344 research outputs found

    A lower bound on blowup rates for the 3D incompressible Euler equation and a single exponential Beale-Kato-Majda type estimate

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    We prove a Beale-Kato-Majda type criterion for the loss of regularity for solutions of the incompressible Euler equations in Hs(R3)H^{s}({\mathbb R}^3), for s>52s>\frac52. Instead of double exponential estimates of Beale-Kato-Majda type, we obtain a single exponential bound on u(t)Hs\|u(t)\|_{H^s} involving the length parameter introduced by P. Constantin in \cite{co1}. In particular, we derive lower bounds on the blowup rate of such solutions.Comment: AMS Latex, 15 page

    The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations

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    We study the blow-up criterion of smooth solutions to the 3D MHD equations. By means of the Littlewood-Paley decomposition, we prove a Beale-Kato-Majda type blow-up criterion of smooth solutions via the vorticity of velocity only, i. e. \sup_{j\in\Z}\int_0^T\|\Delta_j(\na\times u)\|_\infty dt, where Δj\Delta_j is a frequency localization on ξ2j|\xi|\approx 2^j.Comment: 12page

    The relative importance of phytoplankton aggregates and zooplankton fecal pellets to carbon export: insights from free-drifting sediment trap deployments in naturally iron-fertilised waters near the Kerguelen Plateau

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    The first KErguelen Ocean and Plateau compared Study (KEOPS1), conducted in the naturally iron-fertilised Kerguelen bloom, demonstrated that fecal material was the main pathway for exporting carbon to the deep ocean during summer (January–February 2005), suggesting a limited role of direct export via phytodetrital aggregates. The KEOPS2 project reinvestigated this issue during the spring bloom initiation (October–November 2011), when zooplankton communities may exert limited grazing pressure, and further explored the link between carbon flux, export efficiency and dominant sinking particles depending upon surface plankton community structure. Sinking particles were collected in polyacrylamide gel-filled and standard free-drifting sediment traps (PPS3/3), deployed at six stations between 100 and 400 m, to examine flux composition, particle origin and their size distributions. Results revealed an important contribution of phytodetrital aggregates (49 ± 10 and 45 ± 22% of the total number and volume of particles respectively, all stations and depths averaged). This high contribution dropped when converted to carbon content (30 ± 16% of total carbon, all stations and depths averaged), with cylindrical fecal pellets then representing the dominant fraction (56 ± 19%).At 100 and 200 m depth, iron- and biomass-enriched sites exhibited the highest carbon fluxes (maxima of 180 and 84 ± 27 mg C m-2 d-1, based on gel and PPS3/3 trap collection respectively), especially where large fecal pellets dominated over phytodetrital aggregates. Below these depths, carbon fluxes decreased (48 ± 21% decrease on average between 200 and 400 m), and mixed aggregates composed of phytodetritus and fecal matter dominated, suggesting an important role played by physical aggregation in deep carbon export.Export efficiencies determined from gels, PPS3/3 traps and 234Th disequilibria (200 m carbon flux/net primary productivity) were negatively correlated to net primary productivity with observed decreases from ~ 0.2 at low-iron sites to ~ 0.02 at high-iron sites. Varying phytoplankton communities and grazing pressure appear to explain this negative relationship. Our work emphasises the need to consider detailed plankton communities to accurately identify the controls on carbon export efficiency, which appear to include small spatio-temporal variations in ecosystem structure

    Blow-up of critical Besov norms at a potential Navier-Stokes singularity

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    We show that the spatial norm of any strong Navier-Stokes solution in the space X must become unbounded near a singularity, where X may be any critical homogeneous Besov space in which local existence of strong solutions to the 3-d Navier-Stokes system is known. In particular, the regularity of these spaces can be arbitrarily close to -1, which is the lowest regularity of any Navier-Stokes critical space. This extends a well-known result of Escauriaza-Seregin-Sverak (2003) concerning the Lebesgue space L3L^3, a critical space with regularity 0 which is continuously embedded into the spaces we consider. We follow the "critical element" reductio ad absurdum method of Kenig-Merle based on profile decompositions, but due to the low regularity of the spaces considered we rely on an iterative algorithm to improve low-regularity bounds on solutions to bounds on a part of the solution in spaces with positive regularity

