Band 63, Heft 3-4

Starting from an improved mapping approach and a linear variable separation approach, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for the (2+1)-dimensional breaking soliton system are derived. Based on the derived solitary wave solution, we obtain some special folded localized excitations and chaotic patterns.

We solve the inverse nodal problem for the diffusion operator. In particular, we obtain a reconstruction of the potential function and its derivatives using only nodal data. Results are a generalization of Law’s and Yang’s works.

The time-dependent nonlinear Boltzmann equation, which describes the time evolution of a single-particle distribution in a dilute gas of particles interacting only through binary collisions, is considered for spatially homogeneous and inhomogeneous media without external force and energy source. The nonlinear Boltzmann equation is converted to a nonlinear partial differential equation for the generating function of the moments of the distribution function. The variational-iteration method derived by He is used to solve the nonlinear differential equation of the generating function. The moments for both homogeneous and inhomogeneous media are calculated and represented graphically as functions of space and time. The distribution function is calculated from its moments using the cosine Fourier transformation. The distribution functions for the homogeneous and inhomogeneous media are represented graphically as functions of position and time.

He’s homotopy perturbation method (HPM) is applied to linear and nonlinear Schrödinger equations for obtaining exact solutions. The HPM is used for an analytic treatment of these equations. The results reveal that the HPM is very effective, convenient and quite accurate to such types of partial differential equations.

In this paper we present the soliton dynamics in a two port fiber nonlinear directional coupler with periodically modulated dispersion and coupling constant dispersion that arose due to the intermodal dispersion between symmetric and antisymmetric modes of the coupler. The fiber material possessed cubic quintic nonlinearity. The influences of the coupling constant dispersion, periodically modulated dispersion and quintic nonlinearity on the soliton switching dynamics have been comprehensively studied. The expressions for the transmission coefficient, cross talk and extinction ratio have been derived in the context of both quintic nonlinearity and periodically modulated dispersion. It has been found that an increase in the value of the quintic nonlinearity has detrimental influence on the soliton switching. Our analytical results have been supported by numerical simulation.

We argue that fractional order differential equations are more suitable to model complex adaptive systems. Hence they are applied in replicator equations for non-cooperative games. Rock-scissors-paper game is discussed. It is known that its integer order model does not have a stable equilibrium. Its fractional order model is shown to have a locally asymptotically stable internal solution. A fractional order asymmetric game is shown to have a locally asymptotically stable internal solution. This is not the case for its integer order counterpart.

We present an information-theoretic method to measure the structural information content of networks and apply it to chemical graphs. As a result, we find that our entropy measure is more general than classical information indices known in mathematical and computational chemistry. Further, we demonstrate that our measure reflects the essence of molecular branching meaningfully by determining the structural information content of some chemical graphs numerically.

Classical trajectory calculations for various atom-diatomic molecules were preformed using the three-dimensional Monte Carlo method. The reaction probabilities, cross-sections and rate constants of several systems were calculated. Equations of motion, which predict the positions and momenta of the colliding particles after each step, have been integrated numerically by the Runge-Kutta-Gill and Adams-Moulton methods. Morse potential energy surfaces were used to describe the interaction between the atom and each atom in the diatomic molecules. The results were compared with experimental ones and with other theoretical values. Good agreement was obtained between calculated rate constants and those obtained experimentally. Also, reasonable agreement was observed with theoretical rate constants obtained by other investigators using different calculation methods. The effects of the temperature, the nature of the colliding particles and the thermochemistry were studied. The results showed a strong dependence of the reaction rates on these factors.

Recently the CO 4 isomer with C 2v symmetry has been detected in an experiment [C. S. Jamieson et al., Chem. Phys. Lett. 440, 105 (2007)]. To further characterize this isomer, we report its optical excitation and absorption spectra calculated by the time-dependent density functional theory. Its rich spectral features are compared with those of another stable isomer having D 2d symmetry. Their spectral difference can be an evidence to distinguish the isomers in experiments.

The optimized molecular structures, vibrational frequencies and corresponding vibrational assignments of the two planar O- cis and O- trans rotomers of 2,4-, 2,5- and 2,6-difluorobenzaldehyde have been calculated using ab initio Hartree-Fock (HF) and density functional theory (B3LYP) methods with the 6-311++G(d,p) basis set level. The calculations were adapted to the CS symmetries of all the molecules. The O- trans rotomers with lower energy of all the compounds have been found as preferential rotomers in the ground state. The mean vibrational deviations between the vibrational frequency values of the two conformers of all the compounds have been shown to increase while the relative energies increase, and so it has been concluded that the higher the relative energy between the two conformers the bigger is the mean vibrational deviation.

