• Volume 72, Issue 6

June 2009,   pages  915-1062

• The auxiliary elliptic-like equation and the exp-function method

The auxiliary equation method is very useful for finding the exact solutions of the nonlinear evolution equations. In this paper, a new idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the auxiliary elliptic-like equation are derived using exp-function method, and then the exact solutions of the nonlinear evolution equations are derived with the aid of auxiliary elliptic-like equation. As examples, the RKL models, the high-order nonlinear Schrödinger equation, the Hamilton amplitude equation, the generalized Hirota–Satsuma coupled KdV system and the generalized ZK–BBM equation are investigated and the exact solutions are presented using this method.

• Role of asymmetries in the chaotic dynamics of the double-well Duffing oscillator

Duffing oscillator driven by a periodic force with three different forms of asymmetrical double-well potentials is considered. Three forms of asymmetry are introduced by varying the depth of the left-well alone, location of the minimum of the left-well alone and above both the potentials. Applying the Melnikov method, the threshold condition for the occurrence of horseshoe chaos is obtained. The parameter space has regions where transverse intersections of stable and unstable parts of left-well homoclinic orbits alone and right-well orbits alone occur which are not found in the symmetrical system. The analytical predictions are verified by numerical simulation. For a certain range of values of the control parameters there is no attractor in the left-well or in the right-well.

• 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.

• Theoretical studies of mutual diffusivities and surface properties in Cd–Ga liquid alloys

The mutual diffusion coefficients, activation energy for diffusion, surface concentration and surface tension of the liquid Cd–Ga alloys have been calculated throughout the concentration range using energetics obtained from the theoretical model fits of the experimental thermodynamic data. Our calculations show that Cd–Ga liquid alloys showed immiscibility at a temperature of 723 K between 0.4 and 0.5 atomic fraction of Cd. Within this concentration region and temperature, the mutual diffusion coefficients approached zero values and the activation energy for diffusion reached high peak values of 220 J/mol. It was also observed that within the region of immscibility, the diffusion coefficients do not obey Arrhenius relation over a wide range of temperature.

• The corrections to scaling within Mazenko's theory in the limit of low and high dimensions

We consider corrections to scaling within an approximate theory developed by Mazenko for nonconserved order parameter in the limit of low $(d \rightarrow 1)$ and high $(d \rightarrow \infty)$ dimensions. The corrections to scaling considered here follows from the departures of the initial condition from the scaling morphology. Including corrections to scaling, the equal time correlation function has the form: $C(r, t) = f_{0} (r/L) + L^{−\omega} f_{1} (r/L) + \cdots$, where 𝐿 is a characteristic length scale (i.e. domain size). The correction-to-scaling exponent ω and the correction-to-scaling functions $f_{1}(x)$ are calculated for both low and high dimensions. In both dimensions the value of ω is found to be ω = 4 similar to 1D Glauber model and OJK theory (the theory developed by Ohta, Jasnow and Kawasaki).

• Studies of the 𝑔 factors and the superhyperfine parameters for Ni3+ in the fluoroperovskites

The 𝑔 factors and the ligand superhyperfine parameters $A'$ and $B'$ for Ni3+ in KMgF3, CsCaF3 and RbCaF3 are theoretically studied from the formulas of these parameters for a 3d7 ion under octahedral environments in the weak field scheme. The unpaired spin densities for the fluorine 2s, 2p$_{\sigma}$ and 2p$_{\pi}$ orbitals are quantitatively determined from the molecular orbital and configuration interaction coefficients based on the cluster approach. The calculated results show good agreement with the experimental data, based on only one adjustable parameter (i.e., the proportionality factor 𝜌 related to the ligand s- and p-orbitals). The superhyperfine parameters for the axial and planar ligands in RbCaF3:Ni3+ are satisfactorily interpreted from the different impurity–ligand distances due to the elongation of the ligand octahedron during cubic-to-tetragonal phase transition.

