共查询到20条相似文献，搜索用时 24 毫秒
1.
In this paper the unsteady laminar free-convection flow of a viscous incompressible fluid, past an accelerated infinite vertical porous plate subjected to a constant suction (or injection) in considered. Numerical results for the skin-friction on the plate are obtained for the class of accelerated motions whose velocity is of the formU
0
t
n
wheret is time,U
0 a constant, andn is a positive integer. The skin friction tends to zero with increasingt when the Grashof number Gr=2, the Prandtl number =1,n=0, and >0 which corresponds to suction.On leave of absence from the Department of Mathematics, University of Dhaka, Bangladesh.On leave from absence from the Department of Mathematics, University of Dar-es-Salaam, Tanzania. 相似文献
2.
The resistive stability of coronal loops to perturbations with short wavelength across the magnetic field is analysed, taking full account of the line tying effect due to the presence of the photosphere. The results presented are similar to those previously obtained for arcades: configurations with a pressure profile decreasing with distance from the loop axis at some point are found to be always unstable, the growth rate increasing monotonically with the wavenumber (n) and scaling approximately as (n
2
D
r)1/3 in the limit of large n. 相似文献
3.
Numerical and analytical comparisons are made between three methods of obtaining stability information on satellite motion using the model of the restricted problem of three bodies. Kuiper's (1961) and Szebehely's (1978) approximate results are compared with computer solutions obtained by successive iterations. The three methods show close agreement regarding the maximum values of the orbital radii for stability. The lowest result and therefore the most conservative estimate is obtained by the simplest formula, max=(/81)1/3 where is the ratio of the satellite's orbital radius to the distance between the primaries with massesm
1>m
2 and is the mass-ratio given bym
2/(m
1+m
2). 相似文献
4.
Mohamed Adel Sharaf 《Astrophysics and Space Science》1979,63(2):295-317
General integral transform of the exponential integralsE
n
is considered and will be denoted asB
(k)
n
(). Different expressions and the equations satisfied byB
(k)
n
are developed. Two-term recurrence formula forB
(k)
n
(0) and three-term recurrence formula forB
(k)
n
(); 0 will be established for a givenk1 andn=2,3, ...,N. The computational algorithms based on these formulae are also constructed for the casesk=1,2,3, andn2. Finally the numerical results fork=2,3 andn=2(1)25 are presented to 15-digit accuracy 相似文献
5.
The gravitational instability of a nonrotating isothermal gaseous disk permeated by a uniform frozen-in magnetic field is investigated using a fourth-order perturbation technique. From the results it is found that the disk is stable whenn/B
0 < (4/33
G)–1/2, wheren andB are the column density of the disk and unperturbed magnetic field, respectively, andG is the gravitational constant. The disk is gravitationally unstable only whenn/B
0 > (4/33
G)–1/2. 相似文献
6.
This paper is devoted to Force-Free Electromagnetic Oscillations in a constant magnetic field. A correction is made in the derivation of the basic equation. The paper confirms the predicted spectrum of frequencies, namely
n
=
o
(n + 1)1/2;n = 0, 1, 2, .... In addition it is suggested that hybrid frequency
n
= (
n
2
+
H
2
)1/2 should be found in observational data. 相似文献
7.
8.
