Volume 67, Issue 12

In the present study, we deal with the momentum and heat transfer analysis in a horizontal annulus of a composite porous medium. The Darcy-Brinkman model is used to develop the governing equations for the flow and heat transfer phenomenon. The annulus injects the time dependent oscillatory velocity normal to its surface. Both the regions of the flow have their own viscosities, and the heat transfer analysis is carried out by retaining viscous dissipation. The governing equations for flow and heat transfer are solved analytically using a perturbation series for solutions in both regions of the annulus. A brief parametric analysis is performed for the velocity and the temperature profiles through graphs.

In this paper, a new numerical algorithm is introduced to solve the Blasius equation, which is a third-order nonlinear ordinary differential equation arising in the problem of two-dimensional steady state laminar viscous flow over a semi-infinite flat plate. The proposed approach is based on the first kind of Bessel functions collocation method. The first kind of Bessel function is an infinite series, defined on ℝ and is convergent for any x ∊ℝ. In this work, we solve the problem on semi-infinite domain without any domain truncation, variable transformation basis functions or transformation of the domain of the problem to a finite domain. This method reduces the solution of a nonlinear problem to the solution of a system of nonlinear algebraic equations. To illustrate the reliability of this method, we compare the numerical results of the present method with some well-known results in order to show the applicability and efficiency of our method.

This article aims at preferring a new and viable algorithm, specifically a two-step homotopy perturbation transform algorithm (TSHPTA). This novel technique is a feasible way in finding exact solutions with a small amount of calculations. As a simple but typical example, it demonstrates the strength and the great potential of the two-step homotopy perturbation transform method to solve nonlinear Volterra-type integral equations efficiently. The results reveal that the proposed scheme is suitable for the nonlinear Volterra equations.

Metal matrix nanocomposites reinforced with carbon nanotubes (CNTs) have become popular in industrial applications. Due to their excellent thermophysical and mechanical properties, CNTs are considered as attractive filler for the improvement in properties of metals. In the present work, we have synthesized noncovalently functionalized CNT reinforced nanosilver composites by using a modified molecular level mixing method. The structure and morphology of nanocomposites are characterized by X-ray diffraction, scanning electron microscopy, transmission electron microscopy, and energy dispersive spectroscopy. The electrical conductivity of silver-CNT nanocomposites measured by the four-point probe method is found to be more than that of the pure nanosilver. The significant improvement in electrical conductivity of Ag=CNT nanocomposites stems from homogenous and embedded distribution of CNTs in a silver matrix with intact structure resulting from noncovalent functionalization. The low temperature sintering also enhances the electrical conductivity of Ag=CNT nanocomposites.

Dufour and Soret effects on the convection in a horizontal layer of Rivlin-Ericksen elastico- viscous fluid in porous medium are considered. For the porous medium, the Darcy model is used. A linear stability analysis based upon normal mode analysis is employed to find a solution of the fluid layer confined between two free boundaries. The onset criterion for stationary and oscillatory convection has been derived analytically, and graphs have been plotted, giving various numerical values to various parameters, to depict the stability characteristics. The effects of the Dufour parameter, Soret parameter, solutal Rayleigh number, and Lewis number on stationary convection have been investigated.

The existence theory for the vector valued stochastic differential equations under G-Brownian motion (G-SDEs) of the type X t = X 0 + ∫ t o (v;X v )dv+ ∫ t 0 g(v;X v )d(B) v + ∫ t 0 h(v;X v )dB v ; t ∊ [0;T]; with first two discontinuous coefficients is established. It is shown that the G-SDEs have more than one solution if the coefficient g or the coefficients f and g simultaneously, are discontinuous functions. The upper and lower solutions method is used and examples are given to explain the theory and its importance.

In this note, the Carathéodory approximation scheme for vector valued stochastic differential equations under G-Brownian motion (G-SDEs) is introduced. It is shown that the Carathéodory approximate solutions converge to the unique solution of the G-SDEs. The existence and uniqueness theorem for G-SDEs is established by using the stated method.

In this work, we develop an imperceptible watermarking technique for images that employ substitution boxes constructed over Galois field GF(2 4 ). The strength of the proposed substitution box (S-box) is analyzed and its suitability is investigated for watermarking applications by applying statistical methods, which include entropy, contrast, correlation, energy, homogeneity, mean of absolute deviation (MAD), mean square error (MSE), peak-to-peak signal to noise ratio (PSNR), and structural similarity (SSIM) paradigm analysis. The application of the proposed S-box is presented for embedding copyright information in images.

The pulse propagation in the picosecond or femtosecond regime of birefringent optical fibers is governed by the coupled mixed derivative nonlinear Schr¨odinger (CMDNLS) equations. A new type of Lax pair associated with such coupled equations is derived from the Wadati-Konno-Ichikawa spectral problem. The Darboux transformation method is applied to this integrable model, and the N-times iteration formula of the Darboux transformation is presented in terms of the compact determinant representation. Starting from the zero potential, the bright vector N-soliton solution of CMDNLS equations is expressed as a compact determinant by N complex eigenvalues and N linearly independent eigenfunctions. The collision mechanisms in two components shows that bright vector solitons can exhibit the standard elastic and inelastic collisions. Such energy-exchange collision behaviours have potential applications in the construction of logical gates, the design of fiber directional couplers, and quantum information processors.

Considering a periodically oscillating harmonic potential, we explored the dynamic properties of bright solitons in a Bose-Einstein condensate by using Darboux transformation. It is found that the soliton movement exhibits a nonperiodic oscillation under a slow oscillating potential, while it is hardly affected under a fast oscillating potential. Furthermore, the head-on and/or ‘chase’ collisions of two solitons have been obtained, which could be controlled by the oscillation frequency of the potential.

The geometrical structures, relative stabilities, electronic and magnetic properties of Au n Ir 2 (n = 1 - 7) clusters have been systematically investigated by using meta-generalized gradient approximation (meta-GGA) Tao-Perdew-Staroverov-Scuseria (TPSS) functional in comparison with pure gold clusters. The optimized geometries show that the two doping iridium atoms can affect the structure of the host cluster. Compared with the pure Au n+2 clusters, the lowest energy Au n Ir 2 (n=1 - 7) clusters favour higher spin multiplicity except for Au 7 Ir 2 . Furthermore, the calculated binding energies, fragmentation energies, second-order difference energies, and the highest occupied-lowest unoccupied energy gaps indicate that the stability of Au n Ir 2 is enhanced. Natural population analysis reveals that the charges transfer from the Au n frames to the iridium atoms for Au 3;4;6;7 Ir 2 clusters. In addition, charges and magnetic moments of 6s, 5d, and 6p states for the iridium atoms in Au n Ir 2 (n = 1 - 7) clusters are also analyzed and compared.