Volume 68, Issue 10-11

The natural modes for one-dimensional (1D) twin square potentials of complex strength g are studied. A global analysis of the natural modes based on the construction of the Riemann surfaces R I g and R II g of the multiple valued function k = k(g), where k(g) defines the poles of the transmission coefficient, is done. To each nonradiative or radiative mode a sheet of the Riemann surface is associated. All the natural modes of the system are identified and treated in a unified way. New classes of resonant state poles with exotic properties are identified on the k-plane images of the sheets of R I g and R II g and the properties of the exotic modes are studied. The traversal time through the 1D twin square potentials is analysed. Subluminal and superluminal traversal times are evidenced. An approximate formula for the frequencies k for which the maximal superluminal velocities are gained as a function of the potential parameters is given.

A set of edges X is subverted from a graph G by removing the closed neighbourhood N[X] from G. We denote the survival subgraph by G=X. An edge-subversion strategy X is called an edge-cut strategy of G if G=X is disconnected, a single vertex, or empty. The edge-neighbour-scattering number of a graph G is defined as ENS(G) = max{ω(G/X)-|X| : X is an edge-cut strategy of G}, where w(G=X) is the number of components of G=X. This parameter can be used to measure the vulnerability of networks when some edges are failed, especially spy networks and virus-infected networks. In this paper, we prove that the problem of computing the edge-neighbour-scattering number of a graph is NP-complete and give some upper and lower bounds for this parameter.

Based on the defect model that the impurity Cu 2+ in TiO 2 on the octahedral Ti 4+ site is associated with one oxygen vacancy VO along the C 2 axis, the electron paramagnetic resonance (EPR) parameters, i. e., the g factors gi ( i = x ; y ; z ) and the hyperfine structure constants At , of the Cu 2+ -VOcenter in TiO2 are calculated by using the perturbation formulas of these parameters for a 3d 9 ion in a rhombically elongated octahedra. From this study, the impurity Cu 2+ is found to be away from VO by a distance D z (≈ 0:33 Å) along the C 2 axis, meanwhile the four O 2- ions in the plane perpendicular to the C 2 axis may be shifted by D x (≈ 0:28 Å) towards VO due to the electrostatic interaction between these ions and VO. The theoretical results based on the above local structure distortions show good agreement with the experimental data.

Ultrapure hafnium metal (110 ppm zirconium) was neutron activated with a thermal neutron flux of 6:6 · 10 12 cm -2 s -1 in order to obtain 181Hf for subsequent time differential perturbed angular correlation (TDPAC) experiments using the nuclear probe 181Hf(β - ) 181Ta. Apart from the expected nuclear quadrupole interaction (NQI) signal for a hexagonal close-packed (hcp) metal, three further discrete NQIs were observed with a few percent fraction each. The TDPAC spectra were recorded for up to 11 half lives with extreme statistical accuracy. The fitted parameters vary slightly within the temperature range between 248 K and 373 K. The signals corresponding to the three additional sites completely disappear after ‘annealing’ at 453 K for one minute. Based on the symmetry of the additional NQIs and their temperature dependencies, they are tentatively attributed to Frenkel pairs produced by recoil due to the emission of a prompt 5:694 MeV -ray following thermal neutron capture and reported by the nuclear probe in three different positions. These Frenkel pairs are stable up to at least 373 K.

In this paper, the generalized diffusion equation with perturbation ut = A(u;u x )u II +eB(u;u x ) is studied in terms of the approximate functional variable separation approach. A complete classification of these perturbed equations which admit approximate functional separable solutions is presented. Some approximate solutions to the resulting perturbed equations are obtained by examples.

The main aim of this work is to present a new reliable approach to compute an approximate solution of the system of nonlinear differential equations governing the problem of two-dimensional and axisymmetric unsteady flows due to normally expanding or contracting parallel plates by the homotopy perturbation method, and the Sumudu transform is adopted in the solution procedure. The method finds the solution without any discretization or restrictive assumptions and avoids the roundoff errors. The numerical solutions obtained by the proposed technique indicate that the approach is easy to implement and computationally very attractive.

In this paper, exact solutions of velocity and stresses are obtained for the magnetohydrodynamic (MHD) flow of a Maxwell fluid in a porous half space by the Laplace transform method. The flows are caused by the cosine and sine oscillations of a plate. The derived steady and transient solutions satisfy the involved differential equations and the given conditions. Graphs for steady-state and transient velocities are plotted and discussed. It is found that for a large value of the time t, the transient solutions disappear, and the motion is described by the corresponding steady-state solutions.

We apply the Gröbner basis to the ansatz method in quantum mechanics to obtain the energy eigenvalues and the wave functions in a very simple manner. There are important physical potentials such as the Cornell interaction which play significant roles in particle physics and can be treated via this technique. As a typical example, the algorithm is applied to the semi-relativistic spinless Salpeter equation under the Cornell interaction. Many other applications of the idea in a wide range of physical fields are listed as well.

