General Relativistic Theory of Light Propagation in the Field of Radiative Gravitational Multipoles

The extremely high precision of current radio/optical interferometric observations and the unparalleled sensitivity of existing (LIGO) and future (LISA, ASTROD) gravitational-wave detectors demand a much better theoretical treatment of relativistic effects in the propagation of electromagnetic signals through variable gravitational fields. Especially important for future gravitational-wave observatories is the problem of propagation of light rays in the field of multipolar gravitational waves emitted by a localized source of gravitational radiation. A consistent approach giving a complete and exhaustive solution to this problem in the first post-Minkowskian approximation of General Relativity is presented in this paper. We derive a set of equations describing propagation of an electromagnetic wave in the retarded gravitational field of a time-dependent localized source emitting gravitational waves with arbitrary multipolarity and show for the first time that they can be integrated analytically in closed form. We also prove that the leading terms in observable relativistic effects depend exclusively on the values of the multipole moments of the isolated system and its time derivatives taken at the retarded instant of time on the null cone and do not depend on their integrated values. By making use of our integration technique we reproduce the known results of integration of equations of light rays both in a stationary field of a gravitational lens and in that of a plane gravitational wave, thereby establishing a relationship between our formalism and the approximations used by previous researches. The gauge freedom of our formalism is carefully studied and all gauge-dependent terms in the expressions for observable quantities are singled out and used for physically meaningful interpretation of observations. Two limiting cases of small and large values of the light-ray impact parameter, d, are elaborated in more detail. We explicitly show that in the case of small impact parameter the leading order terms for any effect of light propagation in the field of an arbitrary multipole depend neither on its radiative nor on its intermediate zone contributions. The main effect rather comes from the near zone terms. This property makes much more difficult any direct detection of gravitational waves by astronomical techniques if general relativity is correct. We also present an analytical treatment of time delay and light-ray bending in large impact parameter case corresponding to the approximation of a plane gravitational wave of arbitrary multipolarity. Explicit expressions for time delay and deflection angle are obtained in terms of the transverse-traceless (TT) part of the space-space components of the metric tensor

Propagation of Light in the Field of Stationary and Radiative Gravitational Multipoles

Extremely high precision of near-future radio/optical interferometric observatories like SKA, Gaia, SIM and the unparalleled sensitivity of LIGO/LISA gravitational-wave detectors demands more deep theoretical treatment of relativistic effects in the propagation of electromagnetic signals through variable gravitational fields of the solar system, oscillating and precessing neutron stars, coalescing binary systems, exploding supernova, and colliding galaxies. Especially important for future gravitational-wave observatories is the problem of propagation of light rays in the field of multipolar gravitational waves emitted by a localized source of gravitational radiation. Present paper suggests physically-adequate and consistent mathematical solution of this problem in the first post-Minkowskian approximation of General Relativity which accounts for all time-dependent multipole moments of an isolated astronomical system

Social Image of the Ural Region Mining Workers at the Post-Reform Time Period

The article dwells upon a transition character of the Ural proletariat at the post-reform time period. Both domestic and foreign historiography define the social image of the Russian worker of the 20th century second part as either proletarian or referring to a “half-worker and half-peasant” type, combining traditional pre-capitalist features with newer ones, characteristic of industrial manufacture. A manufacturer’s being connected to the land as well as forming a certain mentality combined with the professional skills are considered the main criteria while defining the Russian workers’ typology. Taking into consideration the Urals old tradition of industrial manufacture, the process of forming an independent class at the area progressed rather vigorously. Despite of land allotments availability, workers in the Urals got under influence of modernization. Treating scornfully peasant work, industrial workers purposefully separated themselves from peasants. Nevertheless, it will be wrong to speak about complete disappearance of traditional peasant psychology among the Ural proletariat of the said time period. The working class at the region used to belong to a transition type, therefore we can speak about its incomplete establishment as a bourgeois society class

Estimates in Beurling--Helson type theorems. Multidimensional case

We consider the spaces $A_p(\mathbb T^m)$ of functions $f$ on the $m$ -dimensional torus $\mathbb T^m$ such that the sequence of the Fourier coefficients $\hat{f}=\{\hat{f}(k), ~k \in \mathbb Z^m\}$ belongs to $l^p(\mathbb Z^m), ~1\leq p<2$. The norm on $A_p(\mathbb T^m)$ is defined by $\|f\|_{A_p(\mathbb T^m)}=\|\hat{f}\|_{l^p(\mathbb Z^m)}$. We study the rate of growth of the norms $\|e^{i\lambda\varphi}\|_{A_p(\mathbb T^m)}$ as $|\lambda|\rightarrow \infty, ~\lambda\in\mathbb R,$ for $C^1$ -smooth real functions $\varphi$ on $\mathbb T^m$ (the one-dimensional case was investigated by the author earlier). The lower estimates that we obtain have direct analogues for the spaces $A_p(\mathbb R^m)$