The interaction of an e-beam with silica glass has been simulated using the 27SiO 2 cluster, charged from 0 to − 18 by a PM3 semiempirical quantum chemical method. The structures of the charged 27SiO 2 silica clusters and their physicochemical characteristics, namely the heat of formation, relative volume, electron density of states distribution, gap between HOMO and LUMO and charge distribution, have been derived and analyzed in order to study the processes occurring on the atomic level at an e-beam-irradiated surface. The overcharging of the silica cluster led to its expansion by 30% in volume and evaporation of the charged species, followed by cluster densification. The silica cluster expansion should lead to structural changes in the neighbouring silica glass areas.

Taking into account spin-spin (SS), spin-other-orbit (SOO), and orbit-orbit (OO) interactions in addition to general spin-orbit (SO) interactions, the local structures of Ni 2+ in CsMgX 3 (X = Cl, Br, I) are theoretically investigated by using the complete diagonalization method (CDM). On this basis, it is found that the local angles, at the Ni 2+ centres are larger than those, at the hosts. The contributions to the spin-Hamiltonian parameters from spin triplets and slight magnetic interactions are discussed.

The density-of-states effective mass approximation and the conduction-band effective mass approximation are employed to formulate carrier concentrations and the diffusivity-mobility relationship (DMR) for heavily doped n-semiconductors exhibiting band gap narrowing. These are very suitable for the investigation of electrical transport also in heavily doped p-semiconductors. Numerical calculations indicate that the DMR depends on a host of parameters including the temperature, carrier degeneracy, and the non-parabolicity of the band structure.

Au/n-GaAs Schottky barrier diodes (SBDs) have been fabricated. The effect of indentation on Schottky diode parameters such as Schottky barrier height (φ b ) and ideality factor ( n ) was studied by current-voltage ( I-V ) measurements. The method used for indentation was the Vickers microhardness test at room temperature. The experimental results showed that the I-V characteristics move to lower currents due to an increase of φ b with increasing indentation weight, while contacts showed a nonideal diode behaviour.

Empirical equations for the density and molar volume of molten binary mixtures of MCl-LnCl 2 and MCl-MeCl 2 (M = alkali metals; Ln = lanthanoides; Me = Ca, Sr, Ba) based on the density of individual components are suggested. The equations, taking into account the deviations of the molar volumes from their additive values, are applicable to all binary systems involving known rare earth dichlorides.

The actual occupancy of the two available cation sites by luminescent Eu 3+ ions, in the cubic bixbyite-type structure of nanocrystalline sesquioxides, has been investigated by 151 Eu Mössbauer spectroscopy and magnetic susceptibility measurements. It was found that one fourth of the europium ions is in the more symmetric site C 3i and three fourths in the less symmetric site C 2 ; the distribution is random. In the series of the Eu-doped sesquioxides Sc 2 O 3 , Lu 2 O 3 , Y 2 O 3 and Eu 2 O 3 , the covalency of the Eu-O bond and the Eu site distortion increase with the difference in ionic radii between europium and the cation of the host compound. The magnetic susceptibility has been analyzed as sum of the contributions of the free Eu 3+ ion, of the crystal-field effect and of the exchange interaction between europium ions.

The presence of charge transfer in EuSe is analyzed by experimental and theoretical X-ray diffraction data. The direction and amount of charge transfer are inferred by plotting and comparing the structure factor of the components. Thus a charge transfer of 0.22 electrons is obtained in EuSe from europium (Eu) to selenium (Se).

The effects of gamma radiation on tertiary butylhydroquinone (TBHQ) are reported using electron spin resonance (ESR) spectroscopy. While unirradiated (control) TBHQ exhibited no ESR signal, irradiated one presented an ESR spectrum with five characteristic resonance peaks extended over a magnetic field region of 1.5 mT. Variations of the heights of the resonance peaks and the spectrum area as function of the microwave power, applied dose, storage time, and temperature were studied. The kinetic features and spectroscopic parameters of the species responsible for the experimental ESR spectrum were investigated by annealing studies performed at four different temperatures and simulation calculations, respectively. A model based on the presence of two species having different kinetic and spectroscopic features was found to describe best the experimental results. The dosimetric potential of TBHQ was also investigated, and it was concluded that the discrimination of irradiated TBHQ from unirradiated one was possible even long after the radiation treatment, and that radiation doses above 5 kGy could be measured with an accuracy better than 3% by using TBHQ. Two tentative radical species were proposed.

The dielectric relaxation time (τ ) and dipole moment (μ) of binary mixtures of different molar concentrations of N -methylformamide (NMF) in binary mixtures of NMF and tetramethylurea (TMU) in benzene have been calculated at 25, 30, 35 and 40 ◦ C using standard standing wave microwave techniques and following the single frequency (9.885 GHz) concentration variational method of Gopala Krishna. The energy parameters (Δ H ε , Δ F ε , Δ S ε ) for the dielectric relaxation process of binary mixtures containing 30 mol% of NMF have been calculated at different temperatures, and comparison has been made with the corresponding energy parameters (Δ H η , Δ F η , Δ S η ) for the viscous flow process. Based on these studies, it was inferred that the dielectric relaxation process can be treated as a rate process just like the viscous flow process. Solute-solvent and solute-solute molecular associations have been proposed.