Publications

2012

• Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration
  
  • Bouin Emeric
  • Calvez Vincent
  • Meunier Nicolas
  • Mirrahimi Sepideh
  • Perthame Benoît
  • Raoul Gael
  • Voituriez Raphael
  Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2012, 350 (15-16), pp.761–766. Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena of front acceleration (when the motility is unbounded) as well as other quantitative results, such as the selection of the most motile individuals (when the motility is bounded). The key argument for the construction and analysis of traveling fronts is the derivation of the dispersion relation linking the speed of the wave and the spatial decay. When the motility is unbounded we show that the position of the front scales as $t^{3/2}$. When the mutation rate is low we show that the canonical equation for the dynamics of the fittest trait should be stated as a PDE in our context. It turns out to be a type of Burgers equation with source term. (10.1016/j.crma.2012.09.010)
  DOI : 10.1016/j.crma.2012.09.010
• Structure fractale tridimensionnelle
  
  • Colonna Jean-François
  , 2012. Tridimensional fractal structure (Structure fractale tridimensionnelle)
• Structure fractale sphérique tridimensionnelle
  
  • Colonna Jean-François
  , 2012. Tridimensional spherical fractal structure (Structure fractale sphérique tridimensionnelle)
• Structure fractale tridimensionnelle
  
  • Colonna Jean-François
  , 2012. Tridimensional fractal structure (Structure fractale tridimensionnelle)
• Structure fractale tridimensionnelle
  
  • Colonna Jean-François
  , 2012. Tridimensional fractal structure (Structure fractale tridimensionnelle)
• Structure fractale tridimensionnelle -la 'mousse' de l'espace-temps ?
  
  • Colonna Jean-François
  , 2012. Tridimensional fractal structure -the space-time foam ?- (Structure fractale tridimensionnelle -la 'mousse' de l'espace-temps ?-)
• Structure fractale tridimensionnelle
  
  • Colonna Jean-François
  , 2012. Tridimensional fractal structure (Structure fractale tridimensionnelle)
• Structure fractale tridimensionnelle
  
  • Colonna Jean-François
  , 2012. Tridimensional fractal structure (Structure fractale tridimensionnelle)
• Relaxation of fluid systems
  
  • Coquel Frédéric
  • Godlewski Edwige
  • Seguin Nicolas
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2012, 22 (8), pp.52. We propose a relaxation framework for general fluid models which can be understood as a natural ex- tension of the Suliciu approach in the Euler setting. In particular, the relaxation system may be totally degenerate. Several stability properties are proved. The relaxation procedure is shown to be efficient in the numerical approximation of the entropy weak solutions of the original PDEs. The numerical method is particularly simple in the case of a fully degenerate relaxation system for which the solution of the Riemann problem is explicit. Indeed, the Godunov solver for the homogeneous relaxation system results in an HLLC-type solver for the equilibirum model. Discrete entropy inequalities are established under a natural Gibbs principle. (10.1142/S0218202512500145)
  DOI : 10.1142/S0218202512500145
• Structure fractale tridimensionnelle -la 'mousse' de l'espace-temps ?
  
  • Colonna Jean-François
  , 2012. Tridimensional fractal structure -the space-time foam ?- (Structure fractale tridimensionnelle -la 'mousse' de l'espace-temps ?-)
• Entrelacs
  
  • Colonna Jean-François
  , 2012. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2012. Intertwining (Entrelacs)
• Existence and uniqueness of traveling waves for fully overdamped Frenkel-Kontorova models
  
  • Al Haj Mohammad
  • Forcadel Nicolas
  • Monneau Régis
  , 2012. In this article, we study the existence and the uniqueness of traveling waves for a discrete reaction-diffusion equation with bistable non-linearity, namely a generalization of the fully overdamped Frenkel-Kontorova model. This model consists in a system of ODE's which describes the dynamics of crystal defects in a lattice solids. Under very poor assumptions, we prove the existence of a traveling wave solution and the uniqueness of the velocity of propagation of this traveling wave. The question of the uniqueness of the profile is also studied by proving Strong Maximum Principle or some weak asymptotics on the profile at infinity.
• Pseudo anneaux olympiques
  
  • Colonna Jean-François
  , 2012. Pseudo Olympic Rings (Pseudo anneaux olympiques)
• Pseudo anneaux olympiques
  
  • Colonna Jean-François
  , 2012. Pseudo Olympic Rings (Pseudo anneaux olympiques)
• Pseudo anneaux olympiques -un point de vue inhabituel
  
  • Colonna Jean-François
  , 2012. Pseudo Olympic Rings -an unusual point of view- (Pseudo anneaux olympiques -un point de vue inhabituel-)
• Pseudo anneaux olympiques
  
