首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 437 毫秒
1.
This series of papers is devoted to multiple scattering of light in plane parallel, inhomogeneous atmospheres. The approach proposed here is based on Ambartsumyan's method of adding layers. The main purpose is to show that one can avoid difficulties with solving various boundary value problems in the theory of radiative transfer, including some standard problems, by reducing them to initial value problems. In this paper the simplest one dimensional problem of diffuse reflection and transmission of radiation in inhomogeneous atmospheres with finite optical thicknesses is considered as an example. This approach essentially involves first determining the reflection and transmission coefficients of the atmosphere, which, as is known, are a solution of the Cauchy problem for a system of nonlinear differential equations. In particular, it is shown that this system can be replaced with a system of linear equations by introducing auxiliary functions P and S. After the reflectivity and transmissivity of the atmosphere are determined, the radiation field in it is found directly without solving any new equations. We note that this approach can be used to obtain the required intensities simultaneously for a family of atmospheres with different optical thicknesses. Two special cases of the functional dependence of the scattering coefficient on the optical thickness, for which the solutions of the corresponding equations can be expressed in terms of elementary functions, are examined in detail. Some numerical calculations are presented and interpreted physically to illustrate specific features of radiative transport in inhomogeneous atmospheres.  相似文献   

2.
TheF N method of solving problems in radiative transfer for plane-parallel media with anisotropic scattering is established. The method utilizes properties of the exact solution and leads to final equations that are particularly concise and easy to use.  相似文献   

3.
On the ground of the proper wave representation the general theory is developed of radiative transfer in a homogeneous plasma with the strong magnetic field ( B /1). The linear and nonlinear equations are derived which generalize the corresponding equations of scalar radiative transfer theory in isotropic media. The solutions of some problems are given for the cases when the magnetic field is perpendicular to the surface: diffuse reflection of radiation from a semiinfinite medium, provided the sources are placed far from the surface (Milne's problem) and have constant intensity, increase linearly or quadratically with the optical depths, or decrease exponentially from the surface.  相似文献   

4.
S. I. Grachev 《Astrophysics》2001,44(3):369-381
General equations of the Wiener-Hopf type for a matrix source function with nonsymmetrical kernel matrices are considered in the form of continuous superpositions of exponentials. Certain problems in the transfer of polarized radiation reduce to equations of this kind. In general there are two different H-matrices in the theory (which are a generalization of the Ambartsumian-Chandrasekhar scalar H-function), generated by an initial equation of the Wiener-Hopf type and its analog, but with the kernel matrix and the unknown matrix of the source function being transposed. In addition there are two corresponding I-matrices, actually consisting of Laplace transforms of the matrix source functions, through which the Stokes vector of the escaping radiation is directly determined. In the problem of diffuse reflection from a half-space, the I-matrices are expressed in terms of a product of these two H-matrices, and for the latter there is a system of nonlinear equations which is a generalization of the corresponding Ambartsumian-Chandrasekhar scalar equation. In the problem of the emission of partially polarized radiation from a half-space containing uniformly distributed internal sources we have obtained a system of two nonlinear equations for the I-matrices directly. In the special case of a symmetrical kernel matrix, this system of two equations reduces to one equation. It is shown that in the case of resonance scattering in a weak magnetic field (the Hanle effect) in the approximation of complete frequency redistribution, the system of two nonlinear equations for the I-matrices (of dimension 6×6) also reduces to one nonlinear equation, although the kernel matrix for the main integral equation for the matrix source function () is not symmetrical. For this case we have found a matrix generalization of the so-called law, consisting of an equation of the type (0)Â T (0) = (where T denotes transposition) at the boundary of a half-space containing uniformly distributed primary sources of partially polarized radiation.  相似文献   

