Volume 60, Issue 8-9

We find new analytic solitary-wave solutions, having a nonzero background at infinity, of the coupled Korteweg-De Vries equation, using the auxiliary function method. We study the dynamical properties of the solitary-waves by numerical simulations. It is shown that the solitary-waves can be stable or unstable, depending on the coefficients of the model. We study the interaction dynamics by using the solitary-waves as initial profiles to show that the mass and energy of the coupled Korteweg- De Vries can be conserved for a negative third-order dispersion term. - PACS numbers: 03.40.Kf, 02.30.Jr, 47.20.Ky, 52.35.Mw

In this paper, some properties of the elliptic ordinary differential equation, which can be used to find travelling wave solutions of nonlinear evolution equations, are given. - PACS: 03.65.Ge

We have studied, analytically, the Ablowitz-Ladik discrete nonlinear Schr¨odinger system. We have found a set of exact solutions which includes as particular cases periodic solutions in terms of elliptic Jacobian functions, bright and dark soliton solutions, and quasi-periodic solutions. We have also found the range of parameters where each exact solution exists. - PACS: 02.30.Jr, 05.45.Yv, 42.65.Tg, 02.30.Gp.

Thermal instability in a horizontal layer of an electrically conducting fluid heated from below has been investigated under the effects of uniform rotation about a vertical axis and an applied uniform vertical magnetic field. The temperature field between the walls of the fluid layer consists of two parts; a steady part and a time-dependent part, which varies periodically. The effect of modulation of the walls temperature on the onset of convection has been studied using Floquets theory. Stabilizing and destabilizing effects on the onset of convective instability have been found. Some comparisons have been made. - 2000 Mathematics Subject Classification: 76E06, 76R10.

The electronic states of a Kane-type semiconductor anti-wire with and without a magnetic field are theoretically investigated. The eigenvalues and eigenstates of Kane’s Hamiltonian are obtained. The calculations are performed for a hard-wall confinement potential, and electronic states are obtained as functions of the magnetic field applied along the cylinder axis. The size dependences of the effective g-value in InSb for electrons and light holes are calculated. The effective g-values of the electrons and light holes decreased with decreasing anti-wire radius.

Some properties of the Willamowski-Rössler model are studied by numerical simulations. From the original equations a minimal version of the model is derived which also exhibits the characteristic properties of the original model. This minimal model shows that it contains the Volterra-Lotka oscillator as a core component. It thus belongs to a class of generalized Volterra-Lotka systems. It has two steady states, a saddle point, responsible for chaos, and a fixed point, dictating its dynamic behaviour. The chaotic attractor is located close to the surface of the basin of attraction of the saddle node. The mean values of the variables are equal to the (unstable) steady state values during oscillations even under chaos, and the variables are always non-negative as in other generalized Volterra-Lotka systems. Surprisingly this was also the case with the original reversible Willamowski-Rössler model allowing to compare the entropy production during oscillations with the entropy production of the steady states. During oscillations the entropy production was always lower even under chaos. Since under these circumstances less energy is dissipated to produce the same output, the oscillating system is more efficient than the non-oscillatory one.

The molecular structures and vibration frequencies of unidentate and bidentate coordinations of carbonate ions to calcium ions in the zeolite CaA have been investigated, using the Hartree-Fock method implementing 6-31 G and 6-311 G basis sets. From the calculations, for both coordinations the structures give rise to theoretical vibration frequencies corresponding well to the experimental results. Therefore the charge of the divalent calcium ion is distributed in the zeolitic structure, and not near the guest carbonate ion. Optimized structural parameters for the two coordinations have been given.

The hyperfine structure constant A and the superhyperfine interaction parameters Aʹ and Bʹ of Cs 2 GeF 6 :Mn 4+ are theoretically studied by the cluster approach. The orbital mixing coefficients and the unpaired spin densities in 2s, 2p σ and 2p π fluorine orbitals are obtained from the optical spectra and the impurity-ligand distance of the studied system. Based on a uniform scheme, the parameters A, Aʹ and Bʹ (as well as the g factor) are reasonably explained. The results are discussed, and the unpaired spin densities of the 2s, 2p σ and 2p π orbitals of the ligand F − are compared with those in previous works.

The gyromagnetic factors g ∥ , g ⊥ and the hyperfine structure constants A ∥ and A ⊥ of the tetragonal Cu 2+ center in KTaO 3 are theoretically studied in this work. Based on the analyses of the electron paramagnetic resonance results of this center, it is found that the impurity Cu 2+ occupies the octahedral Ta 5+ site, associated with a nearest-neighbouring oxygen vacancy V O along the C 4 axis. Due to the electrostatic repulsion of V O , Cu 2+ is displaced away from V O by ΔZ(≈ −0.29 Å ) along the C4 axis. The theoretical values of the g and A factors based on the above defect structure and the impurity displacement agreee reasonably with the experimental data.

