Regularization of Motion Equations with L-Transformation and Numerical Integration of the Regular Equations

The sets of L-matrices of the second, fourth and eighth orders are constructed axiomatically. The defining relations are taken from the regularization of motion equations for Keplerian problem. In particular, the Levi-Civita matrix and KS-matrix are L-matrices of second and fourth order, respectively. A theorem on the ranks of L-transformations of different orders is proved. The notion of L-similarity transformation is introduced, certain sets of L-matrices are constructed, and their classification is given. An application of fourth order L-matrices for N-body problem regularization is given. A method of correction for regular coordinates in the Runge–Kutta–Fehlberg integration method for regular motion equations of a perturbed two-body problem is suggested. Comparison is given for the results of numerical integration in the problem of defining the orbit of a satellite, with and without the above correction method. The comparison is carried out with respect to the number of calls to the subroutine evaluating the perturbational accelerations vector. The results of integration using the correction turn out to be in a favorable position.     

Delivery of icy planetesimals to inner planets in the Proxima Centauri planetary system

The estimates of the delivery of icy planetesimals from the feeding zone of Proxima Centauri c (with mass equal to 7m_E, m_E is the mass of the Earth) to inner planets b and d were made. They included the studies of the total mass of planetesimals in the feeding zone of planet c and the probabilities of collisions of such planetesimals with inner planets. This total mass could be about 10–15m_E. It was estimated based on studies of the ratio of the mass of planetesimals ejected into hyperbolic orbits to the mass of planetesimals collided with forming planet c. At integration of the motion of planetesimals, the gravitational influence of planets c and b and the star was taken into account. In most series of calculations, planetesimals collided with planets were excluded from integrations. Based on estimates of the mass of planetesimals ejected into hyperbolic orbits, it was concluded that during the growth of the mass of planet c the semi-major axis of its orbit could decrease by at least a factor of 1.5. Depending on possible gravitational scattering due to mutual encounters of planetesimals, the total mass of material delivered by planetesimals from the feeding zone of planet c to planet b was estimated to be between 0.002m_E and 0.015m_E. Probably, the amount of water delivered to Proxima Centauri b exceeded the mass of water in Earth's oceans. The amount of material delivered to planet d could be a little less than that delivered to planet b.     

Macroalgal diversity along the Baltic Sea salinity gradient challenges Remane's species-minimum concept

Remane’s species-minimum concept, which states that the lowest number of taxa occurs at the horohalinicum (5-8 psu), was tested by investigating macroalgal diversity on hard substrates along the natural salinity gradient in the Baltic Sea. Field data on species occurrence and abundance were collected by SCUBA diving along 10 transects of the Finnish, Swedish and German coasts, covering a salinity range from 3.9 to 27 psu. Macroalgal species numbers declined steadily with salinity, decreasing until 7.2 psu was reached, but in the horohalinicum, a marked reduction of species number and a change in diversity were indicated by the Shannon index and evenness values. The non-linear decrease in macroalgal diversity at 5-8 psu and the lack of increase in species numbers at salinities below 5 psu imply a restricted applicability of Remane’s species-minimum concept to macroalgae.     

Palaeomagnetic results from the Lancer 1 stratigraphic drillhole,Officer Basin,Western Australia,and implications for Rodinia reconstructions

A partial record of the positions of Australia during Middle to Late Neoproterozoic time is provided by palaeomagnetic results for samples from the Lancer 1 stratigraphic drillhole in Western Australia. Lancer 1 was drilled vertically to 1501 m, through essentially horizontal Neoproterozoic strata of the western Officer Basin. We studied 123 samples from 28 intervals of drillcore which were oriented by matching features (fractures, cross-beds, etc.) in the core with oriented acoustic scanner images of the drillhole walls. Three new palaeopoles are reported for red mudstones and sandstones (redbeds) of the Browne (44.5°N, 141.7°E, dp = 5.1°, dm = 9.0°), Hussar (62.2°N, 85.8°E, dp = 7.3°, dm = 14.6°), and Kanpa (74.0°N, 128.8°E, dp = 7.7°, dm = 14.8°) Formations of the ca 830 – 720 Ma Buldya Group (Supersequence 1), which exhibit stable, two-polarity magnetisations carried by fine-grained hematite and magnetite. The overlying ca 610 – 590 Ma Wahlgu Formation glaciogenic diamictite (Supersequence 3) yielded dispersed directions and an imprecise palaeopole that overlaps results from the glaciogenic Elatina Formation and other Late Neoproterozoic rock units. The results help to elaborate the Middle to Late Neoproterozoic apparent polar wander path for Australia and indicate, in agreement with palaeoclimatic data and previous palaeomagnetic studies, that the continent was slow-moving and occupied low latitudes at this time. Assuming that Australia and Laurentia were still joined at ca 780 Ma, comparison of the new Hussar Formation palaeopole with coeval Laurentian data favours AUSMEX, rather than SWEAT or AUSWUS, as the most likely configuration of these two continents in Rodinia. This preliminary study of Lancer 1 demonstrates the utility of acoustic scanner logs for orienting drillcores, as well as the scope for additional sampling and palaeomagnetic studies of Lancer 1, and other oriented drillcores, to yield a more continuous record of Australia's past motions and to provide magnetostratigraphic data for enhancing inter-basin correlations.     

