The numerical evaluation of theH-functions of radiative transfer in active amplifying media

The present paper contains extensive tables of the values of theH-functionH(z,<0) and of the moments ofQ(x) (in terms of which the moments ofH(z, ) can be determined) appropriate for transfer of radiation in active amplifying media in which<0. These values have been computed correct to the 7th decimal place for values of in the range (–10^–12)-(–10³⁰) and for values of z[0,1] with the aid of a 48-point gaussian quadrature formula.     

On the numerical evaluation of theH-functions of transfer problems in multiplying media

Extensive tables of the values ofH-functionsH ⁰(z, ) andH ₁ ⁰ (z, ) appropriate for the problems of radiative transfer in multiplying media characterized by >1, have been constructed correctly to the sixth decimal place for values of in the range 1.05–10. This accuracy has been attained with the aid of a 32-point Gaussian quadrature.     

The distribution law of stellarp-modes

We show that the overall densityg() of asymptotic acoustic frequencies of a star obeys a Weyl lawg() ^D–1, whereD is the dimensionality of the oscillating stellar configuration. For realistic stars with a finite non-zero surface sound speed,D is equal to the actual dimensionality of the star,D=3. For formal models with a vanishing sound velocity at the surface, heuristic arguments lead to a dimensionality parameterD=4.5. The empirical frequencies of Eddington's standard model are found to be consistent with the latter distribution, with reasonable agreement already occurring in the low-frequency range > _i 2× fundamental radial mode. We argue that real stars obey this 3.5-power law in some finite frequency interval _i << _f , _f being a very high frequency critically depending on the surface sound velocity, while the full asymptotic law, withD=3, holds for > _f .     

Theory of the Trojan asteroids,IV

In a previous publication (1977) the author has constructed a family () of long-periodic orbits in the Trojan case of the restricted problems of three bodies. Here he constructs the domain of the analytical solution of the problem of the motion, excluding the vicinity of thecritical divisor which vanishes at the exact commensurability of the natural frequencies ₁ and ₂. In terms of thecritical masses m_j(₂), or the associatedcritical energies _j ² (m), is the intersection of the intervals ofshallow resonance, of the form. Inasmuch as the intervals |₂– _j ² |<_j ofdeep resonance aredisjoint, it follows that (1) the disjointed family () embraces the tadpole branch, 0²1, lying in: and (2) despite the clustering of _j ² (m) atj=, the family () includes, for ²=1, an asymptoticseparatrix that terminates the branch in the vicinity of the Lagrangian pointL ₃.In a similar manner, the family () can be extended to the horseshoe branch 1<_{2 2} ² .     

Free convection and mass transfer effects on the hydro-magnetic oscillatory flow past an infinite vertical porous plate

Two-dimensional unsteady free convection and mass transfer, flow of an incompressible viscous dissipative and electrically conducting fluid, past an infinite, vertical porous plate, is considered, when the flow, is subjected in the action of uniform transverse magnetic field. The magnetic Reynolds number is taken to be small enough so that the induced magnetic field is negligible. The solution of the problem is obtained in the form of power series of Eckert numberE, which is very small for incompressible fluids. Analytical expressions for the velocity field and temperature field are given, as well as for the skin friction and the rate of heat transfer for the case of the mean steady flow and for the unsteady one. The influence of the magnetic parameter,M, modified Grashof numberG _c , Schmidt numberS _c and frequency , on the flow field, is discussed with the help of graphs, when the plate is being cooled, by the free convection currents (G _r ,E>0), or heated (G _r ,E<0). A comparative study with hydrodynamic case (M=0) and the hydromagnetic one (M0) is also made whenever necessary.List of symbols B₀ applied magnetic field - |B| amplitude of the skin friction - C concentration inside the boundary layer - C concentration in the free stream - C _w concentration at the porous plate - C _p specific heat at constant pressure - D diffusion coefficient - E Eckert number - g _x acceleration due to gravity - G _c modified Grashof number - G _r Grashof number - M magnetic parameter - N _u Nusselt number - P Prandtl number - |Q| amplitude of the rate of heat transfer - S _c Schmidt number - T temperature of the fluid - T _w temperature of the plate - T temperature of the fluid in the free stream - T _r ,T _i fluctuating parts of the temperature profile - u, v velocity components in thex, y directions - u dimensionless velocity in thex direction - u ₀ mean steady velocity - u ₁ unsteady part of the velocity - u _r ,u _i fluctuating parts of the velocity profile - U dimensionless free stream volocity - U ₀ mean free stream velocity - v ₀ suction velocity - x, y co-rodinate system Greek Symbols phase angle of the skin-friction - coefficient of volume expansion - _* coefficient of expansion with concentration - phase angle of the rate of heat transfer - dimensionless co-ordinate normal to the plate - dimensionless temperature - ₀ mean steady temperature - ₁ unsteady part of temperature - k thermal conductivity - v kinematic viscocity - density of fluid in the boundary layer - density of fluid in the free stream - electrical conductivity of the fluid - skin friction - ₀ mean skin friction - frequency - dimensionless frequency     

