Initial moduli of particulated mass with frictional contacts

The stiffness characteristics of a packing of granules are influenced by the particle interactions at contacts, the void ratio, the co-ordination number and the packing structure. A stress-strain relationship for the packings of spheres is presented. The relationship explicitly includes the contact force-displacement law and the parameters characterizing the packing structure. The initial moduli computed using this relationship are compared with experimental measurements and empirical equations for sands. The theoretical results are also compared with experimental results on packings of glass balls. Closed-form solutions are derived for statistically isotropic packings under initial isotropic stress conditions. Numerical solutions for the stiffness properties are obtained for anisotropic initial stress conditions and anisotropic packing structures.     

Optical observations of GRB 050401 afterglow : a case for double-jet model

The afterglow of GRB 050401 presents several novel and interesting features. (i) An initially faster decay in optical band than in X-rays. (ii) A break in the X-ray light curve after ∼0.06 d with an unusual slope after the break. (iii)The X-ray afterglow does not show any spectral evolution across the break while the R -band light curve does not show any break. We have modelled the observed multiband evolution of the afterglow of GRB 050401 as originating in a two-component jet, and interpreting the break in X-ray light curve as due to lateral expansion of a narrow collimated outflow which dominates the X-ray emission. The optical emission is attributed to a wider jet component. Our model reproduces all the observed features of multiband afterglow of GRB 050401. We present optical observations of GRB 050401 using the 104-cm Sampurnanand Telescope at the Aryabhatta Research Institute of Observational Sciences (ARIES), Nainital. Results of the analysis of multiband data are presented and compared with GRB 030329, the first reported case of double jet.     

Damped harmonic oscillator interpretation of the soft-state power spectra of Cyg X-1

We develop a model of an accretion disc in which the variability induced at a given radius is governed by a damped harmonic oscillator at the corresponding epicyclic frequency. That variability induces both linear and non-linear responses in the locally emitted radiation. The total observed variability of a source is the sum of these contributions over the disc radius weighted by the energy dissipation rate at each radius. It is shown that this simple model, which effectively has only three parameters including the normalization, can explain the range of the power spectra observed from Cyg X-1 in the soft state. Although a degeneracy between the black hole mass and the strength of the damping does not allow a unique determination of the mass, we can still constrain it to  ≲(16–20) M_⊙  . We also show that our model preserves the observed linear rms–flux relationship even in the presence of the non-linear flux response.     

Numerical hindcast of extreme waves

The cyclone wave parameters are predicted using Young’s parametric hurricane wave prediction model. The input cyclone tracks for this work are obtained from Fleet Naval Meteorology and Oceanography Center, USA. Extreme value analysis is carried out to obtain the wave heights and periods for 1 in 5, 10, 50 and 100 years return periods, respectively. The deep-water hindcast wave corresponding to 100 years from probable directions are allowed to propagate to Visakhapatnam coastal waters using nearshore spectral wind-wave mode. The offshore wave height for one in 100-year return period is 11.9 m, and the corresponding nearshore wave height at 10-m water depth varies between 4.6 and 5.6 m depending on the directional spreading. Weibull distribution is chosen to fit the 24 cyclonic data sets over a total period of 30 years (September 1972 to November 2002). This paper demonstrates usefulness of Young’s wave model for deep-water extreme wave hindcasting. Further, the results of the present study would be highly useful for assessing the design wave height for Visakhapatnam coast.     

Geochronological Constraints on Evolution of Singhbhum Mobile Belt and Associated Basic Volcanics of Eastern Indian Shield

