Convergence Acceleration Techniques

This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the acceleration of slowly convergent and the summation of divergent series that are ubiquitous in relevant applications. The computing time is reduced in many cases by orders of magnitude.Comment: 6 pages, LaTeX; provides an easy-to-understand introduction to the field of convergence acceleratio

Feasibility of study magnetic proximity effects in bilayer "superconductor/ferromagnet" using waveguide-enhanced Polarized Neutron Reflectometry

A resonant enhancement of the neutron standing waves is proposed to use in order to increase the magnetic neutron scattering from a "superconductor/ferromagnet"(S/F) bilayer. The model calculations show that usage of this effect allows to increase the magnetic scattering intensity by factor of hundreds. Aspects related to the growth procedure (order of deposition, roughness of the layers etc) as well as experimental conditions (resolution, polarization of the neutron beam, background etc) are also discussed. Collected experimental data for the S/F heterostructure Cu(32nm)/V(40nm)/Fe(1nm)/MgO confirmed the presence of a resonant 60-fold amplification of the magnetic scattering.Comment: The manuscript of the article submitted to Crysstalography Reports. 23 pages, 5 figure

Capacity calculation of the electrotechnical scheme of discharge gap replacement of the ozonizer in the COMSOL environment

The investigation of electrostatic field distribution of ozonator electrode gap caused by inhomogeneous permittivity has been done. The paper presents calculation of electrostatic field energy of ozonator electrode gap. From the energy of electrostatic field distribution the information about electrode system capacity has been extracted. For calculation of the electrostatic field and capacity of electrode system the software integrated environment COMSOL has been used

A hydrodynamic model for asymmetric explosions of rapidly rotating collapsing supernovae with a toroidal atmosphere

We numerically solved the two-dimensional axisymmetric hydrodynamic problem of the explosion of a low-mass neutron star in a circular orbit. In the initial conditions, we assumed a nonuniform density distribution in the space surrounding the collapsed iron core in the form of a stationary toroidal atmosphere that was previously predicted analytically and computed numerically. The configuration of the exploded neutron star itself was modeled by a torus with a circular cross section whose central line almost coincided with its circular orbit. Using an equation of state for the stellar matter and the toroidal atmosphere in which the nuclear statistical equilibrium conditions were satisfied, we performed a series of numerical calculations that showed the propagation of a strong divergent shock wave with a total energy of 0.2x10^51 erg at initial explosion energy release of 1.0x10^51 erg. In our calculations, we rigorously took into account the gravitational interaction, including the attraction from a higher-mass (1.9M_solar) neutron star located at the coordinate origin, in accordance with the rotational explosion mechanism for collapsing supernovae.W e compared in detail our results with previous similar results of asymmetric supernova explosion simulations and concluded that we found a lower limit for the total explosion energy.Comment: 13 pages, 5 figures, 2 table

The Role of Pension Funds in Financing US Federal Debt

The article examines main trends in financing the federal debt, pointing out its structure, with focus on the role of pension funds as a source of financing; because the surplus of Social Security funds is loaned to the rest of the government; interlinks concerning this process and possible problems; the peculiarities of the federal government pension system’s investment in the government bonds. The US public debt as a share of GDP is much less than in many countries, but its volume is near 20 trln. doll. It may be classified by marketable and non-marketable securities, which are mainly owed to certain government trust funds such as the Social Security trust fund. So the Social Security trust fund, in effect is exchanging one type of debt for the other, taking into consideration that the non-marketable securities represent amounts owed to the beneficiaries. The reserves are in effect borrowed for a time by the rest of the government, and then repaid with interest when the trust funds need them back. Looking ahead Social Security will continue to be financed through its own receipts, mainly payroll tax; and Social Security Trust Fund surplus will become diminishing, with less possibilities to finance federal debt