On the MHD effects on the force-free monopole outflow

The stationary axisymmetric outflow from a rotating sphere with a (split) monopole magnetic field is considered. The stream equation describing the outflow is linearized in terms of the Michel magnetization parameter σ⁻¹ ≪ 1, which allows a self-consistent analysis of the direct problem. It is shown that for a finite σ the fast magnetosonic surface is located at a finite distance ∼ σ^1/3 R _L ( R _L =  c /Ω_F is the light cylinder). We have also found that the particle energy at the fast surface is just equal to the Michel value γ ∼ 1/3σ. The particle acceleration and magnetic field collimation are shown to become ineffective outside the fast magnetosonic surface.     

On the potential–density relation for Stäckel discs

The general form of the surface density of an infinitely thin disc is given that generates a Sta¨ckel potential in the disc only, using formulae for the potential of elliptic and hyperbolic strings. This is useful for problems in which a simple form for the potential is important, while the corresponding surface density need only be known to check (numerically) that it is positive. A simple potential with a positive surface density is given. Also, formulae are given to calculate the surface density of such a Sta¨ckel disc, in the case in which the rotation curve is given and all the mass is concentrated in the disc.     

Stability of power-law discs — I. The Fredholm integral equation

The power-law discs are a family of infinitesimally thin, axisymmetric stellar discs of infinite extent. The rotation curve can be rising, falling or flat. The self-consistent power-law discs are scale-free, so that all physical quantities vary as a power of radius. They possess simple equilibrium distribution functions depending on the two classical integrals, energy and angular momentum. While maintaining the scale-free equilibrium force law, the power-law discs can be transformed into cut-out discs by preventing stars close to the origin (and sometimes also at large radii) from participating in any disturbance. This paper derives the homogeneous Fredholm integral equation for the in-plane normal modes in the self-consistent and the cut-out power-law discs. This is done by linearizing the collisionless Boltzmann equation to find the response density corresponding to any imposed density and potential. The normal modes — that is, the self-consistent modes of oscillation — are found by requiring the imposed density to equal the response density. In practice, this scheme is implemented in Fourier space, by decomposing both imposed and response densities in logarithmic spirals. The Fredholm integral equation then relates the transform of the imposed density to the transform of the response density. Numerical strategies to solve the integral equation and to isolate the growth rates and the pattern speeds of the normal modes are discussed.     

Asteroid Mean Elements: Higher Order and Iterative Theories

Mean orbital elements are obtained from osculating ones by removing the short periodic perturbations. Large catalogues of asteroid mean elements need to be computed, as a first step in the computation of proper elements, used to study asteroid families. The algorithms for this purpose available so far are only accurate to first order in the masses of the perturbing planet; the mean elements have satisfactory accuracy for most of the asteroid belt, but degraded accuracy in the neighbourhoods of the main mean motion resonances, especially the 2:1. We investigate a number of algorithms capable of improving this approximation; they belong to the two classes of Breiter-type methods and iterative methods. The former are obtained by applying some higher order numerical integration scheme, such as Runge–Kutta, to the differential equation whose solution is a transformation removing the fast angular variables from the equations; they can be used to compute a full second order theory, however, only if the full second order determining function is explicitly computed, and this is computationally too cumbersome for a complicated problem such as the N-body. The latter are fixed point iterative schemes, with the first order theory as an iteration step, used to compute the inverse map from mean to osculating elements; formally the method is first order, but because they implement a fixed frequency perturbation theory, they are more accurate than conventional single iteration methods; a similar method is already in use in our computation of proper from mean elements. Many of these methods are tested on a sample of asteroid orbits taken from the Themis family, up to the edge of the 2:1 resonance, and the dispersion of the values of the computed mean semimajor axis over 100 000 years is used as quality control. The results of these tests indicate that the iterative methods are superior, in this specific application, to the Breiter methods, in accuracy and reliability. This is understood as the result of the cancellations occurring between second order perturbation terms: the incomplete second order theory, resulting from the use of a Breiter method with the first order determining function only, can be less accurate than complete, fixed frequency theories of the first order. We have therefore computed new catalogues of asteroid mean and proper elements, incorporating an iterative algorithm in both steps (osculating to mean and mean to proper elements). This new data set, significantly more reliable even in the previously degraded regions of Themis and Cybele, is in the public domain. This revised version was published online in July 2006 with corrections to the Cover Date.     

