Modelling the differential rotation of F stars

We model stellar differential rotation based on the mean-field theory of fluid dynamics. DR is mainly driven by Reynolds stress, which is anisotropic and has a non-diffusive component because the Coriolis force affects the convection pattern. Likewise, the convective heat transport is not strictly radial but slightly tilted towards the rotation axis, causing the polar caps to be slightly warmer than the equator. This drives a flow opposite to that caused by differential rotation and so allows the system to avoid the Taylor-Proudman state. Our model reproduces the rotation pattern in the solar convection zone and allows predictions for other stars with outer convection zones. The surface shear turns out to depend mainly on the spectral type and only weakly on the rotation rate. We present results for stars of spectral type F which show signs of very strong differential rotation in some cases. Stars just below the mass limit for outer convection zones have shallow convection zones with short convective turnover times. We find solar-type rotation and meridional flow patterns at much shorter rotation periods and horizontal shear much larger than on the solar surface, in agreement with recent observations. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The azimuthal magnetorotational instability (AMRI)

We consider the flow of an electrically conducting fluid between differentially rotating cylinders, in the presence of an externally imposed current-free toroidal field B₀(R_in/R) ê _ϕ . It is known that the classical, axisymmetric magnetorotational instability does not exist for such a purely toroidal imposed field.We show here that a nonaxisymmetric magnetorotational instability does exist, having properties very similar to the axisymmetric magnetorotational instability in the presence of an axial field. In the nonlinear regime the magnetic energy of the perturbances is shifted (in the sense of an inverse cascade) to the axisymmetric mode rather than to the modes with m > 1. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

How can α 2-dynamos generate axisymmetric magnetic fields?

Inspired by a recently observed axisymmetric field in a fully convective star we investigate the influence of an anisotropic diffusivity on the dynamo. We find that with reasonable assumptions for the anisotropy of the diffusivity and the α -effect the preference of axisymmetric modes is achieved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

岩溶隧道顶板安全厚度的理论探讨与工程应用

在岩溶区隧道施工中,隧道顶部既有较大尺度溶洞引起的隧道顶板跨塌是威胁隧道施工的主要问题之一。从隧道施工引起的既有溶洞与隧道间岩层的受力,岩层力学性质和围岩水文地质条件变化出发,分析了隧道施工中影响岩层稳定的主要因素,在此基础上将隧道顶部既有较大尺度溶洞引起的隧道施工期顶板的破坏问题归结为两端简支或4边固支薄层岩板的失稳问题,建立了相应的力学分析模型。采用弹性板理论,对不同力学模型的受力状态进行分析,推导了建立在岩体抗拉和抗剪强度准则基础上的岩溶隧道顶板岩层最小安全厚度计算公式。采用该公式对武都水库导流洞既有溶洞影响下典型洞段隧道顶板稳定性进行分析,跟踪施工调查的顶板稳定情况性态验证了公式的适用性。     

Modal metasomatism in the Kaapvaal craton lithosphere: constraints on timing and genesis from U–Pb zircon dating of metasomatized peridotites and MARID-type xenoliths

Modal metasomatism in the Kaapvaal craton lithosphere is well documented in upper mantle xenoliths sampled by both group I (mainly late Cretaceous) and group II (mainly early Cretaceous to late Jurassic) kimberlites in the Kimberley area. The metasomatic style is characterized by introduction of K, H and large ion lithophile/high field strength (LIL/HFS) elements into the lithospheric mantle leading to the crystallization of hydrous potassic phases such as phlogopite and/or K-amphibole. Textures indicate that the hydrous phases either replace pre-existing assemblages in peridotites, forming the metasomatized peridotite suite (phlogopite–K-richterite–peridotites: PKPs) or crystallize from K-rich melts, forming the mica–amphibole–rutile–ilmenite–diopside (MARID) suite of xenoliths. These K-rich assemblages become potential low melting source components for alkaline incompatible trace element enriched magmas. The timing of metasomatism and its temporal and possible genetic relation to kimberlite magmatism is poorly constrained because of the rarity of phases in the metasomatic assemblages suitable for precise dating. Here we present precise sensitive high resolution ion microprobe (SHRIMP) U–Pb formation ages of 88 ± 2 (1σ=1 standard deviation) and 82 ± 3 Ma data for zircons from a K-richterite–phlogopite-bearing metasomatized peridotite (PKP) and a MARID xenolith respectively, sampled by a group I kimberlite. Both average PKP and MARID zircon ages are indistinguishable from emplacement ages of group I kimberlites in the Kimberley area dated at 83 ± 4 (2σ) and 84 ± 0.9 Ma. One exceptionally old age spot of 102 ± 5 Ma from a PKP zircon provides evidence for modal metasomatism predating group I kimberlite emplacement by several millions of years with minor resetting of the U–Pb isotopic system of most analyzed PKP zircons to a group I emplacement age. Detailed textural and mineral chemical analysis, including high energy X-ray mapping and analysis of fluid inclusion daughter crystals, indicates a complex reaction history for both PKPs and MARIDs. U–Pb zircon ages from this study combined with literature data and experimentally derived models for MARID formation are used to suggest that MARID-formation is concurrent and genetically related to both group I and II kimberlite magmatism in the Kimberley area. MARID and PKP zircon ages are also consistent with the idea first proposed by Dawson and Smith (Geochim Cosmochim Acta 41: 309–323, 1977) that metasomatized peridotites may form from interaction of hydrous fluids expelled by solidifying MARID-type melts with peridotitic wall rocks. Received: 13 December 1999 / Accepted: 13 April 2000     

