• Volume 87, Issue 4

October 2016

• Various properties of the 0.6BaTiO$_3$–0.4Ni$_{0.5}$Zn$_{0.5}$Fe$_2$O$_4$ multiferroic nanocomposite

Structural, magnetic and ferroelectric properties of 0.6BaTiO$_3$–0.4(Ni$_{0.5}Zn$_{0.5}Fe$_2$O$_4$) multiferroic nanocomposite are presented here. The structural properties of the samples were studied by XRD and Raman spectroscopy which confirm the formation of BaTiO$_3$ (BTO) phase with a tetragonal perovskite structure and asmall secondary spinel phase due to the ferrite content. The magnetic and electric orderings were investigated by vibrating sample magnetometer (VSM) and ferroelectric ($P–E$) loop tracer at room temperature. The inceptionof ferroelectric properties is due to barium titanate. The remnant polarization increases ∼5 times for the composite with Ni$_{0.5}$Zn$_{0.5}$Fe$_2$O$_4$ (NZFO) substitution compared to BTO. The remnant polarization is conducive forswitching applications of multiferroic composite.

• The effect of concentration of H$_2$ physisorption on the current–voltage characteristic of armchair BN nanotubes in CNT–BNNT–CNT set

In this research, we have studied physisorption of hydrogen molecules on armchair boron nitride (BN) nanotube (3,3) using density functional methods and its effect on the current–voltage ($I–V$) characteristic of the nanotube as a function of concentration using Green’s function techniques. The adsorption geometries and energies, charge transfer and electron transport are calculated. It is found that H$_2$ physisorption can suppress the $I–V$ characteristic of the BN nanotube, but it has no effect on the band gap of the nanotube. As the H$_2$concentration increases, under the same applied bias voltage, the current through the BN nanotube first increases and then begins to decline. The current–voltage characteristic indicates that H$_2$ molecules can be detected by aBN-based sensor.

• Cylindrically symmetric cosmological model in the presence of bulk stress with varying $\Lambda$

Cylindrically symmetric non-static space–time is investigated in the presence of bulk stress given by Landau and Lifshitz. To get a solution, a supplementary condition between metric potentials is used. The viscosity coefficient of the bulk viscous fluid is assumed to be a power function of mass density whereas the coefficient of shear viscosity is considered as proportional to the scale of expansion in the model. Also some physical and geometrical properties of the model are discussed.

• Statistical model of stress corrosion cracking based on extended form of Dirichlet energy: Part 2

In the previous paper ({\it Pramana – J. Phys.} 81(6), 1009 (2013)), the mechanism of stress corrosion cracking (SCC) based on non-quadratic form of Dirichlet energy was proposed and its statistical features were discussed. Following those results, we discuss here how SCC propagates on pipe wall statistically. It reveals that SCC growth distribution is described with Cauchy problem of time-dependent first-order partial differential equation characterized by the convolution of the initial distribution of SCC over time. We also discuss the extension of the above results to the SCC in two-dimensional space and its statistical features with a simple example.

• Chaos in discrete fractional difference equations

Recently, the discrete fractional calculus (DFC) is receiving attention due to its potential applications in the mathematical modelling of real-world phenomena with memory effects. In the present paper, the chaotic behaviour of fractional difference equations for the tent map, Gauss map and 2x(mod 1) map are studied numerically. We analyse the chaotic behaviour of these fractional difference equations and compare them with their integer counterparts. It is observed that fractional difference equations for the Gauss and tent maps are more stable compared to their integer-order version.

• Optimal control of vibrational transitions of HCl

Control of fundamental and overtone transitions of a vibration are studied for the diatomic molecule, HCl. Specifically, the results of the effect of variation of the penalty factor on the physical attributes of the system (i.e., probabilities) and pulse (i.e., amplitudes) considering three different pulse durations for each value of the penalty factor are shown and discussed. We have employed the optimal control theory to obtain infrared pulses for selective vibrational transitions. The optimization of initial guess field with Gaussian envelope, phrased as maximization of cost functional, is done using the conjugate gradient method. The interaction of the field with the molecule is treated within the semiclassical dipole approximation. The potential and the dipole moment functions used in the calculations of control dynamics are obtained from high level ab-initio calculations.

• A note on analytical solutions of nonlinear fractional 2D heat equation with non-local integral terms

In this paper, we consider the (2+1) nonlinear fractional heat equation with non-local integral terms and investigate two different cases of such non-local integral terms. The first has to do with the time-dependent non-local integral term and the second is the space-dependent non-local integral term. Apart from the nonlinear nature of these formulations, the complexity due to the presence of the non-local integral terms impelled us to use a relatively new analytical technique called q-homotopy analysis method to obtain analytical solutions to both cases in the form of convergent series with easily computable components. Our numerical analysis enables us to show the effects of non-local terms and the fractional-order derivative on the solutions obtained by this method.