5.
Decomposition of the product of functions like exp (– 0/z)S +(z) [S +(z = 0 1 P(x) dx/(x–z)], obtained by Das Gupta (1978) and relevant to the solution of equations of radiative transfer or of transfer problems in finite media by Wiener-Hopf technique, is reviewed and transformed to quite simple integral forms amenable to easy numerical evaluations. The same forms are then shown to be directly obtainable in one step under a slightly stronger condition consistent with practical cases.  相似文献   

6.
It is assumed that the dynamical system can be represented by equations of the form $$\begin{gathered} \dot x = \varepsilon _i f_i (x,y) \hfill \\ \dot y = u(x,y) + \varepsilon _i g_i (x,y) \hfill \\ \end{gathered} $$ as this is the case for the Lagrange equations in celestial mechanics. The perturbation functionsf i andg i may also depend on the timet. The fast angular variabley is now taken as independent variable. Using perturbation theory and expanding in Taylor series the differential equations for the zeroth, first, second, ... order approximations are obtained. In the stroboscopic method in particular the integration is performed analytically over one revolution, say from perigee to perigee. By the rectification step applied tox andt, the initial values for the next revolution are obtained. It is shown how the second order terms can be determined for the various perturbations occurring in satellite theory. The solution constructed in this way remains valid for thousands of revolutions. An important feature of the method is the small amount of computing time needed compared with numerical integration.  相似文献   

7.
Interaction between planetary atmospheres and small bodies is connected with radiation effects. Submicron particles in the Earth's upper atmosphere strongly influence the scattering of the shortwave solar radiation. Based on the mutual connection between the environmental and radiation field structures it is possible to determine the physical characteristics of the particle set in this environment. Generaly, the diffused radiation field in the real atmosphere is given by a sum of elementary and multiple scattering components. Solving the inverse problems always leads to complicated integral equations. A major part of the diffused radiation field in the upper atmosphere is due to the first order scattering. The paper presents a new method for determination of the effective complex refractive index and size distribution of the particles based on the radiance data. The solution of integral equations is to be found in the space of quadratically integrable and continuous functionsf L 2.  相似文献   

8.
A direct approach of the dynamical equation for the evolution of the two-point density correlation function is given in an expanding flat Friedmann Universe in the Newtonian approximation. If the third and higher moments are neglected, a wave-like equation of third-order for the two-point density correlation function is found. The exact solution of this equation shows, in the large time limit, the usual Jeans instability t 4/3. It is suggested that the highern-point correlation function of the density grow liket 2n/3 in the same approximation. This indicates that every truncation procedure of the hierarchy of the equations is inapplicable at least for large timest.  相似文献   

9.
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   

10.
We consider the evolution of a neutron star binary system under the effect of two factors: gravitational radiation and mass transfer between the components. Gravitational radiation is specified under the justified assumption of a circular orbit and point masses and in the approximation of a weak gravitational field at nonrelativistic velocities of the binary components. During the first evolutionary phase determined only by gravitational radiation, the neutron stars approach each other according to a simple analytical solution. The second evolutionary phase begins at the time of Roche-lobe filling by the low-mass component, when the second factor, mass transfer as a result of mass loss by the latter, also begins to affect the evolution. Under the simplest assumptions of conservative mass transfer and exact equality between the Roche-lobe radius and the radius of the low-mass neutron star, it is still possible to extend the analytical solution of the problem of evolution to its second phase. We present this complete solution at both phases and, in particular, give theoretical light curves of gravitational radiation that depend only on two dimensionless parameters (m t and δ 0). Based on the solution found, we analyze the theoretical gravitational signals from SN 1987A; this analysis includes the hypothesis about the rotational explosion mechanism for collapsing supernovae.  相似文献   

11.
A two-component scheme for the generation of type III fundamental radiation is proposed. The first component of the fundamental arises at a plasma level L t because of the Rayleigh scattering of the plasma waves into electromagnetic radiation. The other component arises at L t /2 because of the decay of the first component into plasma waves and the subsequent rescattering of the plasma waves into electromagnetic radiation t 2( t /2). By its properties (location, directivity, polarization) the second component is essentially the same as the second harmonic radiation produced by a stream of fast electrons at L ( t /2). This scheme is used to solve the main problems (localization and directivity of the source, polarization of type III fundamental) of the harmonic theory of type III solar bursts.  相似文献   

