Local Solution Method for Numerical Solving of the Wave Propagation Problem

A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential increasing (decreasing) is proposed. It is based on approximation of the solution to find in the form of superposition of certain polynomial- exponential basic functions. The method is studied for the Helmholtz equation in comparison with the standard finite difference method. The numerical tests have shown the convergence of the method proposed. In comparison with the finite difference method the same accuracy is obtained on substantially rarer mesh. This advantage becomes more pronounced, if the solution varies very rapidly.Comment: 13 page

Model of multiple Dirac eikonal scattering of protons by nuclei

The model of multiple Dirac eikonal scattering of incident proton by target-nucleus nucleons is developed, in which new expressions for the elastic $pA$-scattering amplitudes are obtained from the multiple scattering Watson series with employing the eikonal approximation for the Dirac propagators of the free proton motion between successive scattering acts on nucleons. Basing on this model, calculations for the complete set of observables of the elastic $p+^{40}$Ca and $p+^{208}$Pb at 800 MeV have been performed with using proton-nucleon amplitudes determined from the phase analysis and the nucleon densities obtained from describing the target-nucleus structure in the relativistic mean-field approximation. A comparison has been made of the results of these calculations with analogous calculations on the basis of the Glauber multiple diffraction theory.Comment: 17 pages, 1 figur

On Brownian motion on the plane with membranes on rays with a common endpoint

We consider a Brownian motion on the plane with semipermeable membranes on n rays that have a common endpoint in the origin. We obtain the necessary and sufficient conditions for the process to reach the origin and we show that the probability of hitting the origin is equal to zero or one.Comment: 21 pages, 4 figure

Multiple Dirac eikonal scattering of polarized intermediate-energy protons by nuclei

An improved model of the multiple Dirac eikonal scattering of proton on nucleons of the target nucleus is considered. In this model, the amplitudes of elastic $p-A$ scattering are found on the basis of the Watson series of multiple scattering by means of the eikonal expansion of the Dirac propagator for the free proton motion between scattering events on nucleons, and the nucleus structure is described in the relativistic mean field model. The calculations have been performed for the complete set of observables for the elastic $p+^{40}$Ca and $p+^{208}$Pb scattering at 800 MeV. The effects of allowing for distinction between the relativistic scalar and vector nucleon densities on the description of the $p-A$ scattering observables have been studied, as well as the results of calculations using nucleon densities obtained in different modern variants of the relativistic mean field model have been compared.Comment: 15 pages, 3 figure

Search for isolated Galactic Centre stellar mass black holes in the IR and sub-mm range

We investigate a possibility to find an accreting isolated black hole (IBH) with mass $1-100~\mathrm{M}_{\odot}$ within Central Galactic Molecular Zone (CMZ) in the submillimetre and IR spectral range with help of planned space observatories James Webb Space Telescope (JWST) and Millimetron (MM). We assume the spherical mode of accretion. We develop the simplest possible quantitative model of the formation of radiation spectrum in this range due to synchrotron emission and show that it fully agrees with the more complicated model of Ipser and Price 1982 for expected values of accretion rate. If a substantial fraction of LIGO events was caused by merger of primordial black holes, the JWST would be able to find them provided that there is a cusp in distribution of dark matter in the Galaxy and that the accretion efficiency parameter $\lambda$ defined as the ratio of accretion rate onto IBH to its Bondi-Hoyle-Lyttleton value is larger than $\sim 10^{-2}$. A comparable amount of IBHs is also predicted by recent models of their formation due to stellar evolution. MM capabilities are hampered by the effect of confusion due to distant submillimetre galaxies, but it can also be used for such purposes if the confusion effect is properly dealt with. In case of efficient accretion with $\lambda \sim 1$, both instruments could detect IBHs even when their number densities are as low as $10^{-6}~\mathrm{pc}^{-3}$.Comment: 29 pages, 12 figures, accepted to MNRA

Anisotropic thermal Sunyaev-Zel'dovich effect and the possibility of an independent measurement of the CMB dipole, quadrupole and octupole

We consider the effect of the cosmic microwave background (CMB) frequency spectral distortions arising due to the Compton scattering of the anisotropic radiation on Sunyaev-Zel'dovich (SZ) clusters. We derive the correction to the thermal SZ effect due to the presence of multipoles with $\ell=1,2,3$ in the anisotropy of the CMB radiation. We show that this effect gives us an opportunity for an independent evaluation of the CMB dipole, quadrupole and octupole angular anisotropy in our location using distorted signal from the nearby galaxy clusters and to distinguish between the Sachs-Wolfe (SW) and the Integrated Sachs-Wolfe (ISW) effects by combining such signals from distant and nearby clusters. The future space mission 'Millimetron' will have unprecedented sensitivity, which will make it possible to observe the spectral distortion we are considering.Comment: 8 pages, 8 figures, accepted in Phys.Rev.

