Modal combination rules for multicomponent earthquake excitation

A response spectrum method for dynamic analysis of linear structures subjected to multicomponent seismic input is developed. The method is based on elementary concepts of stationary random vibration and assumes the existence of a set of principal directions along which components of ground motion are uncorrelated. Modal combination rules in terms of ground response spectra are developed for the mean and standard deviation of peak responses and for rootmean-square responses. These rules account for correlations between modal responses of the structure, as well as correlations between the input components. When the position of principal directions is unknown, two alternative rules are proposed: one uses the direction which is most critical for the response quantity of interest, and the other considers the direction as a random variable. The proposed method is simple for practical implementation and gives more accurate results than other existing methods.     

Scattering of an Electromagnetic Wave on a Dielectric Layer Bounded on Two Sides by Two Different Homogeneous, Semi-Infinite Media

The problem of the passage of a plane electromagnetic wave through an arbitrary, inhomogeneous dielectric layer bounded on two sides by two different homogeneous, semi-infinite media is considered. Algebraic relations are obtained between the amplitudes of transmission and reflection (the scattering amplitudes) for the problem under consideration and the wave scattering amplitudes when the layer is bounded on both sides by a vacuum. It is shown that for s and p polarized fields the scattering problem (a boundary-value problem) can be formulated as a Cauchy problem directly for the s and p wave equations. It is also shown that the problem of finding the field inside the layer also reduces to a Cauchy problem in the general case.     

Spin-down of millisecond pulsars owing to gravitational wave emission

The gravitational radiation from millisecond pulsars owing to glitches in their angular velocity is examined. It is assumed that the energy transferred from interior superfluid regions to the crust of a neutron star is converted into gravitational wave energy by damping oscillations of the matter in the star. The gravitational wave intensity and amplitude are calculated for fourteen millisecond pulsars. Gravitational radiation can explain the observed spin-down of millisecond pulsars and an estimate is given for the magnetic field at which the proposed mechanism predominates in the spin-down of these pulsars. __________ Translated from Astrofizika, Vol. 51, No. 3, pp. 479–486 (August 2008).     

Modal decomposition method for stationary response of non-classically damped systems

The stationary response of multi-degree-of-freedom non-classically damped linear systems subjected to stationary input excitation is studied. A modal decomposition procedure based on the complex eigenvectors and eigenvalues of the system is used to derive general expressions for the spectral moments of response. These expressions are in terms of cross-modal spectral moments and explicitly account for the correlation between modal responses; thus, they are applicable to structures characterized with significant non-classical damping as well as structures with closely spaced frequencies. Closed form solutions are presented for the important case of response to white-noise input. Various quantities of response of general engineering interest can be obtained in terms of these spectral moments. These include mean zero-crossing rate and mean, variance and distribution of peak response over a specified duration. Examples point out several instances where non-classical damping effects become significant and illustrate the marked improvement of the results of this study over conventional analysis based on classical damping approximations.     

Slowly rotating superdense configurations in Rosen's bimetric theory of gravitation

In the limits of the Bimetric Theory of Gravitation the equations of axial-symmetric gravitational field, describing the field of rotating configurations, are obtained and examined. The analytical solutions of these equations out of configurations are found. The equations are solved numerically in the first approximation in the angular velocity for the configurations consisting of the real baryon gas (cf. Sahakian, 1972). The moments of inertia of these configurations in BTG are calculated. It is shown that the equations and the appropriate solution, obtained by Falik and Opher (1979), are incorrect.     

Jumps in pulsar angular velocity and their relaxation with allowance for pinning and depinning of quantum vortex filaments

The dynamics of the rotating two-component system in the core of a neutron star is considered. Equations of motion are derived with allowance for the pinning and depinning of neutron vortices, and general solutions of these equations are found for relatively small changes in the star's angular velocity. It is shown that these solutions can describe both a jump in a pulsar's angular velocity and its subsequent relaxation. The characteristic pinning and depinning times are estimated qualitatively from observational data for jumps in the angular velocity of the Vela pulsar.Translated from Astrofizika, Vol. 39, No. 4, pp. 593–604, October–December, 1996.     

On the election of the flat metric in the bimetric theory of gravitation

The problem of the form of the flat metric in the Rosen bimetric theory is examined in the following work.It is shown, on concrete examples, how necessary it is to write down the flat metric and solve the problem of finding the gravitational field in arbitrary non-inertial frame. It is shown also how to separate the pure gravitational effects from those connected with non-inertiality of the frame by way of comparing both metrics.     

Theory of relaxation of pulsar angular velocity within the framework of the general theory of relativity

The dynamics of the rotation of a two-component system in a neutron star is considered within the framework of the general theory of relativity. Equations for the angular velocities of the normal and superfluid components are obtained in the W approximation. It is shown that the solutions of these equations can describe the relaxation of pulsar angular velocity after a glitch. Translated from Astrofizika, Vol. 42, No. 1, pp. 89–100, January–March, 1999.     

Electric and magnetic fields inside the superconducting core of neutron stars

Feynman's approach has been used to derive the equation of dynamics for type II superconductors from the Schr?dinger equation. A closed set of equations for the study of vortex dynamics has been obtained. These equations have been used for calculating electric and magnetic fields inside the core of neutron stars. In particular, the contribution of vortices to the generation of electric and magnetic fields inside the core of the star is explicitly displayed.     

Generation of a toroidal magnetic field in rotating neutron stars

The electromagnetic properties of neutron stars (pulsars) are studied. It is shown that taking the presence of two angular rotation velocities of the components of neutron stars and the first corrections to the general theory of relativity into account in the equations of hydrodynamic equilibrium for the plasma and in Maxwell’s equations leads to the generation of toroidal magnetic fields in the depths of a neutron star. __________ Translated from Astrofizika, Vol. 49, No. 1, pp. 97–101 (February 2006).