The Singhbhum Mobile Belt (SMB) of the eastern Indian shield represents a roughly east-west-trending arcuate belt of folded supracrustals overlying the granite-greenstone basement of the Singhbhum-Orissa Craton along its northern, eastern and western margins and is bounded by the Chotanagpur Gneissic Complex to further north. The radiometric ages of the basement Singhbhum and equivalent granites and the intrusive anorogenic Mayurbhanj granite pluton constrain the time of evolution of this mobile belt between 3.12 and 3.09 Ga. Hence, the SMB supracrustals also known as Singhbhum Group, is late Mesoarchaean in age and not Proterozoic as thought earlier. The evolution of the SMB was followed by emplacement of some major basic igneous rocks within or adjacent to the supracrustals. These include Simlipal volcanics at >3.09 Ga on the SMB, Mayurbhanj gabbro along with Mayurbhanj granite at 3.09 Ga along the marginal part of the craton near the SMB, and the Dalma volcanics on the SMB along with the Dhanjori volcanics adjacent to SMB at 2.80 Ga. The 2.80 Ga old basic volcanics is also associated with emplacement of some small granite plutons occurring along the marginal part of the craton, one of them, the Tamperkola granite intrudes the SMB. The >3.09 Ga onward igneous activities along the marginal part of Singhbhum-Orissa Craton took place essentially under anorogenic tectonic setting before being affected by a major metamorphism at 2.50 Ga, which is recorded on the Dalma volcanics and on some small granite pluton occurs along the marginal part of the craton. The Jagannathpur and stratigraphically equivalent Malangtoli volcanics, occurring within the Singhbhum-Orissa Craton at the west, were erupted at 2.25 Ga. The boundary between the SMB supracrustals and the Singhbhum-Orissa Craton is demarked by a prominent shear zone known as the Singhbhum Shear Zone, which shows multiple reactivation, the oldest being at 3.09 Ga, followed by subsequent reactivation during Palaeo- and Mesoproterozoic periods at 2.2, 1.8, 1.6-1.5, 1.4 and 1.0 Ga respectively. The Singhbhum Group and the adjacent Chotanagpur Gneissic Complex appear to have evolved from a near shore syn-rift and a distal post-rift stable shelf sedimentary assemblages respectively, which were deposited without any stratigraphic break in a marine basin existed in the present north of the Singhbhum-Orissa Craton. Both of these assemblages were deformed and metamorphosed together during Proterozoic at 2.5 to >2.3 Ga, 1.6 Ga and 1.0 Ga.     

Non-minimum phase wavelet estimation by non-linear optimization of all-pass operators

Convolution of a minimum‐phase wavelet with an all‐pass wavelet provides a means of varying the phase of the minimum‐phase wavelet without affecting its amplitude spectrum. This observation leads to a parametrization of a mixed‐phase wavelet being obtained in terms of a minimum‐phase wavelet and an all‐pass operator. The Wiener–Levinson algorithm allows the minimum‐phase wavelet to be estimated from the data. It is known that the fourth‐order cumulant preserves the phase information of the wavelet, provided that the underlying reflectivity sequence is a non‐Gaussian, independent and identically distributed process. This property is used to estimate the all‐pass operator from the data that have been whitened by the deconvolution of the estimated minimum‐phase wavelet. Wavelet estimation based on a cumulant‐matching technique is dependent on the bandwidth‐to‐central‐frequency ratio of the data. For the cumulants to be sensitive to the phase signatures, it is imperative that the ratio of bandwidth to central frequency is at least greater than one, and preferably close to two. Pre‐whitening of the data with the estimated minimum‐phase wavelet helps to increase the bandwidth, resulting in a more favourable bandwidth‐to‐central‐frequency ratio. The proposed technique makes use of this property to estimate the all‐pass wavelet from the prewhitened data. The paper also compares the results obtained from both prewhitened and non‐whitened data. The results show that the use of prewhitened data leads to a significant improvement in the estimation of the mixed‐phase wavelet when the data are severely band‐limited. The proposed algorithm was further tested on real data, followed by a test involving the introduction of a 90°‐phase‐rotated wavelet and then recovery of the wavelet. The test was successful.     

Representative abundances of a few positive ions in the innermost coma of comet Halley

The production rate of H₂O molecules at a heliocentric distance of 1 AU for comet Halley and the abundance ratio with respect to water (H₂O) of parent molecules at the cometary nucleus from the paper of Yamamoto (1987) have been used to compute the number densities of positive ions viz. H₃O⁺, H₃S⁺, H₂CN⁺, H₃CO⁺, CH₃OH ₂ ⁺ and NH ₄ ⁺ at various cometocentric distances within 600 kms from the nucleus.The role of proton transfer reactions in producing major ionic species is discussed. A major finding of the present investigation is that NH ₄ ⁺ ion which may be produced through proton transfer reactions is the most abundant ion near the nucleus of a comet unless the abundance of NH₃ as a parent is abnormally low. Using the quoted value of Q(NH₃)/Q(H₂O) for comet Halley and the life times of NH₃ and H₂O molecules, the abundance ratio N(NH₃)/N(H₂O) is found to be one-third of that used in the present paper. The consequent proportionate decrease in the NH ₄ ⁺ ions does not, however, affect its superiority in number density over other ions near the nucleus.The number density of the next most abundant ion viz. H₃O⁺ is found to be 4 × 10⁴ cm^-3 at the nucleus of comet Halley and decreases by a factor of two only upto a distance of 600 K ms from the nucleus. The ionic mass peak recorded by VEGA and GIOTTO spacecrafts atm/q = 18 is most probably composite of the minor ionic species H₂O⁺, as its number density = 10² cm^-3 remains virtually constant in the inner coma and of NH ₄ ⁺ , the number density of which at large cometocentric distances may add to the recorded peak atmlq = 18. The number densities of other major ions produced through proton transfer from H₃O⁺ are also discussed in the region within 600 K ms from the nucleus of comet Halley.