The new millennium will see the upcoming of several ground-based interferometric gravitational wave antennas. Within the next decade a space-based antenna may also begin to observe the distant Universe. These gravitational wave detectors will together operate as a network taking data continuously for several years, watching the transient and continuous phenomena occurring in the deep cores of astronomical objects and dense environs of the early Universe where gravity was extremely strong and highly nonlinear. The network will listen to the waves from rapidly spinning non-axisymmetric neutron stars, normal modes of black holes, binary black hole inspiral and merger, phase transitions in the early Universe, quantum fluctuations resulting in a characteristic background in the early Universe. The gravitational wave antennas will open a new window to observe the dark Universe unreachable via other channels of astronomical observations.

We develop a stochastic formulation of cosmology in the early universe, after considering the scatter in the redshift-apparent magnitude diagram in the early epochs as an observational evidence for the non-deterministic evolution of early universe. We consider the stochastic evolution of density parameter in the early universe after the inflationary phase qualitatively, under the assumption of fluctuating w factor in the equation of state, in the Fokker-Planck formalism. Since the scale factor for the universe depends on the energy density, from the coupled Friedmann equations we calculated the two variable probability distribution function assuming a flat space geometry.

In this work we check the validity of the no scalar hair theorem in charged axisymmetric stationary black holes for a wide class of scalar tensor theories.

We consider a collapsing spherically symmetric inhomogeneous dust cloud in higher dimensional space-time. We show that the central singularity of collapse can be a strong curvature or a weak curvature naked singularity depending on the initial density distribution.

We have investigated Bianchi type IX string cosmological models in general relativity. To get a determinate solution, we have assumed a condition ρ=λ i.e. rest energy density for a cloud of strings is equal to the string tension density. The various physical and geometrical aspects of the models are also discussed.

Considering the nucleon as consisting entirely of its valence quarks confined independently in a scalar-vector harmonic potential; unpolarized structure functions F₁(x, μ²) and F₂(x, μ²) are derived in the Bjorken limit under certain simplifying assumptions; from which valence quark distribution functions u_v(x, μ²) and d_v(x, μ²) are appropriately extracted satisfying the normalization constraints. QCD-evolution of these input distributions from a model scale of μ²=0.07 GeV² to a higher Q² scale of Q₀²=15 GeV² yields xu_v(x, Q₀²) and xd_v(x, Q₀²) in good agreement with experimental data. The gluon and sea-quark distributions such as G(x, Q₀²) and q_s(x, Q₀²) are dynamically generated with a reasonable qualitative agreement with the available data; using the leading order renormalization group equations with appropriate valence-quark distributions as the input.

We have calculated pure rotational transitions of water molecule from a kinetic energy operator (KEO) with the z-axis perpendicular to the molecular plane. We have used rotational basis functions which are linear combinations of symmetric top functions so that all matrix elements are real. The calculated spectra agree well with the observed values.

Low energy positron impact ionization of atomic hydrogen is studies theoretically using the hyperspherical partial wave method of Das [1] in constant Θ₁₂, equal energy sharing geometry. The TDCS reveal considerable differences in physics compared to electron impact ionization under the same geometry.

Bounded whistlers are well-known for their efficient plasma production capabilities in thin cylindrical tubes. In this paper we shall present their radio frequency (RF) breakdown and discharge sustaining capabilities in toroidal systems. Pulsed RF power in the electronmagnetohydrodynamic (EMHD) frequency regime is fed to the neutral background medium. After the breakdown stage, discharge is sustained by toroidal bounded whistlers. In these pulsed experiments the behaviour of the time evolution of the discharge could be studied in four distinct phases of RF breakdown, steady state attainment, decay and afterglow. In the steady state average electron density of ≈10¹² per cc and average electron temperature of ≈20 eV are obtained at 10⁻³ mbar of argon filling pressure. Experimental results on toroidal mode structure, background effects and time evolution of the electron distribution function will be presented and their implications in understanding the breakdown mechanism are discussed.

A simple method to generate an effective electron-ion interaction pseudopotential from the energy wave number characteristic obtained by first principles calculations has been suggested. This effective potential has been used, in third order perturbation, to study the effect of three-body forces on the lattice dynamics of noble metals. It is found that three-body forces, in these metals, do play an important role. The inclusion of such three-body forces appreciably improves the agreement between the experimental and theoretical phonon dispersion curves.

Electrical resistivity (ρ) of the amorphous (a-)Fe_100−cZr_c (c=8.5, 9.5 and 10) alloys has been measured in the temperature range 77 to 300 K, which embraces the second-order magnetic phase transition at the Curie temperature point T_c. Analysis of the resistivity data particularly in the critical region reveals that these systems have a much wider range of critical region compared to other crystalline ferromagnetic materials. The value of T_c and specific heat critical exponent, α has the same values as those determined from our earlier magnetic measurements. The value of α for all the present investigated alloys are in close agreement with the values predicted for three-dimensional (3D) Heisenberg ferromagnet systems, which gives contradiction to the earlier results on similar alloys. It is observed from the analysis that the presence of quenched disorder does not have any influence on critical behavior.

The aim of this brief report is to study the behaviour of sheath structure in a multi-component plasma with dust-neutral collisions. The plasma consists of electrons, ions, micron size negatively charged dust particles and neutrals. The sheath-edge potential and sheath width are calculated for collisionally dominated sheath. Comparison of collisionless and collisionally dominated sheath are made.

When observed spectrum of a diatomic molecule is expressed in terms of the Dunham coefficients $Y_{00}$, $Y_{10}$, $Y_{20}$, $Y_{01}$, and $Y_{11}$ only, dissociation energy of the molecule is given by $Y_{00} + Y^{2}_{10}/(-4Y_{20})$. Kaur and Mahajan [1] have used the Dunham coefficients $Y_{10}$, $Y_{20}$, $Y_{01}$, and $Y_{11}$, for 15 vibrational states of 12 diatomic molecules ($Y_{00}$ is zero for the cases accounted for), but their dissociation energy cannot be reproduced by the expression $Y^{2}_{10}/(-4Y_{20})$. Probable reason for the discrepancy has been discussed.