Eugene Rabe 《Celestial Mechanics and Dynamical Astronomy》1970,2(3):358-358
In the ordinary restricted problem of three bodies, the first-order stability of planar periodic orbits may be determined by means of their characteristic exponents, as derived from the condition of a vanishing determinant for the coefficients of an infinite system of homogenous linear equations associated with the exponential series solutionu, v representing any initially small oscillations about the periodic solutionx, y. In the elliptic restricted problem, periodic solutions are possible only for periods which are equal to, or integral multiples of, the periodP of the elliptic motion of the two primary masses. It is shown that the infinite determinant approach to the determination of the characteristic exponents can be extended to the treatment of superposed free oscillations in the elliptic problem, and that in generaltwo exponents appear in any complete solutionu, v for eachone existing in the corresponding ordinary restricted problem. The value of each exponent depends on a series proceeding in even powers of the eccentricitye of the relative orbit of the two primaries, in addition to its basic dependence on the mass ratio . For stable periodic orbits, the oscillation frequenciesn
1 (,e
2),n
2 (,e
2) associated with these two exponents tend, withe0, to certain limiting valuesn
1 (),n
2(), which differ from each other by the amount of the frequencyN=2/P of the orbital motion of the primaries. One of the two frequencies, sayn
1(), is identical with the frequency of the corresponding oscillations in the ordinary restricted problem, while the second one gives rise to oscillations only in the elliptic restricted problem, withe0.The method will be described in more detail, together with its application to two families of small periodie librations about the equilateral points of the elliptic restricted problem (E. Rabe: Two new Classes of Periodic Trojan Librations in the Elliptic Restricted Problem and their Stabilities) in theProceedings of the Symposium on Periodic Orbits, Stability and Resonances, held at the University of São Paulo, Brasil, 4–12 September, 1969.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 17–23, 1969. 相似文献
9.
Cristina Stoica 《Celestial Mechanics and Dynamical Astronomy》2002,84(3):223-229
The present paper offers an alternative point of view of block regularization for the motion of a particle in a central potential field of the form –x
–, where x is the distance between the particle and the source and some positive real number.Working in the physical space, we consider the scattering angle determined by the path of the particle as a function of angular momentum. We prove that a particle flow is passing over the collision singularity preserving differentiability with respect to initial data if and only if = 2(1–1/n), n positive integer, n 2.This result coincides with the outcome of block regularization applied by McGehee to the same dynamical problem. We discuss that this identity was to expect since both methods target the same physical constraint over the flow. 相似文献
10.
R. Caimmi 《Astrophysics and Space Science》1988,140(1):1-32
An approximate analytical method of solving the polytropic equilibrium equations, first developed by Seidov and Kuzakhmedov (1978), has been extended and generalized to equilibrium configurations of axisymmetric systems in rigid rotation, with polytropic index,n =n
p
+
n
, nearn
p
=0, 1, and 5. Though the details of the method depend on the value ofn
p
, acceptable results are obtained for |
n
| 0.5 to describe slowly rotating configurations in the range 0n1.5, 4.5n5. In the limit of rotational equilibrium configurations, when the distorsion may be large enough, a satisfactory approximation holds only in the range 0n, 1n1.5, 4.5n5. 相似文献
11.
With viscous dissipation and Joule heating taken into account, solution of the energy equation is obtained for unsteady hydromagnetic thermal boundary layer flow past a porous wall (e.g., surface of a star) in presence of a transverse magnetic field, under the condition of zero heat transfer between the fluid and the boundary — the so-called plate thermometer problem in MHD. Solution of the problem, in the form of power series, is obtained under certain valid simplifying assumptions, when (i) the wall is subjected to a normal velocity of suction/injection which is proportional tot
–1/2, and (ii) the wall has a velocity given by t
n
. The variation of temperature is shown graphically and is followed by a quantitative discussion therein also signifying the importance of retaining the Joule heating term in the energy equation.Part I is the article inAstrophysics and Space Science, Vol.45, No. 2, 1976, pp. 397–410.On study-leave from Defence Science Laboratory, Delhi, India. 相似文献
12.
Ian W. Walker A. Gordon Emslie Archie E. Roy 《Celestial Mechanics and Dynamical Astronomy》1980,22(4):371-402
An expansion of the force function ofn-body dynamical systems, where the equations of motion are expressed in the Jacobian coordinate system, is shown to give rise naturally to a set of (n–1) (n–2) dimensionless parameters
ki
li
{i = 2,...,n;k = 2,...,i – 1 (i 3);l =i + 1,...,n (i n – 1)}, representative of the size of the disturbances on the Keplerian orbits of the various bodies. The expansion is particularized to the casen=3 which involves the consideration of only two parameters
23 and
32. Further, the work of Szebehely and Zare (1977) is reviewed briefly with reference to a sufficient condition for the stability of corotational coplanar three-body systems, in which two of the bodies form a binary system. This condition is sufficient in the sense that it precludes any possibility of an exchange of bodies, i.e. Hill type stability, however, it is not a necessary condition. These two approaches are then combined to yield regions of stability or instability in terms of the parameters
23 and
32 for any system of given masses and orbital characteristics (neglecting eccentricities and inclinations) with the following result: that there is a readily applicable rule to assess the likelihood of stability or instability of any given triple system in terms of
23 and
32.Treating a system ofn bodies as a set of disturbed three-body systems we use existing data from the solar system, known triple systems and numerical experiments in the many-body problem to plot a large number of triple systems in the
23,
32 plane and show the results agree well with the
23,
32 analysis above (eccentricities and inclinations as appropriate to most real systems being negligible). We further deal briefly with the extension of the criteria to many-body systems wheren>4, and discuss several interesting cases of dynamical systems. 相似文献
13.
