Nonlinear theory of the two-point correlation function

We consider the influence of the nonlinear stage of gravitational instability on the two-point correlation functions of gravitationally bound objects. Based on the theory of nonlinear gravitational contraction of a single density peak of dissipationless matter (Gurevich and Zybin, 1988a,b; 1990) we develop a method for calculating the two-point correlation functions of different objects of any mass. The method works good in the region of strong correlations and can be easily extended to calculate higher correlation functions. We show that the main contribution to the correlation function _i in the region of strong correlations _i 1 is made by pair systems located outside large clusters of objects. In this region the shape of _i is determined only by the nonlinear dynamics of gravitational contraction of dissipationless matter and has the form _i C ^–, where 1.8 is a universal parameter.     

Tests for coalescing binary neutron stars as cosmological origin of gamma-ray bursts

Theoretical logN-logS distributions and (V/V _max) tests of gamma-ray bursts in the model of coalescence of neutron star (NS+NS) and/or NS+black hole (NS+BH) binaries are calculated for a flat Universe (=1) with different values of the cosmological constant and under various assumptions about the star formation history. The observed logN-logS distribution and value of (V/V _max)=0.33 for 411 bursts with knownC _max/C _lim from the 2d BATSE catalogue are best fitted with a model for which = 0.2 and primary star formation occurs at redshiftsz5–6.     

Three-dimensional model of a dispersed-film flow in a cylindrical channel

A mathematical model of the dispersed-film two-phase flow with phase slip in the vertical cylindrical channel is described.     

Magnetospheric and Plasma Science with Cassini-Huygens

Magnetospheric and plasma science studies at Saturn offer a unique opportunity to explore in-depth two types of magnetospheres. These are an ‘induced’ magnetosphere generated by the interaction of Titan with the surrounding plasma flow and Saturn's ‘intrinsic’ magnetosphere, the magnetic cavity Saturn's planetary magnetic field creates inside the solar wind flow. These two objects will be explored using the most advanced and diverse package of instruments for the analysis of plasmas, energetic particles and fields ever flown to a planet. These instruments will make it possible to address and solve a series of key scientific questions concerning the interaction of these two magnetospheres with their environment. The flow of magnetospheric plasma around the obstacle, caused by Titan's atmosphere/ionosphere, produces an elongated cavity and wake, which we call an ‘induced magnetosphere’. The Mach number characteristics of this interaction make it unique in the solar system. We first describe Titan's ionosphere, which is the obstacle to the external plasma flow. We then study Titan's induced magnetosphere, its structure, dynamics and variability, and discuss the possible existence of a small intrinsic magnetic field of Titan. Saturn's magnetosphere, which is dynamically and chemically coupled to all other components of Saturn's environment in addition to Titan, is then described. We start with a summary of the morphology of magnetospheric plasma and fields. Then we discuss what we know of the magnetospheric interactions in each region. Beginning with the innermost regions and moving outwards, we first describe the region of the main rings and their connection to the low-latitude ionosphere. Next the icy satellites, which develop specific magnetospheric interactions, are imbedded in a relatively dense neutral gas cloud which also overlaps the spatial extent of the diffuse E ring. This region constitutes a very interesting case of direct and mutual coupling between dust, neutral gas and plasma populations. Beyond about twelve Saturn radii is the outer magnetosphere, where the dynamics is dominated by its coupling with the solar wind and a large hydrogen torus. It is a region of intense coupling between the magnetosphere and Saturn's upper atmosphere, and the source of Saturn's auroral emissions, including the kilometric radiation. For each of these regions we identify the key scientific questions and propose an investigation strategy to address them. Finally, we show how the unique characteristics of the CASSINI spacecraft, instruments and mission profile make it possible to address, and hopefully solve, many of these questions. While the CASSINI orbital tour gives access to most, if not all, of the regions that need to be explored, the unique capabilities of the MAPS instrument suite make it possible to define an efficient strategy in which in situ measurements and remote sensing observations complement each other. Saturn's magnetosphere will be extensively studied from the microphysical to the global scale over the four years of the mission. All phases present in this unique environment — extended solid surfaces, dust and gas clouds, plasma and energetic particles — are coupled in an intricate way, very much as they are in planetary formation environments. This is one of the most interesting aspects of Magnetospheric and Plasma Science studies at Saturn. It provides us with a unique opportunity to conduct an in situ investigation of a dynamical system that is in some ways analogous to the dusty plasma environments in which planetary systems form. This revised version was published online in August 2006 with corrections to the Cover Date.     

