Mean field fluctuations and the evolution of self-gravitating systems

This paper considers the nonlinear effects of collective fluctuations about a slowly-varying solution of the collisionless Boltzmann equation appropriate for a system of stars with a distribution of masses. It is argued that these effects should be manifest on a time-scalet _M intermediate between the violent and collisional relaxation times, inhibiting the natural progression towards equipartition induced by collisions, and favouring instead a well-mixed state, realized in numerical simulations, in which the mean square velocity is independent of the mass.     

Метагалактические протоны сверхвысоких энергий

, . 2.7°- . . . E3×10¹⁹ (1.6) .     

Containment of an adiabatic plasma on magnetic lines of force by a self-generated electrostatic field

One component of a three-fluid adiabatic plasma is under certain conditions contained in a restricted region of space by a large-scale electrostatic field generated within the plasma. The containment is discussed here for plasma consisting of ions and two populations of electrons characterized by different pitch angle distribution functions.The bouncing motion of electrons along open fieldlines between a magnetic mirror and an electrostatic mirror produces a velocity distribution function similar to that generated by bouncing particles on closed fieldlines.     

The asymptotic limit of the form-factors α and β product for celestial bodies

The applicability of the properties of central configurations proceeding from the many-body problem to study of gaseous sphere cloud evolution during its gravitational contraction is justified. It is shown that the product runs to a constant value in the asymptotic time limit of simultaneous collision of all the particles of the cloud where is a form-factor of the potential energy and is a form-factor of the moment of inertia.The spherical bodies as well as ellipsoids of rotation and general ellipsoids with a one-dimensional mass distribution (k),k[0, 1] are found to possess the property =const.

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. , - , , ., , - =const., , (k),k[0, 1].

     

Рассеяние света на анизотропных частицах

, — . , , . , , .     

Čerenkov radiation in anisotropic plasmas

Following our series of works on anisotropic radiation, we analyze the erenkov condition in magnetized plasmas in this paper. We have discovered that the usual erenkov condition cos =1/n isnot satisfied at a far field point in anisotropic media, implying that when a charge is moving in a magnetized plasma, a linear shock wave front does not form. Thus we can calculate the power received at a far field per unit time in such a medium — this quantity could not be evaluated according to previous theory. Numerical examples are presented to show various relevant characteristics of erenkov radiation in model plasmas.     

Infrared absorption by shape distributions of NH3 ice particles: An application to the Jovian atmosphere

We study how distribution of small NH₃ ice particles over shapes affects the strength of resonant absorption features at 9.4 and 26 m. The T-matrix approach is used to compute optical cross sections for shape distributions of 0.5- and 1-m volume-equivalent radius spheroids in random orientation. It is found that the maximum of the resonant absorption for the shape distributions is 1.5–2 times smaller than that for equal-volume spherical particles, the absorption peak being shifted towards longer wavelengths. The results of our computations support the conclusion of West et al. (1989) that, apparently, small NH₃ ice particles cannot be the principal component of the Jovian troposphere in the 300- to 500-mbar region.     

A model of the 2–4Μm spectrum of Comet Halley

Recent observations of Halley's Comet show a broad absorption band centred at 3.4 m and which can be explained on the basis of a bacterial grain model.     

Eclipse Observations of Compact Sources in the Outer Solar Corona

We report here on high angular resolution observations of solar noise storm sources at a frequency of 75 MHz. The data for the study were obtained at the Gauribidanur Radio Observatory (long.: 77°2612 E, lat.: 13°3612 N) about 100 km north of Bangalore, India, during the solar eclipse of 24 October 1995. Our main conclusion is that there are structures of angular size 2.5 arc min in the outer solar corona.     

Multiple expansion of the tidal potential

The Earth tidal deformation causes an additional gravitational potential. Its effect on the Moon orbital motion has been studied by several authors.In this contribution, we develop this additional potential without specifying the inertial frame chosen.For this purpose, we use the properties of the representation of rotation groups in 3 dimensions space. We finally obtain the interaction potential between the distorted Earth and the Moon which is a necessary preliminary to the study of the evolution of the Earth-Moon system.Nomenclature T.R.O Tide raising object - (, , ) Spherical coordinates of the T.R.O. - (J, _E ) Earth spin axis orientation. _E is the longitude of the ascending node of Earth's equator on thexy-plane - (a ,I ,e , , ,M ) Elliptics elements of the T.R.O     

О форме электронной шапки вращающейся нейтронной звезды с сильным магнитным полем

. , , . . . , . . - , , .     

Перенос резонансного излучения И случайные ълуждания Фотонов

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Transfer of resonance radiation in infinite medium is considered as a process of random walks of photons. Close relation is shown to exist between the problems of transfer of line radiation and the stable distributions of the probability theory. This relation is used as a basis of a new method for the investigation of the asymptotic properties of the radiation field far from the sources.