• Root mean square radii of heavy flavoured mesons in a quantum chromodynamics potential model

We report the results of root mean square (r.m.s.) radii of heavy flavoured mesons in a QCD model with the potential $V (r) = −(4\alpha_{s}/3r) + br + c$. As the potential is not analytically solvable, we first obtain the results in the absence of confinement and Coulomb terms respectively. Confinement and Coulomb effects are then introduced successively in the approach using the Dalgarno’s method of perturbation. We explicitly consider the following two quantum mechanical aspects in the analysis: (a) The scale factor $c$ in the potential should not effect the wave function of the system even while applying the perturbation theory. (b) Choice of perturbative piece of the Hamiltonian (confinement or linear) should determine the effective radial separation between the quarks and antiquarks. The results are then compared with the available theoretical values of r.m.s. radii.

• A generic travelling wave solution in dissipative laser cavity

A large family of cosh-Gaussian travelling wave solution of a complex Ginzburg–Landau equation (CGLE), that describes dissipative semiconductor laser cavity is derived. Using perturbation method, the stability region is identified. Bifurcation analysis is done by smoothly varying the cavity loss coefficient to provide insight of the system dynamics. He’s variational method is adopted to obtain the standard sech-type and the notso-explored but promising cosh-Gaussian type, travelling wave solutions. For a given set of system parameters, only one sech solution is obtained, whereas several distinct solution points are derived for cosh-Gaussian case. These solutions yield a wide variety of travelling wave profiles, namely Gaussian, near-sech, flat-top and a cosh-Gaussian with variable central dip. A split-step Fourier method and pseudospectral method have been used for direct numerical solution of the CGLE and travelling wave profiles identical to the analytical profiles have been obtained. We also identified the parametric zone that promises an extremely large family of cosh-Gaussian travelling wave solutions with tunable shape. This suggests that the cosh-Gaussian profile is quite generic and would be helpful for further theoretical as well as experimental investigation on pattern formation, pulse dynamics and localization in semiconductor laser cavity.

• Calculation of energy spectrum of $^{12}$C isotope with modified Yukawa potential by cluster models

In this paper, we have calculated the energy spectrum of 12C isotope in two-cluster models, $3\alpha$ cluster model and $^8$Be + $\alpha$ cluster model. We use the modified Yukawa potential for interaction between theclusters and solve the Schrödinger equation using Nikiforov–Uvarov method to calculate the energy spectrum. Then, we increase the accuracy by adding spin-orbit coupling and tensor force and solve them by perturbationtheory in both models. Finally, the calculated results for both models are compared with each other and with the experimental data. The results show that the isotope $^{12}$C should be considered as a three-$\alpha$ cluster and themodified Yukawa potential is adaptable for cluster interactions.

• Periodic solutions ofWick-type stochastic Korteweg–de Vries equations

Nonlinear stochastic partial differential equations have a wide range of applications in science and engineering. Finding exact solutions of the Wick-type stochastic equation will be helpful in the theories and numerical studies of such equations. In this paper, Kudrayshov method together with Hermite transform isimplemented to obtain exact solutions of Wick-type stochastic Korteweg–de Vries equation. Further, graphical illustrations in two- and three-dimensional plots of the obtained solutions depending on time and space are also given with white noise functionals.

• Synthesis, characterization and third-order nonlinear optical properties of polydiacetylene nanostructures, silver nanoparticles and polydiacetylene–silver nanocomposites

We have synthesized, characterized and studied the third-order nonlinear optical properties of two different nanostructures of polydiacetylene (PDA), PDA nanocrystals and PDA nanovesicles, along with silver nanoparticles-decorated PDA nanovesicles. The second molecular hyperpolarizability $\gamma (−\omega; \omega,−\omega,\omega$) of the samples has been investigated by antiresonant ring interferometric nonlinear spectroscopic (ARINS) technique using femtosecond mode-locked Ti:sapphire laser in the spectral range of 720–820 nm. The observed spectral dispersion of $\gamma$ has been explained in the framework of three-essential states model and a correlation between the electronic structure and optical nonlinearity of the samples has been established. The energy of two-photon state, transition dipole moments and linewidth of the transitions have been estimated. We have observed that the nonlinear optical properties of PDA nanocrystals and nanovesicles are different because of the influence of chain coupling effects facilitated by the chain packing geometry of the monomers. On the other hand, our investigation reveals that the spectral dispersion characteristic of $\gamma$ for silver nanoparticles-coated PDA nanovesicles is qualitatively similar to that observed for the uncoated PDA nanovesicles but bears no resemblance to that observed in silver nanoparticles. The presence of silver nanoparticles increases the $\gamma$ values of the coated nanovesicles slightly as compared to that of the uncoated nanovesicles, suggesting a definite but weak coupling between the free electrons of the metal nanoparticles and $\pi$ electrons of the polymer in the composite system. Our comparative studies show that the arrangement of polymer chains in polydiacetylene nanocrystals is more favourable for higher nonlinearity.