Density functional calculations have been performed for the carbon monoxide molecule adsorption on Au n Pd + m ( n + m ≤ 6) clusters. In the process of CO adsorption, small Au clusters and Pd clusters tend to be an Au atom and three Pd atoms adsorption, respectively. For the mixed Au-Pd clusters, an Au atom, a Pd atom, two atoms consisted of an Au atom and a Pd atom, two Pd atoms, and three Pd atoms adsorption structures are displayed. The highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps and natural bond orbital charge population are calculated. Moreover, CO adsorption energy, CO stretching frequency, and CO bond length (upon adsorption) are also analysed in detail. The results predict that the adsorption strength of Au clusters with CO and the C-O vibration strength is enhanced and reduced after doping of Pd in the Au n Pd m CO + complexes, respectively

General solutions for the magnetohydrodynamic (MHD) natural convection flow of an incompressible viscous fluid over a moving plate are established when thermal radiation, porous effects, and slip condition are taken into consideration. These solutions, obtained in closed-form by Laplace transform technique, depend on the slip coefficient and the three essential parameters Gr, Preff, and Keff. They satisfy all imposed initial and boundary conditions and can generate a large class of exact solutions corresponding to different fluid motions with technical relevance. For illustration, two special cases are considered and some interesting results from the literature are recovered as limiting cases. The influence of pertinent parameters on the fluid motion is graphically underlined.

The mixed oxides Zn1- x Mg x O were prepared as polycrystalline powders with various compositions ( x = 0:02, 0.04, 0.05, and 0.10) using sol-gel technique. X-ray diffractometer (XRD) was used to characterize the powders for structural and electronic properties. X-ray diffraction analysis reveals that all the prepared samples exhibit the single wurtzite phase of zinc oxide (ZnO), and magnesiumdoping does not induce any secondary phase in the samples. The Bragg peak positions in the XRD patterns are found to be shifted towards higher 2q values with more addition of magnesium in the zinc oxide lattice. Magnesium addition in the zinc oxide lattice is found to enhance the mid bond electron density distribution up to x = 0:05 and then decrease for x = 0:10. Evidence of host lattice as well as interstitial addition of Mg 2+ ions has been realized for x = 0:10, through electron density analysis.

In this work, we consider a nonlinear SEIR (susceptible, exposed, infectious, and removed) endemic model, which describes the dynamics of the interaction between susceptible and infected individuals in a population. The model represents the disease evolution through a system of nonlinear differential equations with variable infectivity which determines that the infectivity of an infected individual may not be constant during the time after infection. To control the spread of infection and to find a vaccination schedule for an endemic situation, we use optimal control strategies which reduce the susceptible, exposed, and infected individuals and increase the total number of recovered individuals. In order to do this, we introduce the optimal control problem with a suitable control function using an objective functional. We first show the existence of an optimal control for the control problem and then derive the optimality system. Finally the numerical simulations of the model is identified to fit realistic measurement which shows the effectiveness of the model.

The influence of electron exchange and quantum shielding on the elastic electron-ion collision is investigated in degenerate quantum plasmas. The second-order eikonal method and effective screened potential are employed to obtain the scattering phase shift and collision cross section as functions of the impact parameter, collision energy, electron-exchange parameter, Fermi energy, and plasmon energy. It is found that the electron-exchange effect enhances the eikonal scattering phase shift as well as the eikonal collision cross section in quantum plasmas. The maximum position of the differential eikonal collision cross section is found to be receded from the collision center with an increase of the electron-exchange effect. It is interesting to note that the influence of the electron exchange on the eikonal collision cross section decreases with increasing collision energy. It is also found that the eikonal collision cross section decreases with an increase of the plasmon energy and, however, increases with increasing Fermi energy.

A steady two-dimensional boundary-layer flow and heat transfer of an upper convected Maxwell fluid near a stagnation-point of a permeable shrinking sheet is studied numerically. The effects of elasticity, shrinking, and suction parameters on the flow and heat transfer characteristics are investigated. A similarity transformation reduces the governing equations to third-order nonlinear ordinary differential equations which are then solved numerically. For a fixed value of elastic parameter, it is found that dual solutions exist for some values of shrinking and suction parameters. The plotted streamlines show that for upper branch solutions, the effects of shrinking and suction are direct and obvious as the flow near the surface is seen to suck through the permeable sheet and drag to the origin of the sheet. However, aligned but reverse flow occurs for the case of lower branch solutions.

The parametric Nikiforov-Uvarov (pNU) and asymptotic iteration method (AIM) are applied to study the approximate analytic bound state eigensolutions (energy levels and wave functions) of the radial Schr¨odinger equation (SE) for the Hellmann potential which represents the superposition of the attractive Coulomb potential (-a/r) and the Yukawa potential bexp(-δ/r)/r of arbitrary strength b and screening parameter d in closed form. The analytical expressions to the energy eigenvalues Enl yield quite accurate results for a wide range of n; l in the limit of very weak screening but the results become gradually worse as the strength b and the screening coefficient d increase. The calculated bound state energies have been compared with available numerical data. Special cases of our solution like pure Coulomb and Yukawa potentials are also investigated.

Energy spectrum and wave functions are obtained numerically with a potential consisting of Woods-Saxon, Coulomb, and spin-orbit coupling parts for the nuclei 15 O, 15 N, 17 O, and 17 F. The radial parts of the wave functions are used to calculate some matrix elements of electromagnetic transitions. These results are applied to calculate half-lives of low-lying exited states in the one-particle 17 O and 17 F as well as in the one-hole 15 O and 15 N isotopes. The calculated half-lives are compared with available experimental and theoretical results based on harmonic oscillator wave functions and Weisskopf units. In comparison with the results calculated from the other methods, our results based on the Woods-Saxon potential indicate a satisfactory agreement with accessible experimental data.