A Razin-Tsytovich effect for bremsstrahlung

It is shown that bremsstrahlung from electrons with Lorentz factor 1 is suppressed for >_p in a plasma with plasma frequency _p compared with emission in vacuo. For _p the ratio of the power emitted per unit frequency in the plasma to that in vacuo varies as ².This suppression effect is analogous to the suppression of synchrotron radiation in a plasma (Razin-Tsytovich effect). It is argued that such suppression is a characteristic property of emission by relativistic particles in a plasma.     

Pulsar radio emission from expanding charge sheets

We semi-quantitatively calculate the distribution of energy in frequency and angle emitted from a sheet of charges that are moving out relativistically along dipolar magnetic field lines originating near the magnetic polar caps of a rotating neutron star. The angular distribution is conical with the angle of maximum intensity varying with frequency as ^–1/4 for _c 2 _c /(R _M ²), whereR_M is the initial angular radius of the charge sheet at the surface of the star of radiusR. At higher frequencies the width of the angular cone remains constant. The radiation is linearly polarized with the polarization vector in the plane of the line of sight and the magnetic axis. A sheet of uniform charge density and finite thickness has a frequency spectrum that varies from ^–3/2 to ^–4 for _c and _c , respectively. These features are in good general agreement with the observed characteristics of the intensity, pulse shape, and frequency spectrum of the radio pulses from pulsars.Operated by Associated Universities, Inc., under contract with the National Science Foundation.     

Systemes hamiltoniens au voisinage d'une solution d'equilibre. II:Stabilité des solutions périodiques

Resume On étudie la stabilité des solutions périodiques d'un couplage de systèmes linéaires au voisinage de résonances. Les valeurs propres distinctes _k de la matrice du système linéaire non perturbé sont telles que _k–_j=iq pour tout couple [k, j]; i=–1, q est un nombre entier, la fréquence de la solution. Une application est faite pour un système à trois degrés de liberté au voisinage de la résonance 221.

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Hamiltonian systems in the neighbourhood of an equilibrium solution. II:The stability of periodic solutions

The stability of the periodic solutions for an Hamiltonian system is investigated. Here the distinct eigen values _k of the matrix of the unperturbated linear system are such that _k–_j=iq for any [k, j]; i=–1, q is an integer, is the frequency of the periodic solution. An application is made for a system with three degrees of freedom, near the resonance 221.

     

A nonlinear tensor field and the second metric tensor

In our preceding paper {see [L. Sh. Grigorian and S. Gottlöber, Astrofizika (in press)]} we investigated a self-gravitating system consisting of a scalar field and a linear tensor field _ik= _ki with minimal coupling and with allowance for the action of vacuum polarization effects. In the present paper we investigate the case of a nonlinear tensor field _ik. The action S ⁽⁾ of the field _ik is determined by the difference R_ik — _ik, where R_ik is the space-time Ricci tensor and Rik is the analogous quantity constructed using the metric _ik=g_ik+_ik induced by _ik ( is a free parameter). Here S ⁽⁾ coincides with the previously known expression for the action of a linear field _ik. Equations of motion are derived for _ik in curved space-time. The energy-momentum metric tensor, determining the contribution of _ik to the gravitational field equations, is calculated.Translated from Astrofizika, Vol. 39, No. 1, pp. 135–144, January-March, 1996.     

Isotropization in Brans-Dicke-Bianchi type-V

In this paper we find that from the exact solution for Bianchi type-V in the Brans-Dicke theory with =0 the Hubble parameters are the same for , so that the Universe will be isotropized.     

Large-amplitude low-frequency electromagnetic waves in pulsar magnetospheres

Nonlinear propagation of strong low-frequency waves, as emitted by pulsars or compact galactic nuclei at their rotation frequencies, in a magnetized plasma is investigated. It is shown that even rather small amplitude waves can drive electrons to ultrarelativistic energies. In the limit when the electrons are ultrarelativistic but the ions are immobile, two types of circularly polarized waves (i.e., ^± modes) are excited. In the wave zone of the Crab pulsar, both the electric field ( 3 V m^–1) and the wavelength (10⁸ m) of the ^- mode are larger, by an order of magnitude, than those of the ⁺ wave mode. Both ^± modes can become modulationally unstable due to their nonlinear interaction with density fluctuations induced by the electrostatic waves.     

