Stable ground states and self-similar blow-up solutions for the gravitational Vlasov-Manev system

In this work, we study the orbital stability of steady states and the existence of blow-up self-similar solutions to the so-called Vlasov-Manev (VM) system. This system is a kinetic model which has a similar Vlasov structure as the classical Vlasov-Poisson system, but is coupled to a potential in $-1/r- 1/r^2$ (Manev potential) instead of the usual gravitational potential in $-1/r$, and in particular the potential field does not satisfy a Poisson equation but a fractional-Laplacian equation. We first prove the orbital stability of the ground states type solutions which are constructed as minimizers of the Hamiltonian, following the classical strategy: compactness of the minimizing sequences and the rigidity of the flow. However, in driving this analysis, there are two mathematical obstacles: the first one is related to the possible blow-up of solutions to the VM system, which we overcome by imposing a sub-critical condition on the constraints of the variational problem. The second difficulty (and the most important) is related to the nature of the Euler-Lagrange equations (fractional-Laplacian equations) to which classical results for the Poisson equation do not extend. We overcome this difficulty by proving the uniqueness of the minimizer under equimeasurabilty constraints, using only the regularity of the potential and not the fractional-Laplacian Euler-Lagrange equations itself. In the second part of this work, we prove the existence of exact self-similar blow-up solutions to the Vlasov-Manev equation, with initial data arbitrarily close to ground states. This construction is based on a suitable variational problem with equimeasurability constraint

Stability of isotropic steady states for the relativistic Vlasov-Poisson system

?In this work, we study the orbital stability of stationary solutions to the relativistic Vlasov-Manev system. This system is a kinetic model describing the evolution of a stellar system subject to its own gravity with some relativistic corrections. For this system, the orbital stability was proved for isotropic models constructed as minimizers of the Hamiltonian under a subcritical condition. We obtain here this stability for all isotropic models by a non-variationnal approach. We use here a new method developed in [23] for the classical Vlasov-Poisson system. We derive the stability from the monotonicity of the Hamiltonian under suitable generalized symmetric rearrangements and from a Antonov type coer- civity property. We overcome here two new difficulties : the first one is the a priori non-continuity of the potentials, from which a greater control of the re- arrangements is necessary. The second difficulty is related to the homogeneity breaking which does not give the boundedness of the kinetic energy. Indeed, in this paper, we does not suppose any subcritical condition satisfied by the steady states

Etude mathématique de modèles cinétiques pour la gravitation, tenant compte d'effets relativistes : stabilité, solutions autosimilaires.

This document is concerned with the behavior of solutions near ground states for gravitational kinetic systems of Vlasov type. In the first chapter we build by variational methods some stationary states of the Vlasov-Manev system and we prove their orbital stability. The second chapter gives the existence of self-similar blow-up solutions to the "pur Vlasov-Manev" system near ground states. In the third chapter we obtain the orbital stability of a large class of ground states. New methods based on the rigidity of the flow are developed in these three chapters. In particular, they provide the uniqueness of ground states by avoiding the study of non-local Euler-Lagrange equations, they solve a variational problem with non finite constraints and they give the orbital stability of ground states which are not necessary obtained from variational methods. In the fourth chapter, we finish our analysis with a numerical study of the radialy symmetric Vlasov-Poisson system : we give numerical finite difference schemes which conserve the mass and the Hamiltonien of the system.Cette thèse propose une étude mathématique du comportement des solutions autour d'états stationnaires pour des systèmes cinétiques gravitationnels de type Vlasov. Les trois premières parties présentent des résultats théoriques. Tout d'abord, par une ap- proche variationnelle, on construit des états stationnaires pour le système de Vlasov-Manev et on montre leur stabilité orbitale. Ensuite, on prouve l'existence de solutions autosimi- laires explosant en temps fini autour d'un état stationnaire pour le système dit de "Vlasov- Manev pur". Enfin on démontre la stabilité orbitale d'une large classe d'états stationnaires pour le système de Vlasov-Poisson relativiste. Ces résultats s'appuient sur de nouvelles méthodes utilisant la rigidité du flot. Celles-ci permettent notamment d'obtenir la séparation d'états stationnaires en évitant l'étude d'équations d'Euler-Lagrange non locales, de résoudre un problème variationnel avec une infinité de contraintes et de prouver la stabilité orbitale de solutions stationnaires non nécessairement obtenues de manière variationnelle. Dans la quatrième et dernière partie, nous étudions numériquement l'équation de Vlasov-Poisson en coordonnées radiales. Après avoir choisi un système de variables adéquates, nous présentons des schémas numériques de différences finies conservant la masse et le Hamiltonien du système

Étude mathématique de modèles cinétiques pour la gravitation, tenant compte d'effets relativistes (stabilité, solutions autosimilaires)

