共查询到20条相似文献，搜索用时 31 毫秒
1.
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
2.
L. G. Luk’yanov 《Astronomy Letters》2012,38(3):201-211
Families of conditionally periodic solutions have been found by a slightly modified Lyapunov method of determining periodic
solutions near the libration points of the restricted three-body problem. When the frequencies of free oscillations are commensurable,
the solutions found are transformed into planar or spatial periodic solutions. The results are confirmed by numerically integrating
the starting nonlinear differential equations of motion. 相似文献
3.
M. A. Sattar 《Astrophysics and Space Science》1992,191(2):323-328
Locally similar solutions of the combined free and forced convection flow in a semi-infinite vertical porous medium are obtained by a perturbation method. The solutions, obtained near the leading edge of the plate, are discussed in comparison with the numerical results obtained by Raptis and Perdikis (1988). 相似文献
4.
Robert A. Van Gorder 《New Astronomy》2011,16(2):65-67
Perturbation solutions are obtained for the Lane–Emden equation of the second kind which describe Bonnor–Ebert gas spheres. In particular, we employ the field-theoretic perturbative procedure due to Bender et al. to obtain analytical solutions to the nonlinear initial value problem. We find that the method allows one to construct perturbation solutions which converge rapidly to the true solutions in many cases, as it allows one to more accurately represent the influence of nonlinear terms in the linearized equations. The rapid convergence of the method results in qualitatively accurate solutions in relatively few iterations. 相似文献
5.
S. R. Das Gupta 《Astrophysics and Space Science》1978,56(1):21-49
In this paper we develop a new method, combined with Laplace transformation and Wiener-Hopf technique, to obtain unique solutions of transport equations in finite media. For this purpose we consider the simple transfer equation for diffuse reflection by a plane-parallel finite atmosphere scattering radiation with moderate anisotropy. It is transformed, by Laplace transformation, into two coupled linear integral equations which are then reduced to two uncoupled Fredholm integral equations admitting of unique solutions by the method of iteration for values of the breadth of the atmosphere greater than that specified, depending on the scattering process. 相似文献
6.
In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal
masses. This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of the Albouy-Chenciner
equations. The existence of exact solutions, in a neighborhood of the approximated ones, is then verified using the Krawczyk
method. Although the Albouy-Chenciner equations for the five-body problem are huge, it is possible to solve them in a reasonable
amount of time. 相似文献
7.
Sarod Yatawatta 《Experimental Astronomy》2012,34(1):89-103
Interferometric calibration always yields non unique solutions. It is therefore essential to remove these ambiguities before the solutions could be used in any further modeling of the sky, the instrument or propagation effects such as the ionosphere. We present a method for LOFAR calibration which does not yield a unitary ambiguity, especially under ionospheric distortions. We also present exact ambiguities we get in our solutions, in closed form. Casting this as an optimization problem, we also present conditions for this approach to work. The proposed method enables us to use the solutions obtained via calibration for further modeling of instrumental and propagation effects. We provide extensive simulation results on the performance of our method. Moreover, we also give cases where due to degeneracy, this method fails to perform as expected and in such cases, we suggest exploiting diversity in time, space and frequency. 相似文献
8.
The principal objections to our paper on Jordan-Brans-Dicke Bianchi-type universes are misleading. The intended solutions assume a power-law form, only in the limit of very large times. Although this is the only one for which we wrote down explicit solutions. The physical point of view behind our paper was to extend the re-scaling method, developed by one of us, to anisotropic universes in general and not to make a detailed study of each of the possible solutions that could be obtained through this process. 相似文献
9.
A. Beesham 《Astrophysics and Space Science》1987,132(2):397-399
A simple method of obtaining exact solutions in the scale-covariant theory of gravitation from the corresponding general relativistic solutions is presented. Some comments are made on some special scale-covariant solutions. 相似文献
10.
S. G. Zhuravlev 《Celestial Mechanics and Dynamical Astronomy》1979,19(1):77-93
A formal method of constructing of conditionally periodic solutions of canonical systems of differential equations in the vicinity of a commemsurability of frequencies is proposed. The method is a union of the rapid convergence method and (well-known in celestial mechanics) Delaunay-Zeipel's method of canonical transformations. For a successful application of the method an existence of stationary resonant solutions of an averaged system of the differential equations is necessary. 相似文献
11.
Virendra Singh 《Celestial Mechanics and Dynamical Astronomy》1977,16(2):137-142
In this article the existence of periodic solutions in Hill's relativistic problem is demonstrated using Poincaré's small parameter method. This method guarantees the convergence of the series representing the periodic solutions. 相似文献
12.
The equations of gas dynamics are solved, quasi-analytically by applying McVittie's method for spherical, cylindrical and plane configurations. The hypothesis of linear wave flow is applied and it is assumed that the final state of collapsing clouds is a hydrostatic equilibrium state, determined by complete polytropes. Complete analytical solutions are found when the generalized (to the three symmetries) Emden equation admits of analytical solutions. Otherwise the solutions are left in terms of the numerical solutions of the Emden equation. Numerical solutions to the Emden equation in the plane case are found and tabulated. A strong dependence of amplification, of density, pressure and temperature of the gas, on the symmetry is found. In addition, it is conclude that the flow remains subsonic, during the collapse, except toward the boundaries of the collapsing clouds. 相似文献
13.
