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Laboratoire Jacques-Louis Lions

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Université Paris Diderot, CNRS

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

[halsde-00790602] Applying ecological and evolutionary theory to cancer: a long and winding road

Date: 20 Feb 2013 - 15:22

Desc: Since the mid 1970s, cancer has been described as a process of Darwinian evolution, with somatic cellular selection and evolution being the fundamental processes leading to malignancy and its many manifestations (neoangiogenesis, evasion of the immune system, metastasis, and resistance to therapies). Historically, little attention has been placed on applications of evolutionary biology to understanding and controlling neoplastic progression and to prevent therapeutic failures. This is now beginning to change, and there is a growing international interest in the interface between cancer and evolutionary biology. The objective of this introduction is first to describe the basic ideas and concepts linking evolutionary biology to cancer. We then present four major fronts where the evolutionary perspective is most developed, namely laboratory and clinical models, mathematical models, databases, and techniques and assays. Finally, we discuss several of the most promising challenges and future prospects in this interdisciplinary research direction in the war against cancer.

[hal-04023026] Mucus and ciliated cells of human lung : splitting strategies for particle methods and 3D stokes flows

Date: 10 Mar 2023 - 10:57

Desc: Lung walls are covered by a film of mucus, whose motility is fundamental for a healthy behavior. Indeed, mucus traps inhaled aerosols (bacteria, dust, ...), and moves from smallest to largest airways, until it reaches esophagus where is it swallowed or expectorated. A lot of biological parameters are responsible for mucus motion [6], such as the vibrations of ciliated cells covering lung walls (cilia height, frequency, ...), mucus/air interaction, water saturation in mucin network, mucus thickness.

[hal-01436949] Incoherent shock waves in long-range optical turbulence

Date: 16 Ene 2017 - 18:21

Desc: Considering the nonlinear Schrödinger (NLS) equation as a representative model, we report a unified presentation of different forms of incoherent shock waves that emerge in the long-range interaction regime of a turbulent optical wave system. These incoherent singularities can develop either in the temporal domain through a highly noninstantaneous nonlinear response, or in the spatial domain through a highly nonlocal nonlinearity. In the temporal domain, genuine dispersive shock waves (DSW) develop in the spectral dynamics of the random waves, despite the fact that the causality condition inherent to the response function breaks the Hamiltonian structure of the NLS equation. Such spectral incoherent DSWs are described in detail by a family of singular integro-differential kinetic equations, e.g. Benjamin–Ono equation, which are derived from a nonequilibrium kinetic formulation based on the weak Langmuir turbulence equation. In the spatial domain, the system is shown to exhibit a large scale global collective behavior, so that it is the fluctuating field as a whole that develops a singularity, which is inherently an incoherent object made of random waves. Despite the Hamiltonian structure of the NLS equation, the regularization of such a collective incoherent shock does not require the formation of a DSW — the regularization is shown to occur by means of a different process of coherence degradation at the shock point. We show that the collective incoherent shock is responsible for an original mechanism of spontaneous nucleation of a phase-space hole in the spectrogram dynamics. The robustness of such a phase-space hole is interpreted in the light of incoherent dark soliton states, whose different exact solutions are derived in the framework of the long-range Vlasov formalism.

[hal-01541093] Distributed synaptic weights in a LIF neural network and learning rules

Date: 17 Jun 2017 - 13:23

Desc: Leaky integrate-and-fire (LIF) models are mean-field limits, with a large number of neurons, used to describe neural networks. We consider inhomogeneous networks structured by a connec-tivity parameter (strengths of the synaptic weights) with the effect of processing the input current with different intensities. We first study the properties of the network activity depending on the distribution of synaptic weights and in particular its discrimination capacity. Then, we consider simple learning rules and determine the synaptic weight distribution it generates. We outline the role of noise as a selection principle and the capacity to memorized a learned signal.