Gravitational collapse of a dust ball — The external observer's point of view

The problem of collapse of a dust ball has been studied in detail from the point of view of an external observer (O). It is seen that although there is no material pressure from the point of view of the comoving observer, there is a non-vanishing material pressure in the ball from the point of view of O. In the early stages of collapse (w.r.t. O), this pressure is positive everywhere inside the ball, while during the later stages, if one goes outwards from the centre towards the surface of the ball, this pressure is negative up to a certain value of the radial coordinate, and then changes its sign thereafter. On the basis of this pressure, one can understand the physics of the whole scenario of collapse w.r.t. O; in particular, the important feature is that in the ultimate stages an event horizon is formed asymptotically and there is no collapse to a point (as takes place from the point of view of the comoving observer).     

Age and geochemistry of the Newania dolomite carbonatites, India: implications for the source of primary carbonatite magma

The Newania carbonatite complex of India is one of the few dolomite-dominated carbonatites of the world. Intruding into Archean basement gneisses, the rocks of the complex have undergone limited diversification and are not associated with any alkaline silicate rock. Although the magmatic nature of the complex was generally accepted, its age of emplacement had remained equivocal because of the disturbed nature of radioisotope systems. Many questions about the nature of its mantle source and mode of origin had remained unanswered because of lack of geochemical and isotopic data. Here, we present results of our effort to date the complex using ¹⁴⁷Sm–¹⁴³Nd, ²⁰⁷Pb–²⁰⁶Pb and ⁴⁰Ar–³⁹Ar dating techniques. We also present mineral chemistry, major and trace element geochemistry and Sr–Nd isotopic ratio data for these carbonatites. Our age data reveal that the complex was emplaced at ~1,473 Ma and parts of it were affected by a thermal event at ~904 Ma. The older ²⁰⁷Pb–²⁰⁶Pb ages reported here (~2.4 Ga) and by one earlier study (~2.3 Ga; Schleicher et al. Chem Geol 140:261–273, 1997) are deemed to be a result of heterogeneous incorporation of crustal Pb during the post-emplacement thermal event. The thermal event had little effect on many magmatic signatures of these rocks, such as its dolomite–magnesite–ankerite–Cr-rich magnetite–magnesio-arfvedsonite–pyrochlore assemblage, mantle like δ¹³C and δ¹⁸O and typical carbonatitic trace element patterns. Newania carbonatites show fractional crystallization trend from high-Mg to high-Fe through high-Ca compositions. The least fractionated dolomite carbonatites of the complex possess very high Mg# (≥80) and have similar major element oxide contents as that of primary carbonatite melts experimentally produced from peridotitic sources. In addition, lower rare earth element (and higher Sr) contents than a typical calcio-carbonatite and mantle like Nb/Ta ratios indicate that the primary magma for the complex was a magnesio-carbonatite melt and that it was derived from a carbonate bearing mantle. The Sr–Nd isotopic data suggest that the primary magma originated from a metasomatized lithospheric mantle. Trace element modelling confirms such an inference and suggests that the source was a phlogopite bearing mantle, located within the garnet stability zone.     

The rotational motion in quiescent prominences

On the basis of Kippenhahn and Schlüter's magnetohydrostatic model of a quiescent prominence we have attempted to study the effect of a rotational velocity field in it. We find that a physically plausible solution is not possible in the vertical plane. A possibility, however, is shown in the horizontal plane, with certain assumptions to get equal velocity contours.     

Morphotectonic Appraisal of Yamuna River Basin in Headwater Region: A Relative Active Tectonics Purview

In the present paper integrated appraisals of landform evolution and their geomorphic features, drainage networks across the upper part of Yamuna river basin have been attempted by using various geomorphic indices such as watershed, drainage density (D), drainage texture, stream-gradient index (SL), hypsometric integral (HI), drainage basin asymmetry (AF), mountain front sinuosity (Smf), sinuosity index (SI), valley floor height and width ratio (Vf) and data of historical earthquakes in characterizing the basin in view of relative index of active tectonics (RIAT) on DEM in geographic information systems (GIS) environment to assess the influence of recent tectonics on geomorphologic growth of the basin.The substantiated RIAT classes through some field observations and corroborated by recent seismicity reveal the recent activation of Yamuna tear faults in the basin with delineation of four RIAT classes such as class-1 (inactive 9.8% of the area), class-2 (low active; 16.40% of the area), class-3 (moderately active; 42.38% of the area) and class-4 (very active; 31.62%). The results suggest that the Himalayan frontal thrust (HFT) and Yamuna tear (YT) located in the basin is morphogenic in nature and got activated several times as evidenced by number of seismic activities in the basin and adjoining regions. The incision, and sharp turning of rivers, crenulations and warping of cross beddings/laminations and silt/clay beds and lenses, megascopic and mesoscopic faulting in sediment sequences suggest a very active nature of the HFT and YT till date in association with three prolific microseismogenic weak zones These active discontinuities appear to support the formation and development of different deformational features in sediment sequences which may be indirectly related to subduction and underthrusting of Indian plate under Eurasian plate below the Himalayan mountain chain.     

Extreme relativistic model for neutron stars and pulsars

Exact solutions have been obtained for a massive fluid sphere under the extreme causality condition (dP/dρ)=1. Radial pulsational stability of these structures has been discussed. It is found that for pulsationally stable configurations the surface to central density ratio is greater than 0.30, the maximum values for surface and central redshifts are 0.85 and 3.40 respectively in the extreme case, and the maximum mass and size are respectively 4.8M _⊙ and 20.1 km. It has also been shown that these structures are gravitationally bound, with a maximum binding energy per unit rest mass equal to 0.25 for a surface to central density ratio ?0.40. Slow rotation of these configurations has also been considered, and the relative drag and moment of inertia have been calculated. These results have been applied to the Crab pulsar and the mass of the pulsar has also been calculated based upon this model.     

