Long-time behavior of the Stokes-transport system in a channel

The coupling between the transport equation for the density and the Stokes equation is considered in a periodic channel. More precisely, the density is advected by pure transport by a velocity field given by the Stokes equation with source force coming from the gravity due to differences in the density. Dirichlet boundary conditions are taken for the velocity field on the bottom and top of the channel, and periodic conditions in the horizontal variable. We prove that the affine stratified density profile is stable under small perturbations in Sobolev spaces and prove convergence of the density to another limiting stratified density profile for large time with an explicit algebraic decay rate. Moreover, we are able to precisely identify the limiting profile as the decreasing vertical rearrangement of the initial density. Finally, we study boundary layers formation to precisely characterize the long-time behavior beyond the constant limiting profile and enlighten the optimal decay rate.Comment: 69 page

Unitary representations of the Galilean line group: Quantum mechanical principle of equivalence

We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on the Galilean line group, the semidirect product of the real line and the group of analytic functions from the real line to the Euclidean group in three dimensions. This group provides transformations between all inertial and non-inertial reference frames and contains the Galilei group as a subgroup. We construct a certain class of unitary representations of the Galilean line group and show that these representations determine the structure of quantum mechanics in non-inertial reference frames. Our representations of the Galilean line group contain the usual unitary projective representations of the Galilei group, but have a more intricate cocycle structure. The transformation formula for the Hamiltonian under the Galilean line group shows that in a non-inertial reference frame it acquires a fictitious potential energy term that is proportional to the inertial mass, suggesting the equivalence of inertial mass and gravitational mass in quantum mechanics

Saliva-based detection of COVID-19 infection in a real-world setting using reagent-free Raman spectroscopy and machine learning

ABSTRACT: SIGNIFICANCE: The primary method of COVID-19 detection is reverse transcription polymerase chain reaction (RT-PCR) testing. PCR test sensitivity may decrease as more variants of concern arise and reagents may become less specific to the virus. AIM: We aimed to develop a reagent-free way to detect COVID-19 in a real-world setting with minimal constraints on sample acquisition. The machine learning (ML) models involved could be frequently updated to include spectral information about variants without needing to develop new reagents. APPROACH: We present a workflow for collecting, preparing, and imaging dried saliva supernatant droplets using a non-invasive, label-free technique-Raman spectroscopy-to detect changes in the molecular profile of saliva associated with COVID-19 infection. RESULTS: We used an innovative multiple instance learning-based ML approach and droplet segmentation to analyze droplets. Amongst all confounding factors, we discriminated between COVID-positive and COVID-negative individuals yielding receiver operating coefficient curves with an area under curve (AUC) of 0.8 in both males (79% sensitivity and 75% specificity) and females (84% sensitivity and 64% specificity). Taking the sex of the saliva donor into account increased the AUC by 5%. CONCLUSION: These findings may pave the way for new rapid Raman spectroscopic screening tools for COVID-19 and other infectious diseases

Effect of Hydrocortisone on Mortality and Organ Support in Patients With Severe COVID-19: The REMAP-CAP COVID-19 Corticosteroid Domain Randomized Clinical Trial.

