Forms of Eulerian correlation functions in the solar wind

Current spacecraft missions such as Wind and ACE can be used to determine magnetic correlation functions in the solar wind. Data sets from these missions can, in principle, also be used to compute so-called Eulerian correlation functions. These temporal correlations are essential for understanding the dynamics of solar wind turbulence. In the current article we calculate these dynamical correlations by using well-established methods. These results are very useful for a comparison with Eulerian correlations obtained from space craft missions.     

A convenient method to obtain stellar eigenfrequencies

The differential equations describing stellar oscillations are transformed into an algebraic eigenvalue problem. Frequencies of adiabatic oscillations are obtained as the eigenvalues of a banded real symmetric matrix. We employ the Cowling-approximation, i.e. neglect the Eulerian perturbation of the gravitational potential, and, in order to preserve selfadjointness, require that the Eulerian pressure perturbation vanishes at the outer boundary. For a solar model, comparison of first results with results obtained from a Henyey method shows that the matrix method is convenient, accurate, and fast.     

An excursion set model for the distribution of dark matter and dark matter haloes

A model of the gravitationally evolved dark matter distribution, in the Eulerian space, is developed. It is a simple extension of the excursion set model that is commonly used to estimate the mass function of collapsed dark matter haloes. In addition to describing the evolution of the Eulerian space distribution of the haloes, the model allows one to describe the evolution of the dark matter itself. It can also be used to describe density profiles, on scales larger than the virial radius of these haloes, and to quantify the way in which matter flows in and out of Eulerian cells. When the initial Lagrangian space distribution is white noise Gaussian, the model suggests that the Inverse Gaussian distribution should provide a reasonably good approximation to the evolved Eulerian density field, in agreement with numerical simulations. Application of this model to clustering from more general Gaussian initial conditions is discussed at the end.     

Stellar models under homoaxial rotation: Eulerian equations and simulation of non-uniformly rotating stars

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.     

A minimizing property of eulerian solutions

In this paper, we prove that the elliptical solutions and collision ejection solutions with the Eulerian collinear configuration for planar 3-body problems are the variational minimizers of the Lagrangian action restricted on a suitable loop space.     

The motion of artificial satellites in the set of Eulerian redundant parameters

In this paper, the connections between orbit dynamics and rigid body dynamics are established throughout the Eulerian redundant parameters, the perturbation equations for any conic motion of artificial satellites are derived in terms of these parameters. A general recursive and stable computational algorithm is also established for the initial-value problem of the Eulerian parameters for satellites prediction in the Earth's gravitational field with axial symmetry. Applications of the algorithm are considered for the two cases of short and long term predictions. For the short-term prediction, we consider the problem of the final state prediction of some typical ballistic missiles in the geopotential model with zonal harmonic terms up to J ₃₆, while for the long-term prediction, we consider the perturbed J ₂ motion of Explorer 28 over 100 revolutions.     

An axially symmetric explosion model in magnetogasdynamics: II

A method using Eulerian coordinate system is developed under a local radiality assumption to study a point explosion in a spheroid with axially symmetric exponential density distribution, including the effect of azimuthal magnetic field.     

Oblateneess and drag effects on the motion of satellites in the set of Eulerian redundant parameters

In this paper, the perturbed motion of the artificial satellites under the effects of the earth's oblateness and atmospheric drag will be established. These equations will be expressed in terms of the Eulerian redundant parameters. Applications of the method for the perturbed motion are illustrated by numerical examples for some test cases of the orbits.     

Orbit computations with the Eulerian topological regular elements with oblateness

In this paper, the Eulerian set of topological regular elements was utilized to develop an orbit computation package for the initial value problem for any conic motion of artificial satellites in the Earth's gravitational field with axial symmetry. Applications for the two types of short- and long-term predictions are considered. The numerical results proved the high efficiency and flexibility of the package.     

Bounded orbits in the elliptic restricted three-body problem

Special solutions of the planar rectilinear elliptic restricted 3-body problem are investigated for the limiting case e=1. Numerical integration is performed for primaries of equal masses. Starting values which define circular orbit solutions lead to bounded solutions if the initial radius a₀ is larger than 3.74 in units of the primaries' semimajor axis a. A comparison with the Eulerian two-fixedcentre problem is presented in order to understand qualitatively the characteristic features of bounded orbits and the transition to escape orbits.     

On the motion of three rigid bodies: Central configurations

In the present paper, the motion of three rigid bodies is considered. With a set of new variables, and the 10 first integrals of the motion, the problem is reduced to a system of order 25 and one quadrature. The plane motions are characterized, and finally, an equation for the existence of central configurations (in particular, Lagrangian and Eulerian solutions) has been found. Besides, the case of three axisymmetric ellipsoids is studied.     

Motion of artificial satellites in the set of Eulerian redundant parameters,II

In this paper the full recurrent power series solution is established for J ₂-gravity perturbed motion in terms of the Eulerian redundant parameters. Applications of the method for the problem of the final state prediction are illustrated by numerical examples of some typical ballistic missiles, a final state of very high accuracy is obtained for each case study.     

Rotational dynamics of a deformable medium: Further generalization

Cauchy's fundamental first law of continuum mechanics is integrated over the whole mass of a self-gravitating deformable finite material continuum, viscolinear (i.e., Newtonian), not necessarily constrained to obey Stokes's condition, with viscosity coefficients given as arbitrary functions of the coordinates. The general Eulerian equation is derived, governing generalized rotation on which certain other cooperating deformations are superimposed. Finally, the explicit form of this equation is given for the case of a viscous gaseous polytrope.     

形变地球对不同驱动力的响应

地球形变位移场和重力场的时空变化无论在基础理论研究,还是在地理空间信息建设中都具有重要的意义.地球在各种力学机制的作用下产生了形变,形变又导致地球引力位的变化,即形变附加位或Euler引力位增量.基于矢量球函数的基本理论,讨论了引潮力、负载力和地表应力对地球形变和引力位增量的影响,给出了均匀不可压缩地球模型的Euler引力位增量的具体表达式和Love数的理论关系.可为地球形变的理论研究提供参考和依据.     

The Eulerian equations of differentially rotating gaseous polytropes

In this paper, we present in detail the whole process by which the Eulerian general equation is obtained, holding in case of a differentially rotating gaseous polytrope. The explicit form of this equation is derived on the basis of a model developed in a previous investigation.     

Rotational evolution of solar-type stars

The aim of the present investigation has been to consider rotational evolution of solar-type stars simulated by a polytropic model that possesses differential rotation of Clement's type. A properly defined reduction factor moderates the effects of such a rotation. The present treatment is based upon the general Eulerian equation, governing nonuniform (i.e., nonrigid-body) rotation, which has been set up in a previous investigation. Nonconservative terms, arising when stellar wind torque is under consideration, are taken into account. Data available for the viscosity of the Sun are used to construct a plausible viscosity model. Certain assumptions are made that remove the mathematical difficulties and simplify the physical ground. The obtained results are compared to corresponding estimates of recent observations.