共查询到20条相似文献，搜索用时 156 毫秒
1.
The equations of neutrino hydrodynamics are derived in two different approximations taking into consideration the neutrino scattering from stellar material. In a thermal-conductivity approximation which holds good when neutrino optical depth with respect to absorption exceeds 1, the neutrino scattering is taken into account, analogously with photon radiative conductivity, by introducing the transport cross-section in the neutrino mean free path. In a practically important case when the neutrino optical thickness with respect to scattering is high enough, whereas that concerning absorption is sufficiently low, another approximation of Comptonized neutrinos is valid. In this case, the neutrino and antineutrino chemical potentials are independent of each other. They have to be calculated from equations of continuity established for neutrino and antineutrino alongside with the diffusion equation expressing the law of lepton-charge conservation. The equations of neutrino hydrodynamics are written out both with and without inclusion of muon neutrinos and antineutrinos.The equations obtained are established to deal properly with neutrino diffusion inside collapsing stars. 相似文献
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3.
Can Battal Kilinç 《Astrophysics and Space Science》2006,301(1-4):83-88
We consider Einstein's equations with variable cosmological constant in the presence of a perfect fluid for the inhomogeneous
cylindrically-symmetric space–time. We find two solutions under this conditions and analyze our solutions with respect to
the constants. 相似文献
4.
J. Baumgarte 《Celestial Mechanics and Dynamical Astronomy》1972,5(4):490-501
A stabilization of the classical equations of two-body motion is offered. It is characterized by the use of the regularizing independent variable (eccentric anomaly) and by the addition of a control-term to the differential equations. This method is related to the KS-theory (Stiefel, 1970) which performed for the first time a stabilization of the Kepler motion. But in contrast to the KS-theory our method does not transform the coordinates of the particle. As far as the theory of stability and the numerical experiments are concerned we restrict ourselves to thepure Kepler motion. But, of course, the stabilizing devices will also improve the accuracy of the computation of perturbed orbits. We list, therefore, also the equations of the perturbed motion. 相似文献
5.
V. G. Sokolov 《Solar System Research》2009,43(1):53-60
The boundaries of the domains of holomorphy of the coordinates of unperturbed elliptic motion with respect to the eccentricities of planetary orbits are determined for the cases when any of the five anomalies of one of the planets-eccentric, true, tangential, or one of two mutual anomalies suggested by M.F. Subbotin—is used as an independent variable. The resulting equations are a generalization of the known equations for the boundaries of the domains of the holomorphy of coordinates for the cases when the time is the independent variable and determine the bisymmetric ovals, whose size and shape depend on the eccentricities and on the ratio of the planetary mean motions. The largest domains of holomorphy are obtained when the tangential anomaly or one of the Subbotin mutual anomalies is used. A function was found that conformally maps the domain of holomorphy to the unit disk. It was demonstrated that the application of any anomaly of the outer planet as the independent variable can result in a significant shrinking of the domain of the holomorphy of the coordinates of the inner planet, so that the analytic continuation of the initial power series with the center at the origin of the coordinates of a complex plane becomes impossible. 相似文献
6.
N. Borderies 《Celestial Mechanics and Dynamical Astronomy》1977,16(3):291-308
This paper deals with the Adams-Moulton-Cowell multistep integrator, as described by Oestwinter and Cohen (1972). In order to evaluate the accuracy of the method, we started to test it in the case of the unperturbed two-body motion; numerical instability may arise by integrating first order systems. The accuracy is improved by applying a Sundmann transformation of the independent variable. The algorithm is then modified such that the equations of pure keplerian motion are integrated with respect to the new independent variable without truncation error; numerical experiments show the considerable improvement of accuracy and the reduction of computing time for Keplerian motion.If terms of the disturbing function of the Earth are added to the central potential, the time-transformation is less effective. With a modification of this time-transformation as given by Moynot in 1971, it is possible to reduce the propagation of the truncation error in the J2 problem. 相似文献
7.
