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

Effects of coexistence between the blue mussel Mytilus edulis and eelgrass Zostera marina on sediment biogeochemistry and plant performance

The habitat-modifying suspension-feeding mussel Mytilus edulis may have facilitating or inhibiting effects on seagrass meadows depending on the environmental conditions. We investigated the effects of M. edulis on sediment biogeochemistry in Zostera marina meadows under eutrophic conditions in Flensborg fjord, Denmark. Sediment and plant samples were collected at 5 stations with Z. marina (Eelgrass), 5 with Z. marina and M. edulis (Mixed), and at 2 unvegetated ones, 1 with mussels (Mussel) and 1 with sand (Sand). The Mixed sediment was en riched in fine particles (2 to 3 times), nutrients and sulphides compared to Eelgrass stations. In creased sediment nutrient availability at the Mixed stations was reflected in increased N and P content in eelgrass. However, the plant biomass did not differ significantly between stations, while shoot features (number of leaves and leaf area) were significantly reduced at Mixed stations, suggesting an inhibiting effect of M. edulis on Z. marina. Negative correlations between eelgrass measures and sediment sulphide at Mixed stations indicate that the presence of mussels increases sulphide invasion in the plants. A survey of 318 stations in Danish fjords suggests a threshold of 1.6 kg M. edulis m(-2) beyond which no coexistence between Z. marina and M. edulis was found.</p

A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation

We consider the problem of identifying sharp criteria under which radial $H^1$ (finite energy) solutions to the focusing 3d cubic nonlinear Schr\"odinger equation (NLS) $i\partial_t u + \Delta u + |u|^2u=0$ scatter, i.e. approach the solution to a linear Schr\"odinger equation as $t\to \pm \infty$. The criteria is expressed in terms of the scale-invariant quantities $\|u_0\|_{L^2}\|\nabla u_0\|_{L^2}$ and $M[u]E[u]$, where $u_0$ denotes the initial data, and $M[u]$ and $E[u]$ denote the (conserved in time) mass and energy of the corresponding solution $u(t)$. The focusing NLS possesses a soliton solution $e^{it}Q(x)$, where $Q$ is the ground-state solution to a nonlinear elliptic equation, and we prove that if $M[u]E[u]<M[Q]E[Q]$ and $\|u_0\|_{L^2}\|\nabla u_0\|_{L^2} < \|Q\|_{L^2}\|\nabla Q\|_{L^2}$, then the solution $u(t)$ is globally well-posed and scatters. This condition is sharp in the sense that the soliton solution $e^{it}Q(x)$, for which equality in these conditions is obtained, is global but does not scatter. We further show that if $M[u]E[u] \|Q\|_{L^2}\|\nabla Q\|_{L^2}$, then the solution blows-up in finite time. The technique employed is parallel to that employed by Kenig-Merle \cite{KM06a} in their study of the energy-critical NLS

On the nonlinear stability of mKdV breathers

A mathematical proof for the stability of mKdV breathers is announced. This proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and instability modes. In order to construct such a functional, we work in a subspace of the energy one. However, our proof introduces new ideas in order to attack the corresponding stability problem in the energy space. Some remarks about the sine-Gordon case are also considered.Comment: 7 p

Mussel production and Water Framework Directive targets in the Limfjord, Denmark: an integrated assessment for use in system-based management

Growth of human activities often conflict with nature conservation requirements and integrated assessments are necessary to build reliable scenarios for management. In the Limfjord, Denmark's largest estuary, nutrient loading reductions are necessary to fulfill EU regulations criteria, such as the Water Framework Directive (WFD). Cuts in nutrient loadings do not necessarily result in corresponding reductions in eutrophication impacts or in improving primary and higher trophic-level production. Similarly, the socioeconomic consequences of a mussel fishery and aquaculture production are complex and hard to predict. This study focuses on the usefulness of a System Approach Framework (SAF) implementation for stakeholder understanding of complex systems and development of sustainable management. Ecological-social-economic (ESE) model simulations clearly demonstrated the potential problems of WFD implementation for mussel fishers and mussel farmers. Simulation of mussel fishery closures resulted in a tenfold increase in the hitherto fishable mussel biomass and a similar decrease in the biomass of shallow-water mussels and medium-sized ones in deep water. A total closure of the mussel fishery could result in an annual profit loss of ~6.2 million. Scenario simulation of the introduction of one, two, three, and four mussel culture farms of ~19 ha showed that the introduction of line-mussels would decrease the biomass of wild mussels both in shallow and deep waters, affecting the catch and profit of fishers. The SAF, which included consultation with stakeholders at all stages, differs from the traditional public consultation process in that (1) communication was verbal and multilateral, (2) discussion among stakeholders was facilitated, and (3) stakeholder opinions and priorities formed the focus of the ESE assessment

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

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

Efficacy, Safety, and Timing of Anticoagulant Thromboprophylaxis for the Prevention of Venous Thromboembolism in Patients With Acute Spinal Cord Injury: A Systematic Review

Study Design: Systematic review. Objectives: The objective of this study was to answer 5 key questions: What is the comparative effectiveness and safety of (1a) anticoagulant thromboprophylaxis compared to no prophylaxis, placebo, or another anticoagulant strategy for preventing deep vein thrombosis (DVT) and pulmonary embolism (PE) after acute spinal cord injury (SCI)? (1b) Mechanical prophylaxis strategies alone or in combination with other strategies for preventing DVT and PE after acute SCI? (1c) Prophylactic inferior vena cava filter insertion alone or in combination with other strategies for preventing DVT and PE after acute SCI? (2) What is the optimal timing to initiate and/or discontinue anticoagulant, mechanical, and/or prophylactic inferior vena cava filter following acute SCI? (3) What is the cost-effectiveness of these treatment options? Methods: A systematic literature search was conducted to identify studies published through February 28, 2015. We sought randomized controlled trials evaluating efficacy and safety of antithrombotic strategies. Strength of evidence was evaluated using the Grading of Recommendations Assessment, Development and Evaluation (GRADE) system. Results: Nine studies satisfied inclusion criteria. We found a trend toward lower risk of DVT in patients treated with enoxaparin. There were no significant differences in rates of DVT, PE, bleeding, and mortality between patients treated with different types of low-molecular-weight heparin or between low-molecular-weight heparin and unfractionated heparin. Combined anticoagulant and mechanical prophylaxis initiated within 72 hours of SCI resulted in lower risk of DVT than treatment commenced after 72 hours of injury. Conclusion: Prophylactic treatments can be used to lower the risk of venous thromboembolic events in patients with acute SCI, without significant increase in risk of bleeding and mortality and should be initiated within 72 hours. © 2017, © The Author(s) 2017