Electron Rydberg wave packets in one-dimensional atoms

An expression for the transition probability or form factor in one-dimensional Rydberg atom irradiated by short half-cycle pulse was constructed. In applicative contexts, our expression was found to be more useful than the corresponding result given by Landau and Lifshitz. Using the new expression for the form factor, the motion of a localized quantum wave packet was studied with particular emphasis on its revival and super-revival properties. Closed form analytical expressions were derived for expectation values of the position and momentum operators that characterized the widths of the position and momentum distributions. Transient phase-space localization of the wave packet produced by the application of a single impulsive kick was explicitly demonstrated. The undulation of the uncertainty product as a function of time was studied in order to visualize how the motion of the wave packet in its classical trajectory spreads throughout the orbit and the system becomes nonclassical. The process, however, repeats itself such that the atom undergoes a free evolution from a classical, to a nonclassical, and back to a classical state.     

Evolution of optical pulses in the presence of third-order dispersion

We model the propagation of femtosecond pulses through optical fibres by a nonlinear Schrödinger (NLS) equation involving a perturbing term arising due to third-order dispersion in the medium. The perturbative effect of this higher-order dispersion causes the usual NLS soliton to emit a radiation field. As a result, the given initial pulse propagating through the fibre exhibits nonsolitonic behaviour. We make use of a variational method to demonstrate how an initial pulse by the interaction with the emitted radiation can evolve into a soliton. We also demonstrate that the effect of interaction between the initial pulse and radiation field can be accounted for by including, in the evolution equation, terms associated with self-steepening and stimulated Raman scattering that characterize the optical medium.     

Effects of three-body atomic interaction and optical lattice on solitons in quasi-one-dimensional Bose-Einstein condensate

We make use of a coordinate-free approach to implement Vakhitov-Kolokolov criterion for stability analysis in order to study the effects of three-body atomic recombination and lattice potential on the matter-wave bright solitons formed in Bose-Einstein condensates. We analytically demonstrate that (i) the critical number of atoms in a stable BEC soliton is just half the number of atoms in a marginally stable Townes-like soliton and (ii) an additive optical lattice potential further reduces this number by a factor of √1 − bg ₃ with g ₃ the coupling constant of the lattice potential and b = 0.7301.      

Peroxovanadium-catalyzed oxidative esterification of aldehydes

The peroxovanadium species generated from V(2)O(5) and hydrogen peroxide, which is liberated from peroxy salts such as sodium perborate (SPB) or sodium percarbonate (SPC), transform aldehydes directly into esters in an alcoholic medium. Monoesters of diols have been achieved directly in one pot from aldehydes. High catalytic turnover number combined with inexpensive, easily available reagents and innocuous side products from the reaction make it a suitable alternative for the synthesis of esters from aldehydes.     

Relaxation in pure and seeded supersonic jets of SF6

Nozzle expansion of pure SF₆ and SF₆ seeded in carrier gases e.g. Ar, He and N₂, is used to study relaxation of the various degrees of freedom. The diode laser absorption spectrum of the Q branch of the ν₃ mode of SF₆ is used to derive the rotational temperature (T_rot). Time-of-flight studies determine the translational temperature (T_tg) while the vibrational temperature (T_vib) is estimated from the energy balance equation. Rotational and translational temperatures follow each other closely while the vibrational temperature lags behind considerably. The effective specific heat ratio (γ) and the collisional effectiveness parameter (e) for SF₆ are determined from these measurements. Seeded-beam data prove argon to be a better refrigerant than He or N₂. Cooling in seeded beams at moderate stagnation pressures is not substantially enhanced even at very high dilution.     

Phase-function method for velocity-dependent potentials

We have adapted the phase-function method for studying on- and off-shell properties of velocity-dependent potentials. The main result presented in this paper is an ansatz for the interpolatingT-matrix function (on- or off- the energy-shell as the case may). Based on this ansatz we have presented an efficient method for computing the off-shell extension function which plays a role in the theories of three particle system. We have demonstrated this by means of a model calculation.     

Scattering contributions to the internal partition function of a diatomic molecular system

An analytical expression for the phase shift contribution to the internal partition function for the Morse potential is derived by using an approximate Jost function. This function is shown to be a convergent sum. The numerical results obtained for H₂ and HCl show the partition function to be a monotonically increasing function of temperature. This observation agrees with the results of Rogers and co-workers. Work supported in part by the Department of Atomic Energy, Government of India.     

Korteweg-de Vries hierarchy using the method of base equations

A base-equation method is implemented to realize the hereditary algebra of the Korteweg-de Vries (KdV) hierarchy and the N-soliton manifold is reconstructed. The novelty of our approach is that, it can in a rather natural way, predict other nonlinear evolution equations which admit local conservation laws. Significantly enough, base functions themselves are found to provide a basis to regard the KdV-like equations as higher order degenerate bi-Lagrangian systems.     

Off-shell extension function from a generalised phase-function method

It is shown that the Combined-variable-phase-off-shell scattering theory or the generalised phase-function method provides efficient algorithms to calculate the off-shell extension function which plays a role in the theories of three-particle scattering. In order to assert this we have chosen to work with a model potential for theα-α interaction. The functions which occur in the context of our approach exhibit certain interesting features with regard to effect of the potential in producing on-and off-shell quantities like the phase shift and quasi-phase. Interpolating off-shell extension function is seen to exhibit a discontinuity where the phase function goes through a zero.     

Mechanical property evaluation of glass–jute fiber reinforced polymer composites

The natural fibers such as jute, coir, hemp, sisal etc. are randomly used as reinforcements for composite materials because of its various advantages such as low cost, low densities, low energy consumption over conventional fibers. In addition, they are renewable as well as biodegradable, and indeed wide varieties of fibers are locally available. In this study, glass–jute fiber reinforced polymer composite is fabricated, and the mechanical properties such as tensile, flexural and impact behavior are investigated. The materials selected for the studies were jute fiber and glass fiber as the reinforcement and epoxy resin as the matrix. The hand lay‐out technique was used to fabricate these composites. Fractured surface were comprehensively examined in scanning electron microscope (SEM) to determine the microscopic fracture mode. A numerical procedure based on the finite element method was then applied to evaluate the overall behavior of this composite using the experimentally applied load. Results showed that by incorporating the optimum amount of jute fibers, the overall strength of glass fiber reinforced composite can be increased and cost saving of more than 30% can be achieved. It can thus be inferred that jute fiber can be a very potential candidate in making of composites, especially for partial replacement of high‐cost glass fibers for low load bearing applications. Copyright © 2016 John Wiley & Sons, Ltd.