Publications

2012

• Modelling and Simulation of Liquid-Vapor Phase Transition in Compressible Flows Based on Thermodynamical Equilibrium.
  
  • Faccanoni Gloria
  • Kokh Samuel
  • Allaire Grégoire
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2012, 46 (05), pp.1029-1054. In the present work we investigate the numerical simulation of liquid-vapor phase change in compressible flows. Each phase is modeled as a compressible fluid equipped with its own Equation of State (EOS). We suppose that inter-phase equilibrium processes in the medium operate at a short time-scale compared to the other physical phenomena such as convection or thermal diffusion. This assumption provides an implicit definition of an equilibrium EOS for the two-phase medium. Within this framework, mass transfer is the result of local and instantaneous equilibria between both phases. The overall model is strictly hyperbolic. We examine properties of the equilibrium EOS and we propose a discretization strategy based on a Finite-Volume relaxation method. This method allows to cope with the implicit definition of the equilibrium EOS, even when the model involves complex EOS's for the pure phases. We present two-dimensional numerical simulations that shows that the model is able to reproduce mechanism such as phase disappearance and nucleation. (10.1051/m2an/2011069)
  DOI : 10.1051/m2an/2011069
• Mean curvature flow with obstacles
  
  • Almeida Luís
  • Chambolle Antonin
  • Novaga Matteo
  Annales de l'Institut Henri Poincaré (C), Analyse non linéaire, EMS, 2012, 29 (5), pp.667 - 681. We consider the evolution of fronts by mean curvature in the presence of obstacles. We construct a weak solution to the flow by means of a variational method, corresponding to an implicit time-discretization scheme. Assuming the regularity of the obstacles, in the two-dimensional case we show existence and uniqueness of a regular solution before the onset of singularities. Finally, we discuss an application of this result to the positive mean curvature flow. (10.1016/j.anihpc.2012.03.002)
  DOI : 10.1016/j.anihpc.2012.03.002
• Quadratic conditions for bang-singular extremals
  
  • Aronna Maria Soledad
  • Bonnans J. Frederic
  • Dmitruk Andrei V.
  • Lotito Pablo
  Numerical Algebra, Control and Optimization, American Institute for Mathematical Sciences, 2012, 2 (3), pp.511-546. This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain second order necessary optimality conditions. Secondly, we derive a second order sufficient condition for the scalar control case. (10.3934/naco.2012.2.511)
  DOI : 10.3934/naco.2012.2.511
• A new class of $({\cal H}^k,1)$-rectifiable subsets of metric spaces
  
  • Ghezzi Roberta
  • Jean Frédéric
  Communications on Pure and Applied Analysis, AIMS American Institute of Mathematical Sciences, 2012, 12 (2), pp.881-898. The main motivation of this paper arises from the study of Carnot--Carathéodory spaces, where the class of $1$-rectifiable sets does not contain smooth non-horizontal curves; therefore a new definition of rectifiable sets including non-horizontal curves is needed. This is why we introduce in any metric space a new class of curves, called continuously metric differentiable of degree $k$, which are Hölder but not Lipschitz continuous when $k>1$. Replacing Lipschitz curves by this kind of curves we define $({\cal H}^k,1)$-rectifiable sets and show a density result generalizing the corresponding one in Euclidean geometry. This theorem is a consequence of computations of Hausdorff measures along curves, for which we give an integral formula. In particular, we show that both spherical and usual Hausdorff measures along curves coincide with a class of dimensioned lengths and are related to an interpolation complexity, for which estimates have already been obtained in Carnot--Carathéodory spaces. (10.3934/cpaa.2013.12.881)
  DOI : 10.3934/cpaa.2013.12.881
• Bocop - A collection of examples
  
  • Bonnans Frédéric J.
  • Martinon Pierre
  • Grélard Vincent
  , 2012. In this document we present a collection of classical optimal control problems which have been implemented and solved with Bocop. We recall the main features of the problems and of their solutions, and describe the numerical results obtained.
• A Local Ordered Upwind Method for Hamilton-Jacobi and Isaacs Equations
  
  • Cacace Simone
  • Cristiani Emiliano
  • Falcone Maurizio
  , 2012, 18. We present a generalization of the Fast Marching (FM) method for the numerical solution of a class of Hamilton-Jacobi equations, including Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations. The method is able to compute an approximation of the viscosity solution concentrating the computations only in a small evolving trial region, as the original FM method. The main novelty is that the size of the trial region does not depend on the dynamics. We compare the new method with the standard iterative algorithm and the FM method, in terms of accuracy and order of computations on the grid nodes. (10.3182/20110828-6-IT-1002.02473)
  DOI : 10.3182/20110828-6-IT-1002.02473
• Sequential design of experiments for parameter estimation with application to numerical dosimetr
  
  • Jala Marjorie
  • Lévy-Leduc Céline
  • Moulines Éric
  • Conil Emmanuelle
  • Wiart Joe
  , 2012.
• Studying isometry groups using the horofunction boundary
  
