Volume 65, Issue 3

Many problems in applied mathematics and engineering are usually formulated as singular two-point boundary value problems. A well-known fact is that the exact solutions in closed form of such problems were not obtained in many cases. In this paper, the exact solutions for a class of nonlinear singular two-point boundary value problems are obtained to the first time by using Adomian decomposition method

The generalized hyperbolic non-Newtonian fluid model first proposed by Al-Zahrani [J. Petroleum Sci. Eng. 17, 211 (1997)] is considered. This model was successfully applied to some drilling fluids with a better performance in relating shear stress and velocity gradient compared to power-law and the Hershel-Bulkley model. Special flow geometries namely pipe flow, parallel plate flow, and flow between two rotating cylinders are treated. For the first two cases, analytical solutions of velocity profiles and discharges in the form of integrals are presented. These quantities are calculated by numerically evaluating the integrals. For the flow between two rotating cylinders, the differential equation is solved by the Runge-Kutta method combined with shooting. For all problems, the power-law approximation of the model is compared with the generalized hyperbolic model, too.

In this paper, non-similarity boundary-layer flow of a Newtonian fluid near an asymmetric plane stagnation point with a dimensionless external flow velocity u e = x/(x+1) is studied. The original boundary-layer equations are transferred into a nonlinear partial differential equation (PDE) with variable coefficients. An analytic technique for strongly nonlinear equations, namely the homotopy analysis method (HAM), is applied to replace the nonlinear PDE by an infinite number of linear ordinary differential equations (ODEs) with constant coefficients. An artificial parameter, called the convergence-control parameter, is introduced to ensure the convergence of solution series. Accurate analytical approximations of skin friction and boundary-layer thickness are obtained, and the effect of the external flow velocity on the non-similarity flows is investigated. This approach has general meanings and can be applied to many other non-similarity boundary-layer flows.

In this work, the generalized (2+1) and (3+1)-dimensional Calogero-Bogoyavlenskii-Schiff equations are studied. We employ the Cole-Hopf transformation and the Hirota bilinear method to derive multiple-soliton solutions and multiple singular soliton solutions for these equations. The necessary conditions for complete integrability of each equation are derived

In the present paper, the approximate analytical solutions of a general diffusion equation with fractional time derivative in the presence of an absorbent term and a linear external force are obtained with the help of the powerful homotopy perturbation method (HPM). By using initial values, the approximate analytical solutions of the equation are derived. The results are deduced for different particular cases. The numerical results show that only a few iterations are needed to obtain accurate approximate solutions and these are presented graphically. The presented method is extremely simple, concise, and highly efficient as a mathematical tool in comparison with the other existing techniques.

This study is concerned with the peristaltic flow of a viscous fluid in a curved channel. Mathematically the problem is governed by two partial differential equations. Closed form solutions of the stream function, axial velocity, and pressure gradient are developed under long wavelength and low Reynolds number assumptions. The influence of curvature is analyzed on various flow quantities of interest.

In this paper, the exp-function method is applied by using symbolic computation to construct a variety of new generalized solitonary solutions for the Chaffee-Infante equation with distinct physical structures. The results reveal that the exp-function method is suited for finding travelling wave solutions of nonlinear partial differential equations arising in mathematical physics

The well-known He’s variational iteration method is an efficient and easy technique for finding the solution of various kinds of problems. In this method the solution of a nonlinear problem is found without any need to solve a linear or nonlinear system of equations. In the current work we present an idea for accelerating the convergence of the resulted sequence to the solution of the problem by choosing a suitable initial term. The efficiency of the method will be shown by testing the new algorithm on several examples.

This paper suggests a generalized F-expansion method for constructing new exact travelling wave solutions of a nonlinear coagulation problem with mass loss. This method can be used as an alternative to obtain analytical and approximate solutions of different types of kernel which are applied in physics. The nonlinear kinetic equation, which is an integro differential equation, is transformed into a differential equation using Laplace’s transformation. The inverse Laplace transformation of the solution gives the size distribution function of the system. As a result, many exact travelling wave solutions are obtained which include new periodic wave solutions, trigonometric function solutions, and rational solutions. The method is straightforward and concise,and it can also be applied to other nonlinear evolution equations arising in mathematical physics.

The problem of thermal instability of compressible, electrically conducting couple-stress fluids in the presence of a uniform magnetic field is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the compressibility, couple-stress, and magnetic field postpone the onset of convection. Graphs have been plotted by giving numerical values of the parameters to depict the stability characteristics. The principle of exchange of stabilities is found to be satisfied. The magnetic field introduces oscillatory modes in the system that were non-existent in its absence. The case of overstability is also studied wherein a sufficient condition for the non-existence of overstability is obtained.

Results of the static and dynamic dielectric investigations of four liquid crystalline compounds consisting of two or three phenyl rings with n-alkoxy and cyano terminals, carboxylic bridging groups, and fluoro lateral substituents in pure state and in the solution of low polar liquid crystalline medium, are presented. These compounds form the nematic phase being a monotropic one in the case of two ring compounds. The dielectric parameters are analyzed in relation to the dipolar structures of the molecules. The dielectric properties of pure substances are strongly influenced by conductivity and dimerization effects, while extracted from the data for solutions are consisted well with the structures. In the nematic phase the compounds exhibit a crossover of the principal permittivity components among the kilo and megahertz frequency range

This investigation deals with the influence of radiation on magnetohydrodynamic (MHD) and mass transfer flow over a porous stretching sheet. Attention has been particularly focused to the unsteadiness. The arising problems of velocity, temperature, and concentration fields are solved by a powerful analytic approach, namely, the homotopy analysis method (HAM). Velocity, temperature, and concentration fields are sketched for various embedded parameters and interpreted. Computations of skin friction coefficients, local Nusselt number, and mass transfer are developed and examined.

The vertex PI index is a distance-based molecular structure descriptor, that recently found numerous chemical applications. Lower and upper bounds for PI are obtained, as well as results of Nordhaus-Gaddum type. Also a relation between the Szeged and vertex PI indices is established

Quantum-chemical calculations of the parameters of the nM + ・ NbF 7 q− type particles, where M stands for Na, K, Cs; q = 2,3 and n = 0 - 7 have been performed. Within the framework of this approximation, compositions for the most stable particles in molten salts were obtained. It is shown that electron transfer onto the particle results in a different redistribution of the electron density with the Na and K-particles on one hand and Cs-containing particles on the other hand. Energies and some other characteristics of the electron structure and particle geometry were determined depending on the n and M values.

On the basis of the crystal- and ligand-field theory, the high-order perturbation formulas of the g factors (g x , g y , g z ) are established for Cu 2+ ions in an orthorhombic tetrahedral field with D 2 symmetry, including the central cationic and ligand anionic spin-orbital coupling interactions. By using these formulas, the anisotropic g factors of Cu 2+ ion in (CuCl 4 ) 2− cluster are calculated. The results are consistent with the experimental values. The calculations show that the contribution from covalency of the central ion and the 3p orbital ligand can not be neglected