Necessary and sufficient condition for hydrostatic equilibrium in general relativity

We present explicit examples to show that the `compatibility criterion' is capable of providing a {\em necessary} and {\em sufficient} condition for any regular configuration to be compatible with the state of hydrostatic equilibrium. This conclusion is drawn on the basis of the finding that the $M-R$ relation gives the necessary and sufficient condition for dynamical stability of equilibrium configurations only when the compatibility criterion for these configurations is appropriately satisfied. In this regard, we construct an appropriate sequence composed of core-envelope models on the basis of compatibility criterion, such that each member of this sequence satisfies the extreme case of causality condition $v = c = 1$ at the centre. The maximum stable value of $u \simeq 0.3389$ (which occurs for the model corresponding to the maximum value of mass in the mass-radius relation) and the corresponding central value of the local adiabatic index, $(\Gamma_1)_0 \simeq 2.5911$, of this model are found fully consistent with those of the corresponding {\em absolute} values, $u_{\rm max} \leq 0.3406$, and $(\Gamma_1)_0 \leq 2.5946$, which impose strong constraints on these parameters of such models. In addition to this example, we also study dynamical stability of pure adiabatic polytropic configurations on the basis of variational method for the choice of the `trial function', $\xi =re^{\nu/4}$, as well as the mass-central density relation, since the compatibility criterion is appropriately satisfied for these models. The results of this example provide additional proof in favour of the statement regarding compatibility criterion mentioned above.Comment: 31 pages (double-spaced) revtex style, 1 figure in `ps' forma

Dynamical stability of strange quark stars

We show that the mass-radius $(M-R)$ relation corresponding to the MIT bag models of strange quark matter (SQM) and the models obtained by Day et al (1998) do not provide the necessary and sufficient condition for dynamical stability for the equilibrium configurations, since such configurations can not even fulfill the necessary condition of hydrostatic equilibrium provided by the exterior Schwarzschild solution. These findings will remain unaltered and can be extended to any other sequence of pure SQM. This study explicitly show that although the strange quark matter might exist in the state of zero pressure and temperature, but the models of pure strange quark `stars' can not exist in the state of hydrostatic equilibrium on the basis of General Relativity Theory. This study can affect the results which are claiming that various objects like - RX J1856.5-3754, SAX J1808.4-3658, 4U 1728-34, PSR 0943+10 etc. might be strange stars.Comment: 7 pages (including 6 tables and 1 figure) in MNRAS styl

Hydrostatic equilibrium of insular, static, spherically symmetric, perfect fluid solutions in general relativity

An analysis of insular solutions of Einstein's field equations for static, spherically symmetric, source mass, on the basis of exterior Schwarzschild solution is presented. Following the analysis, we demonstrate that the {\em regular} solutions governed by a self-bound (that is, the surface density does not vanish together with pressure) equation of state (EOS) or density variation can not exist in the state of hydrostatic equilibrium, because the source mass which belongs to them, does not represent the `actual mass' appears in the exterior Schwarzschild solution. The only configuration which could exist in this regard is governed by the homogeneous density distribution (that is, the interior Schwarzschild solution). Other structures which naturally fulfill the requirement of the source mass, set up by exterior Schwarzschild solution (and, therefore, can exist in hydrostatic equilibrium) are either governed by gravitationally-bound regular solutions (that is, the surface density also vanishes together with pressure), or self-bound singular solutions (that is, the pressure and density both become infinity at the centre).Comment: 16 pages (including 1 table); added section 5; accepted for publication in Modern Physics Letters

Change Vector Analysis using Enhanced PCA and Inverse Triangular Function-based Thresholding

Change vector analysis is a very sophisticated method to evaluate land-use/land-cover changes meaningfully. By making proper choice of input data in the form of bands (for instance, red, NIR etc) or features (for instance, greenness, brightness, wetness etc), information about both the magnitude as well as the type/nature of changes can be extracted. However, improper selection of thresholds is always a hindrance to a good change detection algorithm. The paper has proposed an improved technique to select threshold appropriately by means of principal component difference and inverse triangular function. The changes have been represented using class-based circular wheel representation. Results have been shown to further testify the performance of proposed algorithm.Defence Science Journal, 2012, 62(4), pp.236-242, DOI:http://dx.doi.org/10.14429/dsj.62.107

Generalized Electromagnetic fields in Chiral Medium

The time dependent Dirac-Maxwell's Equations in presence of electric and magnetic sources are written in chiral media and the solutions for the classical problem are obtained in unique simple and consistent manner. The quaternion reformulation of generalized electromagnetic fields in chiral media has also been developed in compact, simple and consistent manner

Defence Electronics Applications Laboratoty, Dehradun

A system has been built and tested for automated change detection between multi-temporal panchromatic images. This paper discusses the implementation issues, associated tools, and finally summarises initial tests on IRS IC/ID and other high-resolution images. Key characteristics of this system are integration of technologies having high degree of registration, normalisation of the effects of radiometry; selectivity to specific type of changes, refinement of changes by thresholding, and assignment of presence and absence of object and tools for updation/deletion of change mask. A semi-automatic technique for selection of control points in an image having affine distortion has been implemented. Linear regression is used for normalisation of the images. Two change detection techniques, namely image subtraction and image ratioing have been used to find the global change mask. Selective threshold is used to generate target mask. Target mask is shown in two colours to depict presence and absence of the object. Method based on ratioing has been found to be more sensitive to spectral variations and provides better detection of changes

Evaluation of Snow Parameters using Passive Microwave Remote Sensing

The study of snow characteristics using conventional techniques for vast, rugged andremote snow covered areas of Himalayas is very difficult. In the present study, the satellite dataof SSM/I sensor has been used. Changes in snow accumulation result in related variations inpassive microwave brightness temperature. This study attempts to develop new algorithms usingbrightness temperature for snow water equivalent (SWE) and snow depth that will suit theIndian Himalayan conditions. The snow and meteorological data recorded in the field is usedto determine the empirical coefficients, which have been further used in the algorithmdevelopment. The parameters evaluated can be used as the input for the avalanche risk analysis,as one can estimate average snow depth and SWE of the area which are main input for avalancheforecasting. Algorithms are further used for the prediction of snow depth and SWE for subsequentwinters using the brightness temperature. A good correlation was found between the predictedand the observed values from the ground observatory data

Systematics of Anti magnetic rotation in even-even Cd isotopes

The lifetimes for the high spin levels of the yrast band of $^{110}$Cd has been measured. The estimated B(E2) values decrease with increase in angular momentum. This is the characteristic of Anti magnetic rotation as reported in $^{106,108}$Cd. However, alignment behavior of $^{110}$Cd is completely different from its even-even neighbors. A model based on classical particle plus rotor has been used to explore the underlying systematics and develop a self consistent picture for the observed behavior of these isotopes.Comment: 18 pages including 6 figures. Accepted to be published in PLB, with some modification in the tex