Annick Bec-Borsenberger 《Celestial Mechanics and Dynamical Astronomy》1982,26(3):271-276
We study a theory for the ninth satellite of Saturn, Phoebe, based on the literal solution we have obtained in the main problem of the lunar theory.These series were computed by solving, by successive approximations, the Lagrange's equations expressed in variables, functions of the elliptic elements.We may consider the case of Phoebe simpler than a lunar case because we seek less precision (1/10 geocentric) than in the Lunar case, although the eccentricity of Phoebe is stronger.Main problem: our series are computed to the complete seventh order and a great part of the perturbations of the eighth and ninth order, where we have attributed to the small lunar parameters the order 1 tom
0=n/n
0,e
0,e, sin (i
0/2), the order 2 to 0=(a
0/a)((M
1–)/(M
1+M)) and the order 4 toµ
0(a
0/a)M
1
M/M
1
2
–M
2.In the case of Phoebe,µ
0 equal zero and ±0 is the ratioa
0/a.We study the further development of these series by using, instead of parameterm
0, the quantity m
0=n/n
0–m
1 wherem
1 is an approached value ofm
0, in order to accelerate the convergence of the series with respect tom
0.Comparison with a numerical integration we are adjusting a numerical integration to the observations. We have already more than 100 observations, for the period 1900–1957.At first, we compare the series of the main problem to a numerical integration of the Keplerian problem.
Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix. Namur, Belgium, 28–31 July, 1980. 相似文献
Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix. Namur, Belgium, 28–31 July, 1980. 相似文献
14.
Yoshihide Kozai 《Celestial Mechanics and Dynamical Astronomy》1981,23(4):365-370
In this paper dynamical characteristics of satellites are outlined by classifying the satellites into three categories according to the values of the solar tidal factor (n/n)2 which is the disturbing factor due to the sun and the oblateness factor of the primary planetJ
2/a
2. For inner satellites (n/n)2 is much smaller thanJ
2/a
2 and there are several pairs among them, for which the mean motions are commensurable to each other, and for some of them secular accelerations in the mean longitudes have been detected. For outer satellites (n/n)2 is much larger and the solar perturbations are dominant. For intermediary satellites the motion of the pole of the orbital plane is not so simple as those of the satellites of the other categories. 相似文献
15.
Using slab model atmospheres that are irradiated from both sides by photospheric, chromospheric, and coronal radiation fields we have determined the ionization and excitation equilibrium for hydrogen.The model atom consists of two bound levels (n = 1 and n = 2) and a continuum. Ly- was assumed to be optically thick with the transition in detailed radiative balance. The Balmer continuum was assumed to be optically thin with the associated radiative ionization dominated by the photospheric radiation field (T
rad = 5940 K). The ionization equilibrium was determined from an exact treatment of the radiative transfer problem for the internally generated Ly-c field and the impressed chromospheric and coronal field (characterized by T
rad = 6500K).Our calculations corroborate the hypothesis that N2, the n = 2 population density, is uniquely determined by the electron density N
e. We also present ionization curves for 6000K, 7500K, and 10000K models ranging in total hydrogen density from 1 × 1010/cm3 to 3 × 1012/cm3. Using these curves it is possible to obtain the total hydrogen density from the n = 2 population density in prominences and spicules.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献
16.
