Stability of equilibrium points in the generalized perturbed restricted three-body problem

This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen that the triangular points are stable for 0<μ<μ _c and unstable for \(\mu_{c}\le\mu <\frac{1}{2}\), where μ _c is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that collinear points remain unstable.     

Adaptive optimal control of an autonomous underwater vehicle in the dive plane using dorsal fins

In this paper, adaptive control of low speed bio-robotic autonomous underwater vehicles (BAUVs) in the dive plane using dorsal fins is considered. It is assumed that the model parameters are completely unknown and only the depth of the vehicle is measured for feedback. Two dorsal fins are mounted in the horizontal plane on either side of the BAUV. The normal force produced by the fins, when cambered, is used for the maneuvering. The BAUV model considered here is non-minimum phase. An indirect adaptive control system is designed for the depth control using the dorsal fins. The control system consists of a gradient based identifier for online parameter estimation, an observer for state estimation, and an optimal controller. Simulation results are presented which show that the adaptive control system accomplishes precise depth control of the BAUV using dorsal fins in spite of large uncertainties in the system parameters.     

Plane Symmetric Domain Wall in Lyra Geometry

In this paper general solutions are found for domain walls in Lyra geometry in the plane symmetric spacetime metric given by Taub. Expressions for the energy density and pressure of domain walls are derived in both cases of uniform and time varying displacement field β. It is also shown that the results obtained by Rahaman et al [IJMPD, 10, 735 (2001)] are particular case of our solutions. Finally, the geodesic equations and acceleration of the test particle are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

State studies of Earth's plasmasphere: A review

The plasmasphere sandwiched between the ionosphere and the outer magnetosphere is populated by up flow of ionospheric cold (∼1 eV) and dense plasma along geomagnetic field lines. Recent observations from various instruments onboard IMAGE and CLUSTER spacecrafts have made significant advances in our understanding of plasma density irregularities, plume formation, erosion and refilling of the plasmasphere, presence of thermal structures in the plasmasphere and existence of radiation belts. Still modeling work and more observational data are required for clear understanding of plasmapause formation, existence of various sizes and shapes of density structures inside the plasmasphere as well as on the surface of the plasmapause, plasmasphere filling and erosion processes; which are important in understanding the relation of the process proceeding in the Sun and solar wind to the processes observed in the Earth's atmosphere and ionosphere.     

FLRW cosmological models with quark and strange quark matters in $$ gravity

In this paper, we have studied the magnetized quark matter (QM) and strange quark matter (SQM) distributions in the presence of \(f(R,T)\) gravity in the background of Friedmann-Lemaître-Robertson-Walker (FLRW) metric. To get exact solutions of modified field equations we have used \(f(R,T ) = R + 2 f(T)\) model given by Harko et al. with two different parametrization of geometrical parameters i.e. the parametrization of the deceleration parameter \(q \), and the scale factor \(a \) in hybrid expansion form. Also, we have obtained Einstein Static Universe (ESU) solutions for QM and SQM distributions in \(f(R,T)\) gravity and General Relativity (GR). All models in \(f(R,T)\) gravity and GR for FRW and ESU Universes with QM also SQM distributions, we get zero magnetic field. These results agree with the solutions of Akta? and Aygün in \(f(R,T)\) gravity. However, we have also discussed the physical consequences of our obtained models.     

Mid-term periodicities and heliospheric modulation of coronal index and solar flare index during solar cycles 22–23

We applied fast Fourier transform techniques and Morlet wavelet transform on the time series data of coronal index, solar flare index, and galactic cosmic ray, for the period 1986–2008, in order to investigate the long- and mid-term periodicities including the Rieger (\({\sim }130\) to \({\sim }190\) days), quasi-period (\({\sim }200\) to \({\sim }374\) days), and quasi-biennial periodicities (\({\sim }1.20\) to \({\sim }3.27\) years) during the combined solar cycles 22–23. We emphasize the fact that a lesser number of periodicities are found in the range of low frequencies, while the higher frequencies show a greater number of periodicities. The rotation rates at the base of convection zone have periods for coronal index of \({\sim }1.43\) years and for solar flare index of \({\sim }1.41\) year, and galactic cosmic ray, \({\sim }1.35\) year, during combined solar cycles 22–23. In relation to these two solar parameters (coronal index and solar flare index), for the solar cycles 22–23, we found that galactic cosmic ray modulation at mid cut-off rigidity (\(\hbox {Rc} = 2.43\hbox {GV}\)) is anti-correlated with time-lag of few months.     

String cosmology with magnetized bulk viscous fluid in Bianchi I universe

The objective of the present paper is to study an anisotropic Bianchi-I cosmological model filled with bulk viscous fluid and magnetic field in string cosmology. The magnetic field is due to an electric current produced along the x-axis. The expansion in the model is considered to be proportional to one of the components of the shear tensor. We obtain two different quadrature forms of volume scale factor by considering two different relations between bulk viscosity and expansion scalar. We discuss the behavior of the classical potential with respect to the volume scale factor in the presence or absence of magnetic field and bulk viscosity in each case. We observe the role of bulk viscosity on the classical potential and also on the choices of bulk viscous pressure. By introduction of magnetic field or bulk viscosity or both into the model it results in changes in the potential as well as in volume scale factors. The physical and geometrical aspects of the solutions are discussed in detail.     

Change in entropy of non-spinning black holes w.r.t. the radius of event horizon in XRBs

The present research paper discusses the derivation for the change in entropy of Non- spinning black holes with respect to the change in the radius of event horizon applying the first law of black hole mechanics ( $\delta M = \frac{\kappa}{8\pi} \delta A + \varOmega\delta J - \upsilon\delta Q$ ) with the relation for the change in entropy δS=8πMδM. When the work is further extended with proper operation, the entropy of black hole is obtained almost the same as the Bekenstein-Hawking entropy of black hole. This is the entirely new method to obtain the change in entropy of Non-spinning black holes w.r.t. the radius of event horizon and Hawking entropy of black hole. We have also calculated their values for different types of test non-spinning black holes having masses 5–20M _⊙ found in X-ray binaries (Narayan, gr-qc/0506078v1, 2005).     

Gravitational Instability of Cylindrical Viscoelastic Medium Permeated with Non Uniform Magnetic Field and Rotation

The self-gravitating instability of an infinitely extending axisymmetric cylinder of viscoelastic medium permeated with non uniform magnetic field and rotation is studied for both the strongly coupled plasma (SCP) and weakly coupled plasma (WCP). The non uniform magnetic field and rotation are considered to act along the axial direction of the cylinder. The normal mode method of perturbations is applied to obtain the dispersion relation. The condition for the onset of gravitational instability has been derived from the dispersion relation under both strongly and weakly coupling limits. It is found that the Jeans criterion for gravitational collapse gets modified due to the presence of shear and bulk viscosities for the SCP, however, the magnetic field and rotation whether uniform or non uniform has no effect on the Jeans criterion of an infinitely extending axisymmetric cylinder of a self-gravitating viscoelastic medium.     

From Nearby Low Luminosity AGN to High Redshift Radio Galaxies: Science Interests with Square Kilometre Array

We present detailed science cases that a large fraction of the Indian AGN community is interested in pursuing with the upcoming Square Kilometre Array (SKA). These interests range from understanding low luminosity active galactic nuclei in the nearby Universe to powerful radio galaxies at high redshifts. Important unresolved science questions in AGN physics are discussed. Ongoing low-frequency surveys with the SKA pathfinder telescope GMRT, are highlighted.