A Mercury orientation model including non-zero obliquity and librations

Planetary orientation models describe the orientation of the spin axis and prime meridian of planets in inertial space as a function of time. The models are required for the planning and execution of Earth-based or space-based observational work, e.g. to compute viewing geometries and to tie observations to planetary coordinate systems. The current orientation model for Mercury is inadequate because it uses an obsolete spin orientation, neglects oscillations in the spin rate called longitude librations, and relies on a prime meridian that no longer reflects its intended dynamical significance. These effects result in positional errors on the surface of ~1.5 km in latitude and up to several km in longitude, about two orders of magnitude larger than the finest image resolution currently attainable. Here we present an updated orientation model which incorporates modern values of the spin orientation, includes a formulation for longitude librations, and restores the dynamical significance to the prime meridian. We also use modern values of the orbit normal, spin axis orientation, and precession rates to quantify an important relationship between the obliquity and moment of inertia differences.     

Sub-micron scale distributions of trace elements in zircon

Sub-micron scale zoning of Ti concentrations and correlations between concentrations of Ti and other trace elements (P, Ce, and Y) and cathodoluminescent (CL) banding is observed in natural zircons. Ion images were made using the Caltech Microanalysis Center’s CAMECA NanoSIMS 50L with an O⁻ primary beam focused to ~300 nm on the sample surface. The high spatial resolution of this technique allows for interrogation of chemical variations at or below the scale of CL banding in natural zircons. Images produced in this manner display two types of correlations among Ti, P, Ce, and Y (which appears to be a proxy for CL intensity): strong (correlation coefficients >0.8) and subtle (correlation coefficients ~0.15–0.4). Strongly correlated images, which display Ti variations of ca. a factor of 3 between adjacent CL bands and overall elevated trace element concentrations in CL-dark bands, were found within an oscillatory-zoned, trace element enriched sector of a CL sector-zoned zircon. Three possible causes for such correlations include: temperature-dependent equilibrium partitioning, trace element partitioning limited by diffusion in the host melt and surface-controlled, non-equilibrium growth. Comparison of our data with the expected results of these processes suggests that: (1) Ti partitioning in zircon is dependent upon non-equilibrium effects in addition to temperature and/or (2) the incorporation of elements that co-vary with Ti in zircon (e.g., Y, P and Ce) is also temperature-dependent. Sub-micron scale, high-Ti regions are also found within Proterozoic Adirondack and >4 Ga Jack Hills zircons as well as trace element enrichments (including Ti) along cracks within Jack Hills zircons.     

A restudy of the Ostracoda <Emphasis Type="Italic">Cypris cylindrica</Emphasis> Sowerby (in Malcolmson, 1840) from the Deccan Intertrappean beds (late cretaceous) of Lakshmipur,Kachchh, Gujarat

Cypris cylindrica was originally described by Sowerby (in Malcolmson, 1840) from the Deccan Intertrappean sedimentary beds of the Sichel Hills, Andhra Pradesh. Whatley and Bajpai (2000) recorded the species during recent years from the Intertrappean of Lakshmipur, Kachchh district, Gujarat and stated that Kachchh specimens are identical with the types of the species housed in the Natural History Museum (NHM), London. They recorded the species as Mongolianella cylindrica. The species, however, lacks distinctive shape and hinge structure of Mongolianella and on the contrary closely resembles Stenocypris cylindrica major (Baird, 1859) in shape and internal characters including having adont hinge, large anterior vestibulum, arcuate lists or striae on free part of inner lamella, numerous short marginal pore canals and 6 large adductor scars, the topmost being much elongated. On these bases the species is herein transferred to the genus Stenocypris Sars, 1889.     