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Effects of mass transfer on the unsteady free convection flow past an accelerated vertical porous plate with variable suction

An exact analysis of the effects of mass transfer on the flow of a viscous incompressible fluid past an uniformly accelerated vertical porous and non-porous plate has been presented on taking into account the free convection currents. The results are discussed with the effects of the Grashof number Gr, the modified Grashof number Sc, the Schmidt number Sc, and the suction parametera for Pr (the Prandtl number)=0.71 representating air at 20°C.Nomenclature a suction parameter - C species concentration - C species concentration at the free stream - g acceleration due gravity - Gc modified Grashof number (vg^*(C –C )/U ₀ ³ ) - Pr Prandtl number (C _p/K) - T temperature of the fluid near the plate - T dimensionless temperature near the plate ((T-T )/(T -T )) - U(t) dimensionless velocity of the plate (U/U ₀) - v normal velocity component - v ₀ suction/injection velocity - x, y coordinate along and normal to the plate - v kinematic viscosity (/gr) - C _p specific heat at constant pressure - C _w species concentration at the plate - C non-dimensional species concentration ((C-C )/(C _w -C )) - Gr Grashof number (g(T _w -T )/U ₀ ³ ) - D chemical molecular diffusivity - K thermal conductivity - Sc Schmidt number (/D) - T _w temperature of the plate - T free stream temperature - t time variable - t dimensionless time (tU ₀ ² /) - U ₀ reference velocity - u velocity of the fluid near the plate - u non-dimensional velocity (u/U ₀) - v dimensionless velocity (v/U ₀) - v ₀ non-dimensionalv ₀ (v ₀ /U₀)=–at^–1/2 - y dimensionless ordinate (yU ₀/) - density of the fluid - coefficient of viscosity     

Спэктр тэплового излучения сверхмассивных звезд и рентгеновских источников

- . ( ) . . F(v)v ^– c>0 . , , .

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In the external layers of supermassive stars and thermal sources of X-ray radiation electron scattering contributes more to the opacity than free-free processes. Therefore, the thermal radiation spectrum of supermassive stars must greatly differ from Planckian, The approximate formulae obtained for the radiation spectra are applicable to any objects with a predominant role of electron scattering in the opacity and power dependence of plasma temperature and density on geometrical depth of the layers.In thermal radiation sources with power dependence of plasma temperature on depth of the layer the formation of power radiation spectraF(v)v ^– with >0 with >0 is possible. Such spectra can imitate the presence of non-thermal radiation mechanisms. This effect takes place also in the case of small optical depth on the Thomson scattering. Possibly, this effect is of interest for the theories of X-ray sources and X-ray solar flares.

     

About the motion of a heavy flexible string attached to the satellite in the central field of attraction

The motion of a heavy inextensible flexible string attached to the satellite in the central gravitational field is discussed. It is supposed that the mass of the string is infinitesimally small compared to the mass of the satellite and hence it does not affect the latter's motion. Under the assumption that the satellite moves along the Keplerian elliptical orbit (in particular circular orbit), the relative motion of the string is investigated. It has been shown that the motion of the flexible string is unstable which is stable in the case of a solidified string.

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, , , . , . , / , /. , , .

     

Effect of perturbations in Coriolis and centrifugal forces on the stability of libration points in the restricted problem

The location and the stability of the libration points in the restricted problem have been studied when small perturbation and are given to the Coriolis and the centrifugal forces respectively. It is seen that the pointsL ₄ andL ₅ form nearly equilateral triangles with the primaries and the pointsL ₁,L ₂,L ₃ remain collinear. It is further observed that for the pointsL ₄ andL ₅, the range of stability increases or decreases depending upon whether the point (, ) lies in one or the other of the two parts in which the (, ) plane is divided by the line 36-19=0 and the stability of the collinear points is not influenced by the perturbations and they remain unstable.     

A study of asymptotic solutions in the vicinity of the collinear libration points of the restricted three-body problem

Some particular solutions of the restricted three-body problem which determine outgoing or incoming orbits near libration points are considered. The solutions are obtained in the form of absolutely convergent Liapounov series. It is proved that these asymptotic solutions are plane curves situated in the orbital plane of the primaries. Each family of asymptotic solutions for every collinear point consists of four solutions which are the separatrices of a saddle point. The angles of inclination of the separatrices are determined.

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aaa a a aa , a. a a a. a, a . . aa, a a aaa. . a . a a , aaa a. . aa aa a .

     

Возникновение полярных и экваториальных конденсаций В плазме вБлизи переменного магнитного диполя

. , . , . , .

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The motion of a plasma in the time-dependent dipole magnetic field is considered. It is shown that the increase of the magnetic moment of the dipole (for example, as the result of the explosion of a magnetic star) leads to the concentration of a plasma in the polar regions. Likewise, a decrease of the magnetic moment (contraction of a star) would lead to the concentration of surrounding plasma in the equatorial plane. This process may be of importance in astrophysics and, particularly, in the dynamics of nebulae and non-stationary star envelopes.

     

турбулентноштб в космологии

=qr, I II (Marochniket al., 1975 a, b), . , II; , . , , ye , . . t _g.     

Effects of Hall current on hydromagnetic free-convective flow through a porous medium

An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c _p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H ₀ applied magnetic field - H magnetic field intensity - (j _x , j _y , j _z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n _e electron number density - P Prandtl number - q velocity vector - (T, T _w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U ₀ uniform velocity - v ₀ suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - _e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - _e charge density - electrical conductivity - _e electron collision time