Publications

2013

• La conjecture de Syracuse -visualisation tridimensionnelle
  
  • Colonna Jean-François
  , 2013. The Syracuse conjecture -tridimensional display- (La conjecture de Syracuse -visualisation tridimensionnelle-)
• La conjecture de Syracuse -visualisation bidimensionnelle
  
  • Colonna Jean-François
  , 2013. The Syracuse conjecture -bidimensional display- (La conjecture de Syracuse -visualisation bidimensionnelle-)
• La conjecture de Syracuse -visualisation monodimensionnelle
  
  • Colonna Jean-François
  , 2013. The Syracuse conjecture -monodimensional display- (La conjecture de Syracuse -visualisation monodimensionnelle-)
• La conjecture de Syracuse -visualisation monodimensionnelle
  
  • Colonna Jean-François
  , 2013. The Syracuse conjecture -monodimensional display- (La conjecture de Syracuse -visualisation monodimensionnelle-)
• La conjecture de Syracuse -visualisation monodimensionnelle
  
  • Colonna Jean-François
  , 2013. The Syracuse conjecture -monodimensional display- (La conjecture de Syracuse -visualisation monodimensionnelle-)
• La conjecture de Syracuse -visualisation monodimensionnelle
  
  • Colonna Jean-François
  , 2013. The Syracuse conjecture -monodimensional display- (La conjecture de Syracuse -visualisation monodimensionnelle-)
• La conjecture de Syracuse -visualisation monodimensionnelle
  
  • Colonna Jean-Francois
  , 2013. The Syracuse conjecture -monodimensional display- (La conjecture de Syracuse -visualisation monodimensionnelle-)
• La conjecture de Syracuse -visualisation monodimensionnelle
  
  • Colonna Jean-Francois
  , 2013. The Syracuse conjecture -monodimensional display- (La conjecture de Syracuse -visualisation monodimensionnelle-)
• Les deux premières itérations de la construction de la courbe de von Koch
  
  • Colonna Jean-Francois
  , 2013. The first two iterations of the construction of the von Koch curve (Les deux premières itérations de la construction de la courbe de von Koch)
• Un cylindre défini à l'aide de trois champs bidimensionnels
  
  • Colonna Jean-Francois
  , 2013. A cylinder defined by means of three bidimensional fields (Un cylindre défini à l'aide de trois champs bidimensionnels)
• Une surface intermédiaire entre une 'double sphère' et un cylindre
  
  • Colonna Jean-Francois
  , 2013. A surface between a 'double sphere' and a cylinder (Une surface intermédiaire entre une 'double sphère' et un cylindre)
• Une surface intermédiaire entre une 'double sphère' et un cylindre
  
  • Colonna Jean-Francois
  , 2013. A surface between a 'double sphere' and a cylinder (Une surface intermédiaire entre une 'double sphère' et un cylindre)
• La conjecture de Goldbach
  
  • Colonna Jean-Francois
  , 2013. The Goldbach conjecture (La conjecture de Goldbach)
• Un 'double sphere' défini à l'aide de trois champs bidimensionnels
  
  • Colonna Jean-Francois
  , 2013. A 'double sphere' defined by means of three bidimensional fields (Un 'double sphere' défini à l'aide de trois champs bidimensionnels)
• L’opérateur de Laplace-Beltrami en Géométrie presque-Riemannienne
  
  • Boscain Ugo
  • Laurent Camille
  Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2013, 63 (5), pp.1739 - 1770. Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. Generically, the singular set is an embedded one dimensional manifold and there are three type of points: Riemannian points where the two vector fields are linearly independent, Grushin points where the two vector fields are collinear but their Lie bracket is not and tangency points where the two vector fields and their Lie bracket are collinear and the missing direction is obtained with one more bracket. Generically tangency points are isolated. In this paper we study the Laplace-Beltrami operator on such a structure. In the case of a compact orientable surface without tangency points, we prove that the Laplace-Beltrami operator is essentially self-adjoint and has discrete spectrum. As a consequence a quantum particle in such a structure cannot cross the singular set and the heat cannot flow through the singularity. This is an interesting phenomenon since when approaching the singular set (i.e. where the vector fields become collinear), all Riemannian quantities explode, but geodesics are still well defined and can cross the singular set without singularities. This phenomenon appears also in sub-Riemannian structure which are not equiregular i.e. in which the grow vector depends on the point. We show this fact by analyzing the Martinet case. (10.5802/aif.2813)
  DOI : 10.5802/aif.2813
• La conjecture de Goldbach
  
  • Colonna Jean-Francois
  , 2013. The Goldbach conjecture (La conjecture de Goldbach)
• Une surface intermédiaire entre une 'double sphère' et un cylindre
  
  • Colonna Jean-Francois
  , 2013. A surface between a 'double sphere' and a cylinder (Une surface intermédiaire entre une 'double sphère' et un cylindre)
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') pour seize éclairages différents -section tridimensionnelle
  
