广义相对论中静态荷电球体的内解

本文在假设荷电球体内部物质密度为ρ_m=μγ~α,电荷密度为ρ_e=ρ_0γ~(b_e-λ/2)的情况下,严格求解Einstein-Maxwell场方程,求得了静态荷电球体的一个较为普遍的内部解。这个解可以看作是Wyman得到的内部解推广到荷电情况下的结果,并且将Wilson,李鉴增,Santos,Pant和Sah等人给出的许多结果作为自己的特例包括在内。     

On Charged Analogues of Buchdahl’S Type Fluid Spheres

In this article the charged analogues of recently derived Buchdahl’s type fluid spheres have been obtained by considering a particular form of electric field intensity. In this process, Einstein–Maxwell field equations yield eight different classes of solutions, joining smoothly with the exterior Reissner–Nordstrom metric at the pressure free intersurface. Out of the eight solutions only seven could be utilized to represent superdense star models with ultrahigh surface density of the order 2×10¹⁴ gm cm⁻³. The maximum masses of the star models were found to be 8.223931M_Θ and 8.460857M_Θ subject to strong and weak energy conditions, respectively, which are much higher than the maximum masses 3.82M_Θ and 4.57M_Θ allowed in the neutral cases. The velocity of sound seen to be less than that of light throughout the star models.     

Stochastic Hill's equations for the study of errant rocket burns in orbit

The problem of errant rocket burns in low Earth orbit is of growing interest, especially in the area of safety analysis of nuclear powered spacecraft. The development of stochastic Hill's equations provides a rigorous mathematical tool for the study of such errant rocket maneuvers. These equations are analyzed within the context of a theory of linear dynamical systems driven by a random white noise. It is established that the trajectories of an errant rocket are realizations of a Gauss-Markov process, whose mean vector is given by the solution of a deterministic rocket problem. The time-dependent covariance matrix of the process is derived in an explicit form.     

Theory of Basin Scale Dynamics of a Stratified Rotating Fluid

The dynamics of a stratified fluid contained in a rotating rectangular box is described in terms of the evolution of the lowest moments of its density and momentum fields. The first moment of the density field also gives the position of the fluids centre-of-mass. The resulting low-order model allows for fast assessment both of adopted parameterisations, as well as of particular values of parameters. In the ideal fluid limit (neglect of viscous and diffusive effects), in the absence of wind, the equations have a Hamiltonian structure that is integrable (non-integrable) in the absence (presence) of differential heating. In a non-rotating convective regime, dynamically rich behaviour and strong dependence on the single (lumped) parameter are established. For small values of this parameter, in a self-similar regime, further reduction to an explicit map is discussed in an Appendix. Introducing rotation in a nearly geostrophic regime leads through a Hopf bifurcation to a limit cycle, and under the influence of wind and salt to multiple equilibria and chaos, respectively.     

Duality properties of Gorringe–Leach equations

In the category of motions preserving the angular momentum direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold–Vassiliev type. The specific associated conserved quantities (Laplace–Runge–Lenz vector and Fradkin–Jauch–Hill tensor) are then dual reflections of each other.     

Analytical solutions for the equations of motion of a space vehicle during the atmospheric re-entry phase on a 2-D trajectory

A practical and important problem encountered during the atmospheric re-entry phase is to determine analytical solutions for the space vehicle dynamical equations of motion. The author proposes new solutions for the equations of trajectory and flight-path angle of the space vehicle during the re-entry phase in Earth’s atmosphere. Explicit analytical solutions for the aerodynamic equations of motion can be effectively applied to investigate and control the rocket flight characteristics. Setting the initial conditions for the speed, re-entering flight-path angle, altitude, atmosphere density, lift and drag coefficients, the nonlinear differential equations of motion are linearized by a proper choice of the re-entry range angles. After integration, the solutions are expressed with the Exponential Integral, and Generalized Exponential Integral functions. Theoretical frameworks for proposed solutions as well as, several numerical examples, are presented.     

Solution of Lane-Emden type equations using Bernstein operational matrix of differentiation

The purpose of this paper is to propose an efficient numerical method for solving Lane-Emden type equations arising in astrophysics using Bernstein polynomials. First Bernstein operational matrix of differentiation is derived using Bernstein polynomials and then applied to solve the linear and nonlinear differential equations of Lane-Emden type. Some illustrative examples are given to demonstrate the efficiency and validity of the proposed algorithm.     

二维圆柱坐标下FDTD法对多频电磁波测井的数值模拟

在介质围绕Z轴旋转对称的情况下,三维直角坐标下的麦克斯韦方程可变成两组分别对应TM波和TE波的二维柱坐标下的偏微分方程.采用线圈作为电磁波测井的发射器和接收器的时候,可采用TE波对应的方程,这时相当于磁极子的情况.而采用电偶极子作为发射和接收器的时候,则对应TM波的方程.采用时间和空间均为二阶精确的有限差分方法,将偏微分方程进行差分化.这样,空间的电磁场可由时间域有限差分法(FDTD)来求解.     

最小二乘定权方法对流动重力计算结果的影响

在处理流动重力观测数据时,采用最小二乘方法解算由权系数和观测值组成的超定方程组,得到最优权值,并利用最优权计算重力值。结果表明,等权方法计算得到的结果点值精度不高,但包含了较全的重力异常地震分析预报信息;不等权方法计算得到的结果点值精度较高,但削弱了有用的重力异常地震分析预报信息;最小二乘方法计算得到的结果不但有较高的点值精度,对M_S4.0及以上地震的分析预报效果也最优。