derivative is computed by an adjointmethod. The cost of our numerical algorithm is moderate since theshape is captured on a fixed Eulerian mesh. Although this method isnot specifically designed for topology optimization, it can easilyhandle topology changes. However, the resulting optimal shape isstrongly dependent on the initial guess. (10.1016/j.jcp.2003.09.032)
  DOI : 10.1016/j.jcp.2003.09.032
• La paléontologie
  
  • Le Douarin Nicole
  • de Lumley Henry
  • Coppens Yves
  • Brunet Michel
  • Senut Brigitte
  • White Tim
  • Malassé Anne Dambricourt
  • Caro Paul
  • Mainguy Gaell
  • Gobet Emmanuel
  • Pagès Gilles
  • Yor Marc
  • Grangier Philippe
  La lettre de l'Académie des Sciences, Académie des sciences, 2004 (13). (10.62686/21)
  DOI : 10.62686/21
• Low thrust minimum-fuel orbital transfer: a homotopic approach
  
  • Haberkorn Thomas
  • Martinon Pierre
  • Gergaud Joseph
  Journal of Guidance, Control, and Dynamics, American Institute of Aeronautics and Astronautics, 2004, 27 (6), pp.1046-1060. We describe in this paper the study of an earth orbital transfer with a low thrust (typically electro-ionic) propulsion system. The objective is the maximization of the final mass, which leads to a discontinuous control with a huge number of thrust arcs. The resolution method is based on single shooting, combined to a homotopic approach in order to cope with the problem of the initial guess, which is actually critical for non-trivial problems. An important aspect of this choice is that we make no assumptions on the control structure, and in particular do not set the number of thrust arcs. This strategy allowed us to solve our problem (a transfer from Low Earth Orbit to Geosynchronous Equatorial Orbit, for a spacecraft with mass of 1500 kgs, either with or without a rendezvous) for thrusts as low as 0.1N, which corresponds to a one-year transfer involving several hundreds of revolutions and thrust arcs. The numerical results obtained also revealed strong regularity in the optimal control structure, as well as some practically interesting empiric laws concerning the dependency of the final mass with respect to the transfer time and maximal thrust.
• Exact approximation rate of killed hypoelliptic diffusions using the discrete Euler scheme
  
  • Gobet Emmanuel
  • Menozzi Stéphane
  Stochastic Processes and their Applications, Elsevier, 2004, 112 (2), pp.201-223. We are interested in approximating a multidimensional hypoelliptic diffusion process $(X_t)_{t\geq 0}$ killed when it leaves a smooth domain $D$. When a discrete Euler scheme with time step $h$ is used, we prove under a non characteristic boundary condition that the weak error is upper bounded by $C_1\sqrt h$, generalizing the result obtained by the first author in Gobet'00 for the uniformly elliptic case. We also obtain a lower bound with the same rate $\sqrt h$, thus proving that the order of convergence is exactly $\frac 12$. This provides a theoretical explanation of the well-known bias that we can numerically observe in that kind of procedure.
• The interior transmission problem for anisotropic Maxwell's equations and its applications to the inverse problem
  
  • Haddar Houssem
  Mathematical Methods in the Applied Sciences, Wiley, 2004, 27 (18), pp.2111--2129. (10.1002/mma.465)
  DOI : 10.1002/mma.465
• Quantum electrodynamics of relativistic bound states with cutoffs
  
  • Barbaroux Jean-Marie
  • Dimassi M.
  • Guillot J. -C.
  Journal of Hyperbolic Differential Equations, World Scientific Publishing, 2004, 1,No.2, pp.271-314. We consider an Hamiltonian with ultraviolet and infrared cutoffs, describing the interaction of relativistic electrons and positrons in the Coulomb potential with photons in Coulomb gauge. The interaction includes both interaction of the current density with transversal photons and the Coulomb interaction of charge density with itself. We prove that the Hamiltonian is self-adjoint and has a ground state for sufficiently small coupling constants. (10.1142/S021989160400010X)
  DOI : 10.1142/S021989160400010X
• High order marching schemes for the wave equation in complex geometry
  
