Scattering and small data completeness for the critical nonlinear Schroediger equation

We prove Asymptotic Completeness of one dimensional NLS with long range nonlinearities. We also prove existence and expansion of asymptotic solutions with large data at infinity

A fate for organic acids, formaldehyde and methanol in cloud water: their biotransformation by micro-organisms

International audienceThe interactions between microbial and chemical contents of cloud water were investigated. First, we observe that the bulk cloud water solution provides a substantial environment where bacteria can develop significantly. Then, a total number of 60 microbial strains originating from seven distinct samples of cloud water and affiliated to various taxonomic groups were looked for their ability to degrade some of the main atmospheric carboxylic compounds: formate, acetate, lactate, succinate, formaldehyde and methanol. Biodegradation tests show that all these compounds can be transformed when used as single carbonaceous substrates, with activities depending on both the strain and the compound. The highest capacities of biodegradation are observed towards formaldehyde, formate and acetate, which are also the more concentrated compounds typically measured in cloud water. Hence, analyses by 1H NMR permitted to establish for instance that compounds like pyruvate or fumarate can be produced and released in the media in relation to the transformation of lactate or succinate. In addition, utilization of 13C labelled formaldehyde showed that it can be transformed through many metabolic pathways, similar to those induced by photochemistry and leading to the production of formate and/or methanol. These results suggest that microorganisms of cloud water can have various behaviours towards the chemical compounds present in the atmosphere: they can represent either a sink or source for organic carbon, and may have to be considered as actors of cloud chemistry

Microbiology and atmospheric processes: chemical interactions of primary biological aerosols

This paper discusses the influence of primary biological aerosols (PBA) on atmospheric chemistry and vice versa through microbiological and chemical properties and processes. Several studies have shown that PBA represent a significant fraction of air particulate matter and hence affect the microstructure and water uptake of aerosol particles. Moreover, airborne micro-organisms, namely fungal spores and bacteria, can transform chemical constituents of the atmosphere by metabolic activity. Recent studies have emphasized the viability of bacteria and metabolic degradation of organic substances in cloud water. On the other hand, the viability and metabolic activity of airborne micro-organisms depend strongly on physical and chemical atmospheric parameters such as temperature, pressure, radiation, pH value and nutrient concentrations. In spite of recent advances, however, our knowledge of the microbiological and chemical interactions of PBA in the atmosphere is rather limited. Further targeted investigations combining laboratory experiments, field measurements, and modelling studies will be required to characterize the chemical feedbacks, microbiological activities at the air/snow/water interface supplied to the atmosphere

Biodegradability standards for carrier bags and plastic films in aquatic environments: A critical review

© 2018 The Authors. Plastic litter is encountered in aquatic ecosystems across the globe, including polar environments and the deep sea. To mitigate the adverse societal and ecological impacts of this waste, there has been debate on whether ‘biodegradable' materials should be granted exemptions from plastic bag bans and levies. However, great care must be exercised when attempting to define this term, due to the broad and complex range of physical and chemical conditions encountered within natural ecosystems. Here, we review existing international industry standards and regional test methods for evaluating the biodegradability of plastics within aquatic environments (wastewater, unmanaged freshwater and marine habitats). We argue that current standards and test methods are insufficient in their ability to realistically predict the biodegradability of carrier bags in these environments, due to several shortcomings in experimental procedures and a paucity of information in the scientific literature. Moreover, existing biodegradability standards and test methods for aquatic environments do not involve toxicity testing or account for the potentially adverse ecological impacts of carrier bags, plastic additives, polymer degradation products or small (microscopic) plastic particles that can arise via fragmentation. Successfully addressing these knowledge gaps is a key requirement for developing new biodegradability standard(s) for lightweight carrier bags.This article is partially based on a Technical Advisory Group report commissioned by the UK Department for Environment, Food and Rural Affairs (summary document delivered to the UK Parliament in December 2015 see: Department for Environment, Food and Rural Affairs (Defra). 2015 Review of standards for biodegradable plastic carrier bags. See http://www.gov.uk/government/publications/carrier-bags-review-of-standards-for-biodegradable-plastic-bags)

Resonance-free Region in scattering by a strictly convex obstacle

We prove the existence of a resonance free region in scattering by a strictly convex obstacle with the Robin boundary condition. More precisely, we show that the scattering resonances lie below a cubic curve which is the same as in the case of the Neumann boundary condition. This generalizes earlier results on cubic poles free regions obtained for the Dirichlet boundary condition.Comment: 29 pages, 2 figure

Interaction of vortices in viscous planar flows

We consider the inviscid limit for the two-dimensional incompressible Navier-Stokes equation in the particular case where the initial flow is a finite collection of point vortices. We suppose that the initial positions and the circulations of the vortices do not depend on the viscosity parameter \nu, and we choose a time T > 0 such that the Helmholtz-Kirchhoff point vortex system is well-posed on the interval [0,T]. Under these assumptions, we prove that the solution of the Navier-Stokes equation converges, as \nu -> 0, to a superposition of Lamb-Oseen vortices whose centers evolve according to a viscous regularization of the point vortex system. Convergence holds uniformly in time, in a strong topology which allows to give an accurate description of the asymptotic profile of each individual vortex. In particular, we compute to leading order the deformations of the vortices due to mutual interactions. This allows to estimate the self-interactions, which play an important role in the convergence proof.Comment: 39 pages, 1 figur

Bounds on the growth of high Sobolev norms of solutions to 2D Hartree Equations

In this paper, we consider Hartree-type equations on the two-dimensional torus and on the plane. We prove polynomial bounds on the growth of high Sobolev norms of solutions to these equations. The proofs of our results are based on the adaptation to two dimensions of the techniques we previously used to study analogous problems on $S^1$, and on $\mathbb{R}$.Comment: 38 page