Importance: Evidence regarding corticosteroid use for severe coronavirus disease 2019 (COVID-19) is limited. Objective: To determine whether hydrocortisone improves outcome for patients with severe COVID-19. Design, Setting, and Participants: An ongoing adaptive platform trial testing multiple interventions within multiple therapeutic domains, for example, antiviral agents, corticosteroids, or immunoglobulin. Between March 9 and June 17, 2020, 614 adult patients with suspected or confirmed COVID-19 were enrolled and randomized within at least 1 domain following admission to an intensive care unit (ICU) for respiratory or cardiovascular organ support at 121 sites in 8 countries. Of these, 403 were randomized to open-label interventions within the corticosteroid domain. The domain was halted after results from another trial were released. Follow-up ended August 12, 2020. Interventions: The corticosteroid domain randomized participants to a fixed 7-day course of intravenous hydrocortisone (50 mg or 100 mg every 6 hours) (n = 143), a shock-dependent course (50 mg every 6 hours when shock was clinically evident) (n = 152), or no hydrocortisone (n = 108). Main Outcomes and Measures: The primary end point was organ support-free days (days alive and free of ICU-based respiratory or cardiovascular support) within 21 days, where patients who died were assigned -1 day. The primary analysis was a bayesian cumulative logistic model that included all patients enrolled with severe COVID-19, adjusting for age, sex, site, region, time, assignment to interventions within other domains, and domain and intervention eligibility. Superiority was defined as the posterior probability of an odds ratio greater than 1 (threshold for trial conclusion of superiority >99%). Results: After excluding 19 participants who withdrew consent, there were 384 patients (mean age, 60 years; 29% female) randomized to the fixed-dose (n = 137), shock-dependent (n = 146), and no (n = 101) hydrocortisone groups; 379 (99%) completed the study and were included in the analysis. The mean age for the 3 groups ranged between 59.5 and 60.4 years; most patients were male (range, 70.6%-71.5%); mean body mass index ranged between 29.7 and 30.9; and patients receiving mechanical ventilation ranged between 50.0% and 63.5%. For the fixed-dose, shock-dependent, and no hydrocortisone groups, respectively, the median organ support-free days were 0 (IQR, -1 to 15), 0 (IQR, -1 to 13), and 0 (-1 to 11) days (composed of 30%, 26%, and 33% mortality rates and 11.5, 9.5, and 6 median organ support-free days among survivors). The median adjusted odds ratio and bayesian probability of superiority were 1.43 (95% credible interval, 0.91-2.27) and 93% for fixed-dose hydrocortisone, respectively, and were 1.22 (95% credible interval, 0.76-1.94) and 80% for shock-dependent hydrocortisone compared with no hydrocortisone. Serious adverse events were reported in 4 (3%), 5 (3%), and 1 (1%) patients in the fixed-dose, shock-dependent, and no hydrocortisone groups, respectively. Conclusions and Relevance: Among patients with severe COVID-19, treatment with a 7-day fixed-dose course of hydrocortisone or shock-dependent dosing of hydrocortisone, compared with no hydrocortisone, resulted in 93% and 80% probabilities of superiority with regard to the odds of improvement in organ support-free days within 21 days. However, the trial was stopped early and no treatment strategy met prespecified criteria for statistical superiority, precluding definitive conclusions. Trial Registration: ClinicalTrials.gov Identifier: NCT02735707

Effect of angiotensin-converting enzyme inhibitor and angiotensin receptor blocker initiation on organ support-free days in patients hospitalized with COVID-19

IMPORTANCE Overactivation of the renin-angiotensin system (RAS) may contribute to poor clinical outcomes in patients with COVID-19. Objective To determine whether angiotensin-converting enzyme (ACE) inhibitor or angiotensin receptor blocker (ARB) initiation improves outcomes in patients hospitalized for COVID-19. DESIGN, SETTING, AND PARTICIPANTS In an ongoing, adaptive platform randomized clinical trial, 721 critically ill and 58 non–critically ill hospitalized adults were randomized to receive an RAS inhibitor or control between March 16, 2021, and February 25, 2022, at 69 sites in 7 countries (final follow-up on June 1, 2022). INTERVENTIONS Patients were randomized to receive open-label initiation of an ACE inhibitor (n = 257), ARB (n = 248), ARB in combination with DMX-200 (a chemokine receptor-2 inhibitor; n = 10), or no RAS inhibitor (control; n = 264) for up to 10 days. MAIN OUTCOMES AND MEASURES The primary outcome was organ support–free days, a composite of hospital survival and days alive without cardiovascular or respiratory organ support through 21 days. The primary analysis was a bayesian cumulative logistic model. Odds ratios (ORs) greater than 1 represent improved outcomes. RESULTS On February 25, 2022, enrollment was discontinued due to safety concerns. Among 679 critically ill patients with available primary outcome data, the median age was 56 years and 239 participants (35.2%) were women. Median (IQR) organ support–free days among critically ill patients was 10 (–1 to 16) in the ACE inhibitor group (n = 231), 8 (–1 to 17) in the ARB group (n = 217), and 12 (0 to 17) in the control group (n = 231) (median adjusted odds ratios of 0.77 [95% bayesian credible interval, 0.58-1.06] for improvement for ACE inhibitor and 0.76 [95% credible interval, 0.56-1.05] for ARB compared with control). The posterior probabilities that ACE inhibitors and ARBs worsened organ support–free days compared with control were 94.9% and 95.4%, respectively. Hospital survival occurred in 166 of 231 critically ill participants (71.9%) in the ACE inhibitor group, 152 of 217 (70.0%) in the ARB group, and 182 of 231 (78.8%) in the control group (posterior probabilities that ACE inhibitor and ARB worsened hospital survival compared with control were 95.3% and 98.1%, respectively). CONCLUSIONS AND RELEVANCE In this trial, among critically ill adults with COVID-19, initiation of an ACE inhibitor or ARB did not improve, and likely worsened, clinical outcomes. TRIAL REGISTRATION ClinicalTrials.gov Identifier: NCT0273570

Well-posedness of the Stokes-transport system in bounded domains and in the infinite strip

