共查询到20条相似文献，搜索用时 0 毫秒
1.
Harendra Singh 《Astrophysics and Space Science》2018,363(4):71
The key purpose of this article is to introduce an efficient computational method for the approximate solution of the homogeneous as well as non-homogeneous nonlinear Lane-Emden type equations. Using proposed computational method given nonlinear equation is converted into a set of nonlinear algebraic equations whose solution gives the approximate solution to the Lane-Emden type equation. Various nonlinear cases of Lane-Emden type equations like standard Lane-Emden equation, the isothermal gas spheres equation and white-dwarf equation are discussed. Results are compared with some well-known numerical methods and it is observed that our results are more accurate. 相似文献
2.
Lane-Emden type equations are well known model equations for the singular nonlinear boundary value problem that arise in the field of astrophysics. In this paper, a new method incorporated by the Legendre wavelet operational matrix of derivatives and block-pulse function approximation is adopted to investigate the solution of Lane-Emden type equations. Illustrative examples are given to demonstrate the simplicity and effectiveness of the proposed method. The obtained results are compared with other available results. 相似文献
3.
Saibal Ray 《Astrophysics and Space Science》2002,280(4):345-355
Static spherically symmetric charged dust models, known as Lane-Emden electromagnetic mass models, having their seed in the
well-known Lane-Emden equations of classical astrophysics, have been derived for Einstein-Cartan theory. The models are of
purely electromagnetic origin. The physical significance of these solutions can be understood from the very fact (i) that
they are generated from the well-known Lane-Emden equations of classical astrophysics having a proven physical foundation
and (ii) that, being the solution of Einstein-Cartan theory, they involve spin and torsion, characteristics which a material
system must possess for its subtle and finer details. PACS number(s): 04.90.+e, 04.20.jb.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
In this paper the problem of representing the numerical solutions of the Lane-Emden equation analytically by means of a convergent power series has been considered. Our results show that it is possible to represent the numerical solutions of the Lane-Emden equation by means of a power series which can be convergent in the whole interior of a polytropic model. 相似文献
5.
The nonlinear integral equations forX- andY-functions have been developed for an inhomogeneous atmosphere scattering anisotropically using the principle of invariance. The anisotropy is represented by means of a phase function expressed in terms of finite-order Legendre polynomials. 相似文献
6.
The partial heat fluxes of thermal radiation in an emitting, absorbing, and scattering finite medium bounded by diffusely-reflecting plates is studied, assuming the medium to scatter isotropically. Two algebraic equations connecting the partial heat fluxes relevant to this problem and the corresponding one with simple boundary conditions are obtained. The intergral equation is solved in a semi-analytical from by collection method, using Legendre polynomials as basis functions. Numerical results are presented and compared. 相似文献
7.
《Planetary and Space Science》2007,55(4):467-474
A theoretical study is made on the generation mechanism of electrostatic Bernstein mode wave in the presence of electromagnetic Kinetic Alfven wave turbulence in magnetized inhomogeneous plasma on the basis of plasma-maser interaction. It is shown that a test high-frequency electrostatic Bernstein mode wave is unstable in the presence of low-frequency Kinetic Alfven wave turbulence. Because of the universal existence of the Kinetic Alfven waves in large-scale plasmas, the result has potential importance in space and astrophysical radiation process. The growth rate of the test high-frequency Bernstein mode wave is obtained with the involvement of spatial density gradient parameter. A comparative study on the role of density gradient in the generation of Bernstein mode on the basis of plasma-maser effect is presented. 相似文献
8.
The Integral Variation (IV) method is a technique to generate an approximate solution to initial value problems involving systems of first-order ordinary differential equations. The technique makes use of generalized Fourier expansions in terms of shifted orthogonal polynomials. The IV method is briefly described and then applied to the problem of near Earth satellite orbit prediction. In particular, we will solve the Lagrange planetary equations including the first three zonal harmonics and drag. This is a highly nonlinear system of six coupled first-order differential equations. Comparison with direct numerical integration shows that the IV method indeed provides accurate analytical approximations to the orbit prediction problem.Advanced Systems Studies; Bldg. 254EElectro-Optical Systems Laboratory; Bldg. 201. 相似文献
9.
