Band 6, Heft 3

A multi-color study of the variability of the magnetic cataclysmic variable BY Cam is presented. The observations were obtained at the Korean 1.8 m and Ukrainian 2.6 m, 1.2 m and 38 cm telescopes in 2003–2005, 56 observational runs cover 189 hours. The variations of the mean brightness in different colors are correlated with a slope dR/dV = 1:29(4), where the number in brackets denotes the error estimates in the last digits. For individual runs, this slope is much smaller ranging from 0.98(3) to 1.24(3), with a mean value of 1.11(1). Near the maximum, the slope becomes smaller for some nights, indicating more “blue” spectral energy distribution, whereas the night-to-night variability has an “infrared” character. For the simultaneous UBVRI photometry, the slopes increase with wavelength from dU/dR = 0:23(1) to dI/dR = 1:18(1). Such wavelength dependence is the opposite of that observed in non-magnetic cataclysmic variables, in agreement with the model of cyclotron emission. The principal component analysis shows two components of variablitity with different spectral energy distributions (with a third at the limit of detection), which possibly correspond to different regions of emission. The highest peak in the scalegram analysis corresponds to the 200 min spin variability, its quarter and to the 30 min and 8 min QPOs. The amplitudes of these components are dependent on wavelength and luminosity state. The light curves were fitted by a statistically optimal trigonometrical polynomial (up to 4th order) to take into account a 4-hump structure. The dependences of these parameters on the phase of the beat period and on mean brightness are discussed. The amplitude of spin variations increases with an increasing wavelength and with decreasing brightness. The linear ephemeris based on 46 mean minima for 2003–2005 is HJD 2453213:010(3) + 0:137123(3)E: The extensive tables of the original observations and of results of analysis are published in an electronic form. The nearby star GSC 4081–1562 was found to be an eclipsing red variable.

The spatial structure of a Bose-Einstein Condensate (BEC) loaded into an optical lattice potential is investigated. We suggest a method for generating chaos in BEC by modulating periodic signals to convert the regular states into chaotic states. The maximal Lyapunov exponent is calculated as a function of modulation intensity and modulation frequency respectively, and the chaotic orbits associated with the positive Lyapunov exponents.

A new theory explaining the intensity of f-f transitions and the crystal field using an approximation of a strong configuration interaction is proposed. The theory enables the anomalous influence of excited configurations with charge transfer on some multiplets of the f shell to be taken into account. With the help of this theory, a satisfactory description of the absorption transitions and luminescence branching ratios from 1 D 2 and 3 P 0 multiplets for the Pr3+ ion in double molybdates has been achieved for the first time. For further validation the theory, was used to provide a description of Stark splitting of Pr3+ — multiplets in elpasolites and determine the covalence parameters; these parameters were found to be in good agreement with values obtained by the other methods.

The energy levels of valence bands (VB) in SbSeBr crystals were calculated for investigation of the photoelectron emission spectra of A5B6C7 — type crystals. The molecular model of this crystal was used for calculation of VB by the Density Functional Theory (DFT) and Unrestricted Hartree — Fock (UHF) methods. The molecular cluster consisting of 20 molecules of SbSeBr was used for calculations of averaged total density of states including atom vibrations. The spectra of averaged total density of states from VB in the SbSeBr cluster were compared with experimental photoelectron emission spectra from VB of A5B6C7 — type crystals. The results of comparison clarify that the atomic vibrations are one of possible reasons for the smoother appearance of the experimental X-ray photoelectron spectrum (XPS).

We used STM to study the conductivity of 32 nucleotide long DNA molecules chemically attached to a gold surface. Two oligonucleotides containing all four base types namely G, A, C, T, one single stranded and one double helical, all showed conductance data significantly higher than DNA containing only T and A that were either single stranded d(T32) or double helical d(T32).d(A32) in confirmation. Within each sequence group, the conductivity of the double helical form was always higher than that of the single strand. We discuss the impact of structure, particular base stacking and affinity to the phase transition.

The motion of spiral waves in excitable media driven by a weak pacing around the spiral tip is investigated numerically as well as theoretically. We presented a