12.
We develop a new method to find solutions of the equations of motion in Hamiltonian Dynamical Systems. The idea of the method is to express the solution of the nonlinear ODE in the formx=N/D n , whereN andD are Fourier series andn is an appropriate constant. We apply this method to a galactic potential with three degrees of freedom.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.  相似文献   

13.
Isentropic oscillations of a star in thermal imbalance are defined as those for which, at every istant, the entropy of each mass element of the configuration in the perturbed motion is equal to that of the same mass element in the unperturbed motion.The solution of the equations describing such isentropic oscillations and written in terms of the infinitesimal displacement r(r 0,t) is presented in terms of asymptotic expansions up to the first order in the parameter /t s where is the adiabatic pulsation period for the fundamental mode andt s , a slow time scale of the order of the Kelvin-Helmholtz time.The solution obtained allows one to define, unambiguously, an isentropic part to the coefficient of vibrational stability of arbitrary stellar models in thermal imbalance, as well as to derive a general formula relating the results of a stability analysis in terms of r and r/r.Application of this general solution to the simple case of homologous motion is also given.  相似文献   

14.
The author's model for anisotropic solar cosmic ray propagation gives 2 coupled, partial differential equations for the intensity and anisotropy of solar cosmic rays propagating with finite speed V in an inhomogeneous medium. The model is used to study the effect of the solar shell on solar cosmic ray propagation. It predicts an exponential decay, regardless of the observer's position. It predicts that when the observer is near the center of the shell, t D/t 0 20 to 30, (t D= decay time, t 0 = onset time) and A m(anisotropy) 15%, if t m/t 0 3 to 5 (t m= time of maximum), consistent with observations of relativistic particles on Feb. 23, 1956. When the observer is between the shell and the sun, the model predicts that oscillations might be observed near maximum intensity. When the observer moves away from the sun and the shell, the propagation is diffusive, but there is an increasingly large persistent anisotropy which serves as a measure of the width of the shell.  相似文献   

15.
A new numerical method is proposed for solving the problems connected with the evolution of spherical clusters. The method is based upon the solution of the algebraic equations describing the motions of spherical shells.The stage of the collapse of a typical cluster is considered. The initial configuration is taken as a system with a uniform density distribution and with velocities much less than the virial ones. The model close to a stationary one has been obtained. The mass of the stationary cluster comprises about 60% of the initial one. The density distribution of the outer part of the cluster approximately corresponds to a profile of R –3.3.  相似文献   

16.
Under the assumption of a power law (k·R n=C,C=const.) between the gravitational constantk and the radius of curvatureR of the Universe and forP=1/3 the exact solution is sought for the cosmological equations of Brans and Dicke. The solution turns out to be valid for closed space and the parameter of the scalar-tensor theory is necessarily negative. The radius of curvature increases linearly with respect to the age of the Universe while the gravitational constant grows with the square of the radius of curvature. It has been shown (Lessner, 1974) that in this case (KR 2) the spatial component of the field equations is independent of the remaining equations. However, our solution satisfies this independent equation. This solution for the radiation-dominated era corresponds to the solution for the matter-dominated era found by Dehnen and one of the authors (Dehnen and Obregón, 1971). Our solution, as is the solution previously obtained for the matter-dominated era, is in contradiction to Dirac's hypothesis in which the gravitational constant should decrease with time in an expanding Universe.  相似文献   