N. K. Sood 《Astrophysics and Space Science》1980,73(1):213-225
The effect of a prevalent magnetic field on static and uniformly rotating self-gravitating cylinders of infinite length is examined. The magnetic field is assumed to consist ofH
andH
z
components, which are taken to be functions of the radial coordinate alone. A variety of magnetic-field configurations are shown to be admissible solutions of equations of motion, from which some feasible cases are presented. A particular magnetic-field configuration having bothH
andH
z
components is studied in detail. The configuration is such that the assumption of a polytropic equation of state reduces the equation governing the density function to a non-homogeneous cylindrical analogue of the Lane-Emden equation for spherical polytropes. The homogeneous case is also studied and shows interesting magnetic-field patterns. 相似文献
10.
A tractable method for investigating the linear stability of line-tied 2-D coronal magnetic fields is introduced. It is based on the Bernstein et al. (1958) energy principle and can be applied to non-isothermal equilibria with gravity, having a translational invariance. The perturbed potential energy integral is manipulated to produce either necessary conditions for stability to localized modes or sufficient conditions for stability to global modes. Each condition only requires the solution of a set of ordinary differential equations, integrated along the magnetic field lines. The tests are employed to two different classes of equilibria. A linear force-free field is shown to be completely stable, regardless of the shear. The role of pressure gradients, footpoint displacements, line-tying and stratification on an isothermal magneto-hydrostatic equilibrium is assessed. 相似文献
11.
Paolo Lanzano 《Earth, Moon, and Planets》1990,48(3):251-278
We establish the equations of motion for a fluid spherical shell which constitutes the upper-most layer of a rotating body and which is heated from below because of radiogenic decay occurring in the lower layers. We solve these equations in terms of series of products of Bessel functions and Gegenbauer polynomials. By the step-wise solution of an infinite-order determinant equation we determine those values for the Taylor and Rayleigh numbers of the flow, up to the 1016 order, that will give rise to convective cells in the liquid layer.Using these eigenvalues, we solve linear systems of equations to determine the coefficients of the series solutions. 相似文献
12.
A model for the generation mechanism for multiple frequency bands in solar spike bursts is extended to predict the degree of circular polarization of the spike burst radiation in the source region. In this model, several adjacent electrostatic Bernstein modes are excited by the electron-cyclotron maser instability and subsequent nonlinear coalescence of Bernstein waves produces transverse magnetoionic waves which freely propagate out of the source region at the foot of a coronal loop to an observer. The emission rates for the coalescence processes between two Bernstein waves to produce transverse x-mode and o-mode waves are compared in order to predict the polarization state of the product radiation. Low degrees of circular polarization favouring the x-mode are predicted to occur over a wide range of parameter space. The range of emission angles is shown to vary between each frequency band, which further constrains the number of simultaneously observable anharmonic bands than predicted in the earlier model. The consistency of these predictions with currently available polarization observations is discussed. 相似文献
13.
H. A. Harutyunian 《Astrophysics》1996,39(4):370-374
The Voigt function and its derivatives are represented by means of series in Hermite polynomials. The equations obtained can be used both for numerical calculations of these functions and for analytical research.Translated from Astrofizika, Vol. 39, No. 4, pp. 619–625, October–December, 1996. 相似文献
14.
Martin Beech 《Astrophysics and Space Science》1987,132(2):393-396
In general, the Lane-Emden equation for an arbitrary polytropic indexn does not admit of an analytic solution. Simple approximation to the numerical results can, however, be found; and, in particular,
affords a hitherto unreported good approximation to then=3 model. This term is accurate to within 10% of the tabulated values over 78% of the polytropic interior. 相似文献
15.
The investigated model supposes Bernstein waves emerging from Harris instabilities at a definite coronal level. The nonlinear process is considered for a higher region, where the quasimonochromatic waves forming the primary spectrum are reflected. Spatial dispersion takes place corresponding to the decreasing magnetic field. Thus each quasimonochromatic wave can be treated separately. According to the nonlinear resonance condition there result electromagnetic waves of twice the primary frequency, the power density of which is calculated. Assuming a coherence time of 480 periods and an oscillation velocity of the electrons of 10-3 times the thermal velocity the effective radiation temperature 1011 K of a type IVmA-burst is obtained at about 180 MHz, if the range of the nonlinear interaction is about 3.9 km long. In the discussion the interpretation of occurring zebra patterns is treated. 相似文献
16.
