On the validity of series expansion being used for the position of a point on a Roche equipotential

The concept of Roche equipotentials has been frequently used in literature to study the problems of rotating stars and stars in binary systems. However in spite of using this simplifying concept, it is still not possible to express the position of a point in the potential field of such a system in a closed analytic form. In order to carry out further analytic studies, Kopal (Adv. Astron. Astrophys. 9:1–65, 1972), therefore, developed a series expansion for it. The series expansion of Kopal has often been used in the analysis of the problem of equilibrium structure and the periods of oscillations of rotating stars and stars in binary systems, but its validity and convergence has not been analytically established. It is important that this aspect of the problem is checked so that one is sure of the correctness of subsequent analysis and results based on this series expansion. In the present brief note, we have addressed ourselves to this problem and validated the correctness of the numerical results obtained through the use of this series expansion.     

A regularized free-form estimator for dark energy

We construct a simple, regularized estimator for the dark energy equation of state by using the recently introduced linear response approximation. We show that even a simple regularization substantially improves the performance of the free-form fitting approach. The use of the linear response approximation allows an analytical construction of the maximum likelihood estimator, in a convenient and easy to use matrix form. We show that, in principle, such regularized free-form fitting can give us an unbiased estimate of the functional form of the equation of state of dark energy. We show the efficacy of this approach on simulated SuperNova Acceleration Probe class data, but it is easy to generalize this method to include other cosmological tests. We provide a possible explanation for the sweet spots seen in other reconstruction methods.     

Impact of geohydrology and neotectonic activity on radon concentration in groundwater of intermontane Doon Valley, Outer Himalaya, India

 Radon concentration was measured in 133 water samples from tubewells, handpumps, dug wells and springs of the Doon Valley, Outer Himalaya, India. The observed radon values were found to vary from 10 to 154 Bq/l whereas radium in selected water samples varied from 0.11 to 0.75 Bq/l. Three different clusters of high radon values were observed in the north-western, central and south-eastern parts of the Doon Valley. These clusters were found to be associated with tectonics (thrust/fault) and associated uranium mineralization in the area. In general, radon concentration in groundwater was found to be positively correlated with the depth of the wells, whereas no significant correlation was observed between radon concentration in groundwater and the water temperature, pH value, conductivity and altitude of the water samples. An attempt has also been made to determine the nature and extent of aquifers in the Doon Valley on radon concentration in groundwater. The variation in radon concentration within the groundwater of the study area was found to be controlled by the neotectonic activity and geohydrological processes that occur in the area. The impact of these activities on radon concentration in groundwater are discussed. Received: 17 September 1999 · Accepted: 11 April 2000     

A Petrological and Geochemical Account of Subsurface Noritic Intrusion in the Western Part of Bundelkhand Massif,Shivpuri District,M.P.

Subsurface exploration for uranium in the northwestern part of Bundelkhand massif, near Khor area, Shivpuri dist., M.P., resulted in intercepting a substantial thickness of mafic rock within Bundelkhand granitoid. Intercepts of this mafic rock at various levels in the boreholes, indicate that the rock mainly occurs as dykelike intrusion and fracture-fills within Bundelkhand granite. It is essentially composed of hypersthene and plagioclase, with or without olivine, leading to the characterisation as hypersthene microdolerite, noritic dolerite and norite (±olivine), depending on the grainsize and variation from intergranular to ophitic texture. Chemically, the rock is characterised by av. 49.09% SiO₂, 2.46%TiO₂, 2.33 Fe₂O₃, 9.45% FeO, 5.75% MgO, 8.37% CaO and 0.96% K₂O. The normative composition ranges from 3.53% quartz, 46.86% plagioclase, 12.58% diopside, 19.24% hypersthene. The olivine normative samples show av. 5.65% olivine. Geochemical plots indicate an intra-plate affinity along with oceanic signature, while presence of mineralogical and normative olivine, together with the REE pattern, point towards a lower crustal or mantle source. The mineralogical and normative presence of either quartz or olivine in these mafic rocks implies that it has an intermediate character between the tholeiitic dolerite dykes and the komatiite-type ultramafics reported from Bundelkhand craton. The complex geochemical signature of the rocks also reveals that both intra-continental as well as a mixture of oceanic- to upper mantle signatures are evident. The present study is a first time report of the occurrence of this hitherto unknown noritic body at depth within the Bundelkhand granite, which has no visible surface expression. The findings may strengthen the existing concept of a continuum between Rajasthan craton in the west and Bundelkhand craton in the east, as a single protocontinent.     