    Antarctic-wide array of high-resolution ice core records reveals pervasive leadpollution began in 1889 and persists today

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    Interior Antarctica is among the most remote places on Earth and was thought to be beyond the reach of human impacts when Amundsen and Scott raced to the South Pole in 1911. Here we show detailed measurements from an extensive array of 16 ice cores quantifying substantial toxic heavy metal lead pollution at South Pole and throughout Antarctica by 1889 – beating polar explorers by more than 22 years. Unlike the Arctic where lead pollution peaked in the 1970s, lead pollution in Antarctica was as high in the early 20th century as at any time since industrialization. The similar timing and magnitude of changes in lead deposition across Antarctica, as well as the characteristic isotopic signature of Broken Hill lead found throughout the continent, suggest that this single emission source in southern Australia was responsible for the introduction of lead pollution into Antarctica at the end of the 19th century and remains a significant source today. An estimated 660 t of industrial lead have been deposited over Antarctica during the past 130 years as a result of mid-latitude industrial emissions, with regional-to-global scale circulation likely modulating aerosol concentrations. Despite abatement efforts, significant lead pollution in Antarctica persists into the 21st century

    Two resistance inducers relevant in coffee plant protection show distinct metabolic adjustments.

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    A good strategy in plant protection is to take advantage of the plant immune system by eliciting the plant?s constitutive defenses. Based on this concept resistance inducers have been developed and are commercially available, such as Bion®. An alternative formulation Greenf orce CuCa was developed by UFLA partners in Brazil which showed promising results for the control of coffee rust ( Hemileia vastatrix ). We established as working hypothesis that resistance inducers impose etabolic adjustments at the cellular level, mainly on photosynthesis and its regulation

    PhOTO Zebrafish: A Transgenic Resource for In Vivo Lineage Tracing during Development and Regeneration

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    Background: Elucidating the complex cell dynamics (divisions, movement, morphological changes, etc.) underlying embryonic development and adult tissue regeneration requires an efficient means to track cells with high fidelity in space and time. To satisfy this criterion, we developed a transgenic zebrafish line, called PhOTO, that allows photoconvertible optical tracking of nuclear and membrane dynamics in vivo. Methodology: PhOTO zebrafish ubiquitously express targeted blue fluorescent protein (FP) Cerulean and photoconvertible FP Dendra2 fusions, allowing for instantaneous, precise targeting and tracking of any number of cells using Dendra2 photoconversion while simultaneously monitoring global cell behavior and morphology. Expression persists through adulthood, making the PhOTO zebrafish an excellent tool for studying tissue regeneration: after tail fin amputation and photoconversion of a ~100µm stripe along the cut area, marked differences seen in how cells contribute to the new tissue give detailed insight into the dynamic process of regeneration. Photoconverted cells that contributed to the regenerate were separated into three distinct populations corresponding to the extent of cell division 7 days after amputation, and a subset of cells that divided the least were organized into an evenly spaced, linear orientation along the length of the newly regenerating fin. Conclusions/Significance: PhOTO zebrafish have wide applicability for lineage tracing at the systems-level in the early embryo as well as in the adult, making them ideal candidate tools for future research in development, traumatic injury and regeneration, cancer progression, and stem cell behavior

    Deep and fast live imaging with two-photon scanned light-sheet microscopy

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    We implemented two-photon scanned light-sheet microscopy, combining nonlinear excitation with orthogonal illumination of light-sheet microscopy, and showed its excellent performance for in vivo, cellular-resolution, three-dimensional imaging of large biological samples. Live imaging of fruit fly and zebrafish embryos confirmed that the technique can be used to image up to twice deeper than with one-photon light-sheet microscopy and more than ten times faster than with point-scanning two-photon microscopy without compromising normal biology
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