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1.
The process of re-escalation of the scalar field as R
3, the energy density as R
3, and the pressurep aspR
3P, lends itself to obtain a reduced equation that represents, for a wide variety of equations of state, the cosmological evolution of an homogeneous and isotropic, flat Universe. A particular solution to this equation is presented. 相似文献
2.
, (DM) (RM). , DM RM N
e
= n
e
ds. M
e
= n
e
H cos ds ; . Lerche (1970a, b) , DM RM N
e
M
e
. . 相似文献
3.
The dispersion equation for hydromagnetic surface waves along a plasma-plasma interface has been solved as a function of the compressibility factor c
1/v
A1, where c
1 and v
A1 are the acoustic and Alfvén wave speed in one of the medium, for general wave propagation direction. Both slow and fast magnetosonic surface waves can exist. The nature and existence of these waves depends on the values of c
1/v
A1 and , the angle of wave propagation. For low- plasmas only fast mode exists. The slow mode does not propagate below a critical value of c
1. When c
1 the phase velocity of the slow wave tend to the Alfvén surface wave velocity in the incompressible media and for large the phase velocity of the fast wave approaches this value. The phase velocity of the slow wave increases whereas for the fast wave it decreases with increase in the angle . 相似文献
4.
A model of a first generation intermediate star of 5M
, with Z=0 has been considered. The model is at an advanced stage of its evolution and has a double shell burning. It burns helium in the inner shell, and hydrogen, via CNO cycle, in the outer shell.
=(log/log)
T
and
T
=(log/logT)
were computed allowing for the oscillations of the relative mass abundance of the reagents in nuclear reactions. Including
=(log/log)
T
and
=(log/logT)
of mean molecular weight and the effect of the oscillations of abundances due to nuclear reactions, stability was studied. Contrary to the results of the static calculations, we found that instability due to the excitation mechanism provided by the high temperature sensitivity of energy generation rate propagates up to the surface. Thus the model in question was found to be unstable against radial adiabatic pulsations, in its fundamental mode. 相似文献
5.
We give here the calculation of density perturbations in a gravitation theory with a scalar field non-minimally coupled to gravity, i.e., the Brans-Dicke theory of gravitation. The purpose is to show the influence of this scalar field on the dynamic behaviour of density perturbations along the eras where the equation of state for the matter can be put under the formp=, where is a constant. We analyse the asymptotic behaviour of this perturbations for the cases =0, =–1, =1/3 and =0. In general, we obtain a decaying and growing modes. In the very important case of inflation, =–1, there is no density perturbation, as it is well known. In the vacuum phase the perturbations on the scalar field and the gravitational field present growing modes at the beginning of the expansion and decaying modes at the end of this phase. In the case =0 it is possible, for some negative values of , to have an amplification of the perturbations with a superluminal expansion of the scale factor. We can also obtain strong growing modes for the density contrast for the case where there is a contraction phase which can have physical interest in some primordial era. 相似文献
6.
S. Kumar 《Astrophysics and Space Science》1984,106(1):53-59
The Chisnell-Chester-Whitham method has been used to investigate the propagation of diverging plane and cylindrical shock waves through an ideal gas in presence of a magnetic field having only constant axial
and variable azimuthal
components, simultaneously for both weak and strong cases. Assuming an initial density distribution 0=r
–w
, where is the density at the plane/axis of symmetry andw is a constant, the analytical expressions for shock velocity and shock strength have been obtained. The expressions for the pressure, the density, and the particle velocity immediately behind the shock have also been derived for both cases. 相似文献
7.
For the region after the recombination era of the Universe the hydrodynamical density waves are analyzed including shear viscosity and heat conduction for =c as well as for <c(c is the critical density of the Universe). Very near to the end of the recombination era (z=1200) we find the well-known Jeans instability. It is shown that the influence of the shear viscosity on the instabilities in negligible, however, a visible influence of the bulk viscosity is present. 相似文献
8.
Hong Wei Li 《Solar physics》1986,104(1):131-136
The variations of the growth rates of ECM at first four harmonics in X-, Z-, and O-modes excited by a hollow beam distribution of weakly relativistic electrons with a parameter
p
/
e
are presented in this paper. The results show that the second harmonic of ECM in X-mode dominates the instability if < 1, and if 1.2 , 2 or 2.2 3 the third or fourth harmonic will dominate. The second and third harmonics of Z-mode waves grow faster only if 2 2.2 and 3 3.2, respectively, so it would not be a competition in most cases. It is suggested that the ECM emission at these harmonics in X-mode is a possible mechanism to produce solar spike emissions with high brightness temperature at shorter and longer decimetric wavelengths.Proceedings of the Workshop on Radio Continua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.On leave from the Department of Astronomy, Nanjing University, Nanjing, The People's Republic of China. 相似文献
9.
