Volume 63, Issue 1-2

A set of relationships between parameters of the Dunham and Murrell-Sorbie potential energy function is developed. By employing Taylor series expansion and comparison of terms arranged in increasing order of bond length, a set of Dunham coefficients is obtained as functions of Murrell- Sorbie parameters. The conversion functions reveal the importance of factorials in extracting Dunham coefficients from Murrell-Sorbie parameters. Plots of both functions, based on parameters of the latter, reveal good correlation near the equilibrium bond length for a group of diatomic molecules. Potential function relations, such as that shown in this paper, are useful when the preferred/reliable data is based on a potential function different from that adopted in available computational software.

First, a function projective synchronization is defined in discrete-time dynamical systems, in which the drive and response state vectors evolve in a proportional scaling function matrix. Second, based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discrete-time chaotic systems. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate the function projective synchronization between the 2D Lorenz discrete-time system and the Fold discrete-time system, as well as between the 3D hyperchaotic Rössler discrete-time system and the Hénon-like map. Numeric simulations are used to verify the effectiveness of our scheme. By choosing different scaling functions, the interesting attractor figures of the drive and response systems are showed in a proportional scaling function.

In this study, after introducing the hyperbolic octonionic (counteroctonion) algebra, which is also expressed in the sub-algebra of sedenions, and differential operator, Proca-Maxwell equations and relevant field equations are derived in compact, simpler and elegant forms using hyperbolic octonions. This formalism demonstrates that Proca-Maxwell equations can be expressed in a single equation.

We propose He’s homotopy perturbation method (HPM) to solve stiff systems of ordinary differential equations. This method is very simple to be implemented. HPM is employed to compute an approximation or analytical solution of the stiff systems of linear and nonlinear ordinary differential equations.

In the present work, treating the arteries as a thin-walled and prestressed elastic tube with a stenosis and the blood as a Newtonian fluid with negligible viscosity, we have studied the amplitude modulation of nonlinear waves in such a composite system by use of the reductive perturbation method. The governing evolution equation was obtained as the variable coefficient nonlinear Schr¨odinger (NLS) equation. By setting the stenosis function equal to zero, we observed that this variable coefficient NLS equation reduces to the conventional NLS equation. After introducing a new dependent variable and a set of new independent coordinates, we reduced the evolution equation to the conventional NLS equation. By seeking a progressive wave type of solution to this evolution equation we observed, that the wave trajectories are not straight lines anymore; they are rather some curves in the (ξ ,τ ) plane. It was further observed that the wave speeds for both enveloping and harmonic waves are variable, and the speed of the enveloping wave increases with increasing axial distance, whereas the speed of the harmonic wave decreases with increasing axial coordinates. The numerical calculations indicated that the speed of the harmonic wave decreases with increasing time parameter, but the sensitivity of wave speed to this parameter is quite weak.

Dense matter, if put under high pressure, can undergo a transformation from an atomic to a molecular configuration, where the electron orbits go into lower energy levels. If the rise in pressure is very sudden, for example by a strong shock wave, the electrons change their orbits rapidly under the emission of photons, which for more than 100 Mbar can reach keV energies. With the opacity of dense matter going in proportion to the density, the photons can be efficiently released from the surface of the compressed matter by a rarefaction wave. The so produced X-ray photons can be used for the fast ignition of a thermonuclear target. The proposed mechanism may be also responsible for the large keV X-ray bursts observed in exploding wire arrays, which can not be explained by conversion of kinetic into thermal energy.

Density functional theory (DFT) calculations have been performed to calculate the optimized geometries of stepwise fluorinated methylenecyclopropanes and 1-methylcyclopropenes. Increasing the number of fluorine atoms caused a destabilization of methylenecycopropane. Perfluorinated 1-methylcyclopropene was found to be present in substantial concentration. This is supported by calculations of the Gibbs free energy, isodesmic reactions and orbital energies (HOMO-LUMO). These results are compared with the fluorinated cyclopropanes keto-enol system. Enthalpies, entropies and dipole moments are reported.

Direct density functional theory (DFT) classical trajectory calculations show that after bissuperoxo FAl(O 2 ) 2 ionization, one of the side-on dioxygen units undergoes a fast intramolecular rearrangement generating a stable radical cation which presents both a peroxo and a peroxyl group bound to the central Al atom, FAl(O 2 )OO ・+ . Molecular properties of this predicted novel species have been estimated at the B3PW91/6-311+G(3df) and G3B3 levels of theory.