Flexible–inflexible: socio-demographic,spatial and temporal dimensions of flat sharing in Leipzig (Germany)

Flat sharers are one of the most distinct representatives of the ‘new’ household types, but have received only very limited attention from researchers. Back in the 1960s shared flats were usually founded with a strong ideological impetus, whereas flat sharing nowadays is just one household type among many others. Typically, this housing arrangement consists of at least two young adult individuals without children. Sharing the flat and the housing costs is the basis of their relationship but living with others is an additional motive. As a rule, flat sharing bridges two distinct events in the course of one’s life: the leaving of the parental home and the foundation of the first independent household. Thus for a restricted period in time, it is a flexible household type adapted to the situational needs of its members. Germany has one of the strongest and longest traditions of flat sharing in Europe, especially among university students. An explorative study was conducted in Leipzig to come to a deeper understanding of what flat sharing means in its ambivalence of being both an economic unit and a social arrangement. Based on qualitative and quantitative evidence from group discussions and Internet adverts, we shed light on the highly under-researched social practice of flat sharing. We will show that despite the structural flexibility of this household type, there is also evidence for its socio-demographic selectivity, spatial concentration and temporal limitation over the individual life courses.     

Bodily tides near spin–orbit resonances

Spin–orbit coupling can be described in two approaches. The first method, known as the “MacDonald torque”, is often combined with a convenient assumption that the quality factor Q is frequency-independent. This makes the method inconsistent, because derivation of the expression for the MacDonald torque tacitly fixes the rheology of the mantle by making Q scale as the inverse tidal frequency. Spin–orbit coupling can be treated also in an approach called “the Darwin torque”. While this theory is general enough to accommodate an arbitrary frequency-dependence of Q, this advantage has not yet been fully exploited in the literature, where Q is often assumed constant or is set to scale as inverse tidal frequency, the latter assertion making the Darwin torque equivalent to a corrected version of the MacDonald torque. However neither a constant nor an inverse-frequency Q reflect the properties of realistic mantles and crusts, because the actual frequency-dependence is more complex. Hence it is necessary to enrich the theory of spin–orbit interaction with the right frequency-dependence. We accomplish this programme for the Darwin-torque-based model near resonances. We derive the frequency-dependence of the tidal torque from the first principles of solid-state mechanics, i.e., from the expression for the mantle’s compliance in the time domain. We also explain that the tidal torque includes not only the customary, secular part, but also an oscillating part. We demonstrate that the lmpq term of the Darwin–Kaula expansion for the tidal torque smoothly passes zero, when the secondary traverses the lmpq resonance (e.g., the principal tidal torque smoothly goes through nil as the secondary crosses the synchronous orbit). Thus, we prepare a foundation for modeling entrapment of a despinning primary into a resonance with its secondary. The roles of the primary and secondary may be played, e.g., by Mercury and the Sun, correspondingly, or by an icy moon and a Jovian planet. We also offer a possible explanation for the “improper” frequency-dependence of the tidal dissipation rate in the Moon, discovered by LLR.     

GPS-TEC variations during low solar activity period (2007–2009) at Indian low latitude stations

The paper is based on the ionospheric variations in terms of vertical total electron content (VTEC) for the low solar activity period from May 2007 to April 2009 based on the analysis of dual frequency signals from the Global Positioning System (GPS) satellites recorded at ground stations Varanasi (Geographic latitude 25°16′ N, Longitude 82°59′ E), situated near the equatorial ionization anomaly crest and other two International GNSS Service (IGS) stations Hyderabad (Geographic latitude 17°20′ N, longitude 78°30′ E) and Bangalore (Geographic latitude 12°58′ N, longitude 77°33′ E) in India. We describe the diurnal and seasonal variations of total electron content (TEC), and the effects of a space weather related event i.e. a geomagnetic storm on TEC. The mean diurnal variation during different seasons is brought out. It is found that TEC at all the three stations is maximum during equinoctial months (March, April, September and October), and minimum during the winter months (November, December, January and February), while obtaining intermediate values during summer months (May, June, July and August). TEC shows a semi-annual variation. TEC variation during geomagnetic quiet as well as disturbed days of each month and hence for each season from May 2007 to April 2008 at Varanasi is examined and is found to be more during disturbed period compared to that in the quiet period. Monthly, seasonal and annual variability of GPS-TEC has been compared with those derived from International Reference Ionosphere (IRI)-2007 with three different options of topside electron density, NeQuick, IRI01-corr and IRI 2001. A good agreement is found between the GPS-TEC and IRI model TEC at all the three stations.     

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.