We present a new approach to Hamilton’s theory of turns for the groups $SO(3)$ and $SU(2)$ which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire construction can be based on binary rotations rather than mirror reflections.

In this paper, we present results of our calculations on the effects of next-to-nearest-neighbour boson hopping ($t'$) energy on Bose–Einstein condensation in cubic lattices. We consider both non-interacting and repulsively interacting bosons moving in the lowest Bloch band. The interacting bosons are studied using Bogoliubov method. We find that the Bose condensation temperature is enhanced by increasing $t'$ for bosons in a simple cubic (sc) lattice and decreases for bosons in body-centred cubic (bcc) and face-centred cubic (fcc) lattices. We also find that interaction-induced depletion of the condensate is reduced for bosons in an sc lattice while it is enhanced for bosons in bcc and fcc lattices.

The bifurcation theory of dynamical systems is applied to an integrable non-linear wave equation. As a result, it is pointed out that the solitary waves of this equation evolve from bell-shaped solitary waves to W/M-shaped solitary waves when wave speed passes certain critical wave speed. Under different parameter conditions, all exact explicit parametric representations of solitary wave solutions are obtained.

The free energy of a quark-gluon plasma fireball in the hadronic medium is calculated in the Ramanathan et al statistical model after incorporating the effect of curvature. The result with the inclusion of curvature is found to produce significant improvements in all the parameters we calculated with respect to the earlier results. The surface tension with this curvature effect is found to be $0.17 T_{c}^{3}$ , which is two times the earlier value of surface tension which is $0.078 T_{c}^{3}$ , and this new result is nearly close to the lattice value $0.24 T_{c}^{3}$. As far as transition is concerned, a thermodynamic variable like entropy shows weakly first-order phase transition and it shows continuity in the behaviour of specific heat.

The branching ratio for $B_{s} \rightarrow \ell^{+} \ell^{−}$ γ mode is of the same order as $B_{s} \rightarrow \ell^{+} \ell^{−}$, since there is no helicity suppression in the 3-body decay mode. New Physics beyond Standard Model may affect these rates favourably for experimental observation at LHC and simultaneous measurements of the modes $B_{s} \rightarrow \mu^{+} \mu^{−}$ and $B_{s} \rightarrow \mu^{+} \mu^{−} \gamma$ at LHC experiment will indicate the basic nature of the interaction at play. A simulation study has been performed to evaluate the potential of CMS detector to observe the more difficult mode of $B_{s} \rightarrow \mu^{+} \mu^{−} \gamma$. An upper limit of $2.08 \times 10^{−7}$ on the branching ratio is expected to be achieved corresponding to an integrated luminosity of 10 fb^-1.

Potential energy curves of various electronic states of CO$^{n+}$ ($0 \leq n \leq 6$) are generated at MRCI/CASSCF level using cc-pvQZ basis set and the results are compared with available experimental and theoretical data.

Using Lie algebraic techniques and simpler expressions of the matrix elements of Majorana and Casimir operators given by us, we obtain an effective Hamiltonian operator which conveniently describes stretching vibrations of biomolecules. For a copper tetramesityl porphyrin molecule, the higher excited vibrational levels are calculated by applying the $U (2)$ algebraic approach.

Thermal effects of a double-end-pumped cubic Nd:YVO₄ laser crystal are investigated in this paper. A detailed analysis of temperature distribution and thermal stress in cubic crystal with circular shape pumping is discussed. It has been shown that by considering the total input powers as constant, the double-end-pumped configurations with equal pump power can be considered as having a minimum thermal effect with respect to the other end-pumped configuration.

In this paper we investigate two-dimensional (2D) Rayleigh–B ́enard convection using direct numerical simulation in Boussinesq fluids with Prandtl number $P = 6.8$ confined between thermally conducting plates. We show through the simulation that in a small range of reduced Rayleigh number $r (770 < r < 890)$ the 2D rolls move chaotically in a direction normal to the roll axis. The lateral shift of the rolls may lead to a global flow reversal of the convective motion. The chaotic travelling rolls are observed in simulations with free-slip as well as no-slip boundary conditions on the velocity field. We show that the travelling rolls and the flow reversal are due to an interplay between the real and imaginary parts of the critical modes.

The dynamic structure factor $S(\mathbf{q}, \omega)$ of a harmonically trapped Bose gas has been calculated well above the Bose–Einstein condensation temperature by treating the gas cloud as a canonical ensemble of non-interacting classical particles. The static structure factor is found to vanish $\varpropto q^{2}$ in the long-wavelength limit. We also incorporate a relaxation mechanism phenomenologically by including a stochastic friction force to study $S(\mathbf{q}, \omega).$ A significant temperature dependence of the density fluctuation spectra is found. The Debye–Waller factor has been calculated for the trapped thermal cloud as a function of q and the number $\mathcal{N}$ of atoms. A substantial difference is found for small- and large-$\mathcal{N}$ clouds.