In this paper we present new and exact analytical and computational developments of Güttler's formulae for composite grains, thereafter applied for the two models:
Literal and analytical expressions have been established for the Riccati-Bessel of the complex functions
n
,
n
, and
n
and their derivatives. The problem is treated in its general form without any restriction and the computer programme is now ready for request. 相似文献
| (1) | Graphite core-ice mantle. |
| (2) | Silicate core-ice mantle. |
17.
We consider the problem of finding the generalized potential function V = U
i(q
1, q
2,..., q
n)q
i + U(q
1, q
2,...;q
n) compatible with prescribed dynamical trajectories of a holonomic system. We obtain conditions necessary for the existence of solutions to the problem: these can be cast into a system of n – 1 first order nonlinear partial differential equations in the unknown functions U
1, U
2,...;, U
n, U. In particular we study dynamical systems with two degrees of freedom. Using adapted coordinates on the configuration manifold M
2 we obtain, for potential function U(q
1, q
2), a classic first kind of Abel ordinary differential equation. Moreover, we show that, in special cases of dynamical interest, such an equation can be solved by quadrature. In particular we establish, for ordinary potential functions, a classical formula obtained in different way by Joukowsky for a particle moving on a surface.Work performed with the support of the Gruppo Nazionale di Fisica Matematica (G.N.F.M.) of the Italian National Research Council. 相似文献
18.
Mohamed Adel Sharaf 《Astrophysics and Space Science》1987,129(1):19-38
In this paper of the series, the third step of the author's regularization approach will be started by establishing the expansions of the functionX
n
(r)
(, ,u) in terms of the sectorial variables
j
(i)
introduced in Paper IV (Sharaf, 1982) to regularize the highly-oscillating perturbation force of some orbital systems. The literal analytical expressions for the Fourier expansion of the function will be explored in terms of
j
(i)
for anyn positive integer,r any real number whatever the types and the number of sectors forming the divisions situation of the elliptic orbits may be. The basic computational materials of the theory will also be given and for which the method of solution, the recurrence formulae, and the general computational sequence for the coefficients are considered. 相似文献
19.
P. G. D. Barkham V. J. Modi A. C. Soudack 《Celestial Mechanics and Dynamical Astronomy》1976,14(4):465-492
A three-body problem is considered in which two masses, forming a close binary, orbit a comparatively distant mass. An asymptotic solution of this problem is presented, where the small parameter is related to the distance separating the binary and the remaining mass. Accepting certain model constraints, this solution is accurate within a constant errorO(11) and uniformly valid for time intervalsO(–3). Two specific examples are chosen to verify the literal solution: one relating to the Sun-Earth-Moon configuration of the solar system, the other to an idealized stellar system where the three masses are in the ratio 20:1:1. In both cases close agreement is found when the analytical solution is compared with an equivalent numerically-generated orbit. 相似文献
20.
A. Lannes 《Experimental Astronomy》1989,1(1):47-76
The minimum-norm least-squares solution of the phase-closure equations of an interferometric array is very stable. Furthermore, this canonical solution can be obtained by simple backprojection, each closure phase leaving its algebraic imprint on the corresponding baselines. More precisely, the generalized inverse of the phase-closure operator C of an n-point array is equal to its adjoint (its Hermitian transpose) divided by n: C
+
=C
*
/n. Likewise, the generalized inverse of the phase-aberration operator B is equal to B
*
/n. These remarkable properties, which have so far remained unnoticed, play an essential part in the algebraic analysis of phase-closure imaging, and thereby in the understanding and the treatment of the inverse problems of aperture synthesis.The applications presented in this paper concern the phase-factor restoration problem in optical interferometry and speckle imaging. We first propose a new iterative procedure for obtaining a particular least-squares solution. In the framework of this nonlinear technique, we then show how to initialize at each iteration the inner process of linear optimization. The backprojection method, which is the obvious choice in the case of weakly-redundant devices, is compared with the recursive techniques used in bispectral analysis for highly-redundant configurations. At the end of the restoration step under consideration, the phase indetermination reduces to a vector lying in the null space of the bispectral operator. The global reconstruction process is closely related to the regularization methods used for band-limited extrapolation. In this context, we outline the final hybrid procedure to be implemented, indicating how certain regularizing constraints can raise the intrinsic indeterminations related to the existence of the null space. 相似文献