  • Colonna Jean-François
  , 2013. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') for sixteen different lightings -tridimensional cross-section- (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') pour seize éclairages différents -section tridimensionnelle-)
• An Optimal Affine Invariant Smooth Minimization Algorithm
  
  • d'Aspremont Alexandre
  • Guzmán Cristóbal
  • Jaggi Martin
  , 2013. We formulate an affine invariant implementation of the algorithm in Nesterov (1983). We show that the complexity bound is then proportional to an affine invariant regularity constant defined with respect to the Minkowski gauge of the feasible set. We also detail matching lower bounds when the feasible set is an ℓp ball. In this setting, our bounds on iteration complexity for the algorithm in Nesterov (1983) are thus optimal in terms of target precision, smoothness and problem dimension.
• The topological derivative in anisotropic elasticity
  
  • Bonnet Marc
  • Delgado Gabriel
  Quarterly Journal of Mechanics and Applied Mathematics, Oxford University Press (OUP), 2013, 66, pp.557-586. A comprehensive treatment of the topological derivative for anisotropic elasticity is presented, with both the background material and the trial small inhomogeneity assumed to have arbitrary anisotropic elastic properties. A formula for the topological derivative of any cost functional defined in terms of regular volume or surface densities depending on the displacement is established, by combining small-inhomogeneity asymptotics and the adjoint solution approach. The latter feature makes the proposed result simple to implement and computationally efficient. Both three-dimensional and plane-strain settings are treated; they differ mostly on details in the elastic moment tensor (EMT). Moreover, the main properties of the EMT, a critical component of the topological derivative, are studied for the fully anisotropic case. Then, the topological derivative of strain energy-based quadratic cost functionals is derived, which requires a distinct treatment. Finally, numerical experiments on the numerical evaluation of the EMT and the topological derivative of the compliance cost functional are reported. (10.1093/qjmam/hbt018)
  DOI : 10.1093/qjmam/hbt018
• A Global Steering Method for Nonholonomic Systems
  
  • Chitour Yacine
  • Jean Frédéric
  • Long Ruixing
  Journal of Differential Equations, Elsevier, 2013, 254, pp.1903-1956. In this paper, we present an iterative steering algorithm for nonholonomic systems (also called driftless control-affine systems) and we prove its global convergence under the sole assumption that the Lie Algebraic Rank Condition (LARC) holds true everywhere. That algorithm is an extension of the one introduced in [21] for regular systems. The first novelty here consists in the explicit algebraic construction, starting from the original control system, of a lifted control system which is regular. The second contribution of the paper is an exact motion planning method for nilpotent systems, which makes use of sinusoidal control laws and which is a generalization of the algorithm described in [29] for chained-form systems. (10.1016/j.jde.2012.11.012)
  DOI : 10.1016/j.jde.2012.11.012
• Second order corrector in the homogenization of a conductive-radiative heat transfer problem
  
  • Allaire Grégoire
  • Habibi Zakaria
  Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2013, 18 (1), pp.1-36. This paper focuses on the contribution of the so-called second order corrector in periodic homogenization applied to a conductive-radiative heat transfer problem. More precisely, heat is diffusing in a periodically perforated domain with a non-local boundary condition modelling the radiative transfer in each hole. If the source term is a periodically oscillating function (which is the case in our application to nuclear reactor physics), a strong gradient of the temperature takes place in each periodicity cell, corresponding to a large heat flux between the sources and the perforations. This effect cannot be taken into account by the homogenized model, neither by the first order corrector. We show that this local gradient effect can be reproduced if the second order corrector is added to the reconstructed solution. (10.3934/dcdsb.2013.18.1)
  DOI : 10.3934/dcdsb.2013.18.1
• Representation, relaxation and convexity for variational problems in Wiener spaces
  
  • Chambolle Antonin
  • Goldman Michael
  • Novaga Matteo
  Journal de Mathématiques Pures et Appliquées, Elsevier, 2013. We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that extends analogous results valid in the classical Euclidean framework.
• Optimisation of cancer drug treatments using cell population dynamics
  
  • Billy Frédérique
  • Clairambault Jean
  • Fercoq Olivier
  , 2013, pp.265. Cancer is primarily a disease of the physiological control on cell population proliferation. Tissue proliferation relies on the cell division cycle: one cell becomes two after a sequence of molecular events that are physiologically controlled at each step of the cycle at so-called checkpoints, in particular at transitions between phases of the cycle [105]. Tissue proliferation is the main physiological process occurring in development and later in maintaining the permanence of the organism in adults, at that late stage mainly in fast renewing tissues such as bone marrow, gut and skin. (10.1007/978-1-4614-4178-6_10)
  DOI : 10.1007/978-1-4614-4178-6_10
• Exponential instability in the inverse scattering problem on the energy interval
  
  • Isaev Mikhail
  Functional Analysis and Its Applications, Springer Verlag, 2013, 47 (3), pp.8. We consider the inverse scattering problem on the energy interval in three dimensions. We are focused on stability and instability questions for this problem. In particular, we prove an exponential instability estimate which shows optimality of the logarithmic stability result of [Stefanov, 1990] (up to the value of the exponent).