This paper describes the effect of 24 MeV proton irradiation on the electrical characteristics of a pnp bipolar junction transistor 2N 2905A. $I–V$, $C–V$ and DLTS measurements are carried out to characterize the transistor before and after irradiation. The properties of deep level defects observed in the bulk of the transistor are investigated by analysing the DLTS data. Two minority carrier levels, $E_{C} – 0.27$ eV and $E_{C} – 0.58$ eV and one majority carrier level, $E_{V} + 0.18$ eV are observed in the base collector junction of the transistor. The irradiated transistor is subjected to isochronal annealing. The influence of isochronal annealing on $I–V$, $C–V$ and DLTS characteristics are monitored. Most of the deep level defects seem to anneal out above $400^{\circ}$ C. It appears that the deep level defects generated in the bulk of the transistor lead to transistor gain degradation. A comparison of proton- and electron-induced gain degradation is made to assess the vulnerability of pnp transistor as against npn transistors.

We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical percolation threshold as a function of the ratio of sizes of discs, for different values of the relative areal densities of two discs, can be described in terms of a scaling function of only one variable. The recent accurate Monte Carlo estimates of critical threshold by Quintanilla and Ziff [Phys. Rev. E76, 051115 (2007)] are in very good agreement with the proposed scaling relation.

n exact diagonalization calculation of the t-J model on 2D square cluster has been studied for the ground state properties of HTSC. Effect of next-nearest-neighbour hopping and magnetic (both antiferromagnetic and ferromagnetic) interaction on $d_{x^{2} −y^{2}}$-wave pairing has been shown. Relative strength of the next-nearest-neighbour interaction with respect to that of near-neighbour interaction for the strongest $d_{x^{2} −y^{2}}$-wave pairing has been estimated. A schematic phase diagram is shown. It is shown that a two-sublattice model with antiferromagnetic interaction between them and a small intra-ferromagnetic-type interaction in one sublattice favours $d_{x^{2} −y^{2}}$-wave superconductivity and moderate negative type NNN hopping adds flavours to this phase.

KALI-1000 pulse power system has been used to generate single pulse nanosecond duration high-power microwaves (HPM) from a virtual cathode oscillator (VIRCATOR) device. HPM power measurements were carried out using a transmitting–receiving system in the presence of intense high frequency (a few MHz) electromagnetic noise. Initially, the diode detector output signal could not be recorded due to the high noise level persisting in the ambiance. It was found that the HPM pulse can be successfully detected using wide band antenna, RF cable and diode detector set-up in the presence of significant electromagnetic noise. Estimated microwave peak power was $\sim 59.8$ dBm ($\sim 1$ kW) at 7 m distance from the VIRCATOR window. Peak amplitude of the HPM signal varies on shot-to-shot basis. Duration of the HPM pulse (FWHM) also varies from 52 ns to 94 ns for different shots.

GaN and AlGaN epitaxial layers are grown by a metalorganic chemical vapour deposition (MOCVD) system. The crystalline quality of these epitaxially grown layers is studied by different characterization techniques. PL measurements indicate band edge emission peak at 363.8 nm and 312 nm for GaN and AlGaN layers respectively. High resolution XRD (HRXRD) peaks show FWHM of 272 and 296 arcsec for the (0 0 0 2) plane of GaN and GaN in GaN/AlGaN respectively. For GaN buffer layer, the Hall mobility is 346 cm²/V-s and carrier concentration is $4.5 \times 10^{16}$ /cm³. AFM studies on GaN buffer layer show a dislocation density of $2 \times 10^{8}$/cm² by wet etching in hot phosphoric acid. The refractive indices of GaN buffer layer on sapphire at 633 nm are 2.3544 and 2.1515 for TE and TM modes respectively.

A numerical study is presented to investigate the role of solitons in the electronic states of double-stranded DNA (dsDNA) molecule in the metal/DNA/metal system. Based on tight-binding Hamiltonian model and within the framework of a generalized Green’s function technique, we consider a ladder model for poly(dG)-poly(dC) DNA molecule containing M cells with four sites (two base pair sites and two backbone sites) in each cell. In the presence of a sublattice of solitons, our results show that the homogeneous soliton distributions induce the electronic states in the band gap of DNA molecule. In addition, the room temperature current–voltage characteristic of the system shows a linear and ohmic-like behaviour.

In this paper, we have provided an overview of cosmic ray effects on terrestrial processes such as electrical properties, global electric circuit, lightning, cloud formation, cloud coverage, atmospheric temperature, space weather phenomena, climate, etc. It is suggested that cosmic rays control short-term and long-term variations in climate. There are many basic phenomena which need further study and require new and long-term data set. Some of these have been pointed out.