Parametrix construction and numerical approximation of resonances of azimuthal harmonics of the charged Klein-Gordon operator on general cosmological slowly accelerating and rotating charged black hole type spacetimes

We show the index 0 Fredholm property of the spectral family of the azimuthal harmonics of the charged Klein-Gordon operator on general cosmological slowly accelerating and rotating charged black hole type spacetimes, including the De Sitter-Kerr-Newman family, using a parametrix construction for abstract totally characteristic operators. We then present a numerical scheme to compute the meromorphic poles of the inverse of the spectral family and provide an explicit estimate of the numerical error

Existence of exponentially growing finite energy solutions for the charged Klein-Gordon equation on the De Sitter-Kerr-Newman metric

We show the existence of exponentially growing finite energy solutions for the charged Klein-Gordon equation on the De Sitter-Kerr-Newman metric for small charge and mass of the field and small angular momentum of the black hole. The mechanism behind is that the zero resonance that exists for zero charge, mass and angular momentum moves into the upper half plane

Hyperoxemia and excess oxygen use in early acute respiratory distress syndrome : Insights from the LUNG SAFE study

Publisher Copyright: © 2020 The Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.Background: Concerns exist regarding the prevalence and impact of unnecessary oxygen use in patients with acute respiratory distress syndrome (ARDS). We examined this issue in patients with ARDS enrolled in the Large observational study to UNderstand the Global impact of Severe Acute respiratory FailurE (LUNG SAFE) study. Methods: In this secondary analysis of the LUNG SAFE study, we wished to determine the prevalence and the outcomes associated with hyperoxemia on day 1, sustained hyperoxemia, and excessive oxygen use in patients with early ARDS. Patients who fulfilled criteria of ARDS on day 1 and day 2 of acute hypoxemic respiratory failure were categorized based on the presence of hyperoxemia (PaO2 > 100 mmHg) on day 1, sustained (i.e., present on day 1 and day 2) hyperoxemia, or excessive oxygen use (FIO2 ≥ 0.60 during hyperoxemia). Results: Of 2005 patients that met the inclusion criteria, 131 (6.5%) were hypoxemic (PaO2 < 55 mmHg), 607 (30%) had hyperoxemia on day 1, and 250 (12%) had sustained hyperoxemia. Excess FIO2 use occurred in 400 (66%) out of 607 patients with hyperoxemia. Excess FIO2 use decreased from day 1 to day 2 of ARDS, with most hyperoxemic patients on day 2 receiving relatively low FIO2. Multivariate analyses found no independent relationship between day 1 hyperoxemia, sustained hyperoxemia, or excess FIO2 use and adverse clinical outcomes. Mortality was 42% in patients with excess FIO2 use, compared to 39% in a propensity-matched sample of normoxemic (PaO2 55-100 mmHg) patients (P = 0.47). Conclusions: Hyperoxemia and excess oxygen use are both prevalent in early ARDS but are most often non-sustained. No relationship was found between hyperoxemia or excessive oxygen use and patient outcome in this cohort. Trial registration: LUNG-SAFE is registered with ClinicalTrials.gov, NCT02010073publishersversionPeer reviewe

Decay of the Local Energy for the Charged Klein–Gordon Equation in the Exterior De Sitter–Reissner–Nordström Spacetime

International audienceWe show decay of the local energy of solutions of the charged Klein–Gordon equation in the exterior De Sitter–Reissner–Nordström spacetime by means of a resonance expansion of the local propagator

