Advective accretion flow properties around rotating black holes – application to GRO J1655-40

We examine the properties of the viscous dissipative accretion flow around rotating black holes in the presence of mass loss. Considering the thin disc approximation, we self-consistently calculate the inflow-outflow solutions and observe that the mass outflow rates decrease with the increase in viscosity parameter (\(\alpha \)). Further, we carry out the model calculation of quasi-periodic oscillation frequency (\(\nu _{\mathrm{QPO}}\)) that is frequently observed in black hole sources and observe that \(\nu ^\mathrm{max}_{\mathrm{QPO}}\) increases with the increase of black hole spin (\(a_k\)). Then, we employ our model in order to explain the High Frequency Quasi-Periodic Oscillations (HFQPOs) observed in black hole source GRO J1655-40. While doing this, we attempt to constrain the range of \(a_k\) based on observed HFQPOs (\(\sim \)300 Hz and \(\sim \)450 Hz) for the black hole source GRO J1655-40.     

Transient loading-related settlement of a square foundation on geogrid-reinforced sand

Summary Laboratory model test results are presented that determine the effectiveness of using layers of geogrids as reinforcement in sand to reduce the settlement of square surface foundations subjected to transient loading. The model tests were conducted with only one type of geogrid at one relative density of compaction of sand. The maximum intensity of the transient load applied always exceeded the static ultimate bearing capacity of the foundation when supported by unreinforced sand. The settlement reduction factors for various depths of reinforcement have been determined.     

Metamorphic reactions in dry and aluminous granulites: a Perple_X <Emphasis Type="Italic">P–T</Emphasis> pseudosection analysis of the influence of effective reaction volume

In high-Mg, Al metapelites, monophase sapphirine corona occur around spinel–corundum aggregates in monomineralic cordierite layers, and bi-phase orthopyroxene–sillimanite aggregates replace locally warped sapphirine in polygonized cordierite aggregates. P–T phase topologies computed (Perple_X software) using compositions of cordierite-rich layers that host the reaction textures did not match the assemblages for the discontinuous reactions spinel + corundum + cordierite → sapphirine and sapphirine + cordierite → orthopyroxene + sillimanite. Instead, the reaction assemblages were reproduced using P–T pseudosection analysis for micro-domain reaction volumes estimated from compositions of product phases in the volume proportion they occur. The results are consistent with known phase relations deduced using Schreinmakers P–T grids. Apparently, the compositions of cordierite-rich layers that hosted the reaction textures were inadequate chemical proxies for determining P–T–X relations of phase-boundary controlled reactions influenced by compositions of the nearest-neighbor minerals in the proportion they react (effective composition), and not in the proportion they existed in the layer/bulk rock. In other words, P–T–X phase topologies and reconstructed P–T paths in dry and aluminous rocks may be best understood by thermodynamic modeling of reactions using effective reaction volume compositions rather than the bulk composition of the rock or the mineralogical layer that host the reaction textures.     

Extended Finite Element Method for the Analysis of Discontinuities in Rock Masses

The strength and deformability of rock mass primarily depend on the condition of joints and their spacing and partially on the engineering properties of rock matrix. Till today, numerical analysis of discontinuities e.g. joint, fault, shear plane and others is conducted placing an interface element in between two adjacent rock matrix elements. However, the applicability of interface elements is limited in rock mechanics problems having multiple discontinuities due to its inherent numerical difficulties often leading to non-convergent solution. Recent developments in extended finite element method (XFEM) having strong discontinuity imbedded within a regular element provide an opportunity to analyze discrete discontinuities in rock masses without any numerical difficulties. This concept is based on partition of unity principle and can be used for cohesive rock joints. This paper summarizes the mathematical frameworks for the implementation of strong discontinuities in 3 and 6 nodded triangular elements and also provides numerical examples of the application of XFEM in one and two dimensional problems with single and multiple discontinuities.     

Some studies on solar microwave bursts in relation to the phases of the associated Hα-flares and their spectral nature

Occurrences of the flare-associated microwave bursts as well as their peak flux and energy excess spectra have been examined in relation to the pre- and post-maximum phases of the respective flares during the period 1969–72. Results obtained are: (i) about 76% of the flare-associated bursts occur in the pre-maximum phase and the remaining 24% occurs in the post-maximum phase irrespective of the flare classification, intensity-wise or area-wise; (ii) ‘impulsive’ and ‘gradual rise and fall’ bursts are relatively more important in the pre-maximum phase while ‘post burst increase’ bursts show comparatively higher occurrences in the post-maximum phase; (iii) peak flux and energy excess spectra of the concurrent microwave bursts in the pre-maximum phase of the flare are mostly of ‘inverted U’ and ‘increasing with frequency’ spectral types. Of these, ‘impulsive’ bursts are predominantly of the ‘inverted U’ and the ‘grf’ bursts are of the ‘increasing with frequency’ spectral type.     