A. K. Singh 《Astrophysics and Space Science》1983,95(2):283-289
The flow past an infinite vertical isothermal plate started impulsively in its own plane in a viscous incompressible and electricalfy conducting fluid has been presented in a rotating system. The magnetic Reynolds number is assumed small so that the induced magnetic field can be neglected. The governing equations of the flow are solved by defining a complex variable with the help of the Laplace transform technique. The influence of the various parameters, occurring into the problem, on the axial and transverse components of the velocity and skin-friction is extensively discussed with the help of graphs and table. 相似文献
8.
A new algorithm is presented for the numerical integration of second-order ordinary differential equations with perturbations
that depend on the first derivative of the dependent variables with respect to the independent variable; it is especially
designed for few-body problems with velocity-dependent perturbations. The algorithm can be used within extrapolation methods
for enhanced accuracy, and it is fully explicit, which makes it a competitive alternative to standard discretization methods. 相似文献
9.
The instability of axisymmetric flows of inviscid compressible fluid with respect to two-dimensional infinitesimal perturbations with the nonconservation of angular momentum is investigated by numerically integrating the differential equations of hydrodynamics. The compressibility is taken into account for a homentropic flow with an adiabatic index varying over a wide range. The problem has been solved for two angular velocity profiles of an initial axisymmetric flow. In the first case, a power-law rotation profile with a finite enthalpy gradient at the flow edges has been specified. For this angular velocity profile, we show that the instability of sonic and surface gravity modes in a nearly Keplerian flow, when a radially variable vorticity exists in the main flow, can be explained by the combined action of the Landau mechanism and mode coupling. We also show that including a radially variable vorticity makes the limiting exponent in the rotation law at which the unstable surface gravity modes vanish dependent on the fluid compressibility. In the second case, a Keplerian rotation law with a quasi-sinusoidal deviation has been specified in such a way that the enthalpy gradient vanished at the flow edges. We have found than the sonic modes are then stabilized and the flow is unstable only with respect to the perturbations that also exist in an incompressible fluid. 相似文献
10.
The dynamical problem for thermal stresses in an infinite isotropic elastic cylinder of radius a with its axis along the z-axis, subject to fixed boundary conditions is studied. The Fourier heat conduction equation has been solved applying the Fourier transform and the theory of complex variable. The thermoelastic equation of motion has been separated into two wave equations which can be solved separately. The temperature, the displacement and the stress components have been obtained in analytical form as series involving Bessel function of first kind and of order zero. 相似文献
11.
Time transformations involving momenta in addition to the coordinates are studied from the points of view of stabilization and regularization of the equations of motion. The generalization of Sundman's transformation by using the potential function to transform the time is further generalized by using the Lagrangian function for the same purpose. The possibility of the stabilization of the equations of motion is investigated similarly to Stiefel's and Baumgarte's recent results but instead of a factorial, an additive control function is introduced in all equations of motion. The relation between the original and new independent variables is integrated by a modification of Ebert's theorem and it is shown that the new independent variable is Hamilton's principal function. Numerical examples illustrate the method and seem to indicate that the computation of close approach trajectories benefit especially by the transformations discussed. The Appendix offers an analytic treatment regarding the stabilization of the constant of energy. 相似文献
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V. A. Shefer 《Solar System Research》2005,39(3):239-246
The motion of minor Solar System bodies having close encounters with major planets is described using the model of motion within the framework of the perturbed restricted three-body problem. The actual motion of a minor body is represented as a combination of two motions, namely, the motion of a fictitious attracting center with a variable mass and the motion with respect to the fictitious center. The position and mass of the fictitious center are chosen so that, when the minor body collides with any of the primaries, the fictitious center carries into the center of inertia of the colliding body and the mass of the fictitious center becomes identical to the mass of this body. The regularizing KS-transformation and Sundman’s time transformation were applied to coordinates and velocities. As a result, a system of differential equations of motion that are quasilinear within the nearest vicinity of each of the primary attracting bodies was obtained. These equations are characterized by a numerical behavior during the encounters of the minor body with the primaries that is essentially better than that of the initial equations of motion. The motion of comets Brooks 2 and Gehrels 3, which have fairly close encounters with Jupiter, is simulated.__________Translated from Astronomicheskii Vestnik, Vol. 39, No. 3, 2005, pp. 272–280.Original Russian Text Copyright © 2005 by Shefer. 相似文献
14.
