Band 64, Heft 9-10

An analysis has been carried out for flow and heat transfer characteristics in a third grade fluid between two porous plates. The electrically conducting fluid fills the porous medium. The solutions have been developed for small porosity and magnetic field. Three flow problems are investigated and analytical expressions for the velocity field and temperature distribution are given for each case. Moreover, we recover and extend the results of Siddiqui et al. [1] by presenting exact solutions for the governing equations derived in [1].

With the aid of symbolic computation and the extended F-expansion method, we construct more general types of exact non-travelling wave solutions of the (2+1)-dimensional dispersive long wave system. These solutions include single and combined Jacobi elliptic function solutions, rational solutions, hyperbolic function solutions, and trigonometric function solutions.

The effects of variable viscosity on the flow and heat transfer in a thin film flow for a third grade fluid has been discussed. The thin film is considered on the outer side of an infinitely long vertical cylinder. The governing nonlinear differential equations of momentum and energy are solved analytically by using homotopy analysis method. The expression for the viscous dissipation and entropy generation are also defined. The graphical results are presented for various physical parameters appearing in the problem

In the present analysis, we have modeled the governing equations of a two dimensional hyperbolic tangent fluid model. Using the assumption of long wavelength and low Reynolds number, the governing equations of hyperbolic tangent fluid for an asymmetric channel have been solved using the regular perturbation method. The expression for pressure rise has been calculated using numerical integrations. At the end, various physical parameters have been shown pictorially. It is found that the narrow part of the channel requires a large pressure gradient, also in the narrow part the pressure gradient decreases with the increase in Weissenberg number We and channel width d.

In this paper, an iterative numerical solution of the higher-dimensional (3+1) physically important nonlinear evolutionary equations is studied by using the homotopy perturbation method (HPM). For this purpose, the Kadomstev-Petviashvili (KP) and the Jumbo-Miwa (JM) equations are analyzed with the HPM and the available exact solutions obtained by the homogenous balance method will be compared to show the accuracy of the proposed numerical algorithm. The results approves the effectiveness and accuracy of the HPM.

An analysis has been carried out to obtain the series solution of boundary layer flow of a micropolar fluid towards a shrinking sheet. The governing equations of micropolar fluid are simplified using suitable similarity transformations and then solved by homotopy analysis method (HAM). The convergence of the HAM solutions has been obtained by using homotopy-pade approximation. The effects of various parameters such as porosity parameter R, the ratio λ and the microinertia K on the velocity and microinertia profiles as well as local skin friction coefficient are presented graphically and in tabulated form.

The main objective of this article is to present a reliable algorithm to determine exact and approximate solutions of the generalized Emden-Fowler type equations. The algorithm mainly is based on He’s variational iteration method (VIM) with an alternative framework designed to overcome the difficulty of the regular singular point at x = 0. In this method, general Lagrange multipliers are introduced to construct a correction for the problem. The multipliers in the functional can be identified optimally via the variational theory. The results reveal that the proposed method is very effective and can be applied for other nonlinear problems.

The influence of temperature dependent viscosity on the flow of a third grade fluid between two coaxial cylinders is carried out. The heat transfer analysis is further analyzed. Homotopy analysis method is employed in finding the series solutions. The effects of pertinent parameters have been explored by plotting graphs.

By means of the generalized direct method, we investigate the (2+1)-dimensional dispersive long wave equations. A relationship is constructed between the new solutions and the old ones and we obtain the full symmetry group of the (2+1)-dimensional dispersive long wave equations, which includes the Lie point symmetry group S and the discrete groups D . Some new forms of solutions are obtained by selecting the form of the arbitrary functions, based on their relationship. We also find an infinite number of conservation laws of the (2+1)-dimensional dispersive long wave equations.

A generalization of He’s Exp-function method for nonlinear equations is introduced in this research. New exact solutions are obtained for Burgers equation

A new technique, the extended ansatz function method, is proposed to seek periodic solitary wave solutions of integrable systems. Exact periodic solitary wave solutions for the (2+1)-dimensional Korteweg-de Vries (KdV) equation are obtained by using this technique. By using the trial function method, Jacobi elliptic function double periodic solutions are also constructed for this equation. This result shows that there exist periodic solitary waves in the different directions for the (2+1)- dimensional KdV equation

The Newcomb-Benford law, also known as Benford’s law or the first-digit law, applies to many tabulated sets of real-world data. It states that the probability that the first significant digit is n, (n ∈ {1,2,3,4,5,6,7,8,9}) is given by log(1+ 1/n). The law has been verified empirically with widely differing data sets. In the present paper it is shown that it does not necessarily follow from the requirement of scale invariance alone, as has been claimed. This condition is necessary, but not sufficient. In addition, it is necessary to consider the properties of certain finite subsets of the set of rational numbers.

