31 research outputs found
On the global evolution of self-gravitating matter. Nonlinear interactions in Gowdy symmetry
We are interested in the evolution of a compressible fluid under its
self-generated gravitational field. Assuming here Gowdy symmetry, we
investigate the algebraic structure of the Euler equations satisfied by the
mass density and velocity field. We exhibit several interaction functionals
that provide us with a uniform control on weak solutions in suitable Sobolev
norms or in bounded variation. These functionals allow us to study the local
regularity and nonlinear stability properties of weakly regular fluid flows
governed by the Euler-Gowdy system. In particular for the Gowdy equations, we
prove that a spurious matter field arises under weak convergence, and we
establish the nonlinear stability of weak solutions.Comment: 37 pages. v2: fix typos to match version published in 201
Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds
Motivated by many applications (geophysical flows, general relativity), we
attempt to set the foundations for a study of entropy solutions to nonlinear
hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold.
The flux of the conservation laws is viewed as a vector-field on the manifold
and depends on the unknown function as a parameter. We introduce notions of
entropy solutions in the class of bounded measurable functions and in the class
of measure-valued mappings. We establish the well-posedness theory for
conservation laws on a manifold, by generalizing both Kruzkov's and DiPerna's
theories originally developed in the Euclidian setting. The class of {\sl
geometry-compatible} (as we call it) conservation laws is singled out as an
important case of interest, which leads to robust estimates independent
of the geometry of the manifold. On the other hand, general conservation laws
solely enjoy the contraction property and leads to a unique contractive
semi-group of entropy solutions. Our framework allows us to construct entropy
solutions on a manifold via the vanishing diffusion method or the finite volume
method.Comment: 30 pages. This is Part 1 of a serie
Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces
For spacetimes containing singularity hypersurfaces we propose a general
notion of junction conditions based on a prescribed singularity scattering map,
as we call it, and we introduce the notion of a cyclic spacetime (also called a
multiverse) consisting of spacetime domains bounded by spacelike or timelike
singularity hypersurfaces, across which our scattering map is applied. A local
existence theory is established here while, in a companion paper, we construct
plane-symmetric cyclic spacetimes. We study the singularity data space
consisting of the suitably rescaled metric, extrinsic curvature, and matter
fields which can be prescribed on each side of the singularity, and for the
class of so-called quiescent singularities we establish restrictions that a
singularity scattering map must satisfy. We obtain a full characterization of
all scattering maps that are covariant and ultralocal, in a sense we define
and, in particular, we distinguish between, on the one hand, three laws of
bouncing cosmology of universal nature and, on the other hand, model-dependent
junction conditions. The theory proposed in this paper applies to spacelike and
timelike hypersurfaces and without symmetry restriction, and encompasses
bouncing-cosmology scenarios, both in string theory and in loop quantum
cosmology, and puts strong restrictions on their possible explicit
realizations.Comment: 56 pages. Construction of plane symmetric cyclic spacetimes moved to
a separate pape
Universal scattering laws for bouncing cosmology
Bouncing cosmologies can arise from various gravity theories. We model them
through a singularity scattering map, as we call it, relating large scale
geometries before and after the bounce. By classifying all suitably local maps
we uncover universal laws (scaling of Kasner exponents, canonical
transformation of matter). We study the singularity scattering map for Bianchi
I bounces in string theory, loop quantum cosmology and modified matter models:
our classification then determines how general spatial inhomogeneities and
anisotropies (without BKL oscillations) are transmitted through bounces.Comment: 5 page
Extracorporeal Membrane Oxygenation for Severe Acute Respiratory Distress Syndrome associated with COVID-19: An Emulated Target Trial Analysis.
RATIONALE: Whether COVID patients may benefit from extracorporeal membrane oxygenation (ECMO) compared with conventional invasive mechanical ventilation (IMV) remains unknown. OBJECTIVES: To estimate the effect of ECMO on 90-Day mortality vs IMV only Methods: Among 4,244 critically ill adult patients with COVID-19 included in a multicenter cohort study, we emulated a target trial comparing the treatment strategies of initiating ECMO vs. no ECMO within 7 days of IMV in patients with severe acute respiratory distress syndrome (PaO2/FiO2 <80 or PaCO2 ≥60 mmHg). We controlled for confounding using a multivariable Cox model based on predefined variables. MAIN RESULTS: 1,235 patients met the full eligibility criteria for the emulated trial, among whom 164 patients initiated ECMO. The ECMO strategy had a higher survival probability at Day-7 from the onset of eligibility criteria (87% vs 83%, risk difference: 4%, 95% CI 0;9%) which decreased during follow-up (survival at Day-90: 63% vs 65%, risk difference: -2%, 95% CI -10;5%). However, ECMO was associated with higher survival when performed in high-volume ECMO centers or in regions where a specific ECMO network organization was set up to handle high demand, and when initiated within the first 4 days of MV and in profoundly hypoxemic patients. CONCLUSIONS: In an emulated trial based on a nationwide COVID-19 cohort, we found differential survival over time of an ECMO compared with a no-ECMO strategy. However, ECMO was consistently associated with better outcomes when performed in high-volume centers and in regions with ECMO capacities specifically organized to handle high demand. This article is open access and distributed under the terms of the Creative Commons Attribution Non-Commercial No Derivatives License 4.0 (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Time to Switch to Second-line Antiretroviral Therapy in Children With Human Immunodeficiency Virus in Europe and Thailand.
Background: Data on durability of first-line antiretroviral therapy (ART) in children with human immunodeficiency virus (HIV) are limited. We assessed time to switch to second-line therapy in 16 European countries and Thailand. Methods: Children aged <18 years initiating combination ART (≥2 nucleoside reverse transcriptase inhibitors [NRTIs] plus nonnucleoside reverse transcriptase inhibitor [NNRTI] or boosted protease inhibitor [PI]) were included. Switch to second-line was defined as (i) change across drug class (PI to NNRTI or vice versa) or within PI class plus change of ≥1 NRTI; (ii) change from single to dual PI; or (iii) addition of a new drug class. Cumulative incidence of switch was calculated with death and loss to follow-up as competing risks. Results: Of 3668 children included, median age at ART initiation was 6.1 (interquartile range (IQR), 1.7-10.5) years. Initial regimens were 32% PI based, 34% nevirapine (NVP) based, and 33% efavirenz based. Median duration of follow-up was 5.4 (IQR, 2.9-8.3) years. Cumulative incidence of switch at 5 years was 21% (95% confidence interval, 20%-23%), with significant regional variations. Median time to switch was 30 (IQR, 16-58) months; two-thirds of switches were related to treatment failure. In multivariable analysis, older age, severe immunosuppression and higher viral load (VL) at ART start, and NVP-based initial regimens were associated with increased risk of switch. Conclusions: One in 5 children switched to a second-line regimen by 5 years of ART, with two-thirds failure related. Advanced HIV, older age, and NVP-based regimens were associated with increased risk of switch
On the global evolution of self-gravitating matter. Functionals for compressible fluids in Gowdy symmetry
We are interested in the evolution of a compressible fluid under its self-generated gravitational field. Assuming here Gowdy symmetry, we investigate the algebraic structure of the Euler equations satisfied by the mass density and velocity field. We exhibit several functionals that provide us with a uniform control on weak solutions in suitable Sobolev norms or in bounded variation. These functionals allow us to study the local regularity and nonlinear stability properties of weakly regular fluid flows governed by the Euler-Gowdy system under consideration. In particular for the Gowdy equations, we prove that a spurious matter field arises under weak convergence, and we establish the nonlinear stability of weak solutions