Volume 63, Issue 9

He’s homotopy perturbation method is adapted to calculate higher-order approximate periodic solutions of conservative nonlinear oscillators for which the elastic force term is an odd nonlinear function. The method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. With carefully constructed iterations, only a few iterations can provide very accurate analytical approximate solutions. An example is presented to illustrate the usefulness and effectiveness of the proposed technique, and comparison of the results obtained using this method with those obtained using other techniques reveals that the former is very effective and convenient.

He’s variational iteration method is proposed to solve nonlinear Volterra’s integro-differential equations. The results reveal that this method is very effective and convenient in comparison with other methods.

We consider the existence, both locally and globally in time, and the blow up of solutions of the Cauchy problem of the generalized damped multidimensional improved modified Boussinesq equation inW s,p (R n ).

Based on the so-called cylindrical brush structure as a fractal model, we derive the generalized fractional diffusion equation in cylindrical symmetry. Moreover, we derive the fractional calculus and also present the usefulness of fractional ideas in diffusion processes that take place in brush polymer, rheology, and complex systems.

To handle electromagnetic wave propagation in a semi-infinite, perfectly conducting, chiral cylinder with a circular base, on which an harmonic Bessel beam impinges, we present a theory relying on the Fourier-Bessel expansion of electromagnetic fields. The chiral medium is successively described by the Tellegen and Post constitutive relations. Conditions of wave propagation are discussed.

A powerful analytic technique for nonlinear problems, the homotopy analysis method (HAM), is employed to give analytic solutions of power-law fluids of second grade. For the so-called secondorder power-law fluids, the explicit analytic solutions are given by recursive formulas with constant coefficients. Also, for the real power-law index in a quite large range an analytic approach is proposed. It is demonstrated that the approximate solution agrees well with the finite difference solution. This provides further evidence that the homotopy analysis method is a powerful tool for finding excellent approximations to nonlinear equations of the power-law fluids of second grade.

We tackle the very fundamental problem of zero-point energy divergence in the context of the Casimir effect. We calculate the Casimir force due to field fluctuations by using standard cavity radiation modes. The validity of convergence generation by means of an exponential energy cut-off factor is discussed in detail.

The effect of time-dependent temperatures on surface waves is investigated. Nonlinear stability analysis is performed to describe waves propagating along the interface between two fluids in the presence of mass and heat transfer. Due to the presence of periodic forces, resonance interaction is balanced. The use of a multiple-scales method yields different nonlinear Schrödinger equations. Two parametric nonlinear Schrödinger equations are derived in resonance cases. One of these equations has not been treated before. Its stability criteria depending on linear perturbation are derived. A classical nonlinear Schrödinger equation is derived in the nonresonance case. Stability conditions are obtained analytically and investigated numerically. It is shown that the resonance point depends on the external frequency and that, for Ω ≈ 2ω and Ω ≈ ω, where Ω and ω are the external and disturbance frequency, the external frequency has stabilizing and destabilizing effects, respectively.

We have investigated the effect of doping concentration on structural, optical and magnetic properties of Mn-doped ZnO thin films deposited on Si (100) substrate by RF magnetron sputtering. The films have been characterized by X-ray diffraction (XRD), photoluminescence (PL) and superconducting quantum interference device (SQUID) magnetometry. It is observed from XRD, that the increase of Mn content increases the FWHM which indicates the degradation of crystalline quality. The photoluminescence spectrum reveals that the incorporation of Mn ions suppresses the deep level emissions considerably in comparison to those observed in pure ZnO. The near band edge (NBE) emission of Mn-doped films is shifted to the lower energy side (red shift) in comparison to pure ZnO film. The room temperature SQUID magnetometer results reveal that all the films show paramagnetic behaviour due to the lack of interactions among Mn moments.