The configuration of a thin,rotating self-similar disk in general relativity

Einstein's equations for a rotating pressure-free space-time are reduced to a system of four first-order non-linear ordinary differential equations in one self-similar dimensionless variable. Numerical results are given for the vacuum solution. A compatible thin disk can be specified by a surface density and an angular velocity . Self-similarity as a statement of the absence of scales implies that and can be written as=c ²/4Gr, =c/r, and demands that and be pure numbers.     

Radiation from a strongly-magnetized plasma: The case of predominant scattering

On the basis of diffusion approach for normal modes, solutions of the radiative transfer problem are obtained and analysed for an optically thick tenuous plasma with a strong magnetic field. The case is considered when the scattering processes without change of photon frequency are dominant. The radiative transfer coefficients as well as spectra, angular dependences and polarization of the outgoing radiation are investigated in detail for a cold plasma,kT _emc ², |–s _B|kT _e/mc ² )^1/2|cos|, whereT _e is the electron plasma temperature, _B=eB/mc the electron cyclotron frequency,s=1,2,... the number of cyclotron harmonic and the angle between the magnetic field and wave vector. The effects of electronpositron vacuum polarization are taken into account and shown to be very significant. Simple analytic solutions are obtained for various limiting cases (small and large vacuum polarization; high, low and close to the cyclotron resonance radiation frequencies; different orientations of the magnetic field, etc). The results obtained are necessary for analysing X-ray and gamma-ray radiation from strongly magnetized neutron stars.     

Moment method for the inverse radiative transfer in inhomogeneous media

In the present paper, an inverse problem of radiative transfer in an inhomogeneous plane medium of scattering albedo =₀ exp(-/s) is solved by a moment method. The results are compared with those obtained by Dunn (1983) using Monte Carlo method.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

Existence of the continuations in theN-body problem

The method of obtaining the estimates of the maximalt-interval ( _–, ₊) on which the solution of theN-body problem exists and which is such that some fixed mutual distance (e. g. ₁₂) exceeds some fixed non-negative lower bound, for allt contained in ( _–, ₊), is considered. For given masses and initial data, the increasing sequences of the numbers _k , each of which provides the estimate ₊ > _k , are constructed. It appears that if ₊ = +, then .     

Discrete Alfvén waves in solar loop prominences

It is shown that a discrete Alfvén wave can explain the natural oscillations of solar loop prominences by considering the existence of a current flow. Discrete Alfvén waves are a new class of Alfvén waves which is described by the inclusion of the finite ion cyclotron frequency (/ _cl 0) and/or the equilibrium plasma current. In this paper we consider only the effect of the current since in solar prominences (/ _cl 0). We have modeled the solar prominences as a cylindrical plasma, surrounded by vacuum (corona), with L a where L and a are the plasma column, length, and radius, respectively. We have calculated the spectrum of the discrete Alfvén waves as function of the magnitude and shape of the plasma current.     

Перенос поляризации излучения В магнитоактивной космической плазме

u , . , .. (1.10), (1.2) ( (1.2)) . (1964) . (1.10), , , , (1.13). , , S _iq ,R _iglm ,K _iqlm (1.10) . , . . , (1.3), (2.3); (2.8)–(2.10). , , , , z (2.20), .. , , (. (2.15)). (K _{e, 0} ) . ^S , ( (2.24)). (2.24a) ^S ±/4. , , (K _{e, o}<0). L, — , , ; , . .     

Astronomy with a mid-infrared echelle spectrograph

Irshell, a mid-infrared echelle spectrograph developed through a collaboration between the University of Texas, the University of California Space Sciences Laboratory, and Hughes Aircraft, has been in regular use for astronomical observations for about five years. It is optimized for high spectral resolution (R10,000) observations of narrow spectral regions (/1/300) and compact sources (a few arcsec), and is sensitive in the 5–25 m region. A wide variety of astronomical objects have been studied. Observing techniques have been developed to achieve maximum sensitivity in those observations for which Irshell is best suited and to allow observations of wide spectral regions and extended objects. We discuss the observing techniques and show some of the data obtained.     

On the stability of the triangular libration points for the photogravitational circular restricted problem of three bodies under the resonances of the third and the fourth order

We investigate the stability of the triangular libration points when both the attracting bodies are radiating under the resonance conditions ₁ = 2₂ and 3₂.     

Stability of the triangular libration points of the circular restricted problem in the presence of resonances

The stability of triangular libration points, when the bigger primary is a source of radiation and the smaller primary is an oblate spheroid. has been investigated in the resonance cases ₁ = 2₂ and ₁ = 3₂. The motion is unstable for all the values of parameters q and A when ₁ = 2₂ and the motion is unstable and stable depending upon the values of the parameters q and A when ₁ = 3₂. Here q is the radiation parameter and A is the oblateness parameter.