Unusual exsolution phenomena in omphacite and partial replacement of phengite by phlogopite + kyanite in an eclogite from the Erzgebirge

In the Erzgebirge Crystalline Complex, eclogites occur in three different high pressure (HP) units (1, 2 and 3) recording contrasting pressure (P)–temperature (T) conditions. Eclogites from HP-unit 1 experienced peak metamorphic conditions in the coesite stability field at about 33 kbar/850 °C. Commonly, these eclogites from HP-unit 1 are all very similar, with an eclogitic peak assemblage of omphacite–garnet–coesite–K-feldspar, rarely accompanied by kyanite, and omphacites systematically deviating from a stoichiometric composition. In contrast, an eclogite recently found near Blumenau, is mineralogically and geochemically different from the typical eclogites of HP-unit 1. This unusual eclogite reveals the eclogitic equilibrium assemblage omphacite–garnet–coesite–phengite–phlogopite–kyanite, and yields metamorphic peak conditions of 870 °C and >29 kbar. There is clear textural evidence of the formation of phlogopite and kyanite under partial consumption of phengite and garnet. Moreover, the omphacite is stoichiometric and contains abundant exsolution lamellae, the thickest of which were identified as quartz by the electron microprobe. The finer lamellae were studied by transmission electron microscopy (TEM). Oligoclase was identified as an exsolution phase. Other lamellae proved to consist of K-white mica, also interpreted as exsolution. Prior to exsolution, the omphacite composition must have been cation-deficient, as that of the other, common HP-unit 1 eclogites. These non-stoichiometric compositions are ascribed to partial substitution by the Ca-Eskola pyroxene component, which calculates to an average of 8 mol% for omphacite in HP-unit 1 eclogites. According to experiments, this substitution becomes significant at P > 30 kbar. Exsolution of K-white mica may indicate hydroxyl defects in the original omphacite, also favoured by high pressure. Oligoclase and K-white mica exsolution from Ca-Eskola-rich clinopyroxene has not previously been reported. The omphacite has a disordered C2/c structure; and in just one case very small (a few tens of nanometres) antiphase domains, resulting from the C2/c to P2/n transformation, are present. These features may indicate a brief thermal history and rapid tectonic processes. Received: 4 January 1999 / Accepted: 20 April 2000     

Precise Real-Time Positioning in WADGPS Networks

In recent years the importance of real-time positioning and navigation with the Global Positioning System (GPS) has grown rapidly. Starting from the establishment of differential GPS (DGPS) reference stations for marine and land navigation, new users and applications have emerged that resulted in a high demand for the establishment of a high-density network of reference stations around the world. Many countries have established their own DGPS service, which is either governmentally or commercially owned. These services are referred to as Local Area DGPS Systems (LADGPS). However, the costs for the establishment and maintenance of a dense network of reference stations are very high. Therefore Wide Area DGPS Systems (WADGPS) are being developed to overcome the main drawbacks of LADGPS. In this case, only a few reference stations are used to cover a large area, such s a continent like Europe. To achieve high positioning accuracies, real-time modeling of the main error sources for long-range baselines is required as errors in the satellite orbit and ionospheric refraction do not cancel entirely in double differencing. In this article, a real-time correction model based on the Kalman filter for WADGPS and networked LADGPS services is discussed and results of field tests in a WADGPS network in Europe are presented. ? 2000 John Wiley & Sons, Inc.     

The stochastic estimation of satellite clock correction information in WADGPS

1 IntroductionChnventional DGPS is limited by the range overwhich the differential corrections are valid due tothe rapid decorrelation of the error sources with in-creasing distance from the reference station to user.In wide area differential GPS (WWPS) errorsources in GPS measurements are medeled sepa-rately,on the basis of a limited number of referencestaitOns, to overcome this drawback. The main er-ror sources are regarded as broadcast ephemeris er-ror,atmospheric refraction and satel…     

From GPS and GLONASS via EGNOS to Galileo – Positioning and Navigation in the Third Millennium

Positioning and navigation – as are presently possible with the American Global Positioning System (GPS) and the Russian GLONASS system – is briefly reviewed. Deficiencies, which have led to augmentations like the European Geostationary Navigation Overlay System (EGNOS), are outlined. Europe's decision to get involved in the definition and possible set-up of a Global Navigation Satellite System (GNSS) of the second generation (GNSS-2), called Galileo, is discussed in detail as well as the GPS modernization program that might take place during the sample phase. Finally, some brief thoughts on the benefit of GNSS-2 for geodesy and surveying are given. ? 2000 John Wiley & Sons, Inc.