Volume 66, Issue 12

The present paper deals with eigenvalue problems for the Schrödinger equation with energy dependent potential and some separated boundary conditions. Using the method of contour integration, we obtain some new regularized traces for this class of Schrödinger operators.

The steady two-dimensional stagnation-point flow of an incompressible viscous fluid over an exponentially shrinking/stretching sheet is studied. The shrinking/stretching velocity, the free stream velocity, and the surface temperature are assumed to vary in a power-law form with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations before being solved numerically by a finite difference scheme known as the Keller-box method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that dual solutions exist for the shrinking case, while for the stretching case, the solution is unique.

Under investigation in this paper is an inhomogeneous nonlinear Schrödinger-Maxwell-Bloch system with variable dispersion and nonlinear effects, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber. Under certain coefficient constraints, multi-soliton solutions are obtained by the Hirota method and symbolic computation. Evolution and interaction of the solitons are plotted, and the self-induced transparency effect caused by the doped erbium atoms is found to lead to the change of the soliton velocity and phase. Overall phase shift can be observed when the parameter accounting for the interaction between the silica and doped erbium atoms is taken as a constant.

In this paper, we study the bifurcations and dynamic behaviour of the travelling wave solutions of the perturbed nonlinear Schrödinger equation (NLSE) with Kerr law nonlinearity by using the theory of bifurcations of dynamic systems. Under the given parametric conditions, all possible representations of explicit exact solitary wave solutions and periodic wave solutions are obtained

In this paper, the generalized sub-equation method is extended to investigate localized nonlinear waves of the one-dimensional nonlinear Schrödinger equation (NLSE) with potentials and nonlinearities depending on time and on spatial coordinates. With the help of symbolic computation, three families of analytical solutions of this NLS-type equation are presented. Based on these solutions, periodically and quasiperiodically oscillating solitons (dark and bright) and moving solitons are observed. Some implications to Bose-Einstein condensates are also discussed

In this work we propose fast and high accuracy numerical methods for the solution of the one dimensional nonlinear Klein-Gordon (KG) equations. These methods are based on applying fourth order time-stepping schemes in combination with discrete Fourier transform to numerically solve the KG equations. After transforming each equation to a system of ordinary differential equations, the linear operator is not diagonal, but we can implement the methods such as for the diagonal case which reduces the time in the central processing unit (CPU). In addition, the conservation of energy in KG equations is investigated. Numerical results obtained from solving several problems possessing periodic, single, and breather-soliton waves show the high efficiency and accuracy of the mentioned methods.

In this paper, some time-dependent flows of a non-Newtonian fluid between two side walls over a plane wall are investigated. The following three problems have been studied: (i) flow due to an oscillating plate, (ii) flow due to an accelerating plate, and (iii) flow due to applied constant stress. The explicit expressions for the velocity field are determined by using the integral transforms. The solutions that have been obtained, depending on the initial and boundary conditions, are written as sum of the steady state and transient solutions. The similar solutions for second-grade and Newtonian fluids can be deduced as limiting cases of our solutions. Furthermore, in absence of the side walls they reduce to the similar solutions over an infinite plate. The effects of some important parameters due to side walls on the flow field are investigated.

General solutions corresponding to the unsteady motion of second-grade fluids induced by an infinite plate that applies a shear stress ƒ (t) to the fluid are established. These solutions can immediately be reduced to the similar solutions for Newtonian fluids. They can be used to obtain known solutions from the literature or any other solution of this type by specifying the function ƒ ( . ). Furthermore, in view of a simple remark, general solutions for the flow due to a moving plate can be developed.

In the current work, the telegraph equation in its general form and with an integral condition is investigated. Also the well-known homotopy analysis method (HAM) is applied and an interesting iterative algorithm is proposed for solving the problem in general form. Some numerical examples are given and compared with the exact solution to show the effectiveness of the proposed method.

We show the existence of new localized nonlinear structures for the electrostatic potential and the electron density in the form of bright and W-shaped solitons in quantum electron plasmas, respectively, which is modelled by the coupled nonlinear Schrödinger-Poisson equations. The robustness and the conservation of the energy of the solitons are demonstrated by numerical simulations. The sensitivity of the coupling constant on the stability of the paired solitons in the quantum electron plasmas are investigated.

Some thermodynamic quantities for the Morse potential are analytically evaluated at an isobaric process. The parameters of Morse gases for 21 substances are obtained by the second virial coefficient data and the spectroscopic data of diatomic molecules. Also some thermodynamic quantities for water are calculated numerically and drawn graphically. The inflexion point of the length L which depends on temperature T and pressure P corresponds physically to a boiling point. L indicates the liquid phase from lower temperature to the inflexion point and the gaseous phase from the inflexion point to higher temperature. The boiling temperatures indicate reasonable values compared with experimental data. The behaviour of L suggests a chance of a first-order phase transition in one dimension.

It was shown that by means of the two-pulse sequence, the spin system of a liquid entrapped into nanosize cavities can be prepared in quasi-equilibrium states of high dipolar order, which relax to thermal equilibrium with the molecular environment with a relaxation time T 1d . Measurements of the inverse dipolar temperature and spin-lattice relaxation time in the local fields provide an important information about the cavity size V, its shape F, and orientation θ (with respect to the external magnetic field) of the nanopores.

Sol-gel barium strontium titanate ( Ba 0.6 Sr 0.4 TiO 3 ) thin films with different grain sizes have been successfully fabricated as metal-insulator-metal (MIM) capacitors. The perovskite structure of the material has been confirmed via X-ray diffraction (XRD). In order to correlate the effect of the grain size to the conduction mechanisms of these films, atomic force microscopy (AFM) results are presented. The grain size shows an important effect on the conduction mechanism for the films. The results show that as the grain size increases, both the impedance and the permittivity of the films decrease, whereas the conductivity shows an inverse variation. The Z* plane for all films shows two regions, corresponding to the bulk mechanism and the distribution of the grain boundaries-electrodes conduction process.M´´ versus frequency plots reveal non-Debye relaxation peaks, which are not able to be observed in the e´´ plots. Alternating current (AC) conductivity versus frequency plots show three regions of conduction processes, i.e. a low-frequency region due to direct current (DC) conduction, a mid-frequency region due to translational hopping motion, and a high-frequency region due to localized hopping and/or reorientational motion.

Alternative explanations to the Michelson-Morley experiment exist and continue to be produced. In the current paper, we will correct a recently published paper concerning a reenactment of the famous experiment. The author of the paper in cause claims the presence of a non-null result though he did not run any experiment himself. Dmitriyev bases his paper on a paper by Demjanov that has already been retracted by the journal where he originally published (V. V. Demjanov, Phys. Lett. A 374, 1110 (2010)). Our paper is organized as follows: in the background section we will give the correct expressions for the relativistic light speed in arbitrary media as opposed to the incorrect ones given in V. P. Dmitriyev, Z. Naturforsch. 66a, 228 (2011). We will follow by explaining the correct equations of the Michelson-Morley experiment in a refractive medium with n > 1, and we will outline the errors in V. P. Dmitriyev, Z. Naturforsch. 66a, 228 (2011). The non-mainstream claims of detecting ‘absolute motion’ are refuted by both theoretical and experimental data.