Band 64, Heft 7-8

We establish a mathematical model for the three-patch diffusion predator-prey system with time delays. The theory of Hopf bifurcation is implemented, choosing the time delay parameter as a bifurcation parameter. We present the condition for the existence of a periodic orbit of the Hopf-type from the positive equilibrium.

With applications in the higher-power and femtosecond optical transmission regime, a generalized variable-coefficient higher-order nonlinear Schrödinger (VC-HNLS) equation is analytically investigated. The multi-solitonic solutions of the generalized VC-HNLS equation in double Wronskian form is constructed and further verified using the Wronskian technique. Additionally, an infinite number of conservation laws for such an equation are presented. Finally, discussions and conclusions on results are made with figures plotted.

In this work, the homotopy perturbation method proposed by Ji-Huan He [1] is applied to solve both linear and nonlinear boundary value problems for fourth-order partial differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solution to show the efficiency of the method. The results show that the homotopy perturbation method is of high accuracy and efficient for solving the fourth-order parabolic partial differential equation with variable coefficients. The results show also that the introduced method is a powerful tool for solving the fourth-order parabolic partial differential equations.

In this paper, a differential equation describing the optimum path of a flying object is derived. The density of the fluid is assumed to be exponentially decaying with altitude. The equation is cast in to a dimensionless form and the exact solution is given. This equation is then analyzed by homotopy analysis method (HAM). The results showed in the figures reveal that this method is very effective and convenient.

In this paper, the variational iteration method is proposed to solve Fredholm’s nth-order integrodifferential equations. The initial approximation is selected wisely which satisfies the initial conditions. The results reveal that this method is very effective and convenient in comparison with other methods.

We consider a Hamilton operator in a finite dimensional Hilbert space with energy level crossing. We discuss the question how energy level crossing and entanglement of states in this Hilbert space are intertwined. Since energy level crossing is related to symmetries of the Hamilton operator we also derive these symmetries and give the reduction to the invariant Hilbert subspaces.

The thermosolutal instability of couple-stress fluid in the presence of uniform vertical rotation is considered. Following the linearized stability theory and normal mode analysis, the dispersion is obtained. For the case of stationary convection, the stable solute gradient and rotation have stabilizing effects on the system, whereas the couple-stress has both stabilizing and destabilizing effects. The dispersion relation is also analyzed numerically. The stable solute gradient and the rotation introduce oscillatory modes in the system, which did not occur in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

The effect of a magnetic field and suspended dust particles on both the Kelvin-Helmholtz (K-H) and the Rayleigh-Taylor (R-T) instability of two superimposed streaming magnetized plasmas is investigated. The magnetized fluids are assumed to be incompressible and flowing on top of each other. The usual magnetohydrodynamic (MHD) equations are considered with suspended dust particles. The basic equations of the problem are linearized and the dispersion relation is obtained using normal mode analysis by applying the appropriate boundary conditions. The general dispersion relation is found to be modified due to the presence of the suspended dust particles and of the magnetic field. The effect of the magnetic field appears in the dispersion relation if three-dimensional perturbations of the system are considered. The general conditions of the K-H instability as well as the R-T instability are derived for the considered medium. The stability of the system for both cases is discussed by applying the Routh-Hurwitz criterion. Numerical analysis is performed to show the effect of various parameters on the growth rates of the K-H and R-T instabilities. Three different cases of the present configurations are considered and the conditions of instability are obtained. It is found that the conditions for the K-H and R-T instabilities depend on the magnetic field, on the suspended dust particles and on the relaxation frequency of the particles. The magnetic field and particle density have stabilizing influence, while the density difference between the fluids has a destabilizing influence on the growth rate of the K-H and R-T configurations.

We systematically analyze the molten salt database of Janz to gain a better understanding of the relationship between molten salts and their properties. Due to the multivariate nature of the database, the intercorrelations amongst the molten salts and their properties are often hidden and defining them is challenging. Using principal component analysis (PCA), a data dimensionality reduction technique, we have effectively identified chemistry-property relationships. From the various patterns in the PCA maps, it has been demonstrated that information extracted with PCA not only contains chemistryproperty relationships of molten salts, but also allows us to understand bonding characteristics and mechanisms of transport and melting, which are difficult to otherwise detect.

Dynamic nuclear polarization experiments were performed to study the solutions of the stable free radicals Galvinoxyl and α,γ -Bisdiphenylene-β -phenyl allyl complex with benzene (1 : 1) in some highly fluorinated aliphatic and aromatic solvents. The measurements were performed at four different temperatures to test the dipolar and the scalar part of the coupling between the fluorine nucleus ( 19 F) and the unpaired electron. It was found that in the samples with Galvinoxyl the dipolar interactions are more effective for the aromatic solvents, while the scalar interactions are more effective for the aliphatics. An alteration from negative to positive region for the nuclear-electron coupling parameter informing on scalar or dipole-dipole interaction was observed only for 2,2,3,4,4,4-Hexafluoro- 1-butanol solvent with increasing temperature. The nuclear-electron coupling parameter varies between −0.003 and 0.228 in all aliphatic solvents and between 0.180 and 0.318 in aromatic solvents. Overhauser enhancement was not observed in the samples prepared with Hexadecafluoroheptane, Heptafluorobutyric acid, and Nonafluoropentanoic acid for both free radicals in all temperatures. These solvents may have scavenging effects on the radicals due to their behaviour.

