共查询到20条相似文献，搜索用时 31 毫秒
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Abdul Ahmad 《Celestial Mechanics and Dynamical Astronomy》1995,61(2):181-196
The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable. 相似文献
3.
Han Ji-chang 《Chinese Astronomy and Astrophysics》1981,5(3):357-364
For the Robertson-Walker metric for a homogeneous and isotropic universe, I have derived explicit solutions of the Einstein-Yang equation (interior torsion-free solutions for a spin-less ideal fluid) and hence found certain solutions of the Einstein field equation for the radiation-dominated phase of the early universe. 相似文献
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We study the self-similar magnetohydrodynamics (MHD) of a quasi-spherical expanding void (viz. cavity or bubble) surrounding the centre of a self-gravitating gas sphere with a general polytropic equation of state. We show various analytic asymptotic solutions near the void boundary in different parameter regimes and obtain the corresponding void solutions by extensive numerical explorations. We find novel void solutions of zero density on the void boundary. These new void solutions exist only in a general polytropic gas and feature shell-type density profiles. These void solutions, if not encountering the magnetosonic critical curve (MCC), generally approach the asymptotic expansion solution far from the central void with a velocity proportional to radial distance. We identify and examine free-expansion solutions, Einstein–de Sitter expansion solutions, and thermal-expansion solutions in three different parameter regimes. Under certain conditions, void solutions may cross the MCC either smoothly or by MHD shocks, and then merge into asymptotic solutions with finite velocity and density far from the centre. Our general polytropic MHD void solutions provide physical insight for void evolution, and may have astrophysical applications such as massive star collapses and explosions, shell-type supernova remnants and hot bubbles in the interstellar and intergalactic media, and planetary nebulae. 相似文献
5.
Pranab Ghosh 《Monthly notices of the Royal Astronomical Society》2000,315(1):89-97
We introduce a multipolar scheme for describing the structure of stationary, axisymmetric, force-free black hole magnetospheres in the '3+1' formalism. We focus here on Schwarzschild spacetime, giving a complete classification of the separable solutions of the stream equation. We show a transparent term-by-term analogy of our solutions with the familiar multipoles of flat-space electrodynamics. We discuss electrodynamic processes around disc-fed black holes in which our solutions find natural applications: (i) 'interior' solutions in studies of the BlandfordZnajek process of extracting the rotational energy of holes, and of the formation of relativistic jets in active galactic nuclei and 'microquasars'; (ii) 'exterior' solutions in studies of accretion disc dynamos, disc-driven winds and jets. On the strength of existing numerical studies, we argue that the poloidal field structures found here are also expected to hold with good accuracy for rotating black holes, except for the cases of the maximum possible rotation rates. We show that the closed-loop exterior solutions found here are not in contradiction with the MacdonaldThorne theorem, as these solutions, which diverge logarithmically on the horizon of the hole , only apply to those regions that exclude . 相似文献
6.
Two basic problems of dynamics, one of which was tackled in the extensive work of Z. Kopal (see e.g. Kopal, 1978, Dynamics of Close Binary Systems, D. Reidel Publication, Dordrecht, Holland.), are presented with their approximate general solutions. The ‘penetration’ into
the space of solution of these non-integrable autonomous and conservative systems is achieved by application of ‘The Last Geometric Theorem of Poincaré’ (Birkhoff, 1913, Am. Math. Soc. (rev. edn. 1966)) and the calculation of sub-sets of ‘solutions précieuses’ that are covering densely the spaces of all solutions
(non-periodic and periodic) of these problems. The treated problems are: 1. The two-dimensional Duffing problem, 2. The restricted
problem around the Roche limit. The approximate general solutions are developed by applying known techniques by means of which
all solutions re-entering after one, two, three, etc, revolutions are, first, located and then calculated with precision.
The properties of these general solutions, such as the morphology of their constituent periodic solutions and their stability
for both problems are discussed. Calculations of Poincaré sections verify the presence of chaos, but this does not bear on
the computability of the general solutions of the problems treated. The procedure applied seems efficient and sufficient for
developing approximate general solutions of conservative and autonomous dynamical systems that fulfil the PoincaréBirkhoff
theorems. The same procedure does not apply to the sub-set of unbounded solutions of these problems. 相似文献
7.
