共查询到20条相似文献，搜索用时 15 毫秒
1.
The hydromagnetic flow in a vertical channel with heat and mass transfer is studied when chemical reaction is present. For the general integral equation for radiative flux and in the absence of the Dufour term, the problem is reduced to a set of coupled integral equations which are solved iteratively. The results are compared with the solutions obtained when chemical reaction is absent. 相似文献
2.
A. I. Shapiro 《Astrophysics》2002,45(2):215-222
A model problem in the theory of line formation in an optically thick, purely scattering, stellar atmosphere is considered. The integral equation of radiation transfer at line frequencies is solved numerically for a two-level atom in the approximation of complete frequency redistribution in scattering. The numerical results are compared with those calculated from equations of the asymptotic theory. On the basis of the asymptotic theory, the positions of intensity maxima in a line are found for different absorption profiles. 相似文献
3.
The paper studies the hydromagnetic flow of a thermally-radiating binary mixture of an incompressible fluid. Both the Soret and Dufour effects are considered when the fluid is not chemically reacting. When the gas is optically thin the resultant system of ordinary differential equations could be solved in a closed form. Generally the problem is reduced to a set of integral equations which are tackled by perturbation and iteration. The problem is worthy of note in the re-entry problem. 相似文献
4.
Rabindra Nath Das 《Astrophysics and Space Science》1978,58(2):419-425
The basic integro-differential equation is subjected to a one-sided finite Laplace transform to obtain linear integral equations of angular distribution of bounding faces. These linear integral equations have been transformed into linear singular integral equations which have been solved exactly to get the emergent distributions from the bounding faces by the theory of linear singular operators. Some solutions of linear singular integral equations have also been derived for future use in radiative transfer problems. 相似文献
5.
S. Ueno 《Astrophysics and Space Science》1976,44(1):151-158
In a series of our preceding papers (cf. Bellman and Ueno, 1971a, 1971b, 1972a, 1972b, 1972c; Ueno 1972), with the aid of invariant imbedding technique, we transformed the two point boundary value problem for integral equations into the initial-value problem. In this paper, extending the procedure to the Milne's integral equation, whose kernel is expanded into a double Fourier cosine series, we show how to find a Cauchy system for the required solution of Milne's integral equation and the Fredholm resolvent. The obtained integro-differential equations are reduced to large system of ordinary differential equations with known initial conditions. Then, they are suitable for the numerical computation of the solution by the modern high-speed computer. 相似文献
6.
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
7.
H. F. Machali 《Astrophysics and Space Science》1993,208(1):33-39
The time-dependent equation of radiative transfer for a finite, plane-parallel, non-radiating, and isotropically scattering atmosphere of arbitrary stratification is solved by using the integral equation method. The medium is taken to be inhomogeneous. The Laplace transform is used in the time domain. It is seen that the obtained solutions are reducible to the corresponding ones for steady-state problems by simply changing the Laplace transform parameter to zero. 相似文献
8.
P. C. W. Fung 《Astrophysics and Space Science》1969,5(4):448-458
In this investigation, the polarization transfer equations in terms of the Stokes parameters are derived for electromagnetic waves propagating in an arbitrary direction in an inhomogeneous magnetized plasma. This system of transfer equations is then solved analytically in the case when the magnetized plasma is homogeneous. For simplicity in presentation, the source term in the equation of transfer has been omitted. Transitting to the special case of quasi-longitudinal propagation, the results obtained here are shown to be in agreement to that derived by Zheleznyakov earlier. 相似文献
9.
Pamela Woo Arun K. Misra Mehdi Keshmiri 《Celestial Mechanics and Dynamical Astronomy》2013,117(3):263-277
Relative motion of binary asteroids, modeled as the full two-body planar problem, is studied, taking into account the shape and mass distribution of the bodies. Using the Lagrangian approach, the equations governing the motion are derived. The resulting system of four equations is nonlinear and coupled. These equations are solved numerically. In the particular case where the bodies have inertial symmetry, these equations can be reduced to a single equation, with small nonlinearity. The method of multiple scales is used to obtain a first-order solution for the reduced nonlinear equation. The solution is shown to be sufficient when compared with the numerical solution. Numerical results are provided for different example cases, including truncated-cone-shaped and peanut-shaped bodies. 相似文献
10.
Alex Konopliv 《Celestial Mechanics and Dynamical Astronomy》1989,47(4):305-320
For differential equations with one fast variable, a perturbation method is introduced that transforms a solution valid over only a short time interval to a new solution composed of averaged variables plus a periodic function of the averaged variables. The averaged variables are governed by a set of differential equations where the fast variable has been removed and thus can be numerically integrated quickly or solved directly. This method is applied to a perturbed harmonic oscillator with a cubic perturbation, van der Pol's equation, coorbital motion in the restricted three-body problem, and to nearly circular motion of a particle near one of the primaries in the restricted three-body problem. 相似文献
11.
H. M. Yehia 《Celestial Mechanics and Dynamical Astronomy》1987,41(1-4):289-295
The problem of motion of a dynamically symmetric gyrostat acted upon by non-symmetric potential forces admitting a cyclic integral is considered. This problem is brought into equivalence with another one concerning the motion of a similar gyrostat under the action of axisymmetric potential forces. Using this analogy, new integrable cases of each of the two problems are obtained from the known cases of the other. The equations of motion are reduced to a single equation of the second order. 相似文献
12.
