High-Speed Cylindrical Collapse of Two Perfect Fluids

In this paper, the study of the gravitational collapse of cylindrically distributed two perfect fluid system has been carried out. It is assumed that the collapsing speeds of the two fluids are very large. We explore this condition by using the high-speed approximation scheme. There arise two cases, i.e., bounded and vanishing of the ratios of the pressures with densities of two fluids given by $c_s, d_s$. It is shown that the high-speed approximation scheme breaks down by non-zero pressures $p_1, p_2$ when $c_s, d_s$ are bounded below by some positive constants. The failure of the high-speed approximation scheme at some particular time of the gravitational collapse suggests the uncertainity on the evolution at and after this time. In the bounded case, the naked singularity formation seems to be impossible for the cylindrical two perfect fluids. For the vanishing case, if a linear equation of state is used, the high-speed collapse does not break down by the effects of the pressures and consequently a naked singularity forms. This work provides the generalisation of the results already given by Nakao and Morisawa [1] for the perfect fluid.Comment: 11 pages, 1 figure, accepted for publication in Gen. Rel. Gra

Quantum singularities in a model of f(R) Gravity

The formation of a naked singularity in a model of f(R) gravity having as source a linear electromagnetic field is considered in view of quantum mechanics. Quantum test fields obeying the Klein-Gordon, Dirac and Maxwell equations are used to probe the classical timelike naked singularity developed at r=0. We prove that the spatial derivative operator of the fields fails to be essentially self-adjoint. As a result, the classical timelike naked singularity remains quantum mechanically singular when it is probed with quantum fields having different spin structures.Comment: 12 pages, final version. Accepted for publication in EPJ

Dynamic wormholes, anti-trapped surfaces, and energy conditions

Adapting and extending a suggestion due to Page, we define a wormhole throat to be a marginally anti-trapped surface, that is, a closed two-dimensional spatial hypersurface such that one of the two future-directed null geodesic congruences orthogonal to it is just beginning to diverge. Typically a dynamic wormhole will possess two such throats, corresponding to the two orthogonal null geodesic congruences, and these two throats will not coincide, (though they do coalesce into a single throat in the static limit). The divergence property of the null geodesics at the marginally anti-trapped surface generalizes the ``flare-out'' condition for an arbitrary wormhole. We derive theorems regarding violations of the null energy condition (NEC) at and near these throats and find that, even for wormholes with arbitrary time-dependence, the violation of the NEC is a generic property of wormhole throats. We also discuss wormhole throats in the presence of fully antisymmetric torsion and find that the energy condition violations cannot be dumped into the torsion degrees of freedom. Finally by means of a concrete example we demonstrate that even temporary suspension of energy-condition violations is incompatible with the flare-out property of dynamic throats.Comment: 32 pages in plain LaTex, no figures. Additional text and references adde

Accelerating electromagnetic magic field from the C-metric

Various aspects of the C-metric representing two rotating charged black holes accelerated in opposite directions are summarized and its limits are considered. A particular attention is paid to the special-relativistic limit in which the electromagnetic field becomes the "magic field" of two oppositely accelerated rotating charged relativistic discs. When the acceleration vanishes the usual electromagnetic magic field of the Kerr-Newman black hole with gravitational constant set to zero arises. Properties of the accelerated discs and the fields produced are studied and illustrated graphically. The charges at the rim of the accelerated discs move along spiral trajectories with the speed of light. If the magic field has some deeper connection with the field of the Dirac electron, as is sometimes conjectured because of the same gyromagnetic ratio, the "accelerating magic field" represents the electromagnetic field of a uniformly accelerated spinning electron. It generalizes the classical Born's solution for two uniformly accelerated monopole charges.Comment: 22 pages, 5 figure

Database of diazotrophs in global ocean: abundance, biomass and nitrogen fixation rates