The occurrence of magnetoacoustic surface waves at a single magnetic interface one side of which is field-free is explored for the case of non-parallel propagation. Phase-speeds and penetration depths of the waves are investigated for various Alfvén speeds, sound speeds and angles of propagation to the applied field. Both slow and fast magnetoacoustic surface waves can exist depending on the values of sound speeds and propagation angle. The fast waves penetrate more than the slow waves.The parallel propagation of fast and slow magnetoacoustic surface waves on a magnetic-magnetic interface is investigated. The slow surface wave is unable to propagate below a critical sound speed. In a low -plasma, only the fast mode exists (0 0). 相似文献
10.
Г. Н. Дубошин 《Celestial Mechanics and Dynamical Astronomy》1970,2(4):454-466
(, 1969). ( ), ( ), , , . , (=), , , .. , . , , - ( ), ( ). , .
This paper is a continuation and a generalization of one published earlier (Duboshin, 1969): it discusses the problem whether there exist the Lagrangian and the Eulerian solutions of the generalized three-body (material points) problem. Every point in this generalized problem acts on another, one with a force (attractive or repulsive) directed along the straight line passing through these points, and in an arbitrary manner depending on time, mutual distance and its derivatives, the first and the second. Here, generally speaking, the third axiom of dynamics (law of action and reaction) is not presupposed as fulfilled, that is, it is supposed that every two material points interact in a different way.This most general assumption being made, we establish the conditions which must dictate the laws of the interactions, so that the three points can always remain at the apexes of the equilateral triangle (Langrangian solution), or remain always on a straight line (Eulerian solution).The author believes that such general treatment of the three-body problem can be useful for theoretical studies in celestial mechanics and also for practical applications in the study of isolated stellar systems.相似文献
11.
Max K. Wallis 《Astrophysics and Space Science》1973,20(1):3-18
The interaction processes governing the penetration of the interstellar gas into the solar neighbourhood are re-examined — as well as photo-ionization and charge-exchange processes, proton elastic collisions and electron ionizations help reduce the nearby gas densities. The total destruction rate varies little during the solar cycle, by perhaps 10%. Particle heating, particularly via the elastic collisions, determines the gas characteristics in the gravitationally focussed tail—enhanced H-density is prevented, while the He-tail is effectively hotter than 103 K.Termination of the solar wind is rediscussed in the light of both electron heating and the stronger gas/plasma interaction. The spiral interplanetary field is taken to break up and the subsonic plasma flow to be controlled by the pressure of slowly cooling electrons. The terminating collisionless shock is then, if it exists at all, very weak (M
1<1.4), subcritical, and energetically unimportant. Cosmic rays are little affected by this sonic transition, but at least the electron component should be modulated by plasma turbulence throughout the ionizing flow.
. , . , . . .相似文献
12.
-- () ., , , , , . , , . , . 相似文献
13.
Cosmic ray (c. r.) propagation in interstellar magnetic fields is often considered in the diffusion approximation, i.e. by the diffusion equation in the coordinate space. Cosmic ray momentum distribution in this case is considered isotropic when the space gradients of c.r density are absent. This approach, with the use of an unfixed effective diffusion coefficientD independent of the energyE enables one to describe all the data available However, neither the diffusion mechanism nor the limits of applicability of the diffusion approximation is clear particularly ifD is independent ofE. Furthermore, the diffusion coefficientD must be expressed through the characteristics of the interstellar medium and possibly through the flux velocity and density of c.r. etc. One of the possible approaches for the analysis of the mechanism and characteristic features of c.r. distribution and isotropization is the account taken of the plasma effects and specifically, the study of c.r. flux instability arising when c.r. are moving in the interstellar plasma. As a result of such instability c.r. may generate waves of different types (magnetohydrodynamic, high-frequency plasma and other waves). Generation of waves and scattering on them result in isotropization of cosmic rays while their propagation under certain conditions turns out similar to that under diffusion.An attempt is made here to systematically analyse the avove mentioned plasma effects and to find out to what extent they are responsible for the behaviour of c.r. in the Galaxy. It turns out that c.r. In any case this is true if this mechanism is regarded as the only c.r. isotropization mechanizm within a wide energy range from 1 to 1000 GeV. Isotropization and spatial diffusion of c.r. up toE100–1000 GeV on the waves from external sources (for example, on the waves from the supernova shells) also proved impossible if the diffusion coefficient is assumed to be independent of c.r. energy. Some new possibilities of c.r. isotropization are also considered.A List of Notations
D
cosmic ray (c.r.) space diffusion coefficient
-
degree of c.r. anyisotropy
-
E,E
kin
total and kinetic particle energy
- p,p
particle momentum and its absolute value
-
angle between the particle momentum direction and the magnetic field direction (z-axis)
-
cos
- v,
particle velocity and its absolute value
-
c
light velocity
-
f(p),f(E)
momentum and energy particle distribution function
-
N( > E) = N( > p) = f(p) dp/(2)3 =
E
f dE
c.r. particle density
-
c.r. spectrum index,N(>E)=KE
–+1
-
n
H
neutral particle density
-
n=n
e=n
i
ion and electron density
-
H
niagnetic field
-
T
temperature
-
thermal velocities of electrons and ions
-
Boltzmann constant
-
Alfén velocity
-
M, m
proton and electron masses
-
e
electron charge
-
wave frequency
-
H
=eH/Mc, =
H
(Mc
2/E)
gyrofrequency of a plasma proton and relativistic particle
-
H
=eH/mc
gyrofrequency of an electron
-
plasma frequency
-
v
ii,v
ei,v
en,v
in
collision frequencies between ions, electrons and ions, electrons and neutrals, ions and neutrals
-
growth rate of wave amplitude
- k,k
wave vector and its absolute value
-
angle between the directions of the vectorsk andH
-
wave energy density 相似文献
14.
