A Two-Dimensional Hydrostatically Equilibrium Atmosphere of a Neutron Star with Given Differential Rotation

An analytic solution has been found in the Roche approximation for the axially symmetric structure of a hydrostatically equilibrium atmosphere of a neutron star produced by collapse. A hydrodynamic (quasione-dimensional) model for the collapse of a rotating iron core in a massive star gives rise to a heterogeneous rotating protoneutron star with an extended atmosphere composed of matter from the outer part of the iron core with differential rotation (Imshennik and Nadyozhin, 1992). The equation of state of a completely degenerate iron gas with an arbitrary degree of relativity is taken for the atmospheric matter. We construct a family of toroidal model atmospheres with total masses $M \approx 0.1 \div 0.2 M_{\odot}$ and total angular momenta $J \approx (1 \div 5.5) \cdot 10^{49} erg \cdot s$, which are acceptable for the outer part of the collapsed iron core, in accordance with the hydrodynamic model, as a function of constant parameters $\omega_{0} and r_{0}$ of the specified differential rotation law $\Omega = \omega_{0}\exp{\Big[-\frac{(r\sin{\Theta})^{2}}{r_{0}^{2}}\Big]}$ in spherical coordinates. The assumed rotation law is also qualitatively consistent with the hydrodynamic model for the collapse of an iron core.Comment: 9 pages, 6 figures, 1 tabl

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

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

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

Topological phases induced by charge fluctuations in Majorana wires

One of the problems concerning topological phases in solid-state systems which still remains urgent is an issue of many-body effects. In this study we address it within perturbative theory framework by considering topological phase transitions related to charge correlations in the extended Kitaev chain model that belongs to the BDI symmetry class. Obtained corrections to a zero-frequency quasiparticle Green's function allow to separate the mean-field and fluctuation contributions to a total winding number. As a result, the phase transitions caused solely by the latter are unveiled. We thoroughly analyze the mechanism of such transitions in terms of fluctuation-induced nodal points and spectrum renormalization. Additionally, features of other quasiparticle properties such as effective mass and damping are discussed in the context of topological phase transitions.Comment: 20 pages, 15 figure

A Convenient Way to Quinoxaline Derivatives through the Reaction of 2-(3-Oxoindolin-2-yl)-2-phenylacetonitriles with Benzene-1,2-diamines

Microwave-assisted reaction between 2-(3-oxoindolin-2-yl)-2-phenylacetonitriles andbenzene-1,2-diamines leads to the high-yielding formation of the corresponding quinoxalines as sole, easily isolaable products. The featured transformation involves unusual extrusion of phenylacetonitrile molecule and could be performed in a short sequence starting from commonly available indoles and nitroolefins