Anisotropic Bianchi Type-I cosmological models have been studied on the basis of Lyra’s geometry. Two types of models, one with constant deceleration parameter and the other with variable deceleration parameter have been derived by considering a time-dependent displacement field.

We derive a number of local identities involving Jacobi elliptic functions and use them to obtain several new results. First, we present an alternative, simpler derivation of the cyclic identities discovered by us recently, along with an extension to several new cyclic identities. Second, we obtain a generalization to cyclic identities in which successive terms have a multiplicative phase factor exp(2iπ/s), wheres is any integer. Third, we systematize the local identities by deriving four local ‘master identities’ analogous to the master identities for the cyclic sums discussed by us previously. Fourth, we point out that many of the local identities can be thought of as exact discretizations of standard non-linear differential equations satisfied by the Jacobi elliptic functions. Finally, we obtain explicit answers for a number of definite integrals and simpler forms for several indefinite integrals involving Jacobi elliptic functions.

We discuss the method of calculating the reflection coefficient using complex trajectory WKB (CWKB) approximation to understand the non-reflecting nature of the potentialU(x) = -U₀/cosh²(x/a). We show that the repeated reflections between the turning points whose paths are in conformity with Bogolubov transformation technique are essential in obtaining the non-reflecting condition. We also discuss the implications of the results when applied to the particle production scenario. We use the CWKB technique developed by one of the authors (SB) to obtain the results which agree very well with those obtained by exact quantum mechanical calculations.

Neutrino-photon processes, forbidden in vacuum, can take place in the presence of a thermal medium and/or an external electro-magnetic field, mediated by the corresponding charged leptons (real or virtual). Such interactions affect the propagation of neutrinos through a magnetized plasma. We investigate the neutrino-photon absorptive processes, at the one-loop level, for massless neutrinos in a weakly magnetized plasma. We find that there is no correction to the absorptive part of the axial-vector-vector amplitude due to the presence of a magnetic field, to the linear order in the field strength.

Electromagnetic theoretic analysis of shielded homogeneous and isotropic dielectric spheres has been made. Characteristic equations for the TE and TM modes have been derived. Dielectric spheres of radii of the order of μm size are found suitable for the optical frequency region whereas for the microwave region radii of the order of mm size are found suitable. Parameters suitable for their application in the optical and microwave frequency ranges have been used to compute the frequencies corresponding to the normal modes for the TE and TM modes. Expressions for the quality factors for realistic resonators, i.e., for a dielectric sphere with a non-zero conductivity and a metal shield with a finite conductivity have also been derived for the TE and TM modes. Computations of the quality factors have been made for resonators with parameters suitable for the optical and the microwave regions.

We re-examine the dual symmetry between absorbing and amplifying random media. By analysing the physically allowed choice of the sign of the square root to determine the complex wave vector in a medium, we draw a broad set of conclusions that enables us to resolve the apparent paradox of the dual symmetry and also to anticipate the large local electromagnetic field enhancements in amplifying random media.

The present paper reports the dislocation unpinning model of acoustic emission (AE) from alkali halide crystals. Equations are derived for the strain dependence of the transient AE pulse rate, peak value of the AE pulse rate and the total number of AE pulse emitted. It is found that the AE pulse rate should be maximum for a particular strain of the crystals. The peak value of the AE pulse rate should depend on the volume and strain rate of the crystals, and also on the pinning time of dislocations. Since the pinning time of dislocations decreases with increasing strain rate, the AE pulse rate should be weakly dependent on the strain rate of the crystals. The total number of AE should increase linearly with deformation and then it should attain a saturation value for the large deformation. By measuring the strain dependence of the AE pulse rate at a fixed strain rate, the time constantτ_s for surface annihilation of dislocations and the pinning timeτ_p of the dislocations can be determined. A good agreement is found between the theoretical and experimental results related to the AE from alkali halide crystals.

GaN on sapphire was grown by MOCVD technique. Rutherford backscattering spectra together with channeling along [0 0 0 1] axis were recorded to study the defects at the interface. Detailed calculation shows that the defects at GaN/sapphire interface are due to dislocations which are distributed into the whole thickness of the film and are mainly aligned on the growth direction.

An emission band system in the region 5700–6700 Å from Dergaon stoney iron meteorite which fell at Dergaon, India on March 2, 16.40 local time (2001) was excited with the help of a continuous 500 mW Ar⁺ laser. The band system is attributed to silicate (olivine), a major component of the meteorite.

The fraction of simultaneous K plus L shell ionized atoms is estimated in Fe, Co and Cu elements using carbon ions at different projectile energies. The present results indicate that the fraction of simultaneous K plus L shell ionization probability decreases with increase in projectile energy as well as with increase in the atomic number of the targets atoms.

Usefulness of a material in thermoelectric devices is temperature specific. The central problem in thermoelectric material research is the selection of materials with high figure-of-merit in the given temperature range of operation. It is of considerable interest to know the utility range of the material, which is decided by the degrading effect of minority carrier conduction. Lead telluride is among the best-known materials for use in the temperature range 400–900 K. This paper presents a detailed theoretical investigation of the role of minority carriers in degrading the thermoelectric properties of lead telluride and outlines the temperature range for optimal performance.

Depth dependent concentration profiles for bilayer film of Sn (500 Å)/Cu (500 A) are determined at different temperatures by X-ray photoelectron spectroscopy (XPS). Although the nature of the diffusion profile for the sample studied immediately after deposition could be explained by the existing laws, the profiles for others are found to be distinctly different and are not explained by the theories of nucleation and growth of the inter-metallic phases. Measured value of the inter-diffusion coefficient for Cu points out to the grain boundary as well as interstitial diffusion processes. It is also observed that the compositions across the bulk of the films become uniform on annealing at higher temperatures and the width of this region increases with annealing. However, the composition close to the surface is found to be entirely different from that of the bulk even on prolonged heating. The findings possibly demonstrate the importance of physical surface in influencing the solid-state reactions.

Energy cascade rates and Kolmogorov’s constant for non-helical steady magnetohydrodynamic turbulence have been calculated by solving the flux equations to the first order in perturbation. For zero cross helicity and space dimension $d = 3$, magnetic energy cascades from large length-scales to small length-scales (forward cascade). In addition, there are energy fluxes from large-scale magnetic field to small-scale velocity field, large-scale velocity field to small-scale magnetic field, and large-scale velocity field to large-scale magnetic field. Kolmogorov’s constant for magnetohydrodynamics is approximately equal to that for fluid turbulence $(\approx 1.6)$ for Alfvén ratio $0.5\leq r_{A}\leq \infty$. For higher space-dimensions, the energy fluxes are qualitatively similar, and Kolmogorov’s constant varies as $d^{1/3}$. For the normalized cross helicity $\sigma_{c}\to 1$, the cascade rates are proportional to $(1-\sigma_{c})/(1+\sigma_{c})$, and the Kolmogorov’s constants vary significantly with $\sigma_{c}$.