A new method for the determination of the equation of state is investigated and applied for MgO crystals. The method is developed by using the Hildebrand approximation and an analytical potential form for the overlap repulsive energy derived by Harrison from quantum mechanical considerations. The bulk modulus is also evaluated for MgO in the temperature range 300 - 200 K and down to a compression of V/V0 = 0.6 using an expression based on the Chopelas-Boehler approximation. The results obtained agree well with the ab-initio values determined by Isaak et al.

The errors in viscosity measurements by the oscillating cup method were calculated as a function of the limit of accuracy imposed by the uncertainty in determining the constants of the oscillating system R, I, T 0 , δ 0 and the limit of precision resulting from errors in determining the experimental parameters δ , T , h, ρ. Thus, by evaluating the fractional error of each of the parameters and implicitly its distinct contribution to the total standard error, it was established that the “meniscus error” Δh, which is difficult to be controlled or avoided, represents the major source of imprecision of oscillating cup viscometers.

The temperatures T liq of molten xWO 3 -(1−x)KPO 3 mixtures with a molar content between x = 0 and x=0.60 have been determined by differential thermal analysis. The surface tension of the xWO 3 - (1−x)KPO 3 melts in the interval from x = 0 to x = 0.5 has been measured by ring tensiometry for temperatures 10 K- 20 K above the melting points, up to 1373 K. The data obtained for KPO 3 were fitted by a linear dependence on the temperature and compared with data available in the literature. The surface tension of the xWO 3 -(1−x)KPO 3 melts was found to decrease non-monotonously with x. Three bends at x ~ 0.15, 0.30, and 0.45 were observed in the surface tension vs. molar fraction curve. The first and the third bends correspond to eutectic compositions; the second one is related to the formation of congruently melting K 2 WO 2 P 2 O 7 . Equations describing the temperature and concentration dependences of the surface tension are proposed.

A series of ionic liquids consisting of 1-butyl-1-methylpyrrolidinium chloride (Pyr 14 Cl) and TaCl 5 at molar ratios of Pyr 14 Cl in the range of 0.85 - 0.20 was synthesized. They exhibit potential application as electrolytes for the electrochemical deposition of tantalum. The thermal behaviour of the Pyr 14 Cl-TaCl 5 mixtures was investigated, using differential scanning calorimetry (DSC) to estimate the range of thermal stability and to determine the optimal compositions for electrochemical trials. The Pyr 14 Cl-TaCl 5 mixtures formed stoichiometric 3 : 2 and 2 : 3 crystalline phases with melting points of 70 °C and 130 °C, respectively, characterized by entropies of fusion of 13.6 JK −1 mol −1 and 10.1 JK −1 mol −1 . The mixtures with molar fractions of Pyr 14 Cl equal to 0.60 and 0.40 were clear and transparent liquids and had the lowest viscosity; they were the most suitable for electrochemical applications. FTIR spectra of the Pyr 14 Cl-TaCl 5 mixtures allowed to get insight into inter-ionic interactions and the nature of formation of these ionic liquids as a function of the molar ratio of the components.

FTIR spectroscopic and electrochemical characterizations of tantalum(V) in 1-butyl-1-methylpyrrolidinium trifluoromethanesulfonate (Pyr 14 TFMS)-TaCl 5 ionic liquids are performed with 5, 15, and 35 mol% TaCl 5 as the media for potential electrochemical application. On the basis of FTIR spectra the electrochemical active species are identified as follows: [TaOCl 4 ] − , [TaOCl 5 ] 2− , [TaCl 5 F] − , and [TaCl 5 F 2 ] 2− . The dominant species are the oxochloride complexes of tantalum(V). Cyclic voltammograms of Pyr 14 TFMS-TaCl 5 mixtures at 80 °C exhibit three reduction peaks: at −0.8 V, −0.9 V, and −2.4 V. The first reduction peak corresponds to the reduction of the oxochloride species of tantalum(V), the second is assigned to the reduction of the mixed chloride-fluoride species of tantalum(V), and the third peak to the further reduction of tantalum. The spectroscopic data confirm the suggestion that oxochloride complexes of tantalum(V) become the dominant species in ionic liquids with the oxygen-containing functional group [CF 3 SO 3 ]−, possibly restricting the process of tantalum metal deposition from these ionic liquids.

