Resonance stability of triangular equilibrium points in elliptical restricted three body problem under the radiating primaries

The main aim of this paper is to study the existence of resonance and linear stability of the triangular equilibrium points of the planar elliptical restricted three body problem considering the photo gravitational effect of both the primaries in circular and elliptical case. A practical application of this case could be the study of the dynamical system around the binary systems. For this the Hamiltonian function, convergent in nature and describing the motion of the infinitesimal body in the neighborhood of the triangular equilibrium solutions is derived. Also, the Hamiltonian for the system is expanded in powers of the generalized components of momenta. Further, canonical transformation has also been used to study the stability of the triangular equilibrium points. The study primarily focuses on establishing the relation for determining the range of stability at and near the resonance frequency ω ₂=1/2 around the binary systems using simulation technique. It is observed that the parametric resonance is only possible at the resonance frequency ω ₂=1/2 in both circular and elliptical cases.     

A new look at pulsar statistics — Birthrate and evidence for injection

We make a statistical analysis of the periodsP and period-derivativesP of pulsars using a model independent theory of pulsar flow in theP-P diagram. Using the available sample ofP andP values, we estimate the current of pulsars flowing unidirectionally along theP-axis, which is related to the pulsar birthrate. Because of radio luminosity selection effects, the observed pulsar sample is biased towards lowP and highP. We allow for this by weighting each pulsar by a suitable scale factor. We obtain the number of pulsars in our galaxy to be 6.05_−2.80 ^+3.32 × 10⁵ and the birthrate to be 0.048_−0.011 ^+0.014 pulsars yr⁻¹ galaxy⁻¹. The quoted errors refer to 95 per cent confidence limits corresponding to fluctuations arising from sampling, but make no allowance for other systematic and random errors which could be substantial. The birthrate estimated here is consistent with the supernova rate. We further conclude that a large majority of pulsars make their first appearance at periods greater than 0.5 s. This ‘injection’, which runs counter to present thinking, is probably connected with the physics of pulsar radio emission. Using a variant of our theory, where we compute the current as a function of pulsar ‘age’ (1/2P/P), we find support for the dipole braking model of pulsar evolution upto 6 × 10⁶ yr of age. We estimate the mean pulsar braking index to be 3.7_−0.8 ^+0.8.     

Propagation of Extremely Low Frequency Waves Through the Ionosphere

The propagation features of extremely low frequency electromagnetic waves through the multicomponent ionospheric plasma are studied. It is shown that at relatively lower frequencies refractive index for right hand mode is higher than the left-hand mode, which is reversed at higher frequencies. The thermal temperature of plasma particle causes decrease in phase and group velocities of both right and left-hand modes. The crossover frequencies for different plasma models are computed and variation with ion concentration and thermal velocity is studied. Explicit expression for group velocity and travel time has been derived and studied numerically. Finally, we have presented simulation of the ion whistler spectrograms for Hydrogen, Helium and Oxygen ions present in the ionospheric plasma. The results are compared with the experimentally detected hydrogen and helium ion whistlers. The importance of the present study in the exploration of ionospheric plasma is illustrated.     

Solution of Lane-Emden type equations using Bernstein operational matrix of differentiation

The purpose of this paper is to propose an efficient numerical method for solving Lane-Emden type equations arising in astrophysics using Bernstein polynomials. First Bernstein operational matrix of differentiation is derived using Bernstein polynomials and then applied to solve the linear and nonlinear differential equations of Lane-Emden type. Some illustrative examples are given to demonstrate the efficiency and validity of the proposed algorithm.     

High-energy afterglow emission from gamma-ray bursts

We calculate the very high-energy (sub-GeV to TeV) inverse Compton emission of GRB afterglows. We argue that this emission provides a powerful test of the currently accepted afterglow model. We focus on two processes: synchrotron self-Compton emission within the afterglow blast wave, and external inverse Compton emission which occurs when flare photons (produced by an internal process) pass through the blast wave. We show that if our current interpretations of the Swift X-ray telescope (XRT) data are correct, there should be a canonical high-energy afterglow emission light curve. Our predictions can be tested with high-energy observatories such as GLAST , Whipple, HESS and MAGIC. Under favourable conditions we expect afterglow detections in all these detectors.     