The X-ray imaging telescopes on Exosat

The instrument configuration and performance characteristics of the X-ray imaging telescopes on EXOSAT are described. The instrument comprises two fully independent Wolter I imaging telescopes. Each telescope can be used in either of two principal modes: (i) an imaging mode with either a position sensitive proportional counter or a channel multiplier array plate in the focal plane, (ii) a spectrometer mode which features a 500 lines/mm and/or a 1000 lines/mm transmission grating as dispersive element.Preliminary results from the calibration of the fully integrated experiment indicate an ultimate angular resolution of 8.5 arc sec full width at half maximum or 17.5 arc sec half-power beam width. The ultimate wavelength resolution in the spectrometer mode ranges from 1Å for wavelengths below 50Å, to 5Å at wavelengths near 300Å.A method for estimating the telescope performance is given which reasonably accounts for the influence of the X-ray source spectrum and the degree of interstellar absorption on the counting statistics.A comparison between EXOSAT and the EINSTEIN telescope in terms of band width/resolution and minimum source detectability shows an enhanced potential for EXOSAT relative to EINSTEIN for sources with T 10⁷K and low column densities (< 4 × 10²⁰cm^–2) and a reduced potential for sources with hard, or heavily cut-off, spectra.     

The intersection of a Loxodrome with a great circle

The intersections of a loxodrome (rhumb line) and a great circle are of interest for some navigational problems, but a closed-form solution cannot be formulated. An algorithm is given for computing approximations to any desired degree of accuracy using Newton's method. By using the equatorial angle φ as an independent variable all solutions can be found rapidly using the modest computational capabilities of a personal computer     

Digital accumulators in phase and frequency tracking loops

Results on the effects of digital accumulators in phase and frequency tracking loops are presented. Digital accumulators or summers are used extensively in digital signal processing to perform averaging or to reduce processing rates to acceptable levels. For tracking the Doppler of high-dynamic targets at low carrier-to-noise ratios, it is shown through simulation and experiment that digital accumulators can contribute an additional loss in operating threshold. This loss was not considered in any previous study and needs to be accounted for in performance prediction analysis. Simulation and measurement results are used to characterize the loss due to the digital summers for three different tracking loops: a digital phase-locked loop, a cross-product automatic frequency tracking loop, and an extended Kalman filter. The tracking algorithms are compared with respect to their frequency error performance and their ability to maintain lock during severe maneuvers at various carrier-to-noise ratios. It is shown that failure to account for the effect of accumulators can result in an inaccurate performance prediction, the extent of which depends highly on the algorithm used     

Urodelean amphibians in studies on microgravity: effects upon organ and tissue regeneration.

Results obtained from nine experiments performed onboard Russian biosatellites have shown that microgravity promotes tissue regeneration in the newt, Pleurodeles waltl. The effect has been reproduced in all flights and on a clinostat as well for eye tissues (lens and retina), limbs and tail. The effect was demonstrated in 1.5- to 2-fold increase in cell proliferation in the early stages of regeneration in space flight. Animals "flown" intact and operated after flight regenerated faster than control ones and showed long-lasting micro-"g" effect. The most recent experiment flew aboard the Bion-11 biosatellite. This test was performed for study on microgravity effect on neural retina regeneration after optic nerve lesioning in the newt. Obtained results confirmed our previous information about intensification of regenerative processes in detached neural retina in urodela exposed to simulated weightlessness (Grigoryan et al., 1998). In particular, we found the increase and activation of cell populations participating in neural retina restoration and maintenance of retinal structure. Our findings suggest that promoting effect of microgravity upon regeneration could be influenced by several factors, largely influenced by a response of the whole organism to changed gravity vector. We hypothesized the synthesis of the specific range of stress proteins induced by micro-"g" and their regulative role in cell proliferation. Such a hypothesis for the existence of "altered gravity stress proteins" is discussed.     

Experimental and mathematical modeling of the consumer's influence on productivity of algae in a model aquatic ecosystem.

A "producer-consumer" (Chlorella vulgaris-Paramecium caudatum) closed aquatic system has been investigated experimentally and theoretically. It has been found that there is a direct relationship between the growth of the paramecia population and their release of ammonia nitrogen, which is the best form of nitrogen for Chlorella growth. The theoretical study of a model of a "producer-consumer" aquatic biotic cycle with spatially separated compartments has confirmed the contribution of paramecia to nitrogen cycling. It has been shown that an increase in the concentration of nitrogen released as metabolites of paramecia is accompanied by an increase in the productivity of microalgae.