Exact solution of the problem of diffuse reflection and transmission by the method of Laplace transform and linear singular operators

The basic integro-differential equation is subjected to a one-sided finite Laplace transform to obtain linear integral equations of angular distribution of bounding faces. These linear integral equations have been transformed into linear singular integral equations which have been solved exactly to get the emergent distributions from the bounding faces by the theory of linear singular operators. Some solutions of linear singular integral equations have also been derived for future use in radiative transfer problems.     

On transfer equation in a semi-infinite atmosphere with albedo ω>1

In this note we derive an exact solution of transfer equation in a plane-parallel semiinfinite atmosphere with albedo >1, by the method of Laplace transform and Wiener-Hopf technique. The emergent intensityI(0, ) is obtained in terms of theH ⁰-functionH ⁰() (Das Gupta, 1978) for which some good approximations are given. Intensity at any depth is also obtained.I(0, )/I(0, 0) is plotted in graphs against [0,1], and shows a maximum which drops and shifts towards the origin as increases.     

The structure and oscillations of low-mass stars in the presence of a magnetic field

The equilibrium structure and oscillations of a partially degenerate standard model in the presence of a poloidal magnetic field have been studied. The magnetic field in the interior has been matched with an outside dipole field. The effect of magnetic field on the various structural parameters, e.g., mass, central condensation, moment of inertia, and oblateness has been computed for different values of the central degeneracy of the model. We have also studied the effect of magnetic field on radial oscillations of the configuration. A variational formulation is used to compute the changes in the frequency of radial mode of oscillation. It has been shown that the changes in frequency computed for various models using a two-parameter eigenfunction are in fair agreement with the values obtained by using the exact eigenfunction.     

An Appraisal of the 2001 Bhuj Earthquake (Mw 7.7, India) Source Zone: Fractal Dimension and b Value Mapping of the Aftershock Sequence

We examined seismic characteristics, b value and fractal dimension of the aftershock sequence of the January 26, 2001 Bhuj earthquake (Mw 7.7) that occurred in the Kutch failed rift basin, western margin of the Stable Continental Region (SCR) of India. A total of about 2,000 events (M?≥?2.0) were recorded within two and a half months, immediately after the main shock. Some 795 events were precisely relocated by simultaneous inversion. These relocated events are used for mapping the frequency-magnitude relation (b value) and fractal correlation dimension (Dc) to understand the seismic characteristics of the aftershocks and the source zone of the main shock. The surface maps of the b value and Dc reveal two distinct tectonic arms or zones of the V-shaped aftershock area, western zone and eastern zone. The b value is relatively higher (~1.6) in the western zone compared to a lower value (~1.4) in the eastern zone. The Dc map also shows a higher value (1.2–1.35) in the western zone compared to a lower Dc (0.80–1.15) in the eastern zone; this implies a positive correlation between Dc and b value. Two cross sections, E–W and N–S, are examined. The E–W sections show similar characteristics, higher b value and higher Dc in the western zone and lower in the eastern zone with depth. The N–S sections across the fault zones, however, show unique features; it imaged both the b and Dc characteristics convincingly to identify two known faults, the Kutch Mainland fault and the South Wagad fault (SWF), one stepping over the other with a seismogenic source zone at depth (20–35?km). The source zone at depth is imaged with a relatively lower b and higher Dc at the ‘fault end’ of the SWF showing a negative correlation. These observations, corroborated with the seismic tomography as well as with the proposed geological/tectonic model, shed a new light to our understanding on seismogenesis of the largest SCR earthquake in India in the recent years.     

Delineation of the 85°E ridge and its structure in the Mahanadi Offshore Basin,Eastern Continental Margin of India (ECMI), from seismic reflection imaging

The passive Eastern Continental Margin of India (ECMI) evolved during the break up of India and East Antarctica in the Early Cretaceous. The 85°E ridge is a prominent linear aseismic feature extending from the Afanasy Nikitin Seamounts northward to the Mahanadi basin along the ECMI. Earlier workers have interpreted the ridge to be a prominent hot spot trail. In the absence of conclusive data, the extension of the ridge towards its northern extremity below the thick Bengal Fan sediments was a matter of postulation. In the present study, interpretation of high resolution 2-D reflection data from the Mahanadi Offshore Basin, located in the northern part of the ridge, unequivocally indicates continuation of the ridge across the continent–ocean boundary into the slope and shelf tracts of the ECMI. Its morphology and internal architecture suggest a volcanic plume related origin that can be correlated with the activity of the Kerguelen hot spot in the nascent Indian Ocean. In the continental region, the plume related volcanic activity appears to have obliterated all seismic features typical of continental crust. The deeper oceanic crust, over which the hot spot plume erupted, shows the presence of linear NS aligned basement highs, corresponding with the ridge, underlain by a depressed Moho discontinuity. In the deep oceanic basin, the ridge influences the sediment dispersal pattern from the Early Cretaceous (?)/early part of Late Cretaceous times till the end of Oligocene, which is an important aspect for understanding the hydrocarbon potential of the basin.