Lattice dynamic theory of compressed rare-gases crystals in the deformed atom model

Lattice dynamics of rare-gas crystals is built on the base of adiabatic approximation when the deformation of electron shells of atoms of dipole and quadrupole types depending on nucleus shift and simultaneously arising Van-der-Vaals forces. The dipole forces are the most long-range ones. The obtained oscillation equations are studied in long-wave approximation. The role of three-body interaction and quadrupole deformation in the violation of Cauchy relation is discussed. Birch elastic moduli calculated for Xe and deviations from Cauchy relation are in good agreement with the experiment in a wide pressure range.Comment: 20 pages,3 figures and 1 Tabl

A Model of the Cosmic Infrared Background Produced by Distant Galaxies

The extragalactic background radiation produced by distant galaxies emitting in the far infrared limits the sensitivity of telescopes operating in this range due to confusion. We have constructed a model of the infrared background based on numerical simulations of the large-scale structure of the Universe and the evolution of dark matter halos. The predictions of this model agree well with the existing data on source counts. We have constructed maps of a sky field with an area of 1 deg$^2$ directly from our simulated observations and measured the confusion limit. At wavelengths $100-300$ $\mu$m the confusion limit for a 10-m telescope has been shown to be at least an order of magnitude lower than that for a 3.5-m one. A spectral analysis of the simulated infrared background maps clearly reveals the large-scale structure of the Universe. The two-dimensional power spectrum of these maps has turned out to be close to that measured by space observatories in the infrared. However, the fluctuations in the number of intensity peaks observed in the simulated field show no clear correlation with superclusters of galaxies; the large-scale structure has virtually no effect on the confusion limit.Comment: 10 pages, 4 figure

Pushing down the low-mass halo concentration frontier with the Lomonosov cosmological simulations

We introduce the Lomonosov suite of high-resolution N-body cosmological simulations covering a full box of size 32 $h^{-1}$ Mpc with low-mass resolution particles ($2\times10^7$ $h^{-1}\,M_\odot$) and three zoom-in simulations of overdense, underdense and mean density regions at much higher particle resolution ($4\times10^4$ $h^{-1}\,M_\odot$). The main purpose of this simulation suite is to extend the concentration-mass relation of dark matter halos down to masses below those typically available in large cosmological simulations. The three different density regions available at higher resolution provide a better understanding of the effect of the local environment on halo concentration, known to be potentially important for small simulation boxes and small halo masses. Yet, we find the correction to be small in comparison with the scatter of halo concentrations. We conclude that zoom simulations, despite their limited representativity of the volume of the Universe, can be effectively used for the measurement of halo concentrations at least at the halo masses probed by our simulations. In any case, after a precise characterization of this effect, we develop a robust technique to extrapolate the concentration values found in zoom simulations to larger volumes with greater accuracy. All together, Lomonosov provides a measure of the concentration-mass relation in the halo mass range $10^7-10^{10}$ $h^{-1}\,M_\odot$ with superb halo statistics. This work represents a first important step to measure halo concentrations at intermediate, yet vastly unexplored halo mass scales, down to the smallest ones. All Lomonosov data and files are public for community's use.Comment: 11 pages, accepted by MNRA

Monte-Carlo sensitivity study for sterile neutrino search with 144^{144}Ce - 144^{144}Pr source and liquid scintillation detectors of various geometries

Expected energy spectra calculations for large volume liquid scintillation detectors to inverse $\beta$-decay for antineutrinos produced by $^{144}$Ce -- $^{144}$Pr artificial source have been performed. The calculations were carried out through Monte-Carlo method within GEANT4.10 framework and were purposed to search for neutrino oscillation to sterile eigenstate with mass about 1 eV. The analysis of relative sensitivity to oscillation parameters for different detector shapes has been performed.Comment: 4 pages, 3 figure