Structural and luminescent characterisation of uraniferous fluorapatite and haematite associated with phosphatic rocks of the Bijawar group in Sagar District,Madhya Pradesh (India)

The structural and spectroscopic characteristics of phosphatic ferruginous shale samples from the Bijawar Group rocks from Sagar District of Madhya Pradesh (India) have been probed for identification of uranium species. Fluorapatite (\(\hbox {Ca}_{5}\hbox {(PO}_{4})_{3}\hbox {F}\), FAP) and haematite (\(\upalpha \)-\(\hbox {Fe}_{2}\hbox {O}_{3}\)) were identified as the main phases in the separated mineral concentrates. The photoluminescence (PL) and X-ray absorption near edge spectroscopy (XANES) studies pointed to a strong experimental evidence of both U(IV) and U(VI) oxidation states in the mineral concentrate portion obtained from the same parent host rock. The PL spectrum has confirmed the charge transfer (f–d) transition bands in UV and near-UV regions with emission peaks at ca. 290, 313, 336, 399 and 416 nm, which has been attributed to the substitution of \(\hbox {Ca}^{2+}\) ions by U(IV) in FAP and broad structureless emission due to stabilisation of U(VI) as \(\hbox {UO}_{6}^{6-}\) in haematite. Time-resolved spectroscopy studies have revealed biexponential decay components lasting 2–5 ns for U(IV) species and \(10\,\upmu \hbox {s}\) for U(VI) species. These characterisations revealed the fundamental information about the oxidation state and form of uranium in this region. Remediation measures for the Bijawar region are also suggested.     

Analysis of thermo-hydrologic-mechanical impact of repository for high-level radioactive waste in clay host formation: an Indian reference disposal system

In our study, a coupled hydrologic-mechanical analysis is done of the excavation damaged zone, before the emplacement of nuclear waste. This is followed by a coupled thermal-hydrologic-mechanical analysis to evaluate the impact of nuclear waste repository in porous water containing rock mass. This analysis has been under taken in accordance with the Indian reference disposal system. The paper considers the changes in pore pressure and stresses due to excavation of disposal holes. A critical study of rock mass permeability, porosity, thermally induced stresses, strains, and temperature distribution after the emplacement of nuclear spent fuels in disposal holes has also been done. Coupling to the mechanical constitutive equations is done via ??effective?? normal strain rates.     

Rapid Determination of Trace and Ultra Trace Level Elements in Diverse Silicate Rocks in Pressed Powder Pellet Targets by LA‐ICP‐MS using a Matrix‐Independent Protocol

A simple, single sample preparation involving pressed rock powder pellets was utilised to determine the trace and ultra trace abundances of petrogenetically important elements including high field‐strength elements and REEs by laser ablation‐ICP‐MS. One of the elements predetermined by XRF spectrometry served as an internal standard. The influence of sample preparation parameters (grain size, pellet compactness and amount of binding media) on analytical performance was also investigated, including sample homogeneity issues at the laser sampling scale. Line scanning with a high repetition frequency (20 Hz) and large beam diameter (200 μm) ensured ablation from a larger sample surface area, eliminating issues related to sample heterogeneity. A median grain size of about 10 μm for silicate rock powders was found to be sufficiently representative at this scale of laser sampling. Granitic rocks or samples containing resistant minerals such as zircon needed extra grinding to achieve grain sizes down to < 5 μm for better precision for elements that are concentrated in these phases. Using ¹³⁷Ba as an internal standard, reasonable accuracies within 15–20% for most of the high mass trace elements were achieved; in the case of low mass elements, it may deviate up to 40%. Precision of measurements rarely exceeded 15% RSD.     

Preparation and Characterisation of Two Geochemical Reference Materials: DG‐H (Granite) and AM‐H (Amphibolite) from the Himalayan Orogenic Belt

Two geochemical reference materials of Himalayan origin named DG‐H (a granite) and AM‐H (an amphibolite) prepared by the Wadia Institute of Himalayan Geology Dehradun are described. Both samples were collected from the NW Himachal Himalaya in India. With the participation of analysts from more than forty international laboratories, element determination data collected during the past 10 years for characterisation of the samples was processed to assign working values using statistical procedures in use for this purpose. Earlier work published on these samples is incorporated in the present communication making it an updated document. The typical chemical and petrological characteristics of these two samples may prove useful for method validation and calibration of analytical instruments used for analysing similar rock types, and for widening the analytical range of several analytical methods used for geochemical analysis.     

Evaluation of hydrogeochemical processes in arsenic-contaminated alluvial aquifers in parts of Mid-Ganga Basin,Bihar, Eastern India

The study region covers 1,650 km² of the Mid-Ganga Basin in Bihar, experiencing intensive groundwater draft. The area forms a part of the Gangetic alluvial plain where high incidence of arsenic groundwater contamination (>50 μg/l) has recently been detected. Seventy-seven groundwater samples have been collected and analysed for major ions, iron and arsenic. Arsenic contamination (max 620 μg/l) is confined in hand pump zones (15–35 m) within the newer alluvium deposited during Middle Holocene to Recent age. The older alluvial aquifers are arsenic-safe and recorded maximum concentration as 9 μg/l. Out of 12 hydrochemical facies identified, four have been found arsenic-affected: Ca–HCO₃, Mg–HCO₃, Ca–Mg–HCO₃ and Mg–Ca–HCO₃. The geochemical evolution of groundwater, as investigated by graphical interpretation and statistical techniques (correlation, principal component analysis) revealed that dissolution of detrital calcite, dolomite and infiltration of rainwater are the major processes shaping the groundwater chemistry in the newer alluvium. Arsenic and iron showed strong positive correlation. Rainfall infiltration, carrying organic matter from recently accumulated biomass from this flood-prone belt, plays a critical role in releasing arsenic and iron present in the sediments. Geochemical evolution of groundwater in older alluvium follows a different path, where cation-exchange has been identified as a significant process.