• Volume 78, Issue 4

April 2012,   pages  499-665

• New exact solutions to the generalized KdV equation with generalized evolution

In this paper, by using a transformation and an application of Fan subequation, we study a class of generalized Korteweg–de Vries (KdV) equation with generalized evolution. As a result, more types of exact solutions to the generalized KdV equation with generalized evolution are obtained, which include more general single-hump solitons, multihump solitons, kink solutions and Jacobian elliptic function solutions with double periods.

• Exact solutions of some physical models using the ($G'/G$)-expansion method

The ($G'/G$)-expansion method and its simpliﬁed version are used to obtain generalized travelling wave solutions of ﬁve nonlinear evolution equations (NLEEs) of physical importance, viz. the ($2+1$)-dimensional Maccari system, the Pochhammer–Chree equation, the Newell–Whitehead equation, the Fitzhugh–Nagumo equation and the Burger–Fisher equation. A variety of special solutions like periodic, kink–antikink solitons, bell-type solitons etc. can easily be derived from the general results. Three-dimensional proﬁle plots of some of the solutions are also drawn.

• Energy–momentum localization for Bianchi type-IV Universe in general relativity and teleparallel gravity

In this study we have investigated the energy–momentum distributions for homogeneous and anisotropic Bianchi type-IV in B class Universe. For this purpose, we have used energy–momentum complexes of Einstein, Bergmann–Thomson, Landau–Lifshitz (LL), Papapetrou, Tolman and Møller in general relativity (GR) as also Einstein, Bergmann–Thomson, Landau–Lifshitz and Møller in teleparallel gravity (TG). From the obtained results we have found that Einstein and Bergmann–Thomson distributions are exactly giving the same results in GR and TG but the Landau–Lifshitz, Papapetrou Tolman and Møller energy–momentum distributions do not provide the same results with Einstein and Bergmann–Thomson in GR and TG. Furthermore, Einstein, Bergmann–Thomson and LL results are the same in different gravitation theories and we get that both GR and TG are equivalent theories for these prescriptions. From the obtained solutions, we could say that these are equivalent theories. Also, Møller energy–momentum distributions do not give the same results in GR and TG. However, we have found that all energy prescriptions are negative and our results agree with Nester et al.

• Nonlinear fractional relaxation

We deﬁne a nonlinear model for fractional relaxation phenomena. We use 𝜖-expansion method to analyse this model. By studying the fundamental solutions of this model we ﬁnd that when $t \to 0$ the model exhibits a fast decay rate and when $t \to \infty$ the model exhibits a power-law decay. By analysing the frequency response we ﬁnd a logarithmic enhancement for the relative ratio of susceptibility.

• Isgur–Wise function in a quantum chromodynamicsinspired potential model with conﬁnement as parent in the variationally improved perturbation theory

We have recently reported the calculation of slope and curvature of Isgur–Wise function based on variationally improved perturbation theory (VIPT) in a quantum chromodynamics (QCD)-inspired potential model. In that work, Coulombic potential was taken as the parent while the linear one as the perturbation. In this work, we choose the linear one as the parent with Coulombic one as the perturbation and see the consequences.

• Design of a superconducting low beta niobium resonator

The proposed high current injector for the superconducting Linac at the InterUniversity Accelerator Centre will have several accelerating structures, including a superconducting module which will contain low beta niobium resonators. A prototype resonator for the low beta module has been designed. The resonator has been carefully modelled to optimize the electromagnetic parameters. In order to validate them, a room-temperature copper model has been built and tested. In this paper we present details of the electromagnetic design of the low beta resonator, brieﬂy discuss the mechanical and engineering design, and present results from the measurements on the room-temperature copper model.

• Magnetic ﬁeld modulation spectroscopy of rubidium atoms

The magnetically modulated saturation absorption proﬁle is studied for a wide range of external DC magnetic ﬁeld. The salient features of Doppler-free signal generated by laser frequency modulation and atomic energy level modulation are compared. The DC offset of the signal proﬁle is found to be unstable as the external DC magnetic ﬁeld is changed. The technical difﬁculty of tuning laser frequency under locked condition over a large frequency span is discussed along with possible solutions.

• Light squeezing in optical parametric ampliﬁcation beyond the slowly-varying amplitude approximation

Optical parametric ampliﬁcation (OPA) described usually by the coupled-wave equations with the ﬁrst-order derivatives of the signal and idler waves, is solved under the slowly-varying amplitude approximation (SVA). In this article, by keeping the second-order derivatives in the coupled-wave equations, we obtained an analytical solution for the output signal and idler waves up to the ﬁrst order of $(\kappa/k)^1$; the ratio of coupling constant to the wave number. Furthermore, here the signal and the idler waves are distinguished only by their polarizations with the same frequency. Light squeezing is observed in normally ordered variances of the two quadrature operators of the output combined mode when plotted against $\kappa L$, where 𝜅 is the coupling constant and 𝐿 the interaction length. The variances have different signs for a range of values of $\kappa L$ and their variations are in opposite directions. We also show that this property is strongly dependent on the relative refractive index of the medium (𝑛). It is worth mentioning that the relative index dependency is not an explicit feature in squeezing of OPA under SVA approximation. Furthermore, the squeezing vanishes when $n \to 1$ and $\kappa /k \to 0$.