The effect of Berry’s phase on the nuclear quadrupole resonance (NQR) spectra of rotating powder samples is studied experimentally, and its application for the determination of the electric field gradient asymmetry η is demonstrated. The NQR frequency splittings, which are observed for the spin 3/2 nucleus of 35 Cl in powder samples of p-dichlorobenzene (C 6 H 4 Cl 2 ) and cyanuric chloride (C 3 N 3 Cl 3 ), are interpreted as a manifestation of Berry’s phase, associated with the adiabatically changing Hamiltonian due to sample rotation. The accumulation of Berry’s phase during the rotation process is responsible for the observed dependence of the NQR line shape on the rotation frequency and the asymmetry parameter. The proposed method for the determination of η involves the analysis of the NQR powder patterns of the rotating samples.

The temperature dependence of the 14 N NQR frequencies has been measured in a polycrystalline sample of diphenylamine by nuclear quadrupole double resonance. Two non-equivalent diphenylamine molecules have been observed. The NQR parameters in diphenylamine were related to the NQR parameters obtained in other amines and to the molecular and crystal structure.

Dielectric relaxation of different molar concentrations of ethanol (C 2 H 5 OH) in binary mixtures of ethanol and chlorobenzene in benzene solutions has been studied at 9.883 GHz by using standard standing microwave techniques and Gopala Krishna’s single frequency concentration variation method at different temperatures (25 °C, 30 °C, 35 °C, and 40 °C). It was found that the dielectric relaxation time varies linearly with variation in the molar concentration of ethanol in the whole concentration range of the binary mixture. Based upon these results the absence of solute-solute and the presence of solute-solvent type of molecular associations could be assumed. The energy parameters for the dielectric relaxation process of binary mixtures containing 50 mol% of ethanol have been calculated at the given temperatures. Comparison has been made with the corresponding energy parameters for viscous flow processes. It was found that the dielectric relaxation process can be treated as the rate process like the viscous flow process.

The electrochemistry of molten LiCl-KCl-GdCl 3 at a reactive Al electrode has been studied at 723 to 823 K. Electrochemical techniques such as cyclic voltammetry and chronopotentiometry have been used in order to identify the intermetallic compounds formed. Cyclic voltammetry showed that, while at an inert W electrode GdCl 3 is reduced to Gd metal in a single step at a potential close to the reduction of the solvent, at an Al electrode a shift towards more positive values occurs. This shift of the cathodic potential indicated a reduction of the activity of Gd in Al with respect to that ofW, due to the formation of alloys. The surface characterization of samples formed by both galvanostatic and potentiostatic electrolysis has shown the presence of two intermetallic compounds: GdAl 3 and GdAl 2 . Using open-circuit chronopotentiometry it has been possible to measure the potentials at which these compounds are transformed into each other. The values of these potential plateaus, once transformed into e. f. m. values, allowed to determine the thermodynamic properties of the GdAl 3 intermetallic compound.

The electrochemical properties of the chlorides of the actinides U, Pu, Np and Am (AnCl 3 ) were investigated by transient electrochemical techniques in the LiCl-KCl eutectic at 400 - 550 °C. The diffusion coefficients of the cations and the apparent standard potentials of the redox systems on an inert W electrode were measured. The Gibbs energy of dilute solutions of AnCl 3 as well as the activity coefficients were derived from electrochemical measurements. In addition, the electrochemical behaviour of the actinides on an Al electrode was investigated. They formed AnAl 4 alloys, the formation potentials of which allowed a quantitative recovery of the actinides and their separation from fission products and especially from lanthanides. In addition, the thermochemical properties of the AnAl 4 alloys were determined by electrochemical measurements.

UV spectrophotometric measurements were done on mixtures of the ubiquinones Ub,0 and Ub,10 in their monomeric form (c < 10 −5 mol/l) with the nucleosides; adenosine, cytidine, 2′-desoxyadenosine, 2′-desoxy-quanosine, guanosine and thymidine, as well as the nucleic acid bases; adenine, cytosine, hypoxanthine, thymine and uracil. Applying the Liptay method, it was found that both ubiquinones form 1 : 1 interaction complexes with the nucleic acid components. The complexation constants were found in the order of 10 5 mol −1 . The calculated ΔG values were negative (∼−7.0 kcal/mol), suggesting a favoured hydrogen bridge formation. This is confirmed by the positive change of the entropy ΔS. The complexation enthalpies ΔH for all complexes are negative, suggesting exothermal interactions.