The pure rotational spectra in the ground vibrational state of (1,2- 13 C)ketene, H 2 13 C= 13 CO, (D 2 ,1- 13 C)ketene, D 2 C= 13 CO, (D 2 ,2- 13 C)ketene, D 2 13 C=CO, and (D 2 , 18 O)ketene, D 2 C=C 18 O, have been observed in the frequency region 200 - 350 GHz. All the spectral lines have been measured in natural abundances with a source modulated millimeterwave spectrometer. From the measured R-branch transitions a set of rotational and centrifugal distortion constants for each isotopomer could be derived, using the Watson S-reduction formalism. Further, the rotational spectra of the two isotopomers (4,5-D)ketene, D2CCO, and (4-D)ketene, DHCCO, which were already measured several years ago, have been extended to higher J-values and higher frequencies, as it is the case for all investigated isotopomers of this work. As a result of these studies a calculation of a mass-dependent structure will be the topic of a next paper.

New Hofmann-T d type complexes in the form of Ni(4-Phenylpyridine) 2 M(CN) 4 (M= Cd or Hg) were prepared in powder form and their infrared spectra are reported in the region of 4000 - 200 cm −1 . From the spectral findings, these compounds are similar in structure to the Hofmann-T d type complexes.

The adsorption of 1,5-pentanedithiol (1,5-PDT) and 1,6-hexanedithiol (1,6-HDT) in liquid phases on NaA (or 4A-type), CaA (or 5A-type) and NaY zeolites has been studied by using infrared spectroscopy. From the IR spectra it is found that the peak positions of the symmetric as well as the antisymmetric modes of the methylene (CH 2 ) groups are observed at almost the same band values for the title dithiolates adsorbed on the A-type and NaY zeolites. On the other hand, the weak SH stretching vibration, observed for all samples, can be attributed to the sulphure atoms of 1,5-PDT and 1,6-HDT coordinatively adsorbed on cationic sites of the zeolites.

Infrared spectroscopy has been used to investigate the adsorption of liquid benzoyl chloride on A-type zeolites. The data show that at room temperature the Fermi resonance phenomenon occurs in the adsorption on KA, NaA and CaA zeolites which are little acidic aluminosilicates.

A simple liquid solution model is proposed to describe the effect of solvent-solute interactions on the solubility of nonpolar and slightly polar substances in supercritical solvents. Treating the system as an ideal solution, the effect of pressure on the solubility is zero or nearly zero, as it is governed by the difference in molar volume of the pure supercooled liquid solute and the pure solid solute, and this may be nearly zero. Deviations from ideal behavior are given by activity coefficients of the Margules type with the interaction parameter w interpreted as interchange energy as in the lattice theory. The hypothesis is put forward that the interchange energy is of the same form as a function proposed by Liptay and others to describe the effect of the solvent on the wavelength of the absorption maximum of the solute dissolved in the solvent. The function consists of a radius of interaction a and a function g(ε ) of the dielectric constant ε of the solvent, treated as a continuum. The function g depends on pressure through the pressure dependence of the dielectric constant ε (P). The attractive feature of this formalism, introduced by Baumann et al. and here justified thermodynamically, is that plots of the logarithm of solubility vs. g are linear, except for polar solutes near the solvent’s critical point. Changes in slope then admit interpretation as changes in the radius of interaction a with possible clues about the mechanism of solvation of these molecules.

Molten Gd-Si and Y-Si alloys were examined calorimetrically at 1760 and 1770 K, respectively. The partial enthalpies of mixing of gadolinium (Δ mix H̅ Gd ), yttrium (Δ mix H̅ Y ) and silicon (Δ mix H̅ Si ) were measured. The integral enthalpy of mixing (Δ mix H) was calculated by Darken’s method. The available thermodynamic data of liquid (Gd,Y)-Si alloys were compared. The partial enthalpies of mixing of Gd and Y, and appropriate integral enthalpies of mixing, were described by polynomial dependencies versus mole fraction of Gd or Y.

The solvation characteristic of 2-methoxy-4-aminobenzoic acid methyl ester (MABAE) and 2- methoxy-4-dimethylaminobenzoic acid methyl ester (MDABAE) in the S 0 , S 1 (LE) and S 1 (ICT) states has been determined by means of solvatochromic shifts in neat and binary solvent mixtures. The multiple linear regression analysis of Kamlet et al. indicates that non-specific dielectric dipoledipole and specific hydrogen-bonding interactions play almost an equal role in defining the position of the absorption and fluorescence maxima. On the basis of the performed analysis of normalized solvatochromic shifts, it has been shown that both solutes are preferentially solvated. For cyclohexane-ethanol (CH-EtOH) binary mixtures the preferential solvation characteristics in the S 0 , S 1 (LE) and S 1 (ICT) states are determined predominantly by the hydrogen-bonding interactions. For both molecules under study the electric dipole moment in the S 0 , S 1 (LE) and S 1 (ICT) states as well as the outer-sphere solvent reorganization energy (λ out ), intramolecular reorganization energy (λ in ), and destabilization energy (E dest. ) have been determined.

The rate of the oxidation of triethylamine by ferricyanide ions in sodium hydroxide or potassium hydroxide solutions has been determined spectrophotometrically at 25℃. Analysis of the kinetic data indicates that the hydroxide ion does not appear in the rate law. Strong retardation of the oxidation of triethylamine, caused by the addition of ferrocyanide ions, has been observed. A plausible mechanism is suggested, and a suitable rate law, congruent with the experimental observations, has been derived.