We continue to analyze the periodic solutions of the singly averaged Hill problem. We have numerically constructed the families of solutions that correspond to periodically evolving satellite orbits for arbitrary initial values of their eccentricities and inclinations to the plane of motion of the perturbing body. The solutions obtained are compared with the numerical solutions of the rigorous (nonaveraged) equations of the restricted circular three-body problem. In particular, we have constructed a periodically evolving orbit for which the well-known Lidov-Kozai mechanism manifests itself, just as in the doubly averaged problem. 相似文献
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《天文和天体物理学研究(英文版)》2015,(10)
We revisit the problem of the maximum masses of magnetized white dwarfs(WDs).The impact of a strong magnetic field on the structure equations is addressed.The pressures become anisotropic due to the presence of the magnetic field and split into parallel and perpendicular components.We first construct stable solutions of the Tolman-Oppenheimer-Volkoff equations for parallel pressures and find that physical solutions vanish for the perpendicular pressure when B(?) 10~(13) G.This fact establishes an upper bound for a magnetic field and the stability of the configurations in the(quasi) spherical approximation.Our findings also indicate that it is not possible to obtain stable magnetized WDs with super-Chandrasekhar masses because the values of the magnetic field needed for them are higher than this bound.To proceed into the anisotropic regime,we can apply results for structure equations appropriate for a cylindrical metric with anisotropic pressures that were derived in our previous work.From the solutions of the structure equations in cylindrical symmetry we have confirmed the same bound for B ~ 10~(13) G,since beyond this value no physical solutions are possible.Our tentative conclusion is that massive WDs with masses well beyond the Chandrasekhar limit do not constitute stable solutions and should not exist. 相似文献
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R. E. Grundy 《Solar physics》1975,40(1):227-230
This paper deals with shock conditions for the progressing wave (or similarity) solutions of one-dimensional, unsteady gas dynamics. These solutions have hitherto been used to deal with the flow behind shocks moving into stationary atmospheres. By generalising the shock conditions to the case of moving atmospheres, it is shown that the progressing wave solutions can be used to describe a certain class of flows, and a new shock locus can be constructed in the phase plane of the solutions. It is hoped that such solutions will be of use in describing the unsteady flow behind shocks propagating into the ambient solar wind. 相似文献
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In this paper we have obtained interior solutions of the field equations for anisotropic sphere in the bimetric general relativity theory formulated by Rosen (Lett. Nuovo Cimento 25, 1979). A class of solutions for a uniform energy-density source of the field equations is presented. The analytic solutions obtained are physically reasonable, well behaved in the interior of the sphere. The solutions agree with the Einstein’s general relativity for a physical system compared to the size of the universe such as the solar system. 相似文献
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基于NNR-NUVEL-1A地球板块运动模型和ITRF2000地球参考架的三维VLBI站速度矢量,采用实测的VLBI基线长度变化率作为约束,重新估计了部分国际VLBI站的局部或区域性地壳的垂直形变,并与国际地球参考架ITRFs解和VLBI全球解GLB2003,VTRF2003和VTRF2005的结果进行了比较。结果表明,欧亚板块的URUMQI站和太平洋板块的KWAJAL26站,南极OHIGGINS站的垂直形变率、ITRFs解和VLBI全球解存在6-15mm/a的差异,北美YUMA站可能有15-31mm/a 的垂直形变率,而美国西部太平洋板块的San Francisco(PRESIDIO)站的垂直形变率还有待进一步的研究。此外,SC-VLBA,CRIMEA和EFLSBERG站的垂直形变率、ITRFs解和VLBI全球解的差约为1-6mm/a。用不同方法得到的VLBI站的水平形变率解有较好的一致性。 相似文献
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Bifurcations of nonlinear electron acoustic solitary waves and periodic waves in an unmagnetized quantum plasma with cold and hot electrons and ions has been investigated. The one dimensional quantum hydrodynamic model is used to study electron acoustic waves (EAWs) in quantum plasma. Applying the well known reductive perturbation technique (RPT), we have derived a Korteweg-de Vries (KdV) equation for EAWs in an unmagnetized quantum plasma. By using the bifurcation theory and methods of planar dynamical systems to this KdV equation, we have presented the existence of two types of traveling wave solutions which are solitary wave solutions and periodic traveling wave solutions. Under different parametric conditions, some exact explicit solutions of the above waves are obtained. 相似文献
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Previously developed solutions for pure toroidal mode Alfvén waves with finite ionosphere conductivities are modified to apply both inside and outside the plasmapause.Detailed diagrams are provided to illustrate the effect of realistic ionosphere conductances on the wave-forms. As well as graphs of wave-period, these include: (a) half-wave solutions showing the effect of dipole field distortion and consequent enhancement of ionosphere electric fields; (b) half-wave solutions with low damping that are symmetric and asymmetric about the equatorial plane; (c) highly-damped half-wave and quarter-wave solutions with wave admittance at the ionosphere nearly equal to the ionosphere conductance; (d) a quarter-wave solution with low damping that has a “near-node” of electric field at one ionosphere and an antinode of electric field at the other. 相似文献
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Utpal Kumar Samanta Asit Saha Prasanta Chatterjee 《Astrophysics and Space Science》2013,347(2):293-298
Bifurcation behavior of nonlinear dust ion acoustic travelling waves in a magnetized quantum dusty plasma has been studied. Applying the reductive perturbation technique (RPT), we have derived a Kadomtsev-Petviashili (KP) equation for dust ion acoustic waves (DIAWs) in a magnetized quantum dusty plasma. By using the bifurcation theory of planar dynamical systems to the KP equation, we have proved that our model has solitary wave solutions and periodic travelling wave solutions. We have derived two exact explicit solutions of the above travelling waves depending on different parameters. 相似文献
15.