The electrorefining of cobalt in NaCl-KCl-K 2 TiF 6 (20 wt%) melt has been investigated. It was shown that complexes of Ti(III) and Co(II) appeared in the melt due to the reaction 2Ti(IV) + Co → 2Ti(III) + Co(II) and this reaction was entirely shifted to the right hand side. On the base of linear sweep voltammetry diagnostic criteria it was found that the discharge of Co(II) to Co metal is controlled by diffusion. The limiting current density of discharge Co(II) to metal in NaCl-KCl-K 2 TiF 6 (20 wt%) melt was determined by steady-state voltammetry. The electrorefining of cobalt was carried out in hermetic electrolyser under argon atmosphere. Initial cathodic current density was changed from 0.2 Acm −2 up to 0.7 Acm −2 , the electrolysis temperature varied within 973 - 1123 K. Behaviour of impurities during cobalt electrorefining was discussed. It was shown that electrorefining led to the elimination of most of the interstitial impurities (H 2 , N 2 , O 2 , C), with the result that the remaining impurity levels below 10 ppm impart high ductility to cobalt.

Langmuir and Langmuir-Blodgett (LB) films formed of some fluorescent dyes, derivatives of 4-aminonaphthalimide, and their binary mixtures with the liquid crystal 4-heptyl-4’-cyanobiphenyl (7CB) have been studied. Surface pressure versus mean molecular area isotherms for Langmuir films have given information about the alignment of molecules in a monomolecular layer at the air/water interface. The absorption and fluorescence spectra of LB films have revealed the occurrence of aggregates among dye molecules. In the ground electronic state some fraction of aggregates of J-type have appeared, while in the excited state the excimers have been created. The latter statement has been confirmed by additional absorption and fluorescence measurements performed for dyes dissolved in 7CB and placed in sandwich cells of 10 μm in thickness.

The paper presents results of the share viscosity measurements performed as a function of temperature and concentration for mixtures of α-tocopherol acetate (vitamine E acetate) and mesitylene, two liquids of essentially different viscosity (four order of magnitude difference at 280 K). The viscosity/ temperature dependence for pure α-tocopherol acetate as well as for the mixtures studied can be well described with the Vogel-Fulcher-Tammann equation. The viscosities of the mixtures exhibit a strong negative deviation from the rule of additive dependence on concentration and for increasing temperature the maximum value of the deviation shows an exponential decreasing.

Recently, many studies for the local structure of 3d 5 ions in octahedrally coordinated compounds are made by simulating the EPR parameters on the basis of the complete energy matrix. However, for the 3d 4 ions in tetrahedrally coordinated compounds, the studies are relatively fewer. In this work, by diagonalizing the complete energy matrix for a d 4 configuration in a tetragonal ligand-field within a strong-field representation, the local structure around Cr 2+ in CdS crystal is studied. Our results show that there exists a compression distortion in the local lattice structure. From our calculations, the distortion parameters ΔR = −0.022 A° and Δθ = −1.410° are obtained.

A theoretical method for studying the inter-relationship between electronic and molecular structure is presented by means of complete energy matrices. As an application, the effects of temperature, concentration and hydrostatic pressure on the local structures of Ni 2+ doped Zn(BF 4 ) 2 ・6H 2 O crystal have been studied. Our results show that the local lattice structures of [Ni(H 2 O) 6 ] 2 + coordination complex have expansion distortions as the temperature rises. Meanwhile, we find that the local structure parameter θ becomes smaller with the increasing concentration of Ni 2+ ions doped in Zn(BF 4 ) 2 ・6H 2 O crystal. Furthermore, the pressure dependence of θ and anisotropic g-factors are discussed and the relationship between zero-field splitting parameter D and Δg is determined.

Dye-sensitized zinc oxide thin films were prepared, characterized and optimized for applications as photoelectrochemically active electrodes. Conditions were established under which crystalline thin films of ZnO with a porous texture were formed by electrochemically induced crystallization controlled by structure-directing agents (SDA). Dye molecules were adsorbed either directly as SDA during this preparation step or, preferably, following desorption of a SDA. The external quantum efficiency (IPCE) could thereby be increased significantly. Particular emphasis was laid on dye molecules that absorb in the red part of the visible spectrum. Model experiments under ultrahigh vacuum (UHV) conditions with dye molecules adsorbed on defined crystal planes of single crystals aimed at a deeper understanding of the coupling of the chromophore electronic π-system within molecular aggregates and to the semiconductor surface. Detailed photoelectrochemical kinetic measurements were used to characterize and optimize the electrochemically prepared dye-sensitized ZnO films. Parallel electrical characterization in vacuum served to distinguish between contributions of charge transport within the ZnO semiconductor matrix and the ions of the electrolyte in the pore system of the electrode.