Laboratoire Jacques-Louis Lions
Présentation
Le laboratoire, créé en 1969, porte le nom de son fondateur Jacques-Louis Lions. il s'agit maintenant d'une unité de recherche conjointe à l’Université Pierre et Marie Curie, à l’université Paris Diderot et au Centre National de la Recherche Scientifique.
Le Laboratoire Jacques-Louis Lions constitue le plus grand laboratoire de France et l'un des principaux au monde pour la formation et la recherche en mathématiques appliquées.
Il accueille l'activités de deux masters deuxième année ce qui représente un centaine d'étudiants. Ses activités recouvrent l’analyse, la modélisation et le calcul scientifique haute performance de phénomènes représentés par des équations aux dérivées partielles.
Fort d’environ 100 enseignants-chercheurs, chercheurs, ingénieurs, personnels administratifs permanents ou émérites, et d’autant de doctorants ou post-doctorants, il collabore avec le monde économique et avec d'autres domaines scientifiques à travers un large spectre d'applications : dynamique des fluides; physique, mécanique et chimie théoriques; contrôle, optimisation et finance; médecine et biologie; traitement du signal et des données.
Thèmes de recherche
- Equations aux dérivées partielles et équations différentielles
- Contrôle, optimisation, calcul des variations
- Calcul scientifique, simulations numériques
- Applications des mathématiques
[hal-00939009] Recent advances in 2D and 3D in vitro systems using primary hepatocytes, alternative hepatocyte sources and non-parenchymal liver cells and their use in investigating mechanisms of hepatotoxicity, cell signaling and ADME.
Date: 29 Ene 2014 - 20:50
Desc: This review encompasses the most important advances in liver functions and hepatotoxicity and analyzes which mechanisms can be studied in vitro. In a complex architecture of nested, zonated lobules, the liver consists of approximately 80 % hepatocytes and 20 % non-parenchymal cells, the latter being involved in a secondary phase that may dramatically aggravate the initial damage. Hepatotoxicity, as well as hepatic metabolism, is controlled by a set of nuclear receptors (including PXR, CAR, HNF-4α, FXR, LXR, SHP, VDR and PPAR) and signaling pathways. When isolating liver cells, some pathways are activated, e.g., the RAS/MEK/ERK pathway, whereas others are silenced (e.g. HNF-4α), resulting in up- and downregulation of hundreds of genes. An understanding of these changes is crucial for a correct interpretation of in vitro data. The possibilities and limitations of the most useful liver in vitro systems are summarized, including three-dimensional culture techniques, co-cultures with non-parenchymal cells, hepatospheres, precision cut liver slices and the isolated perfused liver. Also discussed is how closely hepatoma, stem cell and iPS cell-derived hepatocyte-like-cells resemble real hepatocytes. Finally, a summary is given of the state of the art of liver in vitro and mathematical modeling systems that are currently used in the pharmaceutical industry with an emphasis on drug metabolism, prediction of clearance, drug interaction, transporter studies and hepatotoxicity. One key message is that despite our enthusiasm for in vitro systems, we must never lose sight of the in vivo situation. Although hepatocytes have been isolated for decades, the hunt for relevant alternative systems has only just begun.
[hal-00018874] Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics
Date: 10 Feb 2006 - 15:21
Desc: [...]
[inria-00336911] Results and questions on a nonlinear approximation approach for solving high-dimensional partial differential equations
Date: 5 Nov 2008 - 14:58
Desc: We investigate mathematically a nonlinear approximation type approach recently introduced in [A. Ammar et al., J. Non-Newtonian Fluid Mech., 2006] to solve high dimensional partial differential equations. We show the link between the approach and the greedy algorithms of approximation theory studied e.g. in [R.A. DeVore and V.N. Temlyakov, Adv. Comput. Math., 1996]. On the prototypical case of the Poisson equation, we show that a variational version of the approach, based on minimization of energies, converges. On the other hand, we show various theoretical and numerical difficulties arising with the non variational version of the approach, consisting of simply solving the first order optimality equations of the problem. Several unsolved issues are indicated in order to motivate further research.
[hal-01435054] Discretization error cancellation in electronic structure calculation: toward a quantitative study
Date: 20 Nov 2017 - 15:35
Desc: It is often claimed that error cancellation plays an essential role in quantum chemistry and first-principle simulation for condensed matter physics and materials science. Indeed, while the energy of a large, or even medium-size, molecular system cannot be estimated numerically within chemical accuracy (typically 1 kcal/mol or 1 mHa), it is considered that the energy difference between two configurations of the same system can be computed in practice within the desired accuracy. The purpose of this paper is to provide a quantitative study of discretization error cancellation. The latter is the error component due to the fact that the model used in the calculation (e.g. Kohn-Sham LDA) must be discretized in a finite basis set to be solved by a computer. We first report comprehensive numerical simulations performed with Abinit [1,2] on two simple chemical systems, the hydrogen molecule on the one hand, and a system consisting of two oxygen atoms and four hydrogen atoms on the other hand. We observe that errors on energy differences are indeed significantly smaller than errors on energies, but that these two quantities asymptotically converge at the same rate when the energy cutoff goes to infinity. We then analyze a simple one-dimensional periodic Schrödinger equation with Dirac potentials, for which analytic solutions are available. This allows us to explain the discretization error cancellation phenomenon on this test case with quantitative mathematical arguments.
[hal-00798246] Control of Molecular orientation and alignement by monotonic schemes
Date: 29 Mar 2013 - 10:41
Desc: Many numerical simulations in quantum (bilinear) control use monotonically convergent algorithms. A relevant time discretization has been proposed for these algorithms in [20]. We present here a way to apply these algorithms to the control of orientation and alignment. Numerical results that illustrate some of the properties of these algorithms are given.