A possibility to excite the spin-3/2 quadrupolar nuclei in sites with a non-zero asymmetry parameter of the electric field gradient (EFG) tensor by means of an elliptically polarized radio frequency (RF) magnetic fields is discussed. Closed analytical formulas for the intensities of nuclear quadrupole resonance (NQR) nutation spectra and nutation frequencies of powder samples were obtained. Characteristic singularities in the nutation spectra were determined which allow the measurement of the asymmetry parameter η. It was found that in the general case of η ≠ 0 the excitation of the nuclear spins in + m and −m states by using the circularly polarized RF fields is not fully selective. Keywords Nuclear Quadrupole Resonance; Elliptically Polarized RF Field; Electric Field Gradient Tensor; Asymmetry Parameter

Theoretical investigation of the polaron effects on the third-order susceptibility associated with the intersubband transition in the conduction band in a CdSe/ZnS quantum dot quantum well is presented. Contributions from the confined longitudinal optical (LO) and surface optical phonon modes are considered and the wave function is derived under the frame work of the perturbation theory. We carried a detailed calculation of third-harmonic generation (THG), Quadratic electro-optic effects (QEOE), and electro-absorption (EA) process on such a quantum dot as a function of pump photon energy with different incident photon energy and under different sizes. The results reveal that the polaron effects are quite important especially around the peak value of the third-order susceptibility. By increasing the size of the quantum dots, the peaks of χ (3) THG , χ (3) QEOE , and χ (3) EA will shift to the lower energy, and the intensities of the peaks will increase.

We have explored photovoltaic (PV) reponse for the pyrazoloquinoline and pyrazoloquinoxaline dyes incorporated into the poly(3-decylthiophene) (PDT) polymer matrices. The photovoltaic response correlates generally with the enhancement of the state dipole moments. Generally we have shown that enhanced state dipole moments lead to an increase of the open circuit voltage. The surrounded polymer matrix of the polythiophene enhances the ground state dipole moments and its relative changes are decreased with the increase of the particular state dipole moments. An appearance of the three-phenyl backside groups substantially diminishes the effect.

By introducing the generalized Jacobi elliptic function, a new improved Jacobi elliptic function method is used to construct the exact travelling wave solutions of the nonlinear partial differential equations in a unified way. With the help of the improved Jacobi elliptic function method and symbolic computation, some new exact solutions of the combined Korteweg-de Vries-modified Korteweg-de Vries (KdV-mKdV) equation are obtained. Based on the derived solution, we investigate the evolution of doubly periodic and solitons in the background waves. Also, their structures are further discussed graphically.

A new method of obtaining approximate analytical expressions of zero-field splitting (ZFS) has been proposed. By analyzing the magnetic interaction mechanisms which affect the properties of ZFS of ground 4 A 2 state for 3d 3 ions at trigonal symmetry, and comparing with the calculated results of complete diagonalization method, the approximate analytical expressions of the contribution to zero-field splitting of 4 A 2 state from spin-spin (SS), spin-other-orbit (SOO), and combined mechanisms have been obtained. Also the applicability of these approximate analytical expressions has been analyzed. It is shown that the approximate analytical expressions are suitable in a wide crystal field parameters range.

The feasibility of fixing linear poly(vinyl amine) (PVAm) onto the surface of a poly(ethylene terephthalate) (PET) foil is shown. Pretreatment of the PET foil for PVAm anchoring is UV irradiation generated by an excimer lamp (λ = 222 nm). Thereby newly formed COOH-groups are able to build up in situ an ionic double layer with PVAm by proton transfer. The properties of the modified PET foil like wetting performance and electric conductivity are significantly improved by this treatment.

Copper chalcopyrite based solar cells with different molar gallium to gallium plus indium ratio (GGI) are looked at, using deep level transient spectroscopy (DLTS) and admittance spectroscopy (AS). Depending on the respective measurement parameters, like reverse bias level, height and length of the voltage pulse applied, either a minority carrier or/and a majority carrier deep level signal is/are detected in the temperature range below 200 K. The AS investigations reveal only one trap signal. After a detailed description of the defect properties taking advantage of the two diode model, we discuss the origin of these trap signals in view of our experimental findings

The total cross sections for electron scattering from He, Ne, Ar, Kr and Xe in the energy range from 100 eV to 10 000 eV have been calculated based on the optical-model potential. Our theoretical results are compared with the available experimental data. The consistency between them is also discussed. At higher energies (over 2000 eV for He, over 5000 eV for Ne, Ar, Kr and Xe), the total cross sections of electron scattering from these atoms are scarce, so our calculations will give a reference for further experimental and theoretical studies.