Coordinate gauge conditions in theN-body equations of motion in the first-order post-Newtonian approximation of general relativity

The explicit forms of the metric as well as the equations of motion in the first-order post-Newtonian approximation are worked out under several gauge conditions. It is noted that the so-called EIH (Einstein, Infeld, and Hoffman) equation of motion for an assembly ofN finite mass points mutually interacting via gravitation is identically obtained under three different gauge conditions, namely the harmonic gauge, Chandrasekhar gauge and a composite Chandrasekhar gauge used by Misneret al. (1970), even though the solutions for the metric are found to be all different. In one case the metric has a component apparently diverging, but finally generates regular affine connections so that the equations of motions become free from any singularity. By use of the Chandrasekhar gauge and his formulation, the second-order contribution to the acceleration of planets in the limit of test particle motion around the Sun has been calculated, the inclusion of which in the EIH set of the equations of motion would extend the relative accuracy of computing the total acceleration of any planet to better than one part in 10¹⁷.     

Application of X-ray computed tomography for analyzing cleat spacing and cleat aperture in coal samples

New techniques to determine distributions of cleat aperture, cleat orientation and cleat spacing from CT scans have been developed. For cleat orientation and spacing distributions, two different coal blocks were scanned. The CT scans have been analyzed for the three orthogonal directions. Histograms of the cleat orientations are bimodal, expressing the typical cleat texture of face and butt cleats and bedding perpendicular relaxation fractures. Deviations up to 20° from the peak values in the cleat orientation distributions were used as input for automated image analysis of cleat spacing. Distributions of the cleat spacing measurements are related to the face and butt cleat directions. The term “relevant cleat length” is introduced as a measure to extract the amount of cleat length involved with the cleat spacing measurements. The ratio ranges from 0.03 to 0.38 and expresses the difference in cleat texture in both samples. Cleat spacing versus relevant cleat length shows sample specific patterns for face cleat, butt cleat and bedding. To describe cleat aperture quantitatively, peak height and missing attenuation have been used. The image of a cleat was seen as a convolution of a rectangular fracture profile with a Gaussian point spread function.     

Disturbance produced in a semi-infinite anisotropic elastic medium by an impulsive twist applied on the plane surface

Summary In this paper the displacement due to an impulsive twist produced by impulsive shearing stresses acting on a finite circular area on the plane surface of a semi-infinite solid of homogeneous anisotropic material has been found.Paper presented by Dr. A. K. Mitra of Jadavpur University.     

Using magnetic susceptibility to find Precambrian impact ejecta: A proposal

Layers with high magnetic susceptibility contain heavy minerals that are the most likely to preserve signatures of impact in metamorphosed Precambrian rocks. The following impact indicators are resistant to alteration and metamorphism and are likely to be found in heavy mineral layers: impact diamond, SiC, shocked zircon, high-pressure TiO₂ phases, reidite, and high-pressure chromite. Coesite and stishovite could also be present but are not likely to be preserved in rocks metamorphosed above the greenschist facies. Looking for layers with high magnetic susceptibility will also identify layers that might contain concentrations of zircon for dating.     

Thermodynamics of the universe filled with perfect fluid having variable equation of state

Recently, a field theoretic model for a UV complete theory of gravity has been proposed by Hor̃ava. This theory is a non-relativistic renormalizable gravity theory which coincides with Einstein’s general relativity at large distances. Subsequently Lü et al. have formulated the modified Friedmann equations and have presented a solution in vacuum. In the present work, we rewrite the modified FRW equations in the form of usual FRW equations in Einstein gravity and consequences have been analyzed. Also the thermodynamics of the FRW universe has been studied.     

Geoelectric model and hydrochemistry of salinity affected lower Atrai floodplain aquifer,NW Bangladesh: An approach for irrigation management

