Formulae have been developed for the isotropic averagings in two and three dimensions. Averagings are employed in the cell-dynamical-system simulation of spinodal decomposition for inter-cell coupling. The averagings used in earlier works on spinodal decomposition have been discussed.

Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. The uncertainty relation of the system is always larger than ħ/2 not only in number but also in the thermal state as expected. We used the diagonal elements of density operator satisfying Leouville-von Neumann equation to calculate various expectation values in the thermal state. We applied our theory to a special case which is the forced Caldirola-Kanai oscillator.

The effect of solar features on geospheric conditions leading to geomagnetic storms (GMSs) with planetary index,A^P ≥ 20 and the range of horizontal component of the Earth’s magnetic fieldH such that 250γ <H < 400γ has been investigated using interplanetary magnetic field (IMF), solar wind plasma (SWP) and solar geophysical data (SGD) during the period 1978–99. Statistically, it is observed that maximum number of GMSs have occurred during the maximum solar activity years of 21st and 22nd solar cycles. A peculiar result has been observed during the years 1982, 1994 when sunspot numbers (SSNs) decrease very rapidly while numbers of GMSs increase. No distinct association between yearly occurrence of disturbed days and SSNs is observed. Maximum number of disturbed days have occurred during spring and rainy seasons showing a seasonal variation of disturbed days. No significant correlation between magnitude (intensity) of GMSs and importance ofH_α, X-ray solar flares has been observed. Maximum number of GMSs is associated with solar flares of lower importance, i.e., SF during the period 1978-93.H_α, X-ray solar flares occurred within lower helio-latitudes, i.e., (0–30)°N to (0–30)°S are associated with GMSs. NoH_α, X-ray solar flares have occurred beyond 40°N or 40°S in association with GMSs. In helio-latitude range (10–40)°N to (10–40)°S, the 89.5% concentration of active prominences and disappearing filaments (APDFs) are associated with GMSs. Maximum number of GMSs are associated with solar flares. Coronal mass ejections (CMEs) are related with eruptive prominences, solar flares, type IV radio burst and they occur at low helio-latitude. It is observed that CMEs related GMS events are not always associated with high speed solar wind streams (HSSWSs). In many individual events, the travel time between the explosion on the Sun and maximum activity lies between 58 and 118 h causing GMSs at the Earth.

In the presence of an electric dipole coupling of$$\overline {tt} $$ to a photon, and an analogous ‘weak’ dipole coupling to the Z, CP violation in the process e⁺e⁻ →$$\overline {tt} $$ results in modified polarization of the top and the anti-top. This polarization can be analyzed by studying the angular distributions of decay charged leptons when the top or anti-top decays leptonically. Analytic expressions are presented for these distributions when eithert or$$\overline t $$ decays leptonically, including$$\mathcal{O}$$(α_s) QCD corrections in the soft-gluon approximation. The angular distributions are insensitive to anomalous interactions in top decay. Two types of simple CP-violating polar-angle asymmetries and two azimuthal asymmetries, which do not need the full reconstruction of thet or$$\overline t $$, are studied. Independent 90% CL limits that may be obtained on the real and imaginary parts of the electric and weak dipole couplings at a linear collider operating at √ s = 500 GeV with integrated luminosity 500 fb⁻ and also at √s = 1000 GeV with integrated luminosity 1000 fb⁻ have been evaluated. The effect of longitudinal electron and/or positron beam polarizations has been included.

The variation of fusion cross-section (σJ_fus) with energy in the¹²C+¹²C collision is linked to the underlying resonance phenomenon through the behavior of reaction cross-section (σ) of which σ_fus is taken as a part. The calculation of σ_fus is done through an energy-dependent imaginary potential in the optical model potential (OMP). Through dispersion relation, such an imaginary potential gives rise to energy-dependent real potential which is incorporated in the OMP. In our calculation, a form of potential for the nuclear part which has a soft repulsive in-built core is introduced based on similar works done earlier. The calculated results of σ_fus are used to explain the oscillatory structure, astrophysical S-factor and the decreasing trend at higher energies of the experimental σ_fus data in the case of¹²C+¹²C system with remarkable success. The potential used for fusion calculation is tested for fitting elastic scattering data at some energies and is found good in forward angles. Further improvement of the fitting of these data is obtained by incorporating a coupling potential in the surface region. About twenty resonances are observed in our calculation in the specific partial waves and some of them are found close to the experimentally identified resonances in¹²C+¹²C reaction. Thus, we provide an integrated and comprehensive analysis of fusion, resonance and scattering data in the best studied case of¹²C+¹²C reaction within the framework of optical potential model.

Resonant spin-flavor precession (RSFP) scenario with twisting solar magnetic fields has been confronted with the solar neutrino data from various ongoing experiments. The anticorrelation apparent in the Homestake solar neutrino data has been taken seriously to constrain (Δm²,φ′) parameter space and the twisting profiles of the magnetic field in the convective zone of the Sun. The twisting profiles, thus derived, have been used to calculate the variation of the neutrino detection rates with the solar magnetic activity for the Homestake, Super-Kamiokande and the gallium experiments. It is found that the presence of twisting reduces the degree of anticorrelation in all the solar neutrino experiments. However, the anticorrelation in the Homestake experiment is expected to be more pronounced in this scenario. Moreover, the anticorrelation of the solar neutrino flux emerging from the southern solar hemisphere is expected to be stronger than that for the neutrinos emerging from the northern solar hemispheres.