Marcelo Samuel Berman 《Astrophysics and Space Science》2010,325(2):283-286
After reviewing the scalar-tensor lambda-accelerating power-law solutions by Berman (Astrophys. Space Sci. 323:103, 2009a), we obtain solutions for the amplification of gravitational waves in the models. The solutions consider a perfect gas equation
of state, with cosmic pressure proportional to the energy density, the proportionality constant being smaller than −2/3. 相似文献
16.
S. G. Zhuravlev 《Celestial Mechanics and Dynamical Astronomy》1981,25(3):297-315
In our article (Zhuravlev, 1979) a formal method of constructing conditionally periodic solutions of canonical systems of differential equations with a quick-rotating phase in the case of sharp commensurability was presented. The existence of stationary (or periodic) solutions of an averaged system of differential equations corresponding to the initial system of differential equations is necessary for an effective application of the method for different problems.Evidently, the stationary solutions do not always exist but in numerous papers on stationary solutions (oscillations or motions), the conditions of existence of such solutions are very often not considered at all. Usually a simple assumption is used that the stationary solutions do exist.Otherwise it is well known that Poincaré's theory of periodic solutions (Poincaré, 1892) let one set up conditions of existence of periodic solutions in different systems of differential equations. Particularly, in papers,Mah (1949, 1956), see alsoexmah (1971), the necessary and sufficient conditions of the existence of periodic solutions of (non-canonical) systems of differential equations which are close to arbitrary non-linear systems are given. For canonical autonomous systems of differential equations the conditions of existence of periodic solutions and a method of calculation are presented in the paperMepmah (1952).In our paper another approach is given and the conditions of existence of stationary solutions of canonical systems of differential equations with a quick-rotating phase are proved. For this purpose Delaunay-Zeipel's transformation and Poincaré's small parameter method are used. 相似文献
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The probabilistic method of Sobolev and Case's method of normal mode expansion are combined to predict source-function distributions for radiative transfer in non-conservative, planeparallel atmospheres. The solutions obtained for semi-infinite atmospheres are exact and can be expressed in terms of functions and parameters associated with the non-conservative Milne problem. The predictions for finite atmospheres are approximate and are constructed from the semi-infinite solutions. Tabular values of the requisite functions and parameters are provided to facilitate rapid numerical evaluation of the solutions. Although the finite solutions corresponds to the zeroth-order (optically thick) approximation by Case's method, an assessment of the accuracy indicates that the results are useful for optical thicknesses as small as one or even less. The close connection between the results obtained and the method of point-direction gain of Van de Hulst is discussed. 相似文献
19.
Exact solutions are obtained in (4+1) dimensions for plane symmetric and cylindrically symmetric inhomogeneous spacetimes. In the former case the three space depends on time only while the metric corresponding to the extra dimension is dependent on space as well as time coordinates. The cylindrically symmetric nonstatic solutions for the perfect fluid have no singularity near the axis, but show big bang type of singularity in the finite past. One of the classes of such solutions satisfies the barotropic equation of state of the form =p. Static solutions with cylindrically symmetric solutions are also obtained in 5 dimensions. 相似文献
20.
Pierre Lesaffre Steven A. Balbus † 《Monthly notices of the Royal Astronomical Society》2007,381(1):319-333
Axisymmetric incompressible modes of the magnetorotational instability (MRI) with a vertical wavenumber are exact solutions of the non-linear local equations of motion for a disc (shearing box). They are referred to as 'channel solutions'. Here, we generalize a class of these solutions to include energy losses, viscous, and resistive effects. In the limit of zero shear, we recover the result that torsional Alfvén waves are exact solutions of the non-linear equations. Our method allows the extension of these solutions into the dissipative regime.
These new solutions serve as benchmarks for simulations including dissipation and energy loss, and to calibrate numerical viscosity and resistivity in the zeus3d code. We quantify the anisotropy of numerical dissipation and compute its scaling with time and space resolution. We find a strong dependence of the dissipation on the mean magnetic field that may affect the saturation state of the MRI as computed with zeus3d . It is also shown that elongated grid cells generally preclude isotropic dissipation and that a Courant time-step smaller than that which is commonly used should be taken to avoid spurious anti-diffusion of magnetic field. 相似文献
These new solutions serve as benchmarks for simulations including dissipation and energy loss, and to calibrate numerical viscosity and resistivity in the zeus3d code. We quantify the anisotropy of numerical dissipation and compute its scaling with time and space resolution. We find a strong dependence of the dissipation on the mean magnetic field that may affect the saturation state of the MRI as computed with zeus3d . It is also shown that elongated grid cells generally preclude isotropic dissipation and that a Courant time-step smaller than that which is commonly used should be taken to avoid spurious anti-diffusion of magnetic field. 相似文献