In the salinity affected lower Atrai floodplain aquifer in the NW Bangladesh, geoelectric resistivity survey and hydrochemical analysis are carried out with an aim to identify fresh and saline groundwater zones; investigate the status of salinity; evaluate hydrochemical processes involved and suggest management approaches for irrigation. Here a two-fold aquifer system, inter-layered by silt, clay and silty-clay aquitard and aquiclude is classified as: upper aquifer — spatially affected by salinity of varying degrees; and lower aquifer — generally characterized by high salinity. The aquifer with resistivity values greater than 69 Ωm is safe for irrigation use. Concentrations of major ions vary as: Ca²⁺>Na⁺>Mg²⁺>K⁺ and HCO₃>Cl>NO₃>SO₄ ^2?. Groundwater is dominated by Na-Ca to Ca-Na, HCO₃-Cl-SO₄, Cl-SO₄-HCO₃ and Cl-SO₄ ^2? facies where Ca²⁺, Mg²⁺, SO₄ ^2?, HCO₃ ^?, Cl^? and NO₃ ^2? ion concentrations are statistically dominant and water is of Ca-Mg, HCO₃-SO₄-Cl and NO₃ types. Geochemically, groundwater is hard and saline to fresh water type. Salinity increases with depth, but spatially towards the southern part. Groundwater quality is a product of water-rock interaction, direct mixing and marine spraying, or fall-out of airborne marine salts, where silicate weathering is the primary source of bivalent cations. Sediment provenance of alkaline earth silicates and higher concentrations of alkalis are derived from sources other than precipitation. In general partially or fully salinity affected upper and lower aquifers in the area except in its eastern part are not suitable for tubewell irrigation. As groundwater demand for irrigation is increasing, the saline water has progressively invaded relatively fresher parts of the aquifer by upconning. So, special salinity control management approaches can be adopted through engineering techniques such as groundwater abstraction optimization, as also through scientific behavioral approaches like groundwater demand management, salt tolerant crops production. In this context, surface water conservation and rain water harvesting for domestic and irrigational uses are recommended in the salinity affected area.     

Detection and extraction of signals from the epoch of reionization using higher-order one-point statistics

Detecting redshifted 21-cm emission from neutral hydrogen in the early Universe promises to give direct constraints on the epoch of reionization (EoR). It will, though, be very challenging to extract the cosmological signal (CS) from foregrounds and noise which are orders of magnitude larger. Fortunately, the signal has some characteristics which differentiate it from the foregrounds and noise, and we suggest that using the correct statistics may tease out signatures of reionization. We generate mock data cubes simulating the output of the Low Frequency Array (LOFAR) EoR experiment. These cubes combine realistic models for Galactic and extragalactic foregrounds and the noise with three different simulations of the CS. We fit out the foregrounds, which are smooth in the frequency direction, to produce residual images in each frequency band. We denoise these images and study the skewness of the one-point distribution in the images as a function of frequency. We find that, under sufficiently optimistic assumptions, we can recover the main features of the redshift evolution of the skewness in the 21-cm signal. We argue that some of these features – such as a dip at the onset of reionization, followed by a rise towards its later stages – may be generic, and give us a promising route to a statistical detection of reionization.     

Scalar-tensor theory of gravity and generalized second law of?thermodynamics on?the?event horizon

Here we consider our universe as homogeneous spherically symmetric FRW model and analyze the thermodynamics of this model of the universe in scalar-tensor theory. Assuming the first law of thermodynamics validity of the generalized second law of thermodynamics (GSLT) at the event horizon is examined in both the cases when the universe is filled with perfect fluid and the holographic dark energy.     

Evaluation of the saltation process of bed materials by video imaging under altered bed roughness

The purpose of this paper is to examine the nature of particle saltation and movement over the beds of fixed roughness from flume experiments. A series of experiments are carried out to study the saltation of individual sand particles of different sizes over rough beds under different flow conditions. A 3‐D acoustic Doppler velocimeter is used to record the fluid velocity components; subsequently, under different flow conditions, the images of released sand particles are recorded using high‐speed video imaging technique. Systematic analysis is made with regard to the forces acting on the grains and the variation of their magnitudes along the saltation trajectories of the grains. Relations between the saltation parameters, flow intensity and bed roughness are developed. The distributions of the angle of orientations during a single saltation follows almost a Gaussian distribution. The shape of the Gaussian distribution depends on the particle size and bed roughness. Particle collisions with rough beds and the resulting coefficients of restitution are also discussed. A theoretical framework is developed to compute the mean particle velocity considering the spin in the energy balance equation. Results of the detailed analysis using the imaging technique are much better than in previously reported studies. Copyright © 2013 John Wiley & Sons, Ltd.     

On conformity of the EEJ based ionospheric model to the fountain effect and resulting improvements

The total electron content (TEC) of the equatorial ionosphere is controlled by photochemical processes as well as the transport of the ionospheric plasma near the magnetic equator. The transport phenomenon is initiated by the vertical drift driven by the eastward electric field, which also drives the Equatorial Electrojet. The empirical relation between the Equatorial Electrojet and the anomaly component of the equatorial TEC has already been established. Taking this relation as a reference, a simplified physical model of the anomaly component of equatorial TEC is obtained as a function of Equatorial Electrojet. Influence of other factors like the solar incidence angle and the solar flux are also considered here and the extent of their influence are also investigated. This has been done using TEC data obtained from dual frequency GPS receivers during the low solar activity period of 2005. The derived model is based on the physics of the underlying fountain effect and matches with the observed empirical relation to a fair extent. Obtained results are found to corroborate with previous findings and these physical model values are found to have improved correlation with the observed data than the reference empirical relation. This establishes the conformity between the EEJ based ionospheric model and the physical phenomenon of the fountain effect.