Tōnu Viik 《Astrophysics and Space Science》1992,198(2):265-280
The external field of radiation in Rayleigh-Cabannes atmospheres with constant and linear sources is found using the resolvent matrix approach. If the internal sources are constant the external field may be described by theX-, Y-, andH-matrices. For the case with linear sources we need the derivatives of these matrices with respect to angular variable. The respective scheme for their determination is given.A set of integro-differential equations for theX- andY-matrices is derived and solved numerically. Some relations between the moments of theH-matrix are given and a sample of results for external fields are provided. 相似文献
15.
Two integral equations for the electric field, characterizing the Pierce diode in the cold fluid regime are obtained by using Lagrange transform. These equations agree exactly with those obtained by Godfrey. 相似文献
16.
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
17.
The Eulerian equations are set up for a model subject to homoaxial rotation and suitable for simulation of a non-uniformly rotating star. These equations are formulated in a non-inertial frame of reference, rotating uniformly (i.e., rigidly) with respect to the inertial common frame. 相似文献
18.
Michael E. Hough 《Celestial Mechanics and Dynamical Astronomy》1984,32(4):371-388
An approximate semi-analytic solution of a two-body problem with drag is presented. The solution describesnon-lifting orbital motion in a central, inverse-square gravitational field. Drag deceleration is a non-linear function of velocity relative to a rotating atmosphere due to dynamic pressure and velocity-dependent drag coefficient. Neglected are aerodynamic lift, gravitational perturbations of the inverse-square field, and kinematic accelerations due to coordinate frame rotation at earth angular rate. With these simplifications, it is shown that (i) orbital motion occurs in an earth-fixed invariable plane defined by the radius and relative velocity vectors, and (ii) the simplified equations of motion are autonomous and independent of central angle measured in the invariable plane. Consequently, reduction of the differential equations from sixth to second-order is possible. Solutions for the radial and circumferential components of relative velocity are reduced to quadratures with respect to radial distance. Since the independent variable is radial distance, the solutions are singular at zero radial velocity (e. g., for circular orbits). General atmospheric density and drag coefficient models may be used to evaluate the velocity quadratures. The central angle and time variables are recovered from two additional quadratures involving the velocity quadratures. Theoretical results are compared with numerical simulation results.Presently affiliated with AVCO Systems Division, Wilmington, MA 01887, U.S.A. 相似文献
19.
M. P. Nakada 《Solar physics》1969,7(2):302-320
Some trends in the composition of the lower solar corona due to mixing and diffusion have been examined. Mixing has been treated through plausible inference from the thermal gradient and through analogy with the neutral atmosphere of the earth. These indicate that diffusion may be important in the lower corona. Changes in composition due to pressure and thermal gradients have been calculated with multi-component diffusion equations. Results indicate that (i) large enhancements of heavy elements are possible and (ii) the composition of the corona can show large variations with values of the thermal gradient in the lower corona. 相似文献
20.
Detlev Degenhardt 《Solar physics》1993,148(1):65-84
We suppose the transport of energy in a sunspot (or pore) is described by a diffusion process. The thermal conductivities in the spot and its surroundings are assumed to be constant and isotropic, but with a reduced conductivity in the spot. The sunspot and the ambient medium are represented by semi-infinite strips of variable depth, with one common boundary. This interface is a plane inclined at an arbitrary angle with respect to the vertical in order to simulate the inclined magnetic field at the umbral/penumbral, penumbral/photospheric or pore/photospheric boundary.We show that the region with high conductivity below the interface produces a thermal disturbance in the surface layers of the umbra which manifests itself as a temperature enhancement at the umbral surface in a region near the boundary, resulting in a decreased temperature contrast across the surface. The thermal disturbance in the neighboring medium is confined to a very small region.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献