  • Walsh Cormac
  , 2012.
• Un ensemble de 4x3 stéréogrammes d'une structure fractale filamenteuse tridimensionnelle
  
  • Colonna Jean-François
  , 2012. A set of 4x3 stereograms of a tridimensional filamentous fractal structure (Un ensemble de 4x3 stéréogrammes d'une structure fractale filamenteuse tridimensionnelle)
• Un ensemble de 4x3 stéréogrammes d'une structure fractale filamenteuse tridimensionnelle
  
  • Colonna Jean-François
  , 2012. A set of 4x3 stereograms of a tridimensional filamentous fractal structure (Un ensemble de 4x3 stéréogrammes d'une structure fractale filamenteuse tridimensionnelle)
• Ver circulaire
  
  • Colonna Jean-François
  , 2012. Circular worm (Ver circulaire)
• Structure fractale filamenteuse tridimensionnelle
  
  • Colonna Jean-François
  , 2012. Tridimensional filamentous fractal structure (Structure fractale filamenteuse tridimensionnelle)
• Ver circulaire
  
  • Colonna Jean-François
  , 2012. Circular worm (Ver circulaire)
• Structure fractale filamenteuse tridimensionnelle
  
  • Colonna Jean-François
  , 2012. Tridimensional filamentous fractal structure (Structure fractale filamenteuse tridimensionnelle)
• Structure fractale filamenteuse tridimensionnelle
  
  • Colonna Jean-François
  , 2012. Tridimensional filamentous fractal structure (Structure fractale filamenteuse tridimensionnelle)
• Structure fractale filamenteuse tridimensionnelle
  
  • Colonna Jean-François
  , 2012. Tridimensional filamentous fractal structure (Structure fractale filamenteuse tridimensionnelle)
• Collision analysis for an UAV
  
  • Desilles Anna
  • Zidani Hasnaa
  • Crück Eva
  , 2012, pp.AIAA 2012-4526. The Sense and Avoid capacity of Unmanned Aerial Vehicles (UAV) is one of the key elements to open the access to airspace for UAVs. In order to replace a pilot's See and Avoid capacity such a system has to be certified "as safe as a human pilot on-board". The problem is to prove that an unmanned aircraft equipped with a S and A system can comply with the actual air transportation regulations. This paper aims to provide mathematical and numerical tools to link together the safety objectives and sensors specifications. Our approach starts with the natural idea of a specified "safety volume" around the aircraft: the safety objective is to guarantee that no other aircraft can penetrate this volume. We use a general reachability and viability concepts to define nested sets which are meaningful to allocate sensor performances and manoeuvring capabilities necessary to protect the safety volume. Using the general framework of HJB equations for the optimal control and differential games, we give a rigorous mathematical characterization of these sets. Our approach allows also to take into account some uncertainties in the measures of the parameters of the incoming traffic. We also provide numerical tools to compute the defined sets, so that the technical specifications of a S and A system can be derived in accordance with a small set of intuitive parameters. We consider several dynamical models corresponding to the different choices of maneuvers (lateral, longitudinal and mixed). Our numerical simulations show clearly that the nature of used maneuvers is an important factor in the specifications of sensor's performances. (10.2514/6.2012-4526)
  DOI : 10.2514/6.2012-4526
• Structure fractale filamenteuse tridimensionnelle
  
  • Colonna Jean-François
  , 2012. Tridimensional filamentous fractal structure (Structure fractale filamenteuse tridimensionnelle)
• Un ensemble de 4x3 stéréogrammes d'un ruban de Möbius fractal
  
  • Colonna Jean-François
  , 2012. A set of 4x3 stereograms of a fractal Möbius strip (Un ensemble de 4x3 stéréogrammes d'un ruban de Möbius fractal)
• Un ensemble de 4x3 stéréogrammes d'une sphère fractale
  
  • Colonna Jean-François
  , 2012. A set of 4x3 stereograms of a fractal sphere (Un ensemble de 4x3 stéréogrammes d'une sphère fractale)
• Un ensemble de 4x3 stéréogrammes d'une bouteille de Klein fractale
  
  • Colonna Jean-François
  , 2012. A set of 4x3 stereograms of a fractal Klein bottle (Un ensemble de 4x3 stéréogrammes d'une bouteille de Klein fractale)
• Structure fractale filamenteuse tridimensionnelle
  
  • Colonna Jean-François
  , 2012. Tridimensional filamentous fractal structure (Structure fractale filamenteuse tridimensionnelle)
• Une sphère fractale
  
  • Colonna Jean-François
  , 2012. A fractal sphere (Une sphère fractale)
• Une bouteille de Klein fractale
  
  • Colonna Jean-François
  , 2012. A fractal Klein bottle (Une bouteille de Klein fractale)
• Une bouteille de Klein fractale
  
  • Colonna Jean-François
  , 2012. A fractal Klein bottle (Une bouteille de Klein fractale)