17.
The dynamical expansion and motion of supernova remnants, double radio galaxies, etc., into and through the surrounding interstellar and/or intergalactic gas are processes of some importance in astrophysics for inferring energy, magnetic fields, particle pressure, etc. in a wide variety of astrophysical situations. We are usually hampered by the fact that it is often difficult to obtain a solution to the equations describing the flow of a gas into a surrounding medium starting from a postulated equation of state. The present paper shows how, by starting with a fluid flow that one believes adequately describes the gas, it is possible to solveby quadratures for the associated pressure and density. And in making these remarks we are implicitly assuming plane, cylindrical or spherically symmetric flow velocities which may be unsteady in time. The fluid speed can be chosen to be either non-relativistic or relativistic, but the method is valid only when the resulting gas pressurep, is small compared to c 2, where is the mass density. We illustrate the method by solving a simple problem. In view of the ever increasing number of astrophysical situations where some measure of the fluid flow through an object is becoming available (often from Doppler shifted lines) we believe the present technique shou'd be of some use in helping to unravel the internal dynamical properties of the flowing gas.  相似文献   

18.
Thermal convection has considerable influence on the thermal evolution of terrestrial planets. Previous numerical models of planetary convection have solved the system of partial differential equations by finite difference methods, or have approximated it by parametrized methods. We have evaluated the applicability of a finite element solution of these equations. Our model analyses the thermal history of a self-gravitating spherical planetary body; it includes the effects of viscous dissipation, internal melting, adiabatic gradient, core formation, variable viscosity, decay of radioactive nucleides, and a depth dependent initial temperature profile. Reflecting current interest, physical parameters corresponding to the Moon were selected for the model.Although no initial basalt ocean is assumed for the Moon, partial melting is observed very early in its history; this is presumably related to the formation of the basalt maria. The convection pattern appears to be dominated by an L-2 mode. The present-day lithospheric thickness in the model is 600 km, with core-mantle temperatures close to 1600 K. Surface heat flux is 25.3 mW m–2, higher than the steady state-value by about 16%.The finite element method is clearly applicable to the problem of planetary evolution, but much faster solution algorithms will be necessary if a sufficient number of models are to be examined by this method.Notation coefficient of thermal expansion - ij Kronecker delta - absolute or dynamic viscosity - perturbation in temperature - thermal diffusivity - kinematic viscosity - density - stress tensor - B.P. before present - c specific heat at constant pressure or volume (Boussinesq approximation) - d depth of convection - E * activation energy for creep - g gravity - Ga billions of years - H(t) heat generation per unit mass per unit time at timet - k Boltzmann's constant - K mean thermal conductivity - Ma millions of years - p pressure - q heat flux - q ss steady-state heat flux - Ra Rayleigh number - S volumetric heat sources, includes radioactivity and viscous dissipation - t time - T temperature - u verocity vector - V * activation volume for creep  相似文献   

19.
In this paper, we compare changes in the insolation at Pluto, corresponding to three epochs during the dynamical history of the planet: t = – 1, 0 and 0.5, where t is the time in millions of years A.D. The two extreme values of t coincide respectively with a maximum (126 ) and a minimum (102 ) value of the obliquity (). The other orbital elements i.e. the eccentricity (e) and the longitude of the perihelion ( p ) which affect solar radiation and which are apt to significant periodic changes are also calculated for the times under consideration. In a series of figures, the combined influence of the evolving dynamic parameters on the daily insolation and on the mean (summer, winter, annual) daily insolation is illustrated.  相似文献   

20.
We obtain an approximate analytic solution of a set of nonlinear model -dynamo equations. The reaction of the Lorentz force on the velocity shear which stretches and, hence, amplifies the magnetic field, is incorporated into the model. To single out the effect of the Lorentz force on the -effect, the effect of the Lorentz force on the -effect is neglected in this study. The solution represents a nonlinear oscillation with the amplitude and period determined by the dynamo numberN. The amplitude is proportional toN–1, while the period is almost exactly the same as the dissipation time of the unstable mode [proportional toN; note the linear oscillation period is proportional toN/(N–1) which is quite different for the solar situation whereN1].  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号