Geochronology,paleomagnetism and magnetic fabric of metamorphic rocks in the northeast Fraser Belt,Western Australia

The first zircon U–Pb SHRIMP dating on high-grade meta-igneous units in the northernmost parts of the Fraser Belt along the southern margin of the Western Australian Yilgarn Craton, reveal crystallisation ages between 1299 ± 10 and 1250 ± 23 Ma. A small number of older xenocrystic zircons, incorporated in some samples, indicate the presence of Late Paleoproterozoic crust in the region. Zircon that crystallised within a melt accumulated in the neck of a boudinaged mafic unit was dated at 1296 ± 4 Ma, indicating that the emplacement of the igneous protoliths took place syntectonically. The anisotropy of magnetic susceptibility of the granulites indicates minimum axes with a mean inclination of 4° towards 130°, corresponding to a nearly vertical southwest–northeast (50–230°) magnetic foliation. This is very close to the structural trend of the Fraser Belt suggesting that the magnetic fabric was acquired syntectonically, during the collision between the Yilgarn and Gawler Cratons. The paleomagnetic data on the granulites overlap with published poles for various 1.2 Ga units in the Albany Belt and the 1.2 Ga Fraser dykes, possibly suggesting that the remanence was acquired during the second stage of the Fraser tectonism. A younger magnetisation component resembles a pole of uncertain age published for Bremer Bay in the Albany Belt.     

Early evolution of the Paleoasian ocean: LA-ICP-MS dating of detrital zircon from Late Precambrian sequences of the southern margin of the Siberian craton

We present U–Pb (LA-ICP-MS) data on detrital zircon from the Late Precambrian terrigenous rocks of the Baikal Group and Ushakovka Formation, western Cisbaikalia (southern flank of the Siberian craton). The sources of clastic material for the studied sediments are interpreted. The youngest group of detrital zircon grains from the upper Baikal Group and Ushakovka Formation permits assigning these sediments to the Vendian. The lack of Mesoproterozoic detrital zircon in most of the analyzed samples confirms the hypothesis of a global (~ 1 Gyr) break in endogenic activity within the southern flank of the Siberian craton through the Precambrian. The abundance of Neoproterozoic zircon in sandstones from the upper horizons of the Baikal Group and the Ushakovka Formation might be due to the shrinkage of the ocean basin as a result of the convergence of the craton with the microcontinents and island arcs within the Paleoasian ocean.     

4D Arctic: A Glimpse into the Structure and Evolution of the Arctic in the Light of New Geophysical Maps,Plate Tectonics and Tomographic Models

Knowledge about the Arctic tectonic structure has changed in the last decade as a large number of new datasets have been collected and systematized. Here, we review the most updated, publicly available Circum-Arctic digital compilations of magnetic and gravity data together with new models of the Arctic’s crust. Available tomographic models have also been scrutinized and evaluated for their potential to reveal the deeper structure of the Arctic region. Although the age and opening mechanisms of the Amerasia Basin are still difficult to establish in detail, interpreted subducted slabs that reside in the High Arctic’s lower mantle point to one or two episodes of subduction that consumed crust of possibly Late Cretaceous–Jurassic age. The origin of major igneous activity during the Cretaceous in the central Arctic (the Alpha–Mendeleev Ridge) and in the proximity of rifted margins (the so-called High Arctic Large Igneous Province—HALIP) is still debated. Models of global plate circuits and the connection with the deep mantle are used here to re-evaluate a possible link between Arctic volcanism and mantle plumes.     

Astrodynamical Space Test of Relativity Using Optical Devices I (ASTROD I)—A class-M fundamental physics mission proposal for Cosmic Vision 2015–2025

ASTROD I is a planned interplanetary space mission with multiple goals. The primary aims are: to test general relativity with an improvement in sensitivity of over three orders of magnitude, improving our understanding of gravity and aiding the development of a new quantum gravity theory; to measure key solar system parameters with increased accuracy, advancing solar physics and our knowledge of the solar system; and to measure the time rate of change of the gravitational constant with an order of magnitude improvement and the anomalous Pioneer acceleration, thereby probing dark matter and dark energy gravitationally. It is an international project, with major contributions from Europe and China and is envisaged as the first in a series of ASTROD missions. ASTROD I will consist of one spacecraft carrying a telescope, four lasers, two event timers and a clock. Two-way, two-wavelength laser pulse ranging will be used between the spacecraft in a solar orbit and deep space laser stations on Earth, to achieve the ASTROD I goals. A second mission, ASTROD (ASTROD II) is envisaged as a three-spacecraft mission which would test General Relativity to 1 ppb, enable detection of solar g-modes, measure the solar Lense–Thirring effect to 10 ppm, and probe gravitational waves at frequencies below the LISA bandwidth. In the third phase (ASTROD III or Super-ASTROD), larger orbits could be implemented to map the outer solar system and to probe primordial gravitational-waves at frequencies below the ASTROD II bandwidth.

Dynamic Monte Carlo radiation transfer in SPH: radiation pressure force implementation

We present a new framework for radiation hydrodynamics simulations. Gas dynamics is modelled by smoothed particle hydrodynamics (SPH), whereas radiation transfer is simulated via a time-dependent Monte Carlo approach that traces photon packets. As a first step in the development of the method, in this paper we consider the momentum transfer between radiation field and gas, which is important for systems where radiation pressure is high. There is no fundamental limitation on the number of radiation sources, the geometry or the optical depth of the problems that can be studied with the method. However, as expected for any Monte Carlo transfer scheme, stochastic noise presents a serious limitation. We present a number of tests that show that the errors of the method can be estimated accurately by considering Poisson noise fluctuations in the number of photon packets that SPH particles interact with per dynamical time. It is found that, for a reasonable accuracy, the momentum carried by photon packets must be much smaller than the typical momentum of SPH particles. We discuss numerical limitations of the code, and future steps that can be taken to improve performance and applicability of the method.