On dynamics of velocity vector potential in incompressible fluids

An elegant quaternionic formulation is given for the Lagrangian advection equation for velocity vector potential in fluid dynamics. At first we study the topological significance of a restricted conserved quantity viz., stream-helicity and later more realistic configuration of open streamlines is figured out. Also, using Clebsch parameterisation of the velocity vector potential yet another physical significance for the stream-helicity is provided. Finally we give a Nambu-Poisson formalism of the Lagrangian advection equation for velocity vector potential.     

The Generalized Second Law of Thermodynamics of?the?Universe Bounded by the Event Horizon and?Modified Gravity Theories

In this paper, we investigate the validity of the generalized second law of thermodynamics of the universe bounded by the event horizon. Here we consider homogeneous and isotropic model of the universe filled with perfect fluid in one case and in another case holographic model of the universe has been considered. In the third case the matter in the universe is taken in the form of non-interacting two fluid system as holographic dark energy and dust. Here we study the above cases in the Modified gravity, f(R) gravity.     

Thermodynamics of Lema$$\hat{i}$$ tre−Tolman−Bondi Model

Here we consider our universe as inhomogeneous spherically symmetric Lema [^(i)]{\hat{i}} tre−Tolman−Bondi Model and analyze the thermodynamics of this model of the universe. The trapping horizon is calculated and is found to coincide with the apparent horizon. The Einstein field equations are shown to be equivalent with the unified first law of thermodynamics. Finally assuming the first law of thermodynamics validity of the generalized second law of thermodynamics is examined at the apparent horizon for the perfect fluid and at the event horizon for holographic dark energy.     

On the electron energy spectrum in heavily doped non-parabolic semiconductors

An attempt is made to present a simple theoretical analysis of the energy-wave vector dispersion relation of the conduction electrons in heavily doped non-parabolic semiconductors forming band tails. We observe that the complex energy spectrum in doped small-gap materials whose unperturbed conduction band is described by the three band model of Kane is due to the interaction of the impurity atoms in the tail with the spin-orbit splitting constant of the valence band (Δ), For band-gap (E_g)<Δ the imaginary part predominates which tails in to the conduction band. For the opposite inequality the real part comes in to play which tails in to the split-off band. In the absence of the band tailing effect, the imaginary part of the complex energy spectrum vanishes and the same is also true for doped two-band Kane-type and parabolic energy bands respectively. The present formulation helps us in investigating the Boltzmann transport equation dependent transport properties of degenerate semiconductors and are expected to agree better with experiments. The well-known results of unperturbed three and two band models of Kane together with wide-gap parabolic energy bands have been obtained as special cases of our generalized analysis under certain limiting conditions.     

Laser-induced forward transfer technique for maskless patterning of amorphous V2O5 thin film

A laser-induced forward transfer technique has been applied for the maskless patterning of amorphous V₂O₅ thin films. A sheet beam of a frequency doubled (SHG) Q-switched Nd:YAG laser was irradiated on a transparent glass substrate (donor), the rear surface of which was pre-coated with a vacuum-deposited V₂O₅ 180 nm thick film was either in direct contact with a second glass substrate (receiver) or a 0.14 mm air-gap was maintained between the donor film and the receiving substrate. Clear, regular stripe pattern of the laser-induced transferred film was obtained on the receiver. The pattern was characterized using X-ray diffraction (XRD), optical absorption spectroscopy, scanning electron microscopy (SEM), energy dispersive analysis of X-ray (EDAX), atomic force microscopy (AFM), etc.     

All-optical method of developing a phase encoded latch by using EDFA

Optics has already proved its meaningful application in information processing and computation, where the parallelism of light is exploited to achieve the desired result. In this communication a novel concept of all-optical memory unit based on phase encoding process is proposed. The unit is simple in architecture comprising phase sifters, mirrors (M′) and two blocks of Erbium doped fiber amplifier. The optical feedback is supported by use of beam splitters and mirrors. It is independent of intensity and therefore requires a small switching power and can work at a bit rate far above 100 Gb/s.     

Complex-scaling treatment for high-lying doubly excited resonances for screened Coulomb helium atom

This work presents an investigation on the doubly excited ¹S ^e autoionizing states of screened helium atom lying below the n = 4 threshold of the He⁺ ion. The potential generated in this system is represented by a Yukawa type potential. We have employed complex-coordinate rotation method, as it is a powerful scheme to study high lying resonances. Hylleraas type wave function is used to consider the correlation effect between all the charged particles. Our resonance parameters for the resonances lying below the He⁺ (n = 2) threshold agree well with those of the existing calculations by using the stabilization method. Resonances associated with higher thresholds are new calculations. All the present results are well converged with basis length N = 444.     

Ion beam synthesis of metal-quantum dots for photonic applications

Although electronics technologies have made great advances in device speed, optical devices can function in the time domain inaccessible to electronics. In the time domain less than 1 ps, optical devices have no competition. Photonic or optical devices are designed to switch and process light signals without converting them to electronic form. The major advantages that these devices offer are speed and preservation of bandwidth. The switching is accomplished through changes in refractive index of the material that are proportional to the light intensity. The third-order optical susceptibility, χ⁽³⁾, known as the optical Kerr susceptibility which is related to the non-linear part of the total refractive index, is the nonlinearity which provides this particular feature. Future opportunities in photonic switching and information processing will depend critically on the development of improved photonic materials with enhanced Kerr susceptibilities, as these materials are still in a relatively early stage of development. Different glass systems are now under investigation to increase their nonlinearity by introducing a variety of modifiers into the glass-network. Ion implantation is an attractive method for inducing colloid formation at a high local concentration unattainable by the melt-glass fabrication process and for confining the non-linearities to specific patterned regions in a variety of host matrices. Recent works on metal-ion implanted colloid generation in bulk fused silica glasses have shown that these nanocluster-glass composites under favourable circumstances have significant enhancement of χ⁽³⁾ with picosecond to femtosecond temporal responses.