Volume 70, Issue 8

A mathematical model has been performed for momentum, temperature, and mass concentration of a time-dependent Casson fluid flow between a long vertical wavy wall and a parallel wavy wall subject to convective boundary conditions. Perturbation technique is used to convert the coupled partial differential equations for velocity, temperature, and mass concentration to systems of ordinary differential equations. Analytical results for these differential equations are computed. The effects of various physical parameters such as thermal conductivity, thermal Grashof number, solutal Grashof number, heat absorption parameter, and Biot number are analysed graphically.

We numerically investigate peristaltic transport of incompressible visco-elasto-plastic fluids in a two-dimensional symmetric channel. The constitutive equation used for extra stress tensor is of more general form as it includes a number of well-known models like Maxwell A and B, Johnson–Segalman, Oldroyd-B, and Bingham models as its special cases. A detailed mathematical modelling of the problem is presented. The flow equations in the wave frame reduce to a single nonlinear ordinary differential equation in stream function by the implication of widely taken assumptions of long wavelength and low Reynolds number. The solution of the problem is obtained by two ways; namely, shooting method and Matlab built in routine bvp4c, and their comparison shows an excellent agreement. A parametric study based on bvp4c solution is performed to see the effects of parameters on velocity profile, pressure rise per wavelength, frictional forces, and trapping phenomenon.

We study square matrices F ( α ) over ℂ with α ∈ℝ, where the eigenvalues depend on the parameter α but not the eigenvectors, and vice versa, where the eigenvectors depend on the parameter α but not the eigenvalues. We derive sufficient conditions for such properties. Applications to Lie groups and spin systems are provided. Both normal and nonnormal matrices are investigated.

Based on the first-principles density functional theory calculations combined with the quasi-harmonic Debye model, the pressure dependencies of the structural, elastic, electronic and thermal properties of Li 2 AgSb were systematically investigated. The calculated lattice parameters and unit cell volume of Li 2 AgSb at the ground state were in good agreement with the available experimental data. The obtained elastic constants, the bulk modulus and the shear modulus revealed that Li 2 AgSb is mechanically stable and behaves in a ductile manner under the applied pressure. The elasticity-relevant properties, the Young’s modulus and the Poisson’s ratio showed that pressure can enhance the stiffness of Li 2 AgSb and that Li 2 AgSb is mechanically stable up to 20 GPa. The characteristics of the band structure and the partial density of states of Li 2 AgSb were analysed, showing that Li 2 AgSb is a semiconductor with a direct band gap of 217 meV at 0 GPa and that the increasing pressure can make the band structure of Li 2 AgSb become an indirect one. Studies have shown that, unlike temperature, pressure has little effect on the heat capacity and the thermal expansion coefficient of Li 2 AgSb.

We consider a two-dimensional Dirac oscillator in the presence of a magnetic field in non-commutative phase space in the framework of relativistic quantum mechanics with minimal length. The problem in question is identified with a Poschl–Teller potential. The eigenvalues are found, and the corresponding wave functions are calculated in terms of hypergeometric functions.

The Korteweg–de Vries (KdV)-type equations can describe the shallow water waves, stratified internal waves, ion-acoustic waves, plasma physics and lattice dynamics, while the (2+1)-dimensional Nizhnik–Novikov–Vesselov equations are the isotropic extensions of KdV-type equations. In this paper, we investigate the (2+1)-dimensional modified Nizhnik–Novikov–Vesselov equations. By virtue of the binary Bell polynomials, bilinear forms, multi-soliton solutions and Bäcklund transformations are derived. Effects of some parameters on the solitons and monotonic function are graphically illustrated. We can observe the coalescence of the two solitons in their collision region, where their shapes change after the collision.