Marine N2 fixing microorganisms, termed diazotrophs, are a key functional group in marine pelagic ecosystems. The biological fixation of dinitrogen (N2) to bioavailable nitrogen provides an important new source of nitrogen for pelagic marine ecosystems and influences primary productivity and organic matter export to the deep ocean. As one of a series of efforts to collect biomass and rates specific to different phytoplankton functional groups, we have constructed a database on diazotrophic organisms in the global pelagic upper ocean by compiling about 12 000 direct field measurements of cyanobacterial diazotroph abundances (based on microscopic cell counts or qPCR assays targeting the nifH genes) and N2 fixation rates. Biomass conversion factors are estimated based on cell sizes to convert abundance data to diazotrophic biomass. The database is limited spatially, lacking large regions of the ocean especially in the Indian Ocean. The data are approximately log-normal distributed, and large variances exist in most sub-databases with non-zero values differing 5 to 8 orders of magnitude. Reporting the geometric mean and the range of one geometric standard error below and above the geometric mean, the pelagic N2 fixation rate in the global ocean is estimated to be 62 (52–73) Tg N yr?1 and the pelagic diazotrophic biomass in the global ocean is estimated to be 2.1 (1.4–3.1) Tg C from cell counts and to 89 (43–150) Tg C from nifH-based abundances. Reporting the arithmetic mean and one standard error instead, these three global estimates are 140 ± 9.2 Tg N yr?1, 18 ± 1.8 Tg C and 590 ± 70 Tg C, respectively. Uncertainties related to biomass conversion factors can change the estimate of geometric mean pelagic diazotrophic biomass in the global ocean by about ±70%. It was recently established that the most commonly applied method used to measure N2 fixation has underestimated the true rates. As a result, one can expect that future rate measurements will shift the mean N2 fixation rate upward and may result in significantly higher estimates for the global N2 fixation. The evolving database can nevertheless be used to study spatial and temporal distributions and variations of marine N2 fixation, to validate geochemical estimates and to parameterize and validate biogeochemical models, keeping in mind that future rate measurements may rise in the future. The database is stored in PANGAEA (doi:10.1594/PANGAEA.774851)

Modelling Current and Future Potential Habitats for Plantations of Eucalyptus grandis Hill ex Maiden and E. dunnii Maiden in Uruguay.

ABSTRACT.Eucalyptus grandis and E. dunnii have high productive potential in the South of Brazil, Uruguay, and central Argentina. This is based on the similarity of the climate and soil of these areas, which form an eco-region called Campos. However, previous results show that these species have dierences in their distribution caused by the prioritization of Uruguayan soils for forestry, explained by the particular conditions of each site. In this study, the site variables (climate, soil, and topography) that better explain the distribution of both species were identified, and prediction models of current and future distribution were adjusted for dierent climate change scenarios (years 2050 and 2070). The distribution of E. grandis was associated with soil parameters, whereas for E. dunnii a greater eect of the climatic variables was observed. The ensemble biomod2 model was the most precise with regard to predicting the habitat for both species with respect to the simple models evaluated. For E. dunnii, the average values of the AUC, Kappa, and TSS index were 0.98, 0.88, and 0.77, respectively. For E. grandis, their values were 0.97, 0.86, and 0.80, respectively. In the projections of climatic change, the distribution of E. grandis occurrence remains practically unchanged, even in the scenarios of temperature increase. However, current distribution of E. dunnii shows high susceptibility in a scenario of increased temperature, to the point that most of the area currently planted may be at risk. Our results might be useful to political government and foresters for decision making in terms of future planted areas.© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)

On the role of oxygen for nitrogen fixation in the marine cyanobacterium Trichodesmium sp.

The marine, non-heterocystous, filamentous cyanobacterium Trichodesmium shows a distinct diurnal pattern of nitrogenase activity. In an attempt to reveal the factors that control this pattern, a series of measurements were carried out using online acetylene reduction assay. Light response curves of nitrogenase were recorded applying various concentrations of oxygen. The effect of oxygen depended on the irradiance applied. Above a photon irradiance of 16 μmol m2 s1 nitrogenase activity was highest under anoxic conditions. Below this irradiance the presence of oxygen was required to achieve highest nitrogenase activity and in the dark 5% oxygen was optimal. At any oxygen concentration a photon irradiance of 100 μmol m2 s1 was saturating. When Trichodesmium was incubated in the dark, nitrogenase activity gradually decreased and this decline was higher at higher levels of oxygen. The activity recovered when the cells were subsequently incubated in the light. This recovery depended on oxygenic photosynthesis because it did not occur in the presence of DCMU [3-(3,4-dichlorophenyl)-1,1-dimethylurea]. Recovery of nitrogenase activity in the light was faster at low oxygen concentrations. The results showed that under aerobic conditions nitrogenase activity was limited by the availability of reducing equivalents suggesting a competition for electrons between nitrogenase and respiration.