International audienceWe consider the Stokes-transport system, a model for the evolution of an incompressible viscous fluid with inhomogeneous density. This equation was already known to be globally well-posed for any $L^1\cap L^\infty$ initial density with finite first moment in $\mathbf{R}^3$. We show that similar results hold on different domain types. We prove that the system is globally well-posed for $L^\infty$ initial data in bounded domains of $\mathbf{R}^2$ and $\mathbf{R}^3$ as well as in the infinite strip $\mathbf{R}\times(0,1)$. These results contrast with the ill-posedness of a similar problem, the incompressible porous medium equation, for which uniqueness is known to fail for such a density regularity

Caractère bien posé et comportement en temps long de l’équation de Stokes-transport

The Stokes-transport equation models an incompressible, viscous and inhomogeneous fluid, subject to gravity. It is a reduced model for oceanography and sedimentation. The density is transported by the velocity field, satisfying at any time the momentum balance between viscosity, pressure and gravity effects, namely the Stokes equation. In the first part, we establish the global well-posedness of this system in bounded domains and in the infinite channel, in the weak sense and for Lebesgue initial data. The unbounded channel case is solved in uniformly local Sobolev spaces, with solutions having infinite energy. These results are compared with previous works in the whole space and in the plane. In the second part, we focus on the long-time evolution of the solutions of the Stokes-transport equation in a periodic channel. We show that a class of monotonous stratified density profiles is stable for small and regular enough perturbations. We consider no-slip boundary conditions on the velocity field, which raises mathematical difficulties due to the presence of boundary effects. We obtain explicit algebraic convergence rates and show that the density rearranges vertically and monotonously, in line with the common intuition of sedimentation. We also give a refined description of the density profile, involving a boundary layer expansion in the vicinity of the boundaries. Besides, we extend a previous result obtained for a related problem, proving that any stationary profile is unstable in low regularity topologies. We also highlight properties compatible with the conjecture that the density always stratifies. In the last part, we undertake a numerical study of the evolution of graph density interfaces governed by the Stokes-transport equation. Several behaviours are observed, from the convergence toward the flat rest interface to the graph break. We compare our observations with existing theoretical results.L'équation de Stokes-transport modélise un fluide incompressible, visqueux et inhomogène, soumis à la gravité. Il s'agit d'un modèle réduit d'océanographie et de sédimentation. La densité est transportée par le champ de vitesse du fluide, satisfaisant à tout instant l'équilibre entre les effets de viscosité, de pression et de gravité, d'après l'équation de Stokes. Dans la première partie, nous établissons le caractère bien posé de ce système dans les domaines bornés et dans un canal infini, au sens faible et pour des données intégrables. La cas du canal inclut des solutions d'énergie infinie, impliquant des espaces de fonctions uniformément localement Sobolev. Ces résultats sont comparés à des travaux antérieurs, dans l'espace et le plan. Dans la deuxième partie, nous nous concentrons sur le comportement en temps long des solutions de l'équation de Stokes-transport dans un canal périodique. Nous montrons qu'une classe de profils stratifiés est stable pour des perturbations assez petites et régulières. Nous supposons le fluide non-glissant aux bords, ce qui pose des problèmes particuliers dus aux effets de bords induits. Nous obtenons des taux de convergence algébriques et montrons que la densité se réarrange verticalement et de façon monotone. Nous donnons également un développement de type couche limite du profil de densité à proximité des bords. En outre, nous prouvons, en adaptant un résultat antérieur, que tout profil stationnaire est instable pour des perturbations peu régulières. Nous mettons enfin en évidence des propriétés du système, compatibles avec la conjecture selon laquelle la densité tend toujours à se réordonner. Dans la dernière partie, nous menons une analyse numérique de l'évolution d'interfaces de densité de type graphe, gouvernée par l'équation de Stokes-transport. Plusieurs comportements sont observés, de la convergence vers l'équilibre plat à la rupture de graphe. Nous comparons nos observations à des résultats théoriques existants

SYNTHESIS : une méthodologie outillée d’évaluation et d’optimisation des performances de sûreté de fonctionnement d’un système complexe

International audienceSYNTHESIS makes it possible to assess and then optimize safety performances of a complex system. It involves the decomposition into functional bricks of the components. A dedicated algorithm is used to generate qualitative and quantitative indicators representative of these performances.SYNTHESIS permet d'évaluer, puis d'optimiser les performances de sûreté d'un système complexe. Elle passe par la décomposition en briques fonctionnelles des composants. Un algorithme dédié est utilisé pour la génération d'indicateurs qualitatifs et quantitatifs représentatifs de ces performances