Band 63, Heft 12

The variational iteration method, a well-known method for solving functional equations, is employed to solve a class of eighth-order boundary-value problems, which govern scientific and engineering experimentations. Some special cases of the mentioned equations are solved as examples to illustrate the ability and reliability of the method. The results reveal that the method is very effective and convenient.

A numerical technique is developed for solving Abel’s integral equations. The solutions of such equations may exhibit a singular behaviour in the neighbourhood of the initial point of the interval of integration. The proposed method is based on the shifted Legendre collocation technique. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

We report the existence of a new family of stable stationary solitons in the one-dimensional cubicquintic complex Ginzburg-Landau equation with the viscosity term. By applying the paraxial ray approximation, we obtain the relation between the width and the peak amplitude of the stationary soliton in terms of the model parameters. We find the bistable solitons in the presence of the small viscosity term.We verify the analytical results by direct numerical simulations and show the stability of the stationary solitons. We conclude that the existence condition obtained by the paraxial method may serve as physically more reliable initial condition for stable stationary soliton propagation in the optical system modeled by the one-dimensional cubic-quintic complex Ginzburg-Landau equation with the viscosity term, of which analytical solution is not obtainable with all nonzero parameters.

On the basis of symbolic computation a generalized sub-equation expansion method is presented for constructing some exact analytical solutions of nonlinear partial differential equations. To illustrate the validity of the method, we investigate the exact analytical solutions of the inhomogeneous high-order nonlinear Schrödinger equation (IHNLSE) including not only the group velocity dispersion, self-phase-modulation, but also various high-order effects, such as the third-order dispersion, self-steepening and self-frequency shift. As a result, a broad class of exact analytical solutions of the IHNLSE are obtained. From our results, many previous solutions of some nonlinear Schrödinger-type equations can be recovered by means of suitable selections of the arbitrary functions and arbitrary constants. With the aid of computer simulation, the abundant structure of bright and dark solitary wave solutions, combined-type solitary wave solutions, dispersion-managed solitary wave solutions, Jacobi elliptic function solutions and Weierstrass elliptic function solutions are shown by some figures.

The interesting dynamical behaviours exhibiting in chemical reaction systems, such as multiple steady states and undamped oscillations, often result from unstable steady states. A positive real eigenvalue condition is proposed which gives a necessary and sufficient condition for the determination of an unstable steady state having a positive real eigenvalue in general isothermal reaction networks. Formulas are developed to construct an unstable steady state and a set of positive rate constants. The applications are illustrated by three examples. Two give rise to oscillations and one admits multiple steady states.

The plasmon and screening effects on the occurrence scattering time advance for elastic electronion collisions are investigated in hot quantum plasmas. The effective screening model taking into account the plasmon and screening effects is employed to represent the electron-ion interactions in hot quantum plasmas. The Glauber method is applied to obtain the occurrence scattering time as a function of the scattering angle, impact parameter, plasmon parameter, collision energy, and Debye length. It is shown that the occurrence scattering time advance is enhanced with increasing the plasmon effect and scattering angle. In addition, it is shown that the occurrence scattering time advance decreases with increasing the collision energy. It is also found that the plasmon effect is dominant for the forward scattering domain and, however, the screening effect is getting important with an increase of the scattering angle.

A nonlinear (energy) stability analysis is performed for a magnetized ferrofluid layer, heated and soluted from below, with stress-free boundaries. A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. For ferrofluids we find that the existence of subcritical instabilities is possible, however, it is noted that, in case of a nonferrofluid, the global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of the magnetic parameters, this coincidence is immediately lost. The effects of the magnetic parameter, M 3 , and the solute gradient, S1, on the subcritical instability region have also been analyzed. It is shown that with the increase of the magnetic parameter the subcritical instability region between the two theories decreases quickly, while with the increase of the solute gradient the subcritical region expands. We also demonstrate the coupling between the buoyancy and magnetic forces in the nonlinear energy stability analysis.

The tetrafluoroborate of hexadimethylsulfoxidemanganese(II) was synthesized and studied by differential scanning calorimetry. Five solid phases of [Mn(DMSO) 6 ](BF 4 ) 2 were revealed. Specifically, four phase transitions of the first order were detected between the following solid phases: stable KIb↔stable KIa at T C4 = 215 K; metastable KIII↔overcooled K0 at T C3 = 354 K; metastable KII↔overcooled K0 at T C2 =377 K; stable KIa→stable K0 at T C1 =385 K. [Mn(DMSO) 6 ](BF 4 ) 2 starts to decompose at 400 K with a loss of one DMSO molecule per formula unit and forms [Mn(DMSO) 5 ](BF 4 ) 2 which next decomposes in one step to MnF 2 at the temperature range of 460 - 583 K. From the entropy changes it can be concluded that the phases K0 and metastable KII are orientationally dynamically disordered (ODDIC) crystals. The stable phases KIb and KIa are ordered solid phases.

The dielectric constant, ε′ , and dielectric loss, ε″ , of dilute solutions of benzonitrile (C 6 H 5 CN) in benzene have been measured at 9.885 GHz at 25, 30, 35, and 40 °C using standard standing microwave techniques. Following the single frequency concentration variational method of Gopala Krishna, the dielectric relaxation time, τ , and the dipole moment, μ, at various temperatures have been calculated. It was concluded that dielectric relaxation processes can be treated as rate processes just like the viscous flow process. Based on the above studies, the monomer structure of benzonitrile in benzene has been inferred. The solute-solvent molecular association of benzonitrile in benzene has been found. The energy parameters ΔH ε , ΔF ε , ΔS ε for the dielectric relaxation process of benzonitrile in benzene at different temperatures have been calculated and compared with the corresponding energy parameters ΔH η , ΔF η , ΔS η for the viscous flow process.

Electronic energy transfer between prodan (6-propionyl-2-dimethylaminonaphthalene) and laurdan (6-dodecanoyl-2-dimethylaminonaphthalene) acting as donors and ORB (octadecyl rhodamine B) acting as acceptor in a model system of membranes has been studied by a steady-state fluorescence quenching analysis. Factors determining the energy transfer rate were considered with special attention to the contribution from the spectral heterogeneity of the donor molecules. By analyzing experimental data within the framework of two theoretical models (developed by Stern, Volmer, and Lehrer) of the energy transfer in two-dimensional systems, the limits of the range of possible prodan and laurdan positions with respect to a lipid bilayer have been estimated.

The Hamiltonian matrices for 3d 3 ions in a cubic crystal field are introduced, based on a molecular orbital model, including the electronic Coulomb and tetrahedral crystal-field interactions and the spin-orbit coupling. The optical absorption spectra of V 2+ ions in ZnSe are studied. Moreover, the various additional levels found close to 5680 cm −1 are considered. These levels are assumed to result from the dynamic Jahn-Teller splitting within the excitation levels 2 T 2 and 2 T 1 in ZnSe:V 2+ . The good agreement between the present results and the experimental observations indicates that the contribution of the covalence reduction factors N E and N T2 and of the Racah parameter A to the optical absorption spectra of V 2+ ions in ZnSe is important. However, most of the previous theoretical studies of these spectra in ZnSe:V 2+ have neglected the Racah parameter A, based on the classical crystalfield model. A significant charge-transfer effect found in recent works is confirmed in ZnSe:V 2+ .