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.     

Cosmological models with generalised gravitational and cosmological constants

We consider cosmology with the gravitational and cosmological constants generalized as coupling scalars in Einstein’s theory. A general method of solving the field equations is given. We study here the exact solutions for negative pressure models satisfying G=G ₀(R/R ₀) ⁿ .     

Transient MHD free convection in a rotating system

The classical Rayleigh problem has been extended to the case of the hydromagnetic free-convective flow of an electrically-conducting and incompressible viscous fluid past an infinite vertical naturally permeable wall in a rotating system. The applied transverse magnetic field is fixed with the moving wall and the magnetic Reynolds number of the flow is taken small so that the induced magnetic field can be neglected in comparison to the applied magnetic field. The permeable wall starts moving from rest in the still fluid and thus arises an initial value problem whose solution has been obtained by the Laplace transform method for two important cases impulsive as well as accelerated start of the plate. Mathematical expression for skin friction components have been also obtained in a closed form. Asymptotic behaviour of the solution is analysed for both the cases, and some interesting particular cases have also been encountered. Influence of various physical parameters occurring into the problem has been discussed with the aid of graphs and tables.     

Some anisotropic spatially-homogeneous cosmological models with electromagnetic field

Considering Bianchi type-I metric, cosmological models of a perfect fluid with an electromagnetic field have been obtained, using a supplementary condition between the metric potentials. The four-current is either zero or space-like. The model has expanding and shearing but non-rotating fluid flow which is also geodetic. The requirement of positive conductivity imposes an additional restriction on the model. Various physical and mathematical properties of the model have been discussed.     

Axially-symmetric viscous fluid interacting with the gravitational field

The problem of an axially-symmetric viscous fluid interacting with the gravitational field has been investigated. Exact solutions have been obtained for the pressure and density of the viscous fluid. Physical interpretation of the solutions in respect of the expansion factor, acceleration components reality conditions of the distribution, etc., have been made.     

Some Bianchi-type cosmological models in a new scalar-tensor theory

Bianchi type I, III, V, VI₀, and Kantowski-Sachs type models have been investigated in a scalar tensor theory developed by Saez and Ballester (1985) and Saez (1985). The dynamical behaviour of the models has also been analyzed.     

Stability of two superposed homogeneous fluids under uniform magnetic field

The instability of two superposed homogeneous fluids is discussed under gravitational force and uniform magnetic field. The perturbation propagation is taken simultaneously along and perpendicular to streaming motion in the horizontal plane z=0. The critical wave numberk ^* has been found and some special cases of interest are discussed.     

YO molecule in the sun

Vibrational transition probabilities, namely Franck—Condon factors and -centroids have been evaluated by an approximate analytical method for the (A–X), (A–X), and (A–X) system of YO molecule. Morse potential energy curves forX ²⁺,A ²₂,A²₂, andA²₂, states of YO have been constructed using the latest spectroscopic data. The value of -centroids for the band have been found to decrease linearly with the corresponding wavelengths. We show results for two new transitions of (A–X) and (A–X) and five new bands of (A–X) of YO in the umbral spectrum of the Sun.     

Morse pe-curves of AlH

Morse potential energy curves forC ¹⁺ andC ¹⁺ of AlH have been constructed. The energy values have been found to increase from vibrational levels 0 to 6 and decrease from vibrational levels 7 to 50 with the corresponding centre and half-width in the stateC ¹⁺. InC ¹⁺ state the energy values have been found to increase from vibrational levels 0 to 28 and decrease from vibrational levels 29 to 50 with the corresponding centre and half-width.     

Some aspects related to the asymptotic solutions of the laminar boundary-layer equations with heat flux

The oscillatory, conjugate and asymptotic behaviours of the principal and non-principal solutions of the Blasius and corresponding heat transfer equations governing the compressible laminar boundary-layer flow over a semi-infinite flat plate with heat flux have been studied; the results of the discussion being based on the asymptotic integrations of second-order linear differential equations.