The construction of a millimeterwave spectrometer to study the pure rotational spectra of transient molecules in the gas phase is presented. The spectrometer is a source-modulated system combined with a free space glass discharge cell. Millimeterwave radiation has been produced using a frequency multiplier, the fundamental radiation source being klystrons. The spectrometer has been used to study the millimeterwave spectrum of carbon monosulfide (CS) and fluorine cyanide (FCN) produced inside the cell in a low pressure DC discharge of precursor gases. The quadrupole hyperfine structures of³³S and¹⁴N nucleus of CS and FCN have been resolved, measured and analysed.

An experiment on gain enhancement in the long wavelength band erbium-doped fiber amplifier (L-band EDFA) is demonstrated using dual forward pumping scheme in double-pass system. Compared to a single-stage single-pass scheme, the small signal gain for 1580 nm signal can be improved by 13.5 dB. However, a noise figure penalty of 2.9 dB was obtained due to the backward C-band ASE from second stage and the already amplified signal from the first pass that extracting energy from the forward C-band ASE. The maximum gain improvement of 13.7 dB was obtained at a signal wavelength of 1588 nm while signal and total pump powers were fixed at -30 dBm and 92 mW, respectively.

The inverse problem of the variational calculus for evolution equations characterized by non-linear dispersive terms is analysed with a view to clarify why such a system does not follow from Lagrangians. Conditions are derived under which one could construct similar equations which admit a Lagrangian representation. It is shown that the system of equations thus obtained can be Hamiltonized by making use of the Dirac’s theory of constraints. The specific results presented refer to the third- and fifth-order equations of the so-called distinguished subclass.

The dynamics of a self-gravitating unmagnetized, inhomogeneous, streaming dusty plasma is studied in the present work. The presence of the shear flow causes the coupling between gravitational and electrostatic forces. In the absence of self-gravity, the fluctuations in the plasma may grow at the expense of the density inhomogeneity and for certain wavelengths, such an unstable mode may dominate the usual streaming instability. However, in the presence of self-gravity, the plasma inhomogeneity causes an overlap between Jeans and streaming modes and collapse of the grain will continue at all wavelengths.

The problem of hydrogen diffusion in hydrogenated amorphous silicon (a-Si:H) is studied semiclassically. It is found that the local hydrogen concentration fluctuations-induced extra potential wells, if intense enough, lead to the localized electronic states in a-Si:H. These localized states are metastable. The trapping of electrons and holes in these states leads to the electrical degradation of the material. These states also act as recombination centers for photo-generated carriers (electrons and holes) which in turn may excite a hydrogen atom from a nearby Si-H bond and breaks the weak (strained) Si-Si bond thereby apparently enhancing the hydrogen diffusion and increasing the light-induced dangling bonds.

Double barrier resonant tunneling diode using annealing induced diffusion modified quantum well is proposed as a viable alternative to that using parabolic quantum well which requires complex techniques to fabricate it. The transmission coefficients are calculated using the hybrid incremental airy function plane wave approach. The room temperature current-voltage characteristics have been calculated using transmission coefficients. The current-voltage characteristics are found to be similar in both diodes.

Here we describe the superiority of Bessel function as base function for radial expansion over Zernicke polynomial in the tomographic reconstruction technique. The causes for the superiority have been described in detail. The superiority has been shown both with simulated data for Kadomtsev’s model for saw-tooth oscillation and real experimental x-ray data from W7-AS Stellarator.

Assuming a homogeneous perfect fluid withρ =ρ(t) andp =p(t), we have obtained exact solutions for cosmological models in higher-dimension based on Lyra geometry. Depending on the form of metric chosen, the model is similar to FRW type. The explicit solutions of the scale factor are found via the assumption of an equation of statep =mρ, where m is a constant. Some astrophysical parameters are also calculated.

We demonstrate that the process of matrix factorization provides a systematic mathematical method to investigate the Hamiltonian structure of non-linear evolution equations characterized by hereditary operators with Nijenhuis property.

The structure of theK^π= 2+ gamma vibrational bands and the quasi-gamma bands of even-Z-even-N nuclei is investigated on a global scale, vis-a-vis the variation of band head, the moment of inertia of the band and the odd-even spin staggering. The variation withN andZ and with spinJ of the odd-even spin energy staggering index is studied and a unified view of the same is presented.

Theoretical investigation has been made on two different ultra-low-frequency electrostatic modes, namely, dust-cyclotron mode and dust-lower-hybrid mode, propagating perpendicular to the external magnetic field, in a self-gravitating magnetized two-fluid dusty plasma system. It has been shown that the effect of the self-gravitational force, acting on both dust grains and ions, significantly modifies the dispersion properties of these two electrostatic modes. The implications of these results to some space and astrophysical dusty plasma systems, especially to planetary ring-systems and cometary tails, are briefly mentioned.

The results of electrical resistance measurements under pressure on single crystals of WSe₂ are reported. Measurements up to 8.5 GPa are carried out using Bridgman anvil set up and beyond it using diamond anvil cell (DAC) up to a pressure of 27 GPa. There is no clear indication of any phase transition till the highest pressure is reached in these measurements.