Propagation of Light in the Field of Stationary and Radiative Gravitational Multipoles

Extremely high precision of near-future radio/optical interferometric observatories like SKA, Gaia, SIM and the unparalleled sensitivity of LIGO/LISA gravitational-wave detectors demands more deep theoretical treatment of relativistic effects in the propagation of electromagnetic signals through variable gravitational fields of the solar system, oscillating and precessing neutron stars, coalescing binary systems, exploding supernova, and colliding galaxies. Especially important for future gravitational-wave observatories is the problem of propagation of light rays in the field of multipolar gravitational waves emitted by a localized source of gravitational radiation. Present paper suggests physically-adequate and consistent mathematical solution of this problem in the first post-Minkowskian approximation of General Relativity which accounts for all time-dependent multipole moments of an isolated astronomical system.Comment: 36 pages, no figure

NUMERICAL MODELING OF A STRESS-STRAIN STATE OF A GAS PIPELINE WITH COLD BENDING OFFSETS ACCORDING TO IN-LINE INSPECTION

Knowledge of the current stress-strain state of any section of the pipeline allows you to make informed decisions on its operation, maintenance and repair, as well as on the prediction of the technical condition. The task of determining the characteristics of the stress-strain state of a gas pipeline section that has cold bend offsets (CBO) according to in-line inspection (ILI) is considered. The bent part of CBO is characterized by the presence of residual stresses and deformations in the wall of the offset, which contribute to the overall level of the stress-strain state of the gas pipeline operating under external and internal loads. Using the results of in-line diagnostics, numerical modeling and a solution, the change in the values of longitudinal stresses, is determined and the need to take into account residual stresses in the zone of elastic-plastic deformations of cold bend offsets is shown

Assessment of internal pressure effect, causing additional bending of the pipeline

Article justifies accounting for internal pressure effect in the pipeline, causing additional bending of the pipeline. According to some scientists, there is an erroneously used concept of the equivalent longitudinal axial force (ELAF) Sx, which depends on working pressure, temperature stresses, and joint deformations of pipelines with various types of soils. However, authors of the article use ELAF Sx concept at construction of mathematical model of stress-strain state (SSS) for complex section of the trunk pipeline, and also reveal it when analyzing the results of calculating the durability and stability of the pipeline. Analysis of SSS for calculated section of the pipeline was carried out for two statements of the problem for different values of operation parameters. In the first statement, effect of internal pressure causing bending of the pipeline is taken into account, and in the second it is neglected. It is shown that due to effect of ELAF Sx at p0 = 9.0 MPa, Dt = 29 °C extreme value of bend increases by 54 %, extreme values of bending stresses from span bending moment increase by 74 %, and extreme value of bending stresses from support bending moment double with regard to corresponding SSS characteristics of the pipeline. In case of neglecting the internal pressure effect causing additional bending of the pipeline (second statement of the problem), error in calculating the extreme value of bend is 35 %, extreme value of bending stresses from span bending moments is 44 %, and extreme value of bending stresses from support bending moments is 95 %

Mathematical model of the starter system for a three-stage synchronous generator with a damping cage

В данной статье рассматривается математическая модель стартерной системы для газотурбинных двигателей. Модель исследуемого трехкаскадного синхронного генератора была построена в системе d-q-координат. Полученная модель позволяет сконфигурировать параметры машины в широком диапазоне, а также получить информацию о токах и напряжениях основных электрических узлов машины. Математическое моделирование показало эффективность полученной модели и адекватность предложенного алгоритма электростартерного запуска синхронной машины.This paper, considers a mathematical model the starter system for gas turbine engines. Model of the investigated three-stage synchronous generator has been built in the dq-coordinates. The obtained model allows one to configure the machine parameters in a wide range, as well as receive information about currents and voltages major electrical components of the machine. Mathematical modeling shown efficiency of the resulting model and adequacy of the proposed algorithms electric starter mode synchronous machine