Understanding the behavior of Prometheus and Pandora

We revisit the dynamics of Prometheus and Pandora, two small moons flanking Saturn's F ring. Departures of their orbits from freely precessing ellipses result from mutual interactions via their 121:118 mean motion resonance. Motions are chaotic because the resonance is split into four overlapping components. Orbital longitudes were observed to drift away from predictions based on Voyager ephemerides. A sudden jump in mean motions took place close to the time at which the orbits' apses were antialigned in 2000. Numerical integrations reproduce both the longitude drifts and the jumps. The latter have been attributed to the greater strength of interactions near apse antialignment (every 6.2 yr), and it has been assumed that this drift-jump behavior will continue indefinitely. We re-examine the dynamics of the Prometheus-Pandora system by analogy with that of a nearly adiabatic, parametric pendulum. In terms of this analogy, the current value of the action of the satellite system is close to its maximum in the chaotic zone. Consequently, at present, the two separatrix crossings per precessional cycle occur close to apse antialignment. In this state libration only occurs when the potential's amplitude is nearly maximal, and the “jumps” in mean motion arise during the short intervals of libration that separate long stretches of circulation. Because chaotic systems explore the entire region of phase space available to them, we expect that at other times the Prometheus-Pandora system would be found in states of medium or low action. In a low action state it would spend most of the time in libration, and separatrix crossings would occur near apse alignment. We predict that transitions between these different states can happen in as little as a decade. Therefore, it is incorrect to assume that sudden changes in the orbits only happen near apse antialignment.     

An HLLC Riemann solver for relativistic flows – II. Magnetohydrodynamics

An approximate Riemann solver for the equations of relativistic magnetohydrodynamics (RMHD) is derived. The Harten–Lax–van Leer contact wave (HLLC) solver, originally developed by Toro, Spruce and Spears, generalizes the algorithm described in a previous paper to the case where magnetic fields are present. The solution to the Riemann problem is approximated by two constant states bounded by two fast shocks and separated by a tangential wave. The scheme is Jacobian-free, in the sense that it avoids the expensive characteristic decomposition of the RMHD equations and it improves over the HLL scheme by restoring the missing contact wave.
Multidimensional integration proceeds via the single step, corner transport upwind (CTU) method of Colella, combined with the constrained transport (CT) algorithm to preserve divergence-free magnetic fields. The resulting numerical scheme is simple to implement, efficient and suitable for a general equation of state. The robustness of the new algorithm is validated against one- and two-dimensional numerical test problems.     

Radiative Transfer in Inhomogeneous Atmospheres. III

The approach proposed in the previous parts of this series of papers is used to solve the radiative transfer problem in scattering and absorbing multicomponent atmospheres. Linear recurrence relations are obtained for both the reflectance and transmittance of these kinds of atmospheres, as well as for the emerging intensities when the atmosphere contains energy sources. Spectral line formation in a one-dimensional inhomogeneous atmosphere is examined as an illustration of the possibility of generalizing our approach to the matrix case. It is shown that, in this case as well, the question reduces to solving an initial value problem for linear differential equations. Some numerical calculations are presented.     

Chemical alteration of tephra in the depositional environment: theoretical stability modelling

The study of the chemical stability of vitreous material in aqueous media is well‐established. There has to date been little consideration of the implications of variations in the chemical durability of tephra in Quaternary tephrochronology. Chemical alteration can take the form of cationic leaching from the matrix, or complete destruction of the silica network, either of which could constrain the ability to chemically identify distal tephra. Here we apply established models of vitreous durability to the published chemical analyses of a large number of Icelandic tephras in order to predict their relative durabilities under equivalent conditions. This suggests that some important tephras have relatively poor chemical stability, and that rhyolitic tephras are, in general, more stable than basaltic. We conclude that tephras should be expected to show predictable differential chemical stability in the post‐depositional environment. Copyright © 2003 John Wiley & Sons, Ltd.     

Optical monitoring of the quasar 4C 38.41

The results of a photometric monitoring of the quasar 4C 38.41, performed at the optical R and B bands in 2002 February–March, are presented. With a 60/90 cm Schmidt telescope at the Xinglong station of the National Astronomical Observatories of China, we observed the source exhibiting amplitude variations of up to 0.78 mag in both bands during the whole campaign. Intraday and even intranight variations are detected as well. A typical variability time-scale of about 36 d is derived from our 2-month observations at the optical bands, which is identical to that found at a radio wavelength of 92 cm, suggesting a common origin for the variations in 4C 38.41 from optical to radio bands.     

CCD联合平差方法及其初步实例检验

在常规照相天体测量工作中 ,对暗天体的定位是采用逐级定标星过渡的方法实现的。由于星表系统差和局部差的存在 ,最终定位结果可能包含难以把握的误差积累。在CCD小视场观测情况下时常难以找到足够数量的定标星。鉴于此 ,推导了CCD观测联合平差方法的严格矢量表达式 ,以期通过共同星的过渡 ,实现大天区统一平差。原理上此方法可实现相对于河外天体的定位 ,以削弱星表系统差和局部差对定位结果的影响。讨论了CCD联合平差方法实现中的问题 ,包括底片常数模型选择、切点位置改正、共同星的较差改正和法方程解算方法等 ,并分析了具体的处理措施。用实例初步检验了CCD联合平差方法的效果 ,表明通过对多张CCD观测的联合平差 ,可以削弱单张CCD观测参考星数目过少、单张CCD观测参考星分布不均、个别参考星存在位置偏差和局部区域参考星存在系统性位置偏差等不利因素对归算结果的影响 ,进而达到扩大视场和提高归算精度的目的