• A-site substitution-controlled dielectric dispersion in lead-free sodium bismuth titanate

Effect of doping in Na0.5Bi0.5Ti$_{O3}$ (NBT) with Ce3+ and Sm3+ at the A-site on dielectric behaviour, impedance and conductivity is being reported. Na0.5Bi$_{0.5−x}𝐴_{x}$TiO3 samples (A being Ce and Sm) are studied with varying values of 𝑥. For Na0.5Bi$_{0.5−x}$Ce$_{x}$TiO3 samples 𝑥 is 0.001, 0.005 and 0.007 and for Na0.5Bi$_{0.5−x}$Sm$_{x}$TiO3 samples 𝑥 is 0.05, 0.1 and 0.15. Dielectric constant and loss are studied in the frequency range 10 kHz to 1 MHz and in the temperature range $30–650^{\circ}$C. Impedance and electric modulus studies are undertaken. The relaxations observed in the samples are non-Debye and activation energies for relaxation and conduction are evaluated.

• Dielectric properties of CdS nanoparticles synthesized by soft chemical route

CdS nanoparticles have been synthesized by a chemical reaction route using thiophenol as a capping agent. The frequency-dependent dielectric dispersion of cadmium sulphide (CdS) is investigated in the temperature range of 303–413 K and in a frequency range of 50 Hz–1 MHz by impedance spectroscopy. An analysis of the complex permittivity ($\varepsilon'$ and $\varepsilon''$ ) and loss tangent ($\tan \delta) with frequency is performed by assuming a distribution of relaxation times. The scaling behaviour of dielectric loss spectra suggests that the relaxation describes the same mechanism at various temperatures. The frequency-dependent electrical data are analysed in the framework of conductivity and modulus formalisms. The frequency-dependent conductivity spectra obey the power law. • Simulation of reflectivity spectrum for non-absorbing multilayer optical thin films Reflectivity simulation is an essential tool for the design and optimization of optical thin films. We have developed a reflectivity simulator for non-absorbing dielectric multilayer optical thin films using LabVIEW. The name of the substrate material as well as the material and thickness of each layer of the multilayer stack are fed into the program as input parameters in a pop-up window. The program calculates reflectivity spectrum for the given range of wavelengths using layer thicknesses and dispersion data of refractive indices for the defined stack of dielectric materials. The simulated reflectivity spectra for various combinations of materials in multilayer stacks are presented and compared with the experimental results of the multilayer optical thin films grown by electron-beam evaporation technique. • Transport properties of poly(GACT)–poly(CTGA) deoxyribonucleic acid: A ladder model approach In this paper, based on the tight-binding Hamiltonian model and within the framework of a generalized Green's function technique, the electronic conduction through the poly(GACT)–poly(CTGA) DNA molecule in SWNT/DNA/SWNT structure has been numerically investigated. In a ladder model, we consider DNA as a planar molecule containing 𝑀 cells and four further sites (two base pair sites and two backbone sites) in each cell, sandwiched between two semi-infinite single-walled carbon nanotubes (SWNT) as the electrodes. Having relied on Landauer formalism, we focussed on studying the current–voltage characteristics of DNA, the effect of the coupling strength of SWNT/DNA interface and the role of tube radius of nanotube contacts on the electronic transmission through the foregoing structure. Finally, a characteristic time was calculated for the electron transmission, which measures the delay caused by the tunnelling through the SWNT/DNA interface. The results clearly show that the calculated characteristic time and also the conductance of the system are sensitive to the coupling strength between DNA molecule and nanotube contacts. • Coupling between drainage and coarsening in wet foam Drainage and coarsening are two coupled phenomena during the evolution of wet foam. We show the variation in the growth rate of bubble size, along the height in a column of Gillette shaving foam, by microscope imaging. Simultaneously, the drainage of liquid at the same heights has been investigated by Raman spectroscopic measurements. The observations made in these two sets of experiments indicate the coupling between drainage and coarsening in wet foam. We could explain the correlation between our observed data on drainage and coarsening by the empirical relation, proposed by others, in the literature. • Phonon dispersion relation of liquid metals The phonon dispersion curves of some liquid metals, viz. Na$(Z = 1)$, Mg$(Z = 2)$, Al$(Z = 3)$and Pb$(Z = 4)\$, have been computed using our model potential. The charged hard sphere (CHS) reference system is applied to describe the structural information. Our model potential along with CHS reference system is capable of explaining the phonon dispersion relation for monovalent, divalent, trivalent and tetravalent liquid metals.

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