I I I : Mgas<0.04 Mcor. - . , . 相似文献
15.
Paul S. Wesson 《Astrophysics and Space Science》1978,54(2):489-495
An exact solution of Einstein's equation is stated in which the density (), pressure (p), scale factorS and metric coefficients are functions of only one dimensionless self-similar variable,ct/R, wheret is cosmic time andR is a co-moving radial coordinate. The solution represents a cosmology that begins as a static sphere having R
–2 and evolves into an expanding model which is pressure-free and has a hierarchical type of density law ( R
–, approximately, with =a number, 02). It is suggested that this model should supersede the previous models of Wesson and other workers, since it appears to be the simplest cosmology for a hierarchy. 相似文献
16.
Masaya Saitou 《Astrophysics and Space Science》1989,162(1):47-56
Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity , , respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values , for modeling such fluctuations. Perturbed values
i
=
i
+
i
,v
i
=
i
+ v
i
were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (= v =0,2 =v
2 = 10–8) grow many times in marginally-stable state. 相似文献
17.
The effect of ion–neutral collisions on the propagation of MHD waves and surface waves at a single magnetic interface is investigated. The dispersion equations for MHD waves in a partially ionized medium are derived. There are three damped propagating modes in a uniform unbounded medium: an Alfvén mode, and fast and slow modes. The damping of waves depends on both the collisional frequency and the ionization fraction. Wave damping increases as ionization fraction decreases. Surface waves are discussed in three cases: (a) the incompressible limit, (b) the low plasma, and (c) for parallel propagation. The incompressible limit leads to Alfvén surface waves in a partially ionized medium and the dispersion characteristics are similar to those obtained by Uberoi and Datta. In the low plasma of the Earth's auroral F region there are two damped propagating magnetoacoustic surface waves for =/3. There is only one damped surface mode for =/2, but no surface wave is able to propagate for =0°. For the case of parallel propagation (=0°) the results obtained in the absence of ion-neutral collisions are consistent with the results of Jain and Roberts. It is found that a three-mode structure of damped propagating waves occurs owing to ion–neutral collisions for a comparatively high ionization fraction. For the case of the solar photosphere, where the ionization fraction is low, two weakly damped surface waves are found, though the damping is almost negligible. The pattern of propagation is similar to that found in the case discussed by Jain and Roberts, but the wave speeds are lower due to ion–neutral collisions. The strong collisions tie the ion–neutral species together and reduce the damping. 相似文献
18.
, . 2.7°- . . . E3×1019 (1.6) . 相似文献
19.
S. Selak 《Astrophysics and Space Science》1989,159(1):153-156
In this Letter we propose to consider the four-energy-space whose coordinates are composed as follows: (i) the coordinate 0 refers to the internal energy of the body (it is involved as an unknown function of the rest-energy and the kinetic energy of the body), and (ii) the coordinates 1, 2, 3 relate to the presence of gravitational, electromagnetic, and thermal energy at the location of the body respectively. We involve yet the proper energy interval d2 by analogy to the four-interval ds
2 in general relativity. From such metric field we calculate the Ricci tensor in the simplest case. In addition, we require its form to be the same one as that considered by Schwarzschild. Comparing both solutions we obtain Einstein's relationE=mc
2. 相似文献
20.
V. I. Ferronsky S. A. Denisik S. V. Ferronsky 《Celestial Mechanics and Dynamical Astronomy》1979,20(1):69-81
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.
. , - , , ., , - =const., , (k),k[0, 1].相似文献