V. B. Kuznetsov 《Solar System Research》2016,50(3):211-219
In this paper, the Olbers method for the preliminary parabolic orbit determination (in the Lagrange–Subbotin modification) and the method based on systems of algebraic equations for two or three variables proposed by the author are compared. The maximum number of possible solutions is estimated. The problem of selection of the true solution from the set of solutions obtained both using additional equations and by the problem reduction to finding the objective function minimum is considered. The results of orbit determination of the comets 153P/Ikeya-Zhang and 2007 N3 Lulin are cited as examples. 相似文献
14.
《New Astronomy》2020
The objective of this paper is to find periodic solutions of the circular Sitnikov problem by the multiple scales method which is used to remove the secular terms and find the periodic approximated solutions in closed forms. Comparisons among a numerical solution (NS), the first approximated solution (FA) and the second approximated solution (SA) via multiple scales method are investigated graphically under different initial conditions. We observe that the initial conditions play a vital role in the numerical and approximated solutions behaviour. The obtained motion is periodic, but the difference of its amplitude is directly proportional with the initial conditions. We prove that the obtained motion by the numerical or the second approximated solutions is a regular and periodic, when the infinitesimal body starts its motion from a nearer position to the common center of primaries. Otherwise when the start point distance of motion is far from this center, the numerical solution may not be represent a periodic motion for along time, while the second approximated solution may present a chaotic motion, however it is always periodic all time. But the obtained motion by the first approximated solution is periodic and has regularity in its periodicity all time. Finally we remark that the provided solutions by multiple scales methods reflect the true motion of the Sitnikov restricted three–body problem, and the second approximation has more accuracy than the first approximation. Moreover the solutions of multiple scales technique are more realistic than the numerical solution because there is always a warranty that the motion is periodic all time. 相似文献
15.
考虑周期解的数值延拓问题并提出基于Broyden拟牛顿法来延拓周期解的一种有效算法,先后以布鲁塞尔振子、平面圆型限制性三体问题(Planar Circular Restricted Three-Body Problem, PCRTBP)的周期解为例进行了验证.这里的Broyden方法包含线性搜索、正交三角分解求线性方程组的步骤.对一般的周期解,周期性条件方程组中含有周期作为待延拓参数,可用周期来决定积分时长,将解代入周期性条件得到积分型的非线性方程组,利用Broyden方法迭代延拓直至初值收敛.根据两次垂直通过一个超平面的轨道是对称周期轨道的性质,可采用插值的方法求得再次抵达超平面的解分量,得到周期性条件方程组,再用Broyden方法求解.结合哈密顿系统的对称性和PCRTBP周期轨道的一些分类,对2/1、3/1的内共振周期解族进行了数值研究.最后,对算法和计算结果做了总结和讨论. 相似文献
16.
We developed an iterative method for determining the three-dimensional temperature distribution in a spherical spinning body that is irradiated by a central star. The seasonal temperature change due to the orbital motion is ignored. It is assumed that material parameters such as the thermal conductivity and the thermometric conductivity are constant throughout the spherical body. A general solution for the temperature distribution inside a body is obtained using spherical harmonics and spherical Bessel functions. The surface boundary condition contains a term obtained using the Stefan–Boltzmann law and is nonlinear with respect to temperature because it is dependent on the fourth power of temperature. The coefficients of the general solution are fitted to satisfy the surface boundary condition by using the iterative method. We obtained solutions that satisfy the nonlinear boundary condition within 0.1% accuracy. We calculated the rate of change in the semimajor axis due to the diurnal Yarkovsky effect using the linear and nonlinear solutions. The maximum difference between the rates calculated using the two sets of solutions is 13%. Therefore current understanding of the diurnal Yarkovsky effect based on linear solutions is fairly good. 相似文献
17.
V. Singh 《Celestial Mechanics and Dynamical Astronomy》1976,14(2):167-173
The paper discusses the existence of periodic and quasi-periodic solutions in the space relativistic problem of three bodies with the help of Poincaré's small parameter method starting from non-Keplerian generating solutions, i.e., using Gauss's method. The main peculiarity of these periodic orbits is the fact that they close, in general, after many revolutions. It is worth noticing that these periodic orbits give a new class of periodic solutions of the classical circular problem of three bodies, if relativistic effects are neglected. 相似文献
18.
S. A. Gasanov 《Astronomy Letters》2006,32(3):192-205
The problem of the spatial motion of a star inside an inhomogeneous rotating elliptical galaxy with a homothetic density distribution is considered. Periodic solutions are constructed by the method of a small Poincaré parameter. Linear variational equations with periodic coefficients are used to analyze the Lyapunov stability of these solutions. 相似文献
19.
C. N. Frangakis 《Astrophysics and Space Science》1973,23(1):17-42
The long period problem provides the initial conditions for numerical computation of close periodic solutions separated in three categories. For each type of commensurability a number of periodic solutions are computed and their stability is studied by computing the characteristic exponents of the matrizant. The Runge-Kutta method for the solution of differential equations of motion was used in all cases. The results obtained are presented for a four cases of commensurability. 相似文献
20.
D. N. Pant 《Astrophysics and Space Science》1994,215(1):97-109
In this paper we present a method of obtaining varieties of new classes of exact solutions representing static balls of perfect fluid in general relativity. A number of previously known classes of solutions has been rediscovered in the process. The method indicates the possibility of constructing a plethora of new physically significant models of relativistic stellar interiors with equations of state fairly applicable to the case of extremely compressed stars. To emphasize our point we have derived two new classes of solutions and discussed their physical importance. From the solutions of these classes we have constructed three causal interiors out of which in two models the outward march of pressure, density, pressure-density ratio and the adiabatic sound speed is monotonically decreasing. 相似文献