倾角函数递推公式的误差传递分析

在倾角函数递推关系这个题目上,一些研究者做过工作,如Challe,A(1969),R.H.Googing(1971),J.A.Campbell(1972),G.E.O.Giacaglia(1976)和童付(1979)。最好的结果是由童付获得的,递推关系仅由二个或三个相邻的函数来表达。然而,当倾角较小时,童付的公式存在严重的计算误差传递。本文导出了一个分析公式来估计此种计算误差传递,并在分析计算误差传递机制的基础上,指出可避免计算误差传递的途径,导出的分析公式见文中第(9)式。     

Griffith Taylor and the SE Australian highlands: issues of data sources and testability in interpretations of long‐term drainage history and landscape evolution

Much of the current research on long‐term landscape evolution and drainage history in SE Australia is built in one way or another on the early work of Griffith Taylor. The controversy prompted by several attempts to incorporate Taylor's work in recent plate tectonics interpretations of the long‐term evolution of SE Australia highlights differences of opinion as to the appropriate methodologies for such investigations. These questions, including the issues of data sources in reconstructions of long‐term landscape history, testability of such reconstructions, and the relationship between the landscape history so reconstructed and larger‐scale, regional landscape histories, appear not to have been addressed in recent literature on geomorphological methodology. This literature notes the demise of critical rationalism and appears to espouse a strongly relativist viewpoint, which relies on the shared understanding among the discipline's practitioners as to what are appropriate data sources and tests for hypotheses of long‐term landscape evolution. This offers little hope for resolution of the current disputes about the evolution of the drainage systems of SE Australia, but puts the onus squarely on us, the practitioners, to develop shared understandings of the appropriate data sources and tests for our hypotheses and grand schemes of the type so favoured by Griffith Taylor.     

极射赤平投影中的数学方法

本文提供了严格依据赤平投影原理并利用空间解析几何知识推导出的公式计算方法，可以写出已知产状的线或面的赤平投影方程，也能计算两线所共的面，两面的交线，线或面之间的夹角以及它们的平分线或平分面，可以进行真倾斜和视倾斜的换算，倾斜和侧伏的换算；模拟线面绕轴的旋转以及恢复节理的原始产状；最后阐述用计算机进行节理统计和绘制极点等密图的原理。所用的向量表示方法直观表达了相关构造要素之间的空间关系，可用于计算机辅助教学，也能用于生产实践，精度可达0.01°。     

汉南—米仓山区北东向构造及龙门山推覆构造外缘带

汉南－米仓山区喜马拉雅期的北东向构造与四川盆地西部及荣经－峨边地区的北东向构造一起构成龙门山推覆构造外缘带。本文论述了该带的组成、与其它构造的叠加现象、沿走向的延伸与变化、形成活动时期、剖面结构和整个龙门山推覆构造带与基底构造和莫霍面形态的一致性关系。     

西藏中部念青唐古拉山链中生代以来构造演化

根据对西藏念青唐古拉构造变形分析及地质年代测定资料，将该区构造变形划分为晚侏罗世到早白垩世的伸展拆离，形成区域性面理构造；晚白垩世到渐新世聚敛作用，形成斜向逆冲构造及雁列式褶皱；中新世以来的伸展、隆升，形成念青唐古拉剥离断层及羊八井地堑。     

近十年来分析化学测试技术进展

本文介绍物化探研究所1988～1997年十年中化探分析测试技术的新进展。文章中就地球化学标准物质研制、地球化学样品多元素分析系统、分析仪器的研制、分析测试新方法新技术的研究开发、应用和推广以及专业人才培养诸方面的情况分别进行了论述。