In order to explain a fine structure of parallel ridges in stationary type IV continua, the emission due to the coupling of electrostatic upper hybrid waves and Bernstein waves at the sum frequency of the upper hybrid and harmonics of the gyro frequency has been calculated. If the energy density of these electrostatic waves is of the order of 10-3 times the thermal energy density, then the observed zebra pattern can be emitted by a region with a diameter of 103 km. 相似文献
17.
Richard L. Branham Jr. 《Celestial Mechanics and Dynamical Astronomy》1990,49(2):209-217
Hansen coefficients are used in expansions of the elliptic motion. Three methods for calculating the coefficients are studied: Tisserand's method, the Von Zeipel-Andoyer (VZA) method with explicit representation of the polynomials required to compute the Hansen coefficients, and the VZA method with the values of the polynomials calculated recursively. The VZA method with explicit polynomials is by far the most rapid, but the tabulation of the polynomials only extends to 12th order in powers of the eccentricity, and unless one has access to the polynomials in machine-readable form their entry is laborious and error-prone. The recursive calculation of the VZA polynomials, needed to compute the Hansen coefficients, while slower, is faster than the calculation of the Hansen coefficients by Tisserand's method, up to 10th order in the eccentricity and is still relatively efficient for higher orders. The main advantages of the recursive calculation are the simplicity of the program and one's being able to extend the expansions to any order of the eccentricity with ease. Because FORTRAN does not implement recursive procedures, this paper used C for all of the calculations. The most important conclusion is recursion's genuine usefulness in scientific computing. 相似文献
18.
Cyclotron damping by warm electrons limits the amplitude of high frequency electrostatic waves propagating in discrete auroral arcs. The effect of this damping on whistler VLF hissupper hybrid noise and Bernstein modes is examined by calculating temporal growth rates and power flux intensities of amplified noise produced by precipitating electrons. The auroral electrons are described by a realistic distribution function. The effect of varying ionospheric conditions is also considered. Whistler mode noise is found to be less sensitive to the warm electron model than the upper hybrid mode. Bernstein modes are rapidly absorbed by the ionospheric and warm electrons. The difference in the peak power flux of the whistler and upper hybrid modes is indicative of the local value of the ratio of electron plasma frequency to electron gyrofrequency. For peak upper hybrid noise to exceed peak whistler noisethis ratio should be greater than 1. Ionospheric electron temperature has little effect on the spectrum, and intense narrow beams in the distribution function should be most effective at producing high noise levels for a given warm electron model. 相似文献
19.
Jean Chapront 《Celestial Mechanics and Dynamical Astronomy》1982,28(4):415-430
A new type of approximation is proposed to evaluate Fourier series with a great many terms. It combines Fourier series and Chebychev polynomials to represent time series over a finite time interval. On one side, the high frequencies are approximate multiples of a basic frequency to represent short periodic terms; on the other side, the slowly variable functions of the time, on a given interval, which contain terms with long periods, are approximated by Chebychev polynomials. Application is made in case of the Lunar Theory ELP which contains about 30 000 trigonometric terms. The computing time necessary to evaluate coordinates is very much reduced when we give to series the intermediary representation inF-T form, as compared to a direct substitution of the time in the arguments.One shows also on a numerical example, that the Fourier-Chebychev approximation smoothly degrades outside its range of representation.Bureau des Longitudes. Equipe de Recherche Associée au CNRS 相似文献
20.
《New Astronomy》2022
In this study, we build up a general formalism for tilted N-component fluid form to investigate the isotropization features of the Bianchi-type models excluding Bianchi-IX. We applied this formalism to Bianchi type I and V models analytically and numerically using the metric approach of Einstein field equations. It is found that only the stiff fluid for Bianchi I model does not isotropize, in the absence of cosmological constant. Other Bianchi type I and V models become isotropic regardless of the type of the fluid or how much component it has. The result does not change with the existence of a cosmological constant. 相似文献