• Structural, morphological, optical and antibacterial activity of rod-shaped zinc oxide and manganese-doped zinc oxide nanoparticles

Pure ZnO and Mn-doped ZnO nanoparticles were synthesized by Co-precipitate method. The structural characterizations of the nanoparticles were investigated by X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques. UV–Vis, FTIR and photoluminescence (PL) spectroscopy were used for analysingthe optical properties of the nanoparticles. XRD results revealed the formation of ZnO and Mn-doped ZnO nanoparticles with wurtzite crystal structure having average crystalline size of 39 and 20 nm. From UV–Vis studies, the optical band-gap energy of 3.20 and 3.25 eV was obtained for ZnO and Mn-doped ZnO nanoparticles, respectively. FTIR spectra confirm the presence of ZnO and Mn-doped ZnO nanoparticles. Photoluminescence analysis of all samples showed four main emission bands: a strong UV emission band, a weak blue band, a weak blue–green band and a weak green band indicating their high structural and optical qualities. The antibacterial efficiency of ZnO and Mn-doped ZnO nanoparticles were studied using disc diffusion method. The Mn-dopedZnO nanoparticles show better antibacterial activity when higher doping level is 10 at% and has longer duration of time.

• Overlapping community detection using weighted consensus clustering

Many overlapping community detection algorithms have been proposed. Most of them are unstable and behave non-deterministically. In this paper, we use weighted consensus clustering for combining multiple base covers obtained by classic non-deterministic algorithms to improve the quality of the results. We first evaluate a reliability measure for each community in all base covers and assign a proportional weight to each one. Then we redefine the consensus matrix that takes into account not only the common membership of nodes, but also the reliability of the communities. Experimental results on both artificial and real-world networks show that our algorithm can find overlapping communities accurately.

• The classification of the single travelling wave solutions to the variant Boussinesq equations

The discrimination system for the polynomial method is applied to variant Boussinesq equations to classify single travelling wave solutions. In particular, we construct corresponding solutions to the concrete parameters to show that each solution in the classification can be realized.

• Bose gases in one-dimensional harmonic trap

Thermodynamic quantities, occupation numbers and their fluctuations of a one-dimensional Bose gas confined by a harmonic potential are studied using different ensemble approaches. Combining number theory methods, a new approach is presented to calculate the occupation numbers of different energy levels in microcanonical ensemble. The visible difference of the ground state occupation number in grand-canonical ensemble and microcanonical ensemble is found to decrease by power law as the number of particles increases.

• Relativistic quantum correlations in bipartite fermionic states

The influences of relative motion, the size of the wave packet and the average momentum of the particles on different types of correlations present in bipartite quantum states are investigated. In particular, the dynamics of the quantum mutual information, the classical correlation and the quantum discord on the spincorrelations of entangled fermions are studied. In the limit of small average momentum, regardless of the size of the wave packet and the rapidity, the classical and the quantum correlations are equally weighted. On the otherhand, in the limit of large average momentum, the only correlations that exist in the system are the quantum correlations. For every value of the average momentum, the quantum correlations maximize at an optimal size of the wave packet. It is shown that after reaching a minimum value, the revival of quantum discord occurs with increasing rapidity.

• Effects of thermal stratification on transient free convective flow of a nanofluid past a vertical plate

An analysis of thermal stratification in a transient free convection of nanofluids past an isothermal vertical plate is performed. Nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver having volume fraction of the nanoparticles less than or equal to 0.04 with water as the base fluid are considered. The governing boundary layer equations are solved numerically. Thermal stratification effects and volume fraction of the nanoparticles on the velocity and temperature are represented graphically. It is observed that an increase in the thermal stratification parameter decreases the velocity and temperature profiles of nanofluids. An increase in the volume fraction of the nanoparticles enhances the temperature and reduces the velocity of nanofluids. Also, the influence of thermal stratification parameter and the volume fraction of the nanoparticles of local as well as average skin friction and the rate of heat transfer of nanofluids are discussed and represented graphically.The results are found to be in good agreement with the existing results in literature.

• Homotopy deform method for reproducing kernel space for nonlinear boundary value problems

In this paper, the combination of homotopy deform method (HDM) and simplified reproducing kernel method (SRKM) is introduced for solving the boundary value problems (BVPs) of nonlinear differential equations. The solution methodology is based on Adomian decomposition and reproducing kernel method (RKM). By the HDM, the nonlinear equations can be converted into a series of linear BVPs. After that, the simplified reproducing kernel method, which not only facilitates the reproducing kernel but also avoids the time-consuming Schmidt orthogonalization process, is proposed to solve linear equations. Some numerical test problems including ordinary differential equations and partial differential equations are analysed to illustrate the procedure and confirm the performance of the proposed method. The results faithfully reveal that our algorithm is considerably accurate and effective as expected.

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