  • Li Jing-Rebecca
  • Greengard Leslie
  Journal of Computational Physics, Elsevier, 2004, 198 (1), pp.295--309. We present a new class of explicit marching schemes for the wave equation in complex geometry. They rely on a simple embedding of the domain in a uniform Cartesian grid, which allows for efficient and automatic implementation but creates irregular cells near the boundary. While existing explicit finite difference schemes are generally restricted in the size of the time step that can be taken by the dimensions of the smallest cell, the schemes described here are capable of taking time steps dictated by the uniform grid spacing. This should be of significant benefit in a wide variety of simulation efforts.
• Vector-valued Coherent Risk Measures
  
  • Jouini Elyès
  • Meddeb Moncef
  • Touzi Nizar
  Finance and Stochastics, Springer Verlag (Germany), 2004, 8, pp.531-552. We define a coherent risk measures as set-valued maps satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner, Delbaen, Eber and Heath (1998). We then discuss the aggregation issue, i.e. the passage from valued random portofolio to valued measure of Risk. Necessary and sufficient conditions of coherent aggregation are provided
• FEM/BEM Analysis for SAW devices
  
  • Solal Marc
  • Abboud Toufic
  • Ballandras Sylvain
  • Chamaly Stéphane
  • Laude Vincent
  • Lardat Raphael
  • Pastureaud Thomas
  • Ribbe Jonas
  • Steichen William
  • Ventura Pascal
  , 2004, pp.paper 3a2.
• Quantification by photogrammetric analysis of the normandy and picardy rocky coast dynamic (Normandie, France).
  
  • Costa Stéphane
  • Delahaye Daniel
  • Freire-Diaz Sylviano
  • Di-Nocera L.
  • Davidson Robert
  • Plessis E.
  , 2004, pp.pp.139-148.
• Nonparametric calibration of jump-diffusion option pricing models.
  
  • Cont Rama
  • Tankov Peter
  The Journal of Computational Finance, Incisive Media, 2004, 7, pp.1-49. We present a non-parametric method for calibrating jump-diffusion models to a set of observed option prices. We show that the usual formulations of the inverse problem via nonlinear least squares are ill-posed. In the realistic case where the set of observed prices is discrete and finite, we propose a regularization method based on relative entropy: we reformulate our calibration problem into a problem of finding a risk neutral jump-diffusion model that reproduces the observed option prices and has the smallest possible relative entropy with respect to a chosen prior model. We discuss the numerical implementation of our method using a gradient based optimization and show via simulation tests on various examples that using the entropy penalty resolves the numerical instability of the calibration problem. Finally, we apply our method to empirical data sets of index options and discuss the empirical results obtained.
• Homogenization of periodic systems with large potentials
  
  • Allaire Grégoire
  • Capdeboscq Yves
  • Piatnitski Andrey
  • Siess Vincent
  • Vanninathan Muthusamy
  Archive for Rational Mechanics and Analysis, Springer Verlag, 2004, 174 (2), pp.179--220. We consider the homogenization of a system of second-order equations with a large potential in a periodic medium. Denoting by ε the period, the potential is scaled as ε −2. Under a generic assumption on the spectral properties of the associated cell problem, we prove that the solution can be approximately factorized as the product of a fast oscillating cell eigenfunction and of a slowly varying solution of a scalar second-order equation. This result applies to various types of equations such as parabolic, hyperbolic or eigenvalue problems, as well as fourth-order plate equation. We also prove that, for well-prepared initial data concentrating at the bottom of a Bloch band, the resulting homogenized tensor depends on the chosen Bloch band. Our method is based on a combination of classical homogenization techniques (two-scale convergence and suitable oscillating test functions) and of Bloch waves decomposition. (10.1007/s00205-004-0332-7)
  DOI : 10.1007/s00205-004-0332-7