Fast robust large-scale mapping from video and internet photo collections

This paper presents a system approaching fully automatic 3D modeling of large-scale environments. Our system takes as input either a video stream or collection of photographs obtained from Internet photo sharing web-sites such as Flickr. The system achieves high computational performance through algorithmic optimizations for efficient robust estimation, the use of image-based recognition for efficient grouping of similar images, and two-stage stereo estimation for video streams that reduces the computational cost while maintaining competitive modeling results. In addition to algorithmic advances, we achieve a major improvement in computational speed through parallelization and execution on commodity graphics hardware. These improvements lead to real-time video processing and to reconstruction from tens of thousands of images within the span of a day on a single commodity computer. We demonstrate modeling results on a variety of real-world video sequences and photo collections.     

Computation of ground motion amplification in Kolkata megacity (India) using finite-difference method for seismic microzonation

This paper presents the ground motion amplification scenario along with fundamental frequency (F ₀) of sedimentary deposit for the seismic microzonation of Kolkata City, situated on the world’s largest delta island with very soft soil deposit. A 4th order accurate SH-wave viscoelastic finite-difference algorithm is used for computation of response of 1D model for each borehole location. Different maps, such as for F ₀, amplification at F ₀, average spectral amplification (ASA) in the different frequency bandwidth of earthquake engineering interest are developed for a variety of end-users communities. The obtained ASA of the order of 3–6 at most of the borehole locations in a frequency range of 0.25–10.0 Hz reveals that Kolkata City may suffer severe damage even during a moderate earthquake. Further, unexpected severe damage to collapse of multi-storey buildings may occur in localities near Hoogly River and Salt Lake area due to double resonance effects during distant large earthquakes.     

Numerical Simulation of North Indian Ocean State Prior to the Onset of SW Monsoon Using SSM/I Winds

The Sea Surface Temperatures (SST) and currents are simulated over the north Indian Ocean, during the onset phase of southwest monsoon for the three years 1994, 1995, and 1996, using daily Special Sensor Microwave/Imager (SSM/I) winds and National Center for Environmental Prediction (NCEP) heat fluxes as forcings in the 2½ layer thermodynamic numerical ocean model. The results are discussed for the 30-day period from 16 May to 13 June for all the three years, to determine the ocean state during the onset phase of SW monsoon. The maximum variability in the simulated SST is found along the Somali coast, Indian coasts, and equatorial regions. The maximum SST in the North Arabian Sea is found to be greater than 30°C and minimum SST in the west equatorial region is 25°C during the onset phase of all three years. Model SSTs are in agreement with Reynolds SST. SST gradients in the north-south as well as in the east-west directions, west of 80°E are found to change significantly prior to the onset. It can be inferred from the study that the SST gradient of 2.5°C/2000 km is seen due north and due west of the region 2° - 7°S, 60° - 65°E, about 8 to 10 days prior to the arrival of SW monsoon near Kerala coast. Upper and lower layer circulation fields do not show prominent interannual variability.     

Effects of Impedance Contrast and Soil Thickness on Basin-Transduced Rayleigh Waves and Associated Differential Ground Motion

This paper presents the effects of impedance contrast (IC) across the basin edge, velocity contrast between the basin and underlying bedrock, Poisson’s ratio and soil thickness on the characteristics of basin-transduced Rayleigh (BTR) waves and associated differential ground motion (DGM). Analysis of simulated results for a two-dimensional (2D) basin revealed complex mode transformation of Rayleigh waves after entering the basin. Excellent correlation of frequencies corresponding to different spectral ratio peaks in ellipticity curves of BTR waves and spectral amplification peaks was obtained. However, such correlation was not observed between values of peaks in ellipticity curves and spectral amplification at the corresponding frequencies. An increase of spectral amplification with IC was obtained. The largest spectral amplification was more than twice the IC in the horizontal component and more than the IC in the vertical component in the case of large and same impedance contrast for P- and S-waves. It was concluded that the frequency corresponding to the largest spectral amplification was greater than the fundamental frequency of soil by around 14% and 44% in the vertical and horizontal components, respectively. Spectral amplification of the vertical component was negligible when soil thickness was less than around 15–20 times the S-wave wavelength in the basin. The largest values of peak ground displacement (PGD) and peak differential ground motion (PDGM) were obtained very near the basin edge, and their values with offset from the edge were strongly dependent on the IC across the basin edge, Poisson’s ratio, velocity contrast between the basin and underlying bedrock (dispersion), damping and soil thickness. The obtained value of PDGM for a span of 50 m in the horizontal and vertical components due to the BTR wave was of the order of 0.75 × 10^?3 and 1.32 × 10^?3 for unit amplitude (1.0 cm) in the horizontal component of the Rayleigh wave at rock very near the basin edge.