Cette thèse propose une étude mathématique du comportement des solutions autour d'états stationnaires pour des systèmes cinétiques gravitationnels de type Vlasov. Les trois premières parties présentent des résultats théoriques. Tout d'abord, par une approche variationnelle, on construit des états stationnaires pour le système de Vlasov-Manev et on montre leur stabilité orbitale. Ensuite, on prouve l'existence de solutions autosimilaires explosant en temps fini autour d'un état stationnaire pour le système dit de Vlasov-Manev pur . Enfin on démontre la stabilité orbitale d'une large classe d'états stationnaires pour le système de Vlasov-Poisson relativiste. Ces résultats s'appuient sur de nouvelles méthodes utilisant la rigidité du flot. Celles-ci permettent notamment d'obtenir la séparation d'états stationnaires en évitant l'étude d'équations d'Euler-Lagrange non locales, de résoudre un problème variationnel avec une infinité de contraintes et de prouver la stabilité orbitale de solutions stationnaires non nécessairement obtenues de manière variationnelle. Dans la quatrième et dernière partie, nous étudions numériquement l'équation de Vlasov-Poisson en coordonnées radiales. Après avoir choisi un système de variables adéquates, nous présentons des schémas numériques de différences finies conservant la masse et le Hamiltonien du système.This document is concerned with the behavior of solutions near ground states for gravitational kinetic systems of Vlasov type. In the first chapter we build by variational methods some stationary states of the Vlasov-Manev system and we prove their orbital stability. The second chapter gives the existence of self-similar blow-up solutions to the pur Vlasov- Manev system near ground states. In the third chapter we obtain the orbital stability of a large class of ground states. New methods based on the rigidity of the flow are developed in these three chapters. In particular, they provide the uniqueness of ground states by avoiding the study of non-local Euler-Lagrange equations, they solve a variational problem with non finite constraints and they give the orbital stability of ground states which are not necessary obtained from variational methods. In the fourth chapter, we finish our analysis with a numerical study of the radialy symmetric Vlasov-Poisson system : we give numerical finite difference schemes which conserve the mass and the Hamiltonien of the system.RENNES1-BU Sciences Philo (352382102) / SudocSudocFranceF

The eSpiro Ventilator: An Open-Source Response to a Worldwide Pandemic

International audienceObjective: To address the issue of ventilator shortages, our group (eSpiro Network) developed a freely replicable, open-source hardware ventilator. Design: We performed a bench study. Setting: Dedicated research room as part of an ICU affiliated to a university hospital. Subjects: We set the lung model with three conditions of resistance and linear compliance for mimicking different respiratory mechanics of representative intensive care unit (ICU) patients. Interventions: The performance of the device was tested using the ASL5000 lung model. Measurements and Main Results: Twenty-seven conditions were tested. All the measurements fell within the ±10% limits for the tidal volume (VT). The volume error was influenced by the mechanical condition (p = 5.9 × 10−15) and the PEEP level (P = 1.1 × 10−12) but the clinical significance of this finding is likely meaningless (maximum −34 mL in the error). The PEEP error was not influenced by the mechanical condition (p = 0.25). Our experimental results demonstrate that the eSpiro ventilator is reliable to deliver VT and PEEP accurately in various respiratory mechanics conditions. Conclusions: We report a low-cost, easy-to-build ventilator, which is reliable to deliver VT and PEEP in passive invasive mechanical ventilation

Determination of the absolute configuration of phosphinic analogues of glutamate

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Is metabotropic glutamate receptor mGlu4R a good target to treat Parkinson's disease symptoms? Design and evaluation of potent and selective agonists

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A new Selective Metabotropic Glutamate Receptor type 4 Agonist Reveals New ways to Develop Subtype Selective Orthosteric Ligands with Potential Therapeutic Effects

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A novel selective metabotropic glutamate receptor 4 agonist reveals new possibilities for developing subtype selective ligands with therapeutic potential.

International audienceMetabotropic glutamate (mGlu) receptors are promising targets to treat numerous brain disorders. So far, allosteric modulators are the only subtype selective ligands, but pure agonists still have strong therapeutic potential. Here, we aimed at investigating the possibility of developing subtype-selective agonists by extending the glutamate-like structure to hit a nonconsensus binding area. We report the properties of the first mGlu4-selective orthosteric agonist, derived from a virtual screening hit, LSP4-2022 using cell-based assays with recombinant mGlu receptors [EC(50): 0.11 ± 0.02, 11.6 ± 1.9, 29.2 ± 4.2 μM (n>19) in calcium assays on mGlu4, mGlu7, and mGlu8 receptors, respectively, with no activity at the group I and -II mGlu receptors at 100 μM]. LSP4-2022 inhibits neurotransmission in cerebellar slices from wild-type but not mGlu4 receptor-knockout mice. In vivo, it possesses antiparkinsonian properties after central or systemic administration in a haloperidol-induced catalepsy test, revealing its ability to cross the blood-brain barrier. Site-directed mutagenesis and molecular modeling was used to identify the LSP4-2022 binding site, revealing interaction with both the glutamate binding site and a variable pocket responsible for selectivity. These data reveal new approaches for developing selective, hydrophilic, and brain-penetrant mGlu receptor agonists, offering new possibilities to design original bioactive compounds with therapeutic potential

Automatic removal of identifying information in official EU languages for public administrations : the MAPA Project

The European MAPA (Multilingual Anonymisation for Public Administrations) project aims at developing an open-source solution for automatic de-identification of medical and legal documents. We introduce here the context, partners and aims of the project, and report on preliminary results.peer-reviewe