Generalized and multi-oscillation solitons in the Nonlinear Schr\"odinger Equation with quartic dispersion

We study different types of solitons of a generalized nonlinear Schr\"odinger equation (GNLSE) that models optical pulses traveling down an optical waveguide with quadratic as well as quartic dispersion. A traveling-wave ansatz transforms this partial differential equation into a fourth-order nonlinear ordinary differential equation (ODE) that is Hamiltonian and has two reversible symmetries. Homoclinic orbits of the ODE that connect the origin to itself represent solitons of the GNLSE, and this allows us to study the existence and organization of solitons with advanced numerical tools for the detection and continuation of connecting orbits. In this way, we establish the existence of connections from one periodic orbit to another, called PtoP connections. They give rise to families of homoclinic orbits to either of the two periodic orbits; in the GNLSE they correspond to generalized solitons with oscillating tails whose amplitude does not decay but reaches a nonzero limit. Moreover, PtoP connections can be found in the energy level of the origin, where connections between this equilibrium and a given periodic orbit, called EtoP connections, are known to organize families of solitons. As we show here, EtoP and PtoP cycles can be assembled into different types of heteroclinic cycles that give rise to additional families of homoclinic orbits to the origin. In the GNLSE, these correspond to multi-oscillation solitons that feature several episodes of different oscillations in between their decaying tails. As for solitons organized by EtoP connections only, multi-oscillation solitons are shown to be an integral part of the phenomenon of truncated homoclinic snaking.Comment: 25 Pages, 13 figure

New Class of Organo-Hydrides for Selective Reduction of CO2

The photocatalytic CO2 reduction reaction (P-CO2RR) is one promising way to mitigate CO2 levels in the atmosphere and generate solar fuels such as carbon monoxide (CO), methanol (CH3OH), formic acid (HCOOH) in a way that is inexpensive and environmentally friendly. In nature, photosynthesis is the process that converts CO2 to useful high-energy compounds. It achieves this by a series of hydride transfers from the reduced form of nicotinamide adenine dinucleotide (NADH) to captured CO2 and is driven by sunlight. Mimicking natural photosynthesis, we investigate several catalytic systems composed of a new class of organo-hydride catalysts that accelerate the selective CO2 reduction to formate via a hydride transfer. This work is a significant step towards the selective electrochemical and photochemical reduction of CO2 in a biomimetic approach, using a metal-free catalyst composed of earth-abundant elements. The projects are divided into two main sections. First, this thesis will discuss the “dark” processes that study thermodynamics and kinetics of the CO2 reduction with the new class of hydrides and then the “light-induced” processes that study the photochemical regeneration of organo-hydrides

Anticoagulation Strategies in Non–Critically Ill Patients with Covid-19

BackgroundOptimal thromboprophylaxis for hospitalized patients with coronavirus disease 2019 (Covid-19) is uncertain.MethodsIn an open-label, adaptive platform trial, we randomly assigned hospitalized adults with Covid-19 to low-dose low-molecular-weight heparin thromboprophylaxis or intermediate-dose or low-dose plus aspirin. In response to external evidence, the aspirin intervention was discontinued and a therapeutic-dose arm added. The primary end point was death or the requirement for new organ support by day 28, analyzed with a Bayesian logistic model. Enrolment was closed as a result of operational constraints.ResultsBetween February 2021 and March 2022, 1574 patients were randomly assigned. Among 1526 participants included in the analysis (India, n=1273; Australia and New Zealand, n=138; and Nepal, n=115), the primary outcome occurred in 35 (5.9%) of 596 in low-dose, 25 (4.2%) of 601 in intermediate-dose, 20 (7.2%) of 279 in low-dose plus aspirin, and 7 (14%) of 50 in therapeutic-dose anticoagulation. Compared with low-dose thromboprophylaxis, the median adjusted odds ratio for the primary outcome for intermediate-dose was 0.74 (95% credible interval [CrI], 0.43 to 1.27; posterior probability of effectiveness [adjusted odds ratioConclusionsIn hospitalized non–critically ill adults with Covid-19, compared with low-dose, there was an 86% posterior probability that intermediate-dose, 65% posterior probability that low-dose plus aspirin, and a 7% posterior probability that therapeutic-dose anticoagulation reduced the odds of death or requirement for organ support. No treatment strategy met prespecified stopping criteria before trial closure, precluding definitive conclusions. (Funded by Australian National Health and Medical Research Council or Medical Research Future Fund Investigator and Practitioner Grants and others; ClinicalTrials.gov number, NCT04483960.