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-00983649] Diffusion limit of langevin pdf models in weakly inhomogeneous turbulence
Date: 25 4 月 2014 - 16:33
Desc: In this work, we discuss the modelling of transport in Langevin probability density function (PDF) models used to predict turbulent flows. Our focus is on the diffusion limit of these models, i.e. when advection and dissipation are the only active physical processes. In this limit, we show that Langevin PDF models allow for an asymptotic expansion in terms of the ratio of the integral length to the mean gradient length. The main contribution of this expansion yields an evolution of the turbulent kinetic energy equivalent to that given by a k-epsilon model. In particular, the transport of kinetic energy is given by a gradient diffusion term. Interestingly, the identification between PDF and k-epsilon models raises a number of questions concerning the way turbulent transport is closed in PDF models. In order to validate the asymptotic solution, several numerical simulations are performed.
[hal-01224863] FPGA Implementation Of Diffusive Realization For A Distributed Control Operator
Date: 5 11 月 2015 - 11:15
Desc: We focus on the question of real-time computation for optimal distributed filtering or control applicable to MEMS Arrays. We present an algorithm for the realization of a linear operator solution to a functional equation through its application to a Lyapunov operatorial equation associated to the heat equation in one dimension. It is based on the diffusive realization, and turns to be well suited for fined grained parallel computer architecture as Field Programmable Gate Arrays (FPGA). An effective FPGA implementation has been successfully carried out. Here, we report the main implementation steps and the final measured performances.
[hal-01110657] Protocols for staining of bile canalicular and sinusoidal networks of human, mouse and pig livers, three-dimensional reconstruction and quantification of tissue microarchitecture by image processing and analysis.
Date: 28 1 月 2015 - 15:55
Desc: Histological alterations often constitute a fingerprint of toxicity and diseases. The extent to which these alterations are cause or consequence of compromised organ function, and the underlying mechanisms involved is a matter of intensive research. In particular, liver disease is often associated with altered tissue microarchitecture, which in turn may compromise perfusion and functionality. Research in this field requires the development and orchestration of new techniques into standardized processing pipelines that can be used to reproducibly quantify tissue architecture. Major bottlenecks include the lack of robust staining, and adequate reconstruction and quantification techniques. To bridge this gap, we established protocols employing specific antibody combinations for immunostaining, confocal imaging, three-dimensional reconstruction of approximately 100-μm-thick tissue blocks and quantification of key architectural features. We describe a standard procedure termed 'liver architectural staining' for the simultaneous visualization of bile canaliculi, sinusoidal endothelial cells, glutamine synthetase (GS) for the identification of central veins, and DAPI as a nuclear marker. Additionally, we present a second standard procedure entitled 'S-phase staining', where S-phase-positive and S-phase-negative nuclei (stained with BrdU and DAPI, respectively), sinusoidal endothelial cells and GS are stained. The techniques include three-dimensional reconstruction of the sinusoidal and bile canalicular networks from the same tissue block, and robust capture of position, size and shape of individual hepatocytes, as well as entire lobules from the same tissue specimen. In addition to the protocols, we have also established image analysis software that allows relational and hierarchical quantifications of different liver substructures (e.g. cells and vascular branches) and events (e.g. cell proliferation and death). Typical results acquired for routinely quantified parameters in adult mice (C57Bl6/N) include the hepatocyte volume (5,128.3 ± 837.8 μm(3)) and the fraction of the hepatocyte surface in contact with the neighbouring hepatocytes (67.4 ± 6.7 %), sinusoids (22.1 ± 4.8 %) and bile canaliculi (9.9 ± 3.8 %). Parameters of the sinusoidal network that we also routinely quantify include the radius of the sinusoids (4.8 ± 2.25 μm), the branching angle (32.5 ± 11.2°), the length of intersection branches (23.93 ± 5.9 μm), the number of intersection nodes per mm(3) (120.3 × 103 ± 42.1 × 10(3)), the average length of sinusoidal vessel per mm(3) (5.4 × 10(3) ± 1.4 × 10(3)mm) and the percentage of vessel volume in relation to the whole liver volume (15.3 ± 3.9) (mean ± standard deviation). Moreover, the provided parameters of the bile canalicular network are: length of the first-order branches (7.5 ± 0.6 μm), length of the second-order branches (10.9 ± 1.8 μm), length of the dead-end branches (5.9 ± 0.7 μm), the number of intersection nodes per mm(3) (819.1 × 10(3) ± 180.7 × 10(3)), the number of dead-end branches per mm(3) (409.9 × 10(3) ± 95.6 × 10(3)), the length of the bile canalicular network per mm(3) (9.4 × 10(3) ± 0.7 × 10(3) mm) and the percentage of the bile canalicular volume with respect to the total liver volume (3.4 ± 0.005). A particular strength of our technique is that quantitative parameters of hepatocytes and bile canalicular as well as sinusoidal networks can be extracted from the same tissue block. Reconstructions and quantifications performed as described in the current protocols can be used for quantitative mathematical modelling of the underlying mechanisms. Furthermore, protocols are presented for both human and pig livers. The technique is also applicable for both vibratome blocks and conventional paraffin slices.
[hal-01110684] The virtual liver: state of the art and future perspectives
Date: 28 1 月 2015 - 16:45
Desc: [...]
[hal-01787788] A comparison of refinement indicators for the p-adaptive simulation of steady and unsteady flows with discontinuous Galerkin methods
Date: 7 5 月 2018 - 18:45
Desc: This paper presents an analysis of refinement indicators for the simulation of steady and unsteady flows by means of p-adaptive algorithms for discontinuous Galerkin (DG) methods. Residual-error, discretization-error and feature-based indicators are compared by studying their effect on convergence history, computational gain and refinement regions selected by the adaptive algorithm. The analysis is initially carried out on steady flow configurations. Static p-adaptive simulations of the periodic flow past a cylinder at Re = 100 are then performed. Compared to uniform p-refinement, a reduction between 50% and 75% in the number of degrees of freedom is obtained for all test cases considered. The accuracy and efficiency observed for the VMS [1] and spectral decay [2] indicators demonstrate their great potential for the adaptive simulation of unsteady flows.