A. V. Dementyev 《Astrophysics》2010,53(3):419-433
A matrix transfer equation for multiple resonance scattering of radiation in a spectral line in a semiinfinite atmosphere
with a uniform distribution of primary radiation sources is examined. A nonlinear matrix integral is obtained for this equation
as a generalization of the Rybicki two-point Q-integral. One special case of the matrix [^(Q)] {\mathbf{\hat{Q}}} -integral is the Volterra equation for the matrix source function of the problem discussed here. The Volterra equation is
solved numerically for a Doppler profile of the absorption coefficient. Several polarization characteristics of the emerging
radiation are obtained. 相似文献
13.
J. Hagel 《Celestial Mechanics and Dynamical Astronomy》1990,50(3):209-230
The circular restricted problem of three bodies is investigated analytically with respect to the problem of deriving a second integral of motion besides the well known Jacobian Integral. The second integral is searched for as a correction the angular momentum integral valid in the two body case. A partial differential equation equivalent to the problem is derived and solved approximately by an asymptotic Fourier method assuming either sufficiently small values for the dimensionless mass parameter or sufficiently large distances from the barycentre. The solution of the partial equation then leads to a function of the coordinates, velocities and time being nearly constant, which means that its variation with time is about 40–300 times less than that of the pure angular momentum. By averaging over the remaining fluctuating part of the quasi-integral we are able to integrate the first order equations using a renormalization transformation. This leads to an explicit expression for the approximate solution of the circular problem which describes the motion of the third body orbiting both primaries with nonvanishing initial eccentricity (eccentric planetary type orbits). One of the main results is an explicit formula for the frequency of the perihelion motion of the third body which depends on the mass parameter, the initial distance of the third body from the barycentre and the initial eccentricity. Finally we study orbits of the P-Type, being defined as solutions of the restricted problem with circular initial conditions (vanishing initial eccentricity). 相似文献
14.
Rabindra Nath Das 《Astrophysics and Space Science》1979,60(1):221-232
We have considered six scalar equations which are obtained from the vector transport equation for radiative transfer to the problem of diffuse reflection and transmission in finite plane-parallel Rayleigh scattering atmosphere. By use of the Laplace transform and the theory of linear singular operators these equations have been solved exactly to get the angular distribution of the intensity diffusely reflected from the surface and diffusely transmitted below the surface. 相似文献
15.
The time-dependent equation of radiative transfer for isotropic scattering has been solved by integral equation technique in terms ofX- andY-functions appropriate for the problem. It is seen thatX- andY-functions are reducible to the corresponding function for steady-state problems by simply changing the Laplace transform parameters-i.e., byS0. 相似文献
16.
F. M. El-Sabaa 《Celestial Mechanics and Dynamical Astronomy》1993,55(4):323-330
The equations of motion of a rigid body about a fixed point in a central Newtonian field is reduced to the equation of plane motion under the action of potential and gyroscopic forces, using the isothermal coordinates on the inertia ellipsoid.The construction of periodic solutions near the equilibrium points, by using the Lipaunov theorem of holomorphic integral, is obtained and the necessary and sufficient conditions for the stability of the system are given. 相似文献
17.
Rabindra Nath Das 《Astrophysics and Space Science》2008,317(1-2):119-126
The linear singular integral equation derived from the nonlinear integral equation of Chandrasekhar’s H-function in radiative transfer is considered here to develop a new form of H-function as a solution of a Riemann–Hilbert problem using Plemelj and Cauchy integral formulae for complex domain. This new form of H-function is a simple integral of known functions. Forms of H-function both for conservative and nonconservative cases are obtained. Their numerical evaluations are made by Simpson’s one-third rule to arrive at an accuracy to ninth places of decimals. 相似文献
18.
F. M. El-Sabaa 《Astrophysics and Space Science》1989,162(2):235-242
The equations of motion of a rigid body about a fixed point in a central Newtonian field is reduced to the equation of plane motion under the action of potential and gyroscopic forces, using the isothermal coordinates on the inertia ellipsoid.The construction of periodic solutions nearby equilibrium points, by using the Liapunov theorem of holomorphic integral are obtained and the necessary and sufficient conditions for the stability of the system are given. 相似文献
19.
Rabindra Nath Das 《Astrophysics and Space Science》1980,71(1):25-35
A finite atmosphere having distribution of intensity at both surfaces with definite form of scattering function and source function is considered here. The basic integro-differential equation for the intensity distribution at any optical depth is subjected to the finite Laplace transform to have linear integral equations for the surface quantities under interest. These linear integral equations are transformed into linear singular integral equations by use of the Plemelj's formulae. The solution of these linear singular integral equations are obtained in terms of theX-Y equations of Chandrasekhar by use of the theory of linear singular operators which is applied in Das (1978a). 相似文献
20.
S. K. El-Labany 《Astrophysics and Space Science》1992,191(2):185-194
The propagation of an ion-acoustic soliton in a collisionless plasma with adiabatic positive and negative ions (with equal ion temperature) and hot non-isothermal electrons is studied by use of the renormalization method introduced by Kodama and Taniuti in the reductive perturbation method. The basic set of fluid equations describing the system is reduced to a Korteweg-de Vries (K-dV)-type equation for the first-order perturbed potential and to a linear inhomogeneous differential equation to the second-order of the perturbed potential. A stationary solution of the coupled equations is obtained. 相似文献