Volume 67, Issue 3-4

Two methods are explained to exactly solve Maxwell’s equations where permittivity, permeability, and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one coordinate, general solutions are derived. If the properties depend on two coordinates, geometrically restricted solutions are obtained. Applications to graded reflectors, especially to dielectric mirrors, to filters, polarizers, and to waveguides, plain and cylindrical, are indicated. New foundations for the design of optical instruments, which are centered around an axis, and for the design of invisibility cloaks, plain and spherical, are proposed. The variability of material properties makes possible effects which cannot happen in constant media, e.g. stopping the flux of electromagnetic energy without loss. As a consequence, spherical devices can be constructed which bind electromagnetic waves

This paper is to investigate the (2+1)-dimensional variable-coefficient Konopelchenko- Dubrovsky equations, which can be applied to the phenomena in stratified shear flow, internal and shallow-water waves, plasmas, and other fields. The bilinear-form equations are transformed from the original equations, and soliton solutions are derived via symbolic computation. Soliton solutions and collisions are illustrated. The bilinear-form B¨acklund transformation and another soliton solution are obtained. Wronskian solutions are constructed via the B¨acklund transformation and solution

The Gross-Pitaevskii equation (GPE) describing the dynamics of a Bose-Einstein condensate at absolute zero temperature, is a generalized form of the nonlinear Schr¨odinger equation. In this work, the exact bright one-soliton solution of the one-dimensional GPE with time-dependent parameters is directly obtained by using the well-known Hirota method under the same conditions as in S. Rajendran et al., Physica D 239, 366 (2010). In addition, the two-soliton solution is also constructed effectively

In this paper, a two-dimensional, steady magnetohydrodynamic flow and heat transfer analysis of a non-Newtonian fluid in a channel with a constant wall temperature are considered in the presence of thermal radiation. The steady Navier-Stokes equations are reduced to nonlinear ordinary differential equations by using similarity variables. The homotopy perturbation method is used to solve the nonlinear ordinary differential equations. The effects of the pertinent parameters on the velocity and temperature field are discussed

This article considers the radiation effect on the flow of a Jeffery fluid with variable thermal conductivity. Similarity transformations are employed to convert the partial differential equations into ordinary differential equations. The resulting equations have been computed by the homotopy analysis method (HAM). The numerical values of the local Nusselt numbers are also computed. The comparison with the numerical solutions of qƟ'(0) is presented. The obtained results are displayed and physical aspects have been examined in detail

In this article, the differential transformation method (DTM) is utilized for finding the solution of the regularized long wave (RLW) equation. Not only the exact solutions have been achieved by the known forms of the series solutions, but also for the finite terms of series, and the corresponding numerical approximations have been computed

16 In this paper, we investigate the travelling wave solutions for the Klein-Gordon-Zakharov equations by using the modified trigonometric function series method benefited to the ideas of Z. Y. Zhang, Y. X. Li, Z. H. Liu, and X. J. Miao, Commun. Nonlin. Sci. Numer. Simul. , 3097 (2011). Exact travelling wave solutions are obtained

By Lochak (theory) and Urutskoev (experiment) the hypothesis has been suggested that during electric discharges in water light magnetic monopoles can be created and according to Lochak these monopoles should be looked upon as a kind of excited neutrinos. Based on a quantum field theoretic derivation of an extended (effective) Standard Model, which describes the effects of symmetry breaking caused by the discharge, in Part I and Part II (H. Stumpf, Z. Naturforsch. 66a, 205 and 329 (2011)), the possibility was investigated whether under these circumstances magnetic effects can occur. While in the above two parts the focus of the theory was directed to show the evidence of magnetically active neutrinos, in this part the behaviour of the leptonic doublets (v, e ¯) and (v̅ , e + ) is studied under the (symmetry breaking) conditions of such an electric discharge. The results obtained by the quantum field theoretic treatment of this problem are in agreement with symmetry considerations earlier performed by Lochak

In this paper, we consider the eigenvalue problems for matrix integro-differential operators with separated boundary conditions on the finite interval and find new trace formulae for the matrix integro-differential operators

This paper investigates the effects of heat transfer and pulsatile flow of a Newtonian fluid (blood) through a vertical annulus with mild constriction on the outer wall while the inner wall represents the catheter tube. An analytical expression in terms of Bessel functions of the first and second kind is obtained for the heat and the velocity components. The variation of pressure gradient with steady flow rate is given as well as the wall shear stress distribution for different values of time. The pressure gradient and the wall shear stress are calculated, and their variations are discussed with respect to the Grashof number, the height of the constriction, and the size of the catheter. It is observed that an increase in the catheter size increases the pressure gradient as well as the wall shear stress

This study concentrates on the heat transfer analysis of the steady flow of viscoelastic fluid along an inclined stretching surface. Analysis has been carried out in the presence of thermal radiation and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The equations of continuity, momentum and energy are reduced into the system of governing differential equations and solved by homotopy analysis method (HAM). The velocity and temperature are illustrated through graphs. Exact and homotopy solutions are compared in a limiting sense. It is noticed that viscoelastic parameter decreases the velocity and boundary layer thickness. It is also observed that increasing values of viscoelastic parameter reduces the thickness of momentum boundary layer and increase the heat transfer rate. However, it is found that increasing the radiation parameter has the effect of decreasing the local Nusselt number

In this article, the optimal homotopy-analysis method (HAM) is used to obtain approximate analytic solutions of the time-fractional nonlinear diffusion equation in the presence of an external force and an absorbent term. The fractional derivatives are considered in the Caputo sense to avoid nonzero derivative of constants. Unlike usual HAM this method contains at the most three convergence control parameters which determine the fast convergence of the solution through different choices of convergence control parameters. Effects of proper choice of parameters on the convergence of the approximate series solution by minimizing the averaged residual error for different particular cases are depicted through tables and graphs

The present article deals with the configurational probabilities of a smectogen N-n-undecyl-Dgluconamide (GAM11). The complete neglect differential overlap (CNDO/2) method has been employed to compute the net atomic charge and atomic dipole moment components at each atomic center. The modified Rayleigh-Schr¨odinger perturbation theory along with the multicentered-multipole expansion method has been employed to evaluate the long-range intermolecular interactions, while a ‘6-exp’ potential function has been assumed for short-range interactions. The total interaction energy values obtained during different modes of molecular interactions have been used as input to calculate the configurational probability at room temperature (300 K), and smectic-isotropic transition temperature (429:7 K) using the Maxwell-Boltzmann formula. The various possible geometrical arrangements of molecular pairs have been considered. Further, an attempt has been made to explain the smectic behaviour of GAM11 in terms of their relative order based on the molecular parameters introduced in this paper