Realistic Exact Solution for the Exterior Field of a Rotating Neutron Star

A new six-parametric, axisymmetric and asymptotically flat exact solution of Einstein-Maxwell field equations having reflection symmetry is presented. It has arbitrary physical parameters of mass, angular momentum, mass--quadrupole moment, current octupole moment, electric charge and magnetic dipole, so it can represent the exterior field of a rotating, deformed, magnetized and charged object; some properties of the closed-form analytic solution such as its multipolar structure, electromagnetic fields and singularities are also presented. In the vacuum case, this analytic solution is matched to some numerical interior solutions representing neutron stars, calculated by Berti & Stergioulas (Mon. Not. Roy. Astron. Soc. 350, 1416 (2004)), imposing that the multipole moments be the same. As an independent test of accuracy of the solution to describe exterior fields of neutron stars, we present an extensive comparison of the radii of innermost stable circular orbits (ISCOs) obtained from Berti & Stergioulas numerical solutions, Kerr solution (Phys. Rev. Lett. 11, 237 (1963)), Hartle & Thorne solution (Ap. J. 153, 807, (1968)), an analytic series expansion derived by Shibata & Sasaki (Phys. Rev. D. 58 104011 (1998)) and, our exact solution. We found that radii of ISCOs from our solution fits better than others with realistic numerical interior solutions.Comment: 13 pages, 13 figures, LaTeX documen

Damping of quasi-2D internal wave attractors by rigid-wall friction

The reflection of internal gravity waves at sloping boundaries leads to focusing or defocusing. In closed domains, focusing typically dominates and projects the wave energy onto 'wave attractors'. For small-amplitude internal waves, the projection of energy onto higher wave numbers by geometric focusing can be balanced by viscous dissipation at high wave numbers. Contrary to what was previously suggested, viscous dissipation in interior shear layers may not be sufficient to explain the experiments on wave attractors in the classical quasi-2D trapezoidal laboratory set-ups. Applying standard boundary layer theory, we provide an elaborate description of the viscous dissipation in the interior shear layer, as well as at the rigid boundaries. Our analysis shows that even if the thin lateral Stokes boundary layers consist of no more than 1% of the wall-to-wall distance, dissipation by lateral walls dominates at intermediate wave numbers. Our extended model for the spectrum of 3D wave attractors in equilibrium closes the gap between observations and theory by Hazewinkel et al. (2008)

Faithful transformation of quasi-isotropic to Weyl-Papapetrou coordinates: A prerequisite to compare metrics

We demonstrate how one should transform correctly quasi-isotropic coordinates to Weyl-Papapetrou coordinates in order to compare the metric around a rotating star that has been constructed numerically in the former coordinates with an axially symmetric stationary metric that is given through an analytical form in the latter coordinates. Since a stationary metric associated with an isolated object that is built numerically partly refers to a non-vacuum solution (interior of the star) the transformation of its coordinates to Weyl-Papapetrou coordinates, which are usually used to describe vacuum axisymmetric and stationary solutions of Einstein equations, is not straightforward in the non-vacuum region. If this point is \textit{not} taken into consideration, one may end up to erroneous conclusions about how well a specific analytical metric matches the metric around the star, due to fallacious coordinate transformations.Comment: 18 pages, 2 figure

Nodal and Periastron Precession of Inclined Orbits in the Field of a Rapidly Rotating Neutron Star

We derive a formula for the nodal precession frequency and the Keplerian period of a particle at an arbitrarily inclined orbit (with a minimum latitudinal angle reached at the orbit) in the post-Newtonian approximation in the external field of an oblate rotating neutron star (NS). We also derive formulas for the nodal precession and periastron rotation frequencies of slightly inclined low-eccentricity orbits in the field of a rapidly rotating NS in the form of asymptotic expansions whose first terms are given by the Okazaki--Kato formulas. The NS gravitational field is described by the exact solution of the Einstein equation that includes the NS quadrupole moment induced by rapid rotation. Convenient asymptotic formulas are given for the metric coefficients of the corresponding space-time in the form of Kerr metric perturbations in Boyer--Lindquist coordinates.Comment: 12 page

Smoothening and denoising optical spectra of stars

A comparative analysis of methods for eliminating background noise is attempted. An emphasis on the Savitzky-Golay method, Kaiser filtration and wavelet-based denoising is made; and argued that the behaviour of a singal at different scales (frequencies) plays a crucial role when the spectra are processed with the latter

Investigation of structure of noise component in molecular spectra

© Published under licence by IOP Publishing Ltd. In the work the noise component of molecular spectra is investigated by use the Hurst index which is the quantitative parameter of memory effects. It was shown that the low- frequency noise component predominates. The Hurst index is from 0.6 to 0.7 for the studied FTIR spectra registered at different temperatures

Effect of color noise on the processing of optical signals using the swarm intellect algorithm

© 2016, Allerton Press, Inc.An approach based on stochastic particle swarm optimization is used for the mathematical processing of spectral profiles with noise. Noises with different values of the Hurst index, which characterizes the noise component based on the prevalence of its low- or high-frequency components, is used to test the algorithm’s stability with respect to noise. The Hurst index is varied from 0.1 to 0.9. The effect color noise with levels of 1 to 10% has on the processing of optical signals using the particle swarm optimization algorithm is analyzed. The method is shown to be stable with respect to noise with a level of 10% if the Hurst index does not exceed a value of 0.5

Particle swarm optimization in the problem of decomposing two-component spectral profiles

An approach based on stochastic particle swarm optimization is proposed for the mathematical processing of spectral profiles. It is shown that the proposed approach allows accurate decomposition of complex model spectra and determination of the parameters of spectral components. © 2014 Allerton Press, Inc

Regularization of ill-posed inverse problems in applied spectroscopy

General principles for solving ill-posed inverse problems in applied spectroscopy were considered and an approach to the construction of regularizing functionals for non-Markovian processes was proposed. A regularized algorithm for deconvolution of complex spectra into elementary components was developed. The efficiency of the method was illustrated by the example of the deconvolution of the IR spectrum of 1,2-diphenylethane. © 2007 by Allerton Press, Inc

An evolutionary particle swarm optimization algorithm for mathematical processing of experimental spectra

© 2017, Pleiades Publishing, Ltd.A particle swarm optimization algorithm is applied for mathematical treatment of Fourier-transform IR spectra of branched copolymers of methyl methacrylate. The efficiency of reconstruction of the spectra using the particle swarm optimization algorithm as compared with the least squares method is illustrated by the example of decomposition of a six-component experimental spectrum