# Laboratoire J. A. Dieudonné

## Séminaire de l'équipe EDP Analyse Numérique

Séminaires à venir   -   Liste complète 2017-2018   -   Archives 2009-2017

 07/09/2017 14:00 Salle de conférences
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 14/09/2017 14h Salle de RÃ©union FIZEAU
 Didier Clamond (LJAD) Petviashvilli's method applied to steady surface gravity waves of arbitrary length Petviashvilli's method is a very simple stabilised fixed-point iteration for solving numerically nonlinear PDEs. Its algorithmic complexity is O(N) where $N$ is the number of unknowns, while the Newton--Levenberg--Marquardt complexity is O(N^3). When applied to steady surface gravity waves, this method provides a very efficient algorithm for computing solutions in arbitrary precision and in arbitrary depth, i.e., it works efficiently for short and long periodic waves, as well as for solitary waves. With this algorithm, it is actually not more difficult to solve the Euler equations with a free surface than toy models such as KdV and NLS. A complete theoretical understanding of this algorithm is still lacking, but its efficiency is illustrated via several relevant numerical examples.
 05/10/2017 14h Salle de conferences
 SÃ©minaire->Mini-Cours Axe MTC/NSC, en commun avec l'Ã©quipe Proba/Stat  (Thierry Bal et Alain Destexhe CNRS/UNIC, Gif-sur-Yvette) The stochastic integrative properties of thalamic and cortical neurons In this joint course, we shall overview experimental and theoretical approaches to synaptic noise and oscillation in neurons. After reviewing the stochastic and oscillatory aspects of neuronal activity in vivo, we will overview models of stochastic activity at the cellular and network levels. At the cellular level, models and experiments converge into the dynamic-clamp technique, where a cell-machine interface allows us to "speak the neuronal language" by injection of artificial synaptic activities in real biological neurons, as we show for cortical and thalamic neurons. At the network level, we will illustrate consequences in explaining sensory responses up to perception. E-mail: destexhe@unic.cnrs-gif.fr bal@unic.cnrs-gif.fr
 Ben Schacher (sÃ©minaire commun avec l'Ã©quipe AGD) (Departement of Mathematics, University of Toronto, Toronto, CANADA ) Eulerian calculus on Wasserstein Space RÃ©sumÃ©: The optimal transport problem defines a notion of distance in the space of probability measures over a manifold, the Wasserstein space. In his thesis, McCann discovered that this space is a length space: the distance between probability measures is given by the length of minimizing geodesics called displacement interpolants or Wasserstein geodesics. In 2000, Otto defined a (purely formal) Riemannian calculus allowing the computation of tangent vectors to displacement interpolants and the computation of Hessians of functionals along these geodesics. In this talk, I will present an Eulerian calculus on Wasserstein space, which extends the Otto calculus from a purely Riemannian setting to general Lagrangians. This Eulerian calculus allows for the computation of derivatives and Hessians of functionals involving derivatives of densities, resolving a question of Villani. New first order displacement convex functionals are presented. Finally, I will show how this calculus can be made rigorous via the DiPerna-Lions theory of renormalized solutions. This talk is based on my thesis and ongoing joint work with Almut Burchard.
 SÃ©minaire Analyse des EDP : Thomas Chambrion (UniversitÃ© de Lorraine) et Ugo Boscain (JLL, Paris 6) (organisation D. Chiron, P. RaphaÃ«l, financÃ© par l'ERC SINGWAVE) Adiabatic control of quantum mechanical systems (Ugo Boscain) et ContrÃ´labilitÃ© de l'Ã©quation de SchrÃ¶dinger bilinÃ©aire (Thomas Chambrion) Ugo Boscain: In this talk I will present a technique to control the Schroedinger equation which is based on the adiabatic approximation and the presence of conical intersections between eigenvalues of the Hamiltonian in dependence of the controls seen as parameters (diabolic points). In the case of a Schroedinger equation evolving in a finite dimensional space such a technique allows one to recover the Lie bracket generating condition from purely spectral properties. One of the most interesting features of our technique is that it permits to control a parameter-dependent family of quantum systems (ensemble control). This is work in collaboration with Mario Sigalotti. Page web: http://www.iecl.univ-lorraine.fr/~Thomas.Chambrion/
 Elio Marconi (UniversitÃ© de BÃ¢le) Regularity estimates for scalar conservation laws in one space dimension We consider the scalar conservation law in one space dimension u_t+f(u)_x=0 and we study the regularizing effect that the nonlinearity of the flux f$has on the entropy solution$u$. For a general smooth flux function$f$, the regularity of the solution can be expressed in terms of$BV^\Phi$spaces, where$\Phi$depends on the nonlinearity of$f$. If moreover the set$\{w:f''(w)=0\}$is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that$f'\circ u(t)\in BV_{loc}(\mathbb{R})$for every$t>0$and that this can be improved to$SBV_{loc}(\mathbb{R})\$ regularity except an at most countable set of singular times. As a corollary, we obtain in this setting the sharp regularity of the entropy solution in terms of fractional BV spaces.
 Colloque DENA (22 et 23 Novembre) (Organisation: R Catellier & Y D) DENA 2017 - Workshop on Expanding Networks Dynamics : Modeling, Analysis and Simulation of multi-scale spatial exploration under constraints The main aim of this interdisciplinary Workshop is to bring together researchers from various disciplines for a deeper understanding of the dynamics of constrained expanding networks, in order to analyse, model & characterize both the small-scale and large-scale dynamics of expanding networks of interacting agents. Versatile real-world and/or lab-scale benchmarking toy-models, with various applied constraints, should assess the relevance & robustness of the mathematical/statistical proposed modelings and computations, the expected emergence of an "optimal" (i.e. efficient) resilient design and guide real-world comprehension of the biologic, social, economic, physical, medical... on-going process. Page web: https://workshopdena17.sciencesconf.org/
 30/11/2017 14h Salle 1er Ã©tage Fizeau
 11/01/2018 14h -16h Salle de confÃ©rences
 CÃ©line GRANDMONT (INRIA Paris Projet REO ) TBA E-mail: celine.grandmont@inria.fr Page web: https://team.inria.fr/reo/team-members/celine-grandmont/
 Lisl WEYNANS (IMB , INRIA Bordeaux Sud-Ouest Bordeaux University, ) TBA E-mail: lisl.weynans@math.u-bordeaux.fr Page web: https://www.math.u-bordeaux.fr/~lweynans/
 SÃ©minaire Analyse des EDP : Thierry Gallay ( Institut Fourier, UniversitÃ© Grenoble Alpes) (organisation D. Chiron, P. RaphaÃ«l, financÃ© par l'ERC SINGWAVE) Page web: https://www-fourier.ujf-grenoble.fr/~gallay/
 Michele Botti (IMAG - Institut MontpelliÃ©rain Alexander Grothendieck) TBA TBA E-mail: bottieaffini@gmail.com
 Marie POSTEL (UniversitÃ© Pierre et Marie Curie - LJLL) TBA
 SÃ©minaire Analyse des EDP. (organisation D. Chiron, P. RaphaÃ«l, financÃ© par l'ERC SINGWAVE)
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 Charlotte Perrin (LATP)
 SÃ©minaire Analyse des EDP. (organisation D. Chiron, P. RaphaÃ«l, financÃ© par l'ERC SINGWAVE)
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 SÃ©minaire Analyse des EDP. (organisation D. Chiron, P. RaphaÃ«l, financÃ© par l'ERC SINGWAVE)
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