We studied the electron paramagnetic resonance (EPR) spectra of VO 2+ ions in ammonium hydrogen tartrate (AHT) single crystals at room temperature. We determined the spin Hamiltonian parameters and the molecular bonding coefficients of the complex both in theoretical and experimental ways. The results indicate that the vanadium ion forms a tetragonally compressed octahedron and has a double bond with one of the oxygens in the axial position. This is the reason why the paramagnetic centre in the host crystal is axially symmetric as in most of the vanadyl ion-containing complexes.

We develop the theory of line preserving flows and the magnetic reconnection using the Euler potentials formalism. In addition to our recently proposed model, we formulate new equations describing the time evolution of the Euler potentials in the line preserving regime. We also look at a special case of the flows represented by the ideal plasma flows. We consider the magnetic reconnection as a breakage of the line preservation regime. Because general solutions of the obtained dynamics equations do not have their closed-form expressions, we provide two different approaches to the possible solutions, in particular, a linear approximation and a solution by finding a Lagrangian and a Hamiltonian that generate the dynamics equations. We also provide some simple examples of the physical interpretation of the solutions obtained.

The physical mechanism for the phase invariance of mechanical wave or electromagnetic wave is analysed. For the mechanical wave, the displacement and velocity of oscillation of a mass element together determine the phase invariance. For the electromagnetic wave, the displacement corresponds to the strength of the electric field or magnetic field.

In this article, a novel approach comprising modified homotopy analysis method with Fourier transform has been implemented for the approximate solution of fractional sine-Gordon equation (SGE) utt − DRxαu + sinu = 0,${u_{tt}}\; - \;{}^RD_x^\alpha u\; + \;{\rm{sin}}u\; = \;0,$ where RDxα$^RD_x^\alpha $ is the Riesz space fractional derivative, 1 ≤ α ≤ 2. For α =2, it becomes classical SGE u tt − u xx + sin u =0, and corresponding to α =1, it becomes nonlocal SGE u tt − Hu + sin u =0, which arises in the Josephson junction theory, where H is the Hilbert transform. The fractional SGE is considered as an interpolation between the classical SGE (corresponding to α =2) and nonlocal SGE (corresponding to α =1). Here, the approximate solution of fractional SGE is derived by using modified homotopy analysis method with the Fourier transform. Then, we analyse the results by numerical simulations, which demonstrate the simplicity and effectiveness of the present method.

In this work, we consider the (1+1)-dimensional modified improved Boussinesq (IMBq) equation. As the considered equation is of evolution type, no recourse to a Lagrangian formulation is made. However, we showed that by utilising the partial Lagrangian method and multiplier method, one can construct a number of local and nonlocal conservation laws for the IMBq equation. In addition, by using a solitary wave ansatz method, we obtained exact bright soliton solutions for this equation. The parameters of the soliton envelope (amplitude, widths, velocity) were obtained as function of the dependent model coefficients. Note that, it is always useful and desirable to construct exact solutions especially soliton-type envelope for the understanding of most nonlinear physical phenomena.

This paper presents a meshless method which, at the first step, utilises the radial basis functions collocation scheme to approximate the unknown function at specific nodal points. The difficulty of these biharmonic-type problems is the multiple boundary conditions, as well as high derivatives terms. The inhomogeneous biharmonic equation is replaced by two Poisson equations of an intermediate function where Neumann’s boundary conditions is of second derivatives. It uses the imposed-kernel technique (IKT) to overcome multiple boundary conditions where Neumann’s boundary conditions is of first derivatives. In the next step, our meshless approach uses two- and three-dimensional cubic spline interpolation to get smooth, approximate solutions for the 2-D and 3-D inhomogeneous biharmonic-type problem, respectively. Numerical experiments are included to demonstrate the reliability and efficiency of this method.

The electrical conductivity of molten SnCl 2 was measured in a wide temperature range (Δ T =763 K), from 551 K to temperature as high as 1314 K, that is, 391° above the boiling point of the salt. The specific electrical conductance was found to reach its maximum at 1143 K, after that it decreases with the temperature rising.