Wave operator bounds for 1-dimensional Schr\"odinger operators with singular potentials and applications

Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.Comment: 16 pages, 0 figure

On the 2d Zakharov system with L^2 Schr\"odinger data

We prove local in time well-posedness for the Zakharov system in two space dimensions with large initial data in L^2 x H^{-1/2} x H^{-3/2}. This is the space of optimal regularity in the sense that the data-to-solution map fails to be smooth at the origin for any rougher pair of spaces in the L^2-based Sobolev scale. Moreover, it is a natural space for the Cauchy problem in view of the subsonic limit equation, namely the focusing cubic nonlinear Schroedinger equation. The existence time we obtain depends only upon the corresponding norms of the initial data - a result which is false for the cubic nonlinear Schroedinger equation in dimension two - and it is optimal because Glangetas-Merle's solutions blow up at that time.Comment: 30 pages, 2 figures. Minor revision. Title has been change

Blue carbon stocks in Baltic Sea eelgrass (Zostera marina) meadows

Although seagrasses cover only a minor fraction of the ocean seafloor, their carbon sink capacity accounts for nearly one-fifth of the total oceanic carbon burial and thus play a critical structural and functional role in many coastal ecosystems. We sampled 10 eelgrass (<i>Zostera marina</i>) meadows in Finland and 10 in Denmark to explore seagrass carbon stocks (C_org stock) and carbon accumulation rates (C_org accumulation) in the Baltic Sea area. The study sites represent a gradient from sheltered to exposed locations in both regions to reflect expected minimum and maximum stocks and accumulation. The C_org stock integrated over the top 25 cm of the sediment averaged 627 g C m⁻² in Finland, while in Denmark the average C_org stock was over 6 times higher (4324 g C m⁻²). A conservative estimate of the total organic carbon pool in the regions ranged between 6.98 and 44.9 t C ha⁻¹. Our results suggest that the Finnish eelgrass meadows are minor carbon sinks compared to the Danish meadows, and that majority of the C_org produced in the Finnish meadows is exported. Our analysis further showed that &gt; 40 % of the variation in the C_org stocks was explained by sediment characteristics, i.e. dry density, porosity and silt content. In addition, our analysis show that the root : shoot ratio of <i>Z. marina</i> explained &gt; 12 % and the contribution of <i>Z. marina</i> detritus to the sediment surface C_org pool explained &gt; 10 % of the variation in the C_org stocks. The mean monetary value for the present carbon storage and carbon sink capacity of eelgrass meadows in Finland and Denmark, were 281 and 1809 EUR ha⁻¹, respectively. For a more comprehensive picture of seagrass carbon storage capacity, we conclude that future blue carbon studies should, in a more integrative way, investigate the interactions between sediment biogeochemistry, seascape structure, plant species architecture and the hydrodynamic regime

Last Bite: No Fish Oil No Footnotes

The exponential growth of off-shore mariculture that has occurred worldwide over the last 10 years has raised concern about the impact of the waste produced by this industry on the ecological integrity of the sea bottom. Investigations into this potential source of impact on the biochemistry of the sea floor have provided contrasting results, and no compelling explanations for these discrepancies have been provided to date. To quantify the impact of fish-farm activities on the biochemistry of sediments, we have investigated the quantity and biochemical composition of sediment organic matter in four different regions in the temperate-warm Mediterranean Sea: Akrotiri Bay (Cyprus), Sounion Bay (Greece), Pachino Bay (Italy), and the Gulf of Alicante (Spain). In these four study regions, the concentrations of phytopigments, proteins, carbohydrates, and lipids in the sediments were measured, comparing locations receiving wastes from fish farms to control locations in two different habitats: seagrass beds and soft nonvegetated substrates. Downward fluxes were also measured in all of the regions, up to 200 m from the fish farms, to assess the potential spatial extent of the impact. In all four regions, with the exception of seagrass sediments in Spain, the biochemistry of the sediments showed significant differences between the control and fish-farm locations. However, the variables explaining the differences observed varied among the regions and between habitats, suggesting idiosyncratic effects of fish-farm waste on the biochemistry of sediments. These are possibly related to differences in the local physicochemical variables that could explain a significant proportion of the differences seen between the control and fish-farm locations. Biodeposition derived from the fish farms decreased with increasing distance from the fish-farm cages, but with different patterns in the four regions. Our results indicate that quantitative and qualitative changes in the organic loads of the sediments that arise from intensive aquaculture are dependent upon the ecological context and are not predictable only on the basis of fish-farm attributes and hydrodynamic regimes. Therefore, the siting of fish farms should only be allowed after a case-by-case assessment of the ecological context of the region, especially in terms of the organic matter load and its biochemical composition

Fast soliton scattering by delta impurities

We study the Gross-Pitaevskii equation (nonlinear Schroedinger equation) with a repulsive delta function potential. We show that a high velocity incoming soliton is split into a transmitted component and a reflected component. The transmitted mass (L^2 norm squared) is shown to be in good agreement with the quantum transmission rate of the delta function potential. We further show that the transmitted and reflected components resolve into solitons plus dispersive radiation, and quantify the mass and phase of these solitons.Comment: 32 pages, 3 figure