  • Colonna Jean-François
  , 2012. Pseudo Olympic Rings (Pseudo anneaux olympiques)
• Oiseaux et poissons
  
  • Colonna Jean-François
  , 2012. Birds and fishes (Oiseaux et poissons)
• Stochastic modeling of density-dependent diploid populations and extinction vortex
  
  • Coron Camille
  , 2012. We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a 3-type nonlinear birth-and-death process, in which birth rates are designed to integrate Mendelian reproduction. We are interested in the long term genetic behaviour of the population (adaptive dynamics), and in particular we compute the fixation probability of a slightly non-neutral allele in the absence of mutations, which involves finding the unique sub-polynomial solution of a nonlinear 3-dimensional recurrence relationship. This equation is simplified to a 1-order relationship which is proved to admit exactly one bounded solution. Adding rare mutations and rescaling time, we study the successive mutation fixations in the population, which are given by the jumps of a limiting Markov process on the genotypes space. At this time scale, we prove that the fixation rate of deleterious mutations increases with the number of already fixed mutations, which creates a vicious circle called the extinction vortex.
• Une interpolation entre un rectangle et un cube
  
  • Colonna Jean-François
  , 2012. An interpolation between a rectangle and a cube (Une interpolation entre un rectangle et un cube)
• Une interpolation entre un rectangle et le ruban de Möbius
  
  • Colonna Jean-François
  , 2012. An interpolation between a rectangle and the Möbius strip (Une interpolation entre un rectangle et le ruban de Möbius)
• Nonlinear spectral radii of order-preserving maps and infinite horizon zero-sum two-player stochastic games
  
  • Akian Marianne
  • Gaubert Stéphane
  • Nussbaum R.D.
  , 2012.
• Hamilton-Jacobi-Bellman approach for the climbing problem for heavy launchers
  
  • Bokanowski Olivier
  • Cristiani Emiliano
  • Laurent-Varin Julien
  • Zidani Hasnaa
  , 2012. In this paper we investigate the Hamilton-Jacobi-Bellman (HJB) approach for solving a complex real-world optimal control problem in high dimension. We consider the climbing problem for the European launcher Ariane V: The launcher has to reach the Geostationary Transfer Orbit with minimal propellant consumption under state/control constraints. In order to circumvent the well-known curse of dimensionality, we reduce the number of variables in the model exploiting the specific features concerning the dynamics of the mass. This generates a non-standard optimal control problem formulation. We show that the joint employment of the most advanced mathematical techniques for the numerical solution of HJB equations allows one to achieve practicable results in reasonable time.
• Temps de transitions métastables pour des systèmes dynamiques stochastiques fini et infini-dimensionnels
  
  • Barret Florent
  , 2012. Dans cette thèse, nous nous sommes intéressés à la métastabilité de certains systèmes dynamiques stochastiques. Plus précisément, nous avons étudié des équations différentielles ou des équations aux dérivées partielles perturbées par un bruit blanc additif dans l'asymptotique du bruit faible. Nous avons donné l'expression et le calcul de l'espérance de temps des transitions métastables pour certains types de modèles (formule dite d'Eyring-Kramers). Dans un premier temps, nous avons généralisé des résultats connus pour des diffusions d'Itô dont la dérive est le gradient d'un potentiel. Nous donnons une équivalence entre la géométrie du paysage décrit par le potentiel et des circuits électriques qui nous permet de donner des expressions simples pour le calcul des temps de transition entre des minima du potentiel. Nous utilisons la théorie du potentiel et les capacités dans le calcul de ces temps. Le principal résultat de cette thèse concerne des équations aux dérivées partielles stochastiques scalaires, paraboliques, semi-linéaires et perturbées par un bruit blanc espace-temps sur un intervalle borné réel comme l'équation d'Allen-Cahn. Ce modèle constitue un analogue infini-dimensionnel aux diffusions en dimension finie. Nous avons considéré deux types de conditions au bord, Dirichlet et Neumann, et discutons le cas des conditions périodiques. Sous certaines hypothèses, nous donnons l'expression, analogue à la dimension finie, des temps transitions. La preuve utilise une discrétisation par différence finie de l'équation et un couplage nous permettant d'appliquer les estimations pour la dimension finie. Il a fallu notamment contrôler uniformément ces estimations en fonction de la dimension pour passer à la limite et récupérer le système infini-dimensionnel.
• Une interpolation entre un rectangle et un cylindre
  
  • Colonna Jean-François
  , 2012. An interpolation between a rectangle and a cylinder (Une interpolation entre un rectangle et un cylindre)