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-01413795] Mathematics of Pharmacokinetics and Pharmacodynamics: Diversity of Topics, Models and Methods
Date: 11 Dec 2016 - 10:06
Desc: A short review on pharmacokinetics-pharmacodynamics (PK-PD) presented below aims to show the evolution of some concepts and ideas in this field. Some of them are developed in more detail in the papers of this issue. The key question for a practical application of PK-PD models is the ability to estimate the model parameters using patients data. In [1] a novel approach to an accurate quantification of the uncertainty in parameter estimates attributed to inter-individual variability is proposed. The analyzed PK-PD model is formulated as a compartmental ODE system. The methodology of recognizing and capturing the uncertainty in predicted quantities of interest due to inter-individual variability when the individual is not available for repeated measurements may prove to be invaluable in the risk assessment of future experiments and drug applications. Anticancer molecular PK-PD in a cell population dynamics model with drug delivery optimisation is discussed in [2]. The works [3] and [4] deal with various aspects of hemostasis modelling, and [5] with metabolic aspects in a whole-body setting. These studies represent the diversity of aspects of PK-PD modelling nowadays: theoretical about parameter estimation in general versus applied to medical questions in particular, localised cell population versus whole-body settings, cell population and whole-body versus patient population settings.
[hal-00112592] Monotonic time-discretized schemes in quantum control
Date: 9 Nov 2006 - 11:38
Desc: [...]
[hal-00903715] A Posteriori Analysis of a Non-Linear Gross-Pitaevskii type Eigenvalue Problem
Date: 12 Nov 2013 - 18:55
Desc: In this paper, we provide a first full {\it a posteriori} error analysis for variational approximations of the ground state eigenvector of a non-linear elliptic problems of the Gross-Pitaevskii type, more precisely of the form $-\Delta u + Vu + u^3 = \lambda u$, $\|u\|_{L^2}=1$, with periodic boundary conditions in one dimension. Denoting by $(u_N,\lambda_N)$ the variational approximation of the ground state eigenpair $(u,\lambda)$ based on a Fourier spectral approximation and $(u_N^k,\lambda_N^k)$ the approximate solution at the $k^{th}$ iteration of an algorithm used to solve the non-linear problem, we first provide a precised \textit{a priori} analysis of the convergence rates of $\|u-u_N\|_{H^1}$, $\|u-u_N\|_{L^2}$, $|\lambda-\lambda_N|$ and then present original \textit{a posteriori} estimates in the convergence rates of $\|u_-u_N^k\|_{H^1}$ when $N$ and $k$ go to infinity. We introduce a residue standing for the global error $R_N^k=-\Delta u_N^k+Vu_N^k+(u_N^k)^3-\lambda_N^ku_N^k$ and we divide it into two residues characterizing respectively the error due to the discretization of the space and the finite number of iterations when solving the problem numerically. We show that the numerical results are coherent with this \textit{a posteriori} analysis.
[hal-00174797] A general, multipurpose interpolation procedure: the magic points
Date: 25 Sep 2007 - 13:10
Desc: Lagrangian interpolation is a classical way to approximate general functions by finite sums of well chosen, pre-definite, linearly independent generating functions; it is much simpler to implement than determining the best fits with respect to some Banach (or even Hilbert) norms. In addition, only partial knowledge is required (here values on some set of points). The problem of defining the best sample of points is nevertheless rather complex and is in general not solved. In this paper we propose a way to derive such sets of points. We do not claim that the points resulting from the construction explained here are optimal in any sense. Nevertheless, the resulting interpolation method is proven to work under certain hypothesis, the process is very general and simple to implement, and compared to situations where the best behavior is known, it is relatively competitive.