L'équation chargée de Klein-Gordon en métrique de De Sitter-Reissner-Nordström

In this thesis, we study the charged Klein-Gordon equation in the exterior De Sitter-Reissner-Nordström spacetime. We first show decay in time of the local energy by means of a resonance expansion of the local propagator. Then we construct a scattering theory for the equation and give a geometric interpretation in an extended spacetime of asymptotic completeness in terms of traces at horizons. Exponential decay of local energy for solutions of the wave equation in this extension up to and through horizons is obtained harmonic by harmonic. We next turn to a numerical study of an abstract Klein-Gordon type equation and introduce a scheme which approximate solutions up to an error we can control. Finally, we propose a numerical method to localize low frequency resonances.Many results in the thesis are prerequisite to the construction of the Unruh state satisfying the Hadamard property for the charged Klein-Gordon equation in the De Sitter-Reissner-Nordström spacetime.Dans cette thèse, nous étudions l'équation chargée de Klein-Gordon dans l'espace-temps extérieur de De Sitter-Reissner-Nordström. Nous montrons en premier lieu la décroissance en temps de l'énergie locale aux moyens d'une expansion en termes de résonances du propagateur local. Nous construisons alors une théorie de la diffusion pour l'équation et donnons une interprétation géométrique dans un espace-temps étendu de la complétude asymptotique en termes de traces aux horizons. La décroissance exponentielle de l'énergie locale pour les solutions de l'équation d'onde dans cette extension jusque et au travers des horizons est obtenue harmonique par harmonique. Nous considérons ensuite une étude numérique d'une équation de type Klein-Gordon et introduisons un schéma qui approche les solutions avec une erreur que l'on peut contrôler. Finalement,nous proposons une méthode numérique pour localiser les résonances à basse fréquence.Beaucoup de résultats dans cette thèse sont des prérequis à la construction de l'état de Unruh satisfaisant la propriété de Hadamard pour l'équation de Klein-Gordon chargée dans l'espace-temps extérieur de De Sitter-Reissner-Nordström

Decay of the Local Energy for the Charged Klein-Gordon Equation in the Exterior De Sitter-Reissner-Nordström Spacetime

We show decay of the local energy of solutions of the charged Klein-Gordon equation in the exterior De Sitter-Reissner-Nordström spacetime by means of a resonance expansion of the local propagator.On montre la décroissance de l'énergie locale de solutions de l'équation de Klein-Gordon chargée dans l'espace-temps extérieur de De Sitter-Reissner-Nordström au moyen d'une expansion en terme de résonances du propagateur local

Scattering Theory for the Charged Klein–Gordon Equation in the Exterior De Sitter–Reissner–Nordström Spacetime

International audienceWe show asymptotic completeness for the charged Klein–Gordon equation in the exterior De Sitter–Reissner–Nordström spacetime when the product of the charge of the black with the charge of the Klein-Gordon field is small enough. We then interpret scattering as asymptotic transports along principal null geodesics in a Kaluza–Klein extension of the original spacetime

The charged Klein-Gordon equation in the De Sitter-Reissner-Nordström metric

Dans cette thèse, nous étudions l'équation chargée de Klein-Gordon dans l'espace-temps extérieur de De Sitter-Reissner-Nordström. Nous montrons en premier lieu la décroissance en temps de l'énergie locale aux moyens d'une expansion en termes de résonances du propagateur local. Nous construisons alors une théorie de la diffusion pour l'équation et donnons une interprétation géométrique dans un espace-temps étendu de la complétude asymptotique en termes de traces aux horizons. La décroissance exponentielle de l'énergie locale pour les solutions de l'équation d'onde dans cette extension jusque et au travers des horizons est obtenue harmonique par harmonique. Nous considérons ensuite une étude numérique d'une équation de type Klein-Gordon et introduisons un schéma qui approche les solutions avec une erreur que l'on peut contrôler. Finalement,nous proposons une méthode numérique pour localiser les résonances à basse fréquence.Beaucoup de résultats dans cette thèse sont des prérequis à la construction de l'état de Unruh satisfaisant la propriété de Hadamard pour l'équation de Klein-Gordon chargée dans l'espace-temps extérieur de De Sitter-Reissner-Nordström.In this thesis, we study the charged Klein-Gordon equation in the exterior De Sitter-Reissner-Nordström spacetime. We first show decay in time of the local energy by means of a resonance expansion of the local propagator. Then we construct a scattering theory for the equation and give a geometric interpretation in an extended spacetime of asymptotic completeness in terms of traces at horizons. Exponential decay of local energy for solutions of the wave equation in this extension up to and through horizons is obtained harmonic by harmonic. We next turn to a numerical study of an abstract Klein-Gordon type equation and introduce a scheme which approximate solutions up to an error we can control. Finally, we propose a numerical method to localize low frequency resonances.Many results in the thesis are prerequisite to the construction of the Unruh state satisfying the Hadamard property for the charged Klein-Gordon equation in the De Sitter-Reissner-Nordström spacetime