Volume 67, Issue 8-9

In this paper, we consider eigenvalues and traces of a special Sturm-Liouville problem, which originates from an acoustic scattering problem with a spherically symmetric speed of sound. Regularized trace formulae on transmission eigenvalues of the Sturm-Liouville problem are obtained.

In this paper, three different analytical methods have been successfully used to study a nonlinear oscillator equation arising in the microbeam-based electromechanical resonator. These methods are: variational approach, Hamiltonian approach, and amplitude-frequency formulation. The governing equation is based on the Euler-Bernoulli hypothesis and the partial differential equation (PDE) is simplified into an ordinary differential equartion (ODE) by using the Galerkin method. A frequency analysis is carried out, and the relationship between the angular frequency and the initial amplitude is obtained in closed analytical form. A comparison of the present solutions is made with the existing solutions and excellent agreement is noted.

This paper investigates a cylindrical nonlinear Schrodinger (cNLS) equation, which describes the cylindrically diverging quasi-plane envelope waves in a nonlinear medium. With the Hirota method and symbolic computation, bilinear form and N-soliton solutions in the form of an Nth-order polynomial in N exponentials are obtained for the cNLS equation. By means of the properties of double Wronskian, the N-soliton solutions in terms of the double Wronskian is testified through the direct substitution into the bilinear form. Based on the bilinear form and exchange formulae, the bilinear Backlund transformation is also given. Those solutions are graphically depicted to understand the soliton dynamics of the cylindrically diverging quasi-plane envelope waves. Soliton properties are discussed and physical quantities are also analyzed. Dispersion parameter has the effect that it may extend (or shorten) the periodic time of soliton interaction and change the direction of soliton propagation. Amplitudes of solitons are related to the cubic nonlinearity parameter.

In the present article, an investigation is made on entropy generated within a mixed convective magnetohydrodynamic flow of a viscoelastic fluid over a stretching sheet. In performing the analysis, it is assumed that the flow is steady, laminar, and fully developed. The governing equations for velocity and temperature fields are transformed into nonlinear ordinary differential equations by using suitable similarity transformations and are solved using the homotopy analysis method. The expressions for local entropy generation number Ns, average entropy [Ns] avg , Bejan number Be, and average Bejan number [Be] avg are obtained using the corresponding velocity and temperature data. A comprehensive parametric study is presented through graphs.

This paper outlines a comprehensive study of the two dimensional flow of an incompressible viscoelastic fluid over a shrinking/stretching sheet with temperature dependent viscosity. The governing coupled nonlinear differential equations are solved by means of the homotopy analysis method (HAM). The results are presented graphically to interpret various physical parameters appearing in the problem. The solution procedure explicitly elucidates the remarkable accuracy of the proposed algorithm.

In this paper, we investigate the steady boundary layer flow of a non-Newtonian fluid, represented by a Sisko fluid, over a wedge in a moving fluid. The equations of motion are derived for boundary layer flow of an incompressible Sisko fluid using appropriate similarity variables. The governing equations are reduced to a single third-order highly nonlinear ordinary differential equation in the dimensionless stream function, which is then solved analytically using the homotopy analysis method. Some important parameters have been discussed by this study, which include the power law index n, the material parameter A, the wedge shape factor b, and the skin friction coefficient Cf. A comprehensive study is made between the results of the Sisko and the power-law fluids.

The blow-up of solutions for a class of quasilinear reaction-diffusion equations with a gradient term ut = div(a(u)b(x)▽u)+ f (x;u; |▽u| 2 ; t) under nonlinear boundary condition ¶u=¶n+g(u) = 0 are studied. By constructing a new auxiliary function and using Hopf’s maximum principles, we obtain the existence theorems of blow-up solutions, upper bound of blow-up time, and upper estimates of blow-up rate. Our result indicates that the blow-up time T* may depend on a(u), while being independent of g(u) and f .

We systematically provide a similarity transformation reducing the (3+1)-dimensional inhomogeneous coupled nonlinear Schrodinger (CNLS) equation with variable coefficients and parabolic potential to the (1+1)-dimensional coupled nonlinear Schrodinger equation with constant coefficients. Based on the similarity transformation, we discuss the dynamics of the propagation of the three-dimensional bright-dark soliton, the interaction between two bright solitons, and the feature of the three-dimensional rogue wave with different parameters. The obtained results may raise the possibility of relative experiments and potential applications.

In order to obtain the means to control light polarization, we designed a structure of coupled magnetic resonators and studied its transmission properties by the 4x4 transfer matrix method. The incidence of linearly polarized light results in two transmission resonant peaks of left-handed circular polarization at shorter wavelengths and two transmission resonant peaks of right-handed circular polarization at longer wavelengths, respectively. Through adjusting the magnetizations, the inner left-handed circular polarization and right-handed circular polarization can be merged into one linear polarization, while the two outside resonant peaks keep their circular polarization. The polarized direction of the output linearly polarized light can be controlled by the polarized direction of incidence light. The incidence light with one polarization can output light with three kinds of polarizations through the designed structure.

The paper examines a well-known experimental property of increase of the magnetoresistance effect in a metal observed with a decrease of the metal temperature. This property is explained by the fact that magnetoresistance is a quantity proportional to the relaxation time of the electric conduction of the metal sample which is a parameter observed in the absence of the magnetic field. Since the electric conduction, as well as the corresponding relaxation time, increase with the lowering of temperature, they provide us necessarily with an increase of magnetoresistance. The phenomenon is investigated quantitatively in this paper for numerous metal cases taken as examples.

A version of the optimal homotopy perturbation method (OHPM) is applied in this study to derive highly accurate analytical expressions for the solutions to a non-conservative dynamical system of a rotating electrical machine. The main advantage of this procedure consists of providing us with a convenient and rigorous way to control the approximate solutions by means of some initially unknown parameters which are optimally determined later. Comparisons with numerical results reveal an excellent agreement, which demonstrates the effectiveness of the proposed method in analyzing non-conservative oscillators.

The two-dimensional magnetohydrodynamic (MHD) flow of a Jeffrey fluid is investigated in this paper. The characteristics of heat and mass transfer with chemical reaction have also been analyzed. Convective boundary conditions have been invoked for the thermal boundary layer problem. Exact similarity solutions for flow, temperature, and concentration are derived. Interpretation to the embedded parameters is assigned through graphical results for dimensionless velocity, temperature, concentration, skin friction coefficient, and surface heat and mass transfer. The results indicate an increase in the velocity and the boundary layer thickness by increasing the rheological parameter of the Jeffrey fluid. An intensification in the chemical reaction leads to a thinner concentration boundary layer.