• Three-dimensional simulation of laser–plasma-based electron acceleration

A sequential three-dimensional (3D) particle-in-cell simulation code PICPSI-3D with a user friendly graphical user interface (GUI) has been developed and used to study the interaction of plasma with ultrahigh intensity laser radiation. A case study of laser–plasma-based electron acceleration has been carried out to assess the performance of this code. Simulations have been performed for a Gaussian laser beam of peak intensity $5 \times 10^{19}$ W/cm2 propagating through an underdense plasma of uniform density $1 \times 10^{19}$ cm-3, and for a Gaussian laser beam of peak intensity $1.5 \times 10^{19}$ W/cm2 propagating through an underdense plasma of uniform density $3.5 \times 10^{19}$ cm-3. The electron energy spectrum has been evaluated at different time-steps during the propagation of the laser beam. When the plasma density is $1 \times 10^{19}$ cm-3, simulations show that the electron energy spectrum forms a monoenergetic peak at $\sim 14$ MeV, with an energy spread of $\pm 7$ MeV. On the other hand, when the plasma density is $3.5 \times 10^{19}$ cm-3, simulations show that the electron energy spectrum forms a monoenergetic peak at $\sim 23$ MeV, with an energy spread of $\pm 7.5$ MeV.

• Determination of the optimal parameters for the fabrication of ZnO thin ﬁlms prepared by spray pyrolysis method

In this work, ZnO thin ﬁlms have been prepared by spray pyrolysis deposition method on the glass substrates. The effect of deposition parameters, such as deposition rate, substrate temperature and solution volume has been studied by X-ray diffraction (XRD) method, UV–Vis–NIR spectroscopy, scanning electron microscopy (SEM), and electrical measurements. The XRD patterns indicate polycrystalline wurtzite structure with preferred direction along (0 0 2) planes. Thin ﬁlms have transparency around 90% in the visible range. The optical band gap was determined at 3.27 eV which did not change signiﬁcantly. Evolution of electrical results containing the carriers' density, sheet resistance and resistivity are in agreement with structural results. All the results suggest the best deposition parameters are: deposition rate, $R = 3$ ml/min, substrate temperature, $T_s = 450^\circ$C and thickness of the thin ﬁlms $t = 110–130$ nm.

• Thermal conductivity of large-grain niobium and its effect on trapped vortices in the temperature range 1.8–5 K

Experimental investigation of the thermal conductivity of large grain and its dependence on the trapped vortices in parallel magnetic ﬁeld with respect to the temperature gradient $\nabla T$ was carried out on four large-grain niobium samples from four different ingots. The zero-ﬁeld thermal conductivity measurements are in good agreement with the measurements based on the theory of Bardeen–Rickayzen–Tewordt (BRT). The change in thermal conductivity with trapped vortices is analysed with the ﬁeld dependence of the conductivity results of Vinen et al for low inductions and low-temperature situation. Finally, the dependence of thermal conductivity on the applied magnetic ﬁeld in the vicinity of the upper critical ﬁeld $H_{c2}$ is ﬁtted with the theory of pure type-II superconductor of Houghton and Maki. Initial remnant magnetization in the sample shows a departure from the Houghton–Maki curve whereas the sample with zero trapped ﬂux qualitatively agrees with the theory. A qualitative discussion is presented explaining the reason for such deviation from the theory. It has also been observed that if the sample with the trapped vortices is cycled through $T_c$, the subsequent measurement of the thermal conductivity coincides with the zero trapped ﬂux results.

• String cosmology in LRS Bianchi type-II dusty Universe with time-decaying vacuum energy density 𝛬

A model of a cloud formed by massive strings is used as a source of LRS Bianchi type-II with time-decaying vacuum energy density 𝛬. To construct string cosmological models, we have used the energy–momentum tensor for such strings as formulated by Letelier (1983). The high nonlinear ﬁeld equations have been solved for two types of strings: (i) massive string and (ii) Nambu string. The expansion 𝜃 in the model is assumed to be proportional to the shear 𝜎. This condition leads to $A = \beta B^m$, where 𝐴 and 𝐵 are the metric coefﬁcients, 𝑚 is a constant and 𝛽 is an integrating constant. Our models are in accelerating phase which is consistent with the recent observations of supernovae type-Ia. The physical and geometrical behaviour of these models are also discussed.

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