Origin and geochemical characterization of the glauconites in the Upper Cretaceous Lameta Formation,Narmada Basin,central India

This study presents geochemical characteristics of glauconites in estuarine deposits within the Maastrichtian Lameta Formation in central India. Resting conformably over the Bagh Group, the Lameta Formation consists of ~4-5 m thick arenaceous, argillaceous and calcareous green sandstones underlying the Deccan Traps. The sandstone is friable, medium-to coarse-grained, well-sorted and thoroughly crossstratified, and contains marine fossils. Detailed petrography, spectroscopy and mineral chemistry indicates unique chemical composition of glauconite with high K_2O, MgO, Al_2O_3 and moderate TFe_2O_3. Glauconite is formed by the replacement of K-feldspars, initially as stringers in the cleavages and fractures of feldspars. Incipient glauconite subsequently evolves fully, appearing as pellets. Fully-evolved glauconite pellets often leave tiny relics of K-feldspar. XRD exhibits characteristic peak of 10A from basal(001)reflection of glauconite, indicating the "evolved" character. The K_2O content of glauconites in the Lameta Formation varies from 5.51% to 8.29%, corroborating the "evolved" to "highly-evolved" maturation stage.The TFe_2O_3 content of glauconite varies from 12.56% to 18.90%. The PASS-normalized-REE patterns of glauconite exhibit a "hat-shape" confirming the authigenic origin of glauconites. The slightly-negative to slightly-positive Ce anomaly value and the moderate TFe_2O_3 content of glauconite agree well with a suboxic,estuarine condition. The replacement of K-feldspar by the glauconite contributes towards the high K_2O content. Compositional evolution of glauconites in the Lameta Formation is similar to those observed in many Precambrian sedimentary sequences.     

Inverse modelling of aquifer parameters in basaltic rock with the help of pumping test method using MODFLOW software

The origin and movement of groundwater are the fundamental questions that address both the temporal and spatial aspects of ground water run and water supply related issues in hydrological systems. As groundwater flows through an aquifer, its composition and temperature may variation dependent on the aquifer condition through which it flows. Thus, hydrologic investigations can also provide useful information about the subsurface geology of a region. But because such studies investigate processes that follow under the Earth's shallow, obtaining the information necessary to answer these questions is not continuously easy. Springs, which discharge groundwater table directly, afford to study subsurface hydrogeological processes.The present study of estimation of aquifer factors such as transmissivity (T) and storativity (S) are vital for the evaluation of groundwater resources. There are several methods to estimate the accurate aquifer parameters (i.e. hydrograph analysis, pumping test, etc.). In initial days, these parameters are projected either by means of in-situ test or execution test on aquifer well samples carried in the laboratory. The simultaneous information on the hydraulic behavior of the well (borehole) that provides on this method, the reservoir and the reservoir boundaries, are important for efficient aquifer and well data management and analysis. The most common in-situ test is pumping test performed on wells, which involves the measurement of the fall and increase of groundwater level with respect to time. The alteration in groundwater level (drawdown/recovery) is caused due to pumping of water from the well. Theis (1935) was first to propose method to evaluate aquifer parameters from the pumping test on a bore well in a confined aquifer. It is essential to know the transmissivity (T = Kb, where b is the aquifer thickness; pumping flow rate, Q = TW (dh/dl) flow through an aquifer) and storativity (confined aquifer: S = bS_s, unconfined: S = S_y), for the characterization of the aquifer parameters in an unknown area so as to predict the rate of drawdown of the groundwater table/potentiometric surface throughout the pumping test of an aquifer. The determination of aquifer's parameters is an important basis for groundwater resources evaluation, numerical simulation, development and protection as well as scientific management. For determining aquifer's parameters, pumping test is a main method. A case study shows that these techniques have been fast speed and high correctness. The results of parameter's determination are optimized so that it has important applied value for scientific research and geology engineering preparation.     

Development of a predictive model for <Emphasis Type="Italic">Clostridium difficile</Emphasis> infection incidence in hospitals using Gaussian mixture model and Dempster–Shafer theory

Clostridium difficile infection is one of the major patient safety concerns in hospitals worldwide. Clostridium difficile infection can have high economic burden to patients, hospitals, and government. Limited work has been done in the area of predictive modeling. In this article, A new predictive model based on Gaussian mixture model and Dempster–Shafter theory is proposed to predict Clostridium difficile infection incidence in hospitals. First, the Gaussian mixture model and expectation–maximization algorithms are used to generate explicit probability criteria of risk factors based on the given data. Second, Dempster–Shafter theory is used to predict the Clostridium difficile infection incidence based on the generated probability criteria that have different beliefs attributing to their different credits. The main procedure includes (1) generate the probability criteria model using Gaussian mixture model and expectation–maximization algorithm; (2) determine the credit of the probability criteria; (3) generate the basic probability assignment; (4) discount the evidences; (5) aggregate the evidences using Dempster combining rule; (6) predict Clostridium difficile infection incidence using pignistic probability transformation. Results show that the model has a higher accuracy than an existing model. The proposed model can generate the criteria ratings of risk factors automatically, which would potentially prevent the imprecision caused by the subjective judgement of experts. The proposed model can assist risk managers and hospital administrators in the prediction and control of Clostridium difficile infection incidence with optimizing their resources.