A gated four probe measurement technique to isolate contact resistances in field effect measurements on disordered organic semiconductors was investigated. Organic field effect transistors (OFETs) were prepared with two additional electrodes in the contact geometry protruding into the source-drain channel to monitor the variation in potential across the channel. Two high impedance electrometers were used to determine the potential at the contacts. This technique allows to directly determine the magnitude of the parasitic contact resistances between metal contact and organic semiconductor from the drop in potential at the contact regions. The effects of contact resistances, which can falsify measurements on bulk transport parameters such as the field effect mobility, can be then eliminated during material characterization. Additionally, the temperature and electric field dependence of the contact resistances offers valuable information about the charge injection and extraction processes between metal and organic semiconductor. The effects of the four probe geometry, specifically the effect of the channel electrodes on the current-voltage characteristics, of hole transport in a polythiophene (P3HT) OFET with Au contacts were investigated and found not to influence device performance, except at currents « 1 nA. The IV characteristics were shown to follow the expected FET behaviour. From the variation in potential along the channel it was found that contact resistances at the source contact (charge injecting contact) are minimal while contact resistances at the drain contact (charge extracting contact) are significant, resulting in a much lower effective sourcedrain voltage than that applied to the device.

The thermal stability of FeS 2 cathode material for thermal batteries is investigated in the LiCl-KCl eutectic containing up to 10 wt% Li 2 O (used as anti-peak). The results show that the decomposition of pyrite shifts to higher temperatures in the presence of molten salts as the S 2 gas is repressed by the liquid phase. For high lithium oxide contents the decomposition temperature of pyrite decreases by 100 °C. In addition Li 2 FeS 2 as reaction product is evidenced whereas Li 3 Fe 2 S 4 is expected from literature data.

The rate constants of the hydrolysis of p-substituted benzonitriles with sulfuric acid solutions (18.2 M to 10 M) have been determined spectrophotometrically at (25.1±0.1) °C. It was found that the catalytic activity of sulfuric acid was strongly inhibited by water. The logarithms of the observed rate constants were correlated with different substituent inductive (localized) and resonance (delocalized) constants. The results of the correlation studies indicated that the rate-determining step of the hydrolysis of benzonitriles in 18.2 M sulfuric acid was the addition of a nucleophile, and the hydrolysis was clearly enhanced by the electron-withdrawing inductive effect, while the rate-determining step of the hydrolysis of p-substituted benzonitriles in 10.0 M sulfuric acid was most probably the protonation of benzonitriles, and the rate constants increased by both electron-donating resonance and inductive effects. A mixture of the two mechanisms most probably occurred in 15.3 to 17.0 M sulfuric acid. HSO 4 − rather thanwater most probably acted as nucleophile in the hydrolysis of benzonitriles especially at high concentrations of sulfuric acid solutions.

The local octahedral environment of Ni 2+ in NiTiF 6 ・ 6H 2 O and ZnSiF 6 ・ 6H2O crystals with a trigonal distortion has been studied at different temperatures, based on the complete energy matrices. The calculated results showed that the local lattice structure around an octahedral Ni 2+ centre in NiTiF 6 ・ 6H 2 O and ZnSiF 6 ・ 6H 2 O exhibits a compression distortion. Simultaneously, the orbital reduction effect on the g factors has been studied. The relationship between Δg = g || −g ⊥ and orbital reduction factor k at 4.2, 77 and 298 (302) K has been discussed, suggesting that there is an almost linear relation between k and Δg for the Ni 2+ ion in NiTiF 6 ・ 6H 2 O and ZnSiF 6 ・ 6H 2 O at each temperature.

The formulas for the energy levels and g factors for 3d 9 ions in an orthorhombic field with D 2h symmetry are obtained. They are used to investigate the energy levels and the g-anisotropy of Cu 2+ ions in a bis(L-asparaginato)zinc(II) single crystal. The theoretically calculated values of the energy levels have agree well with the observed optical spectrum of the Cu 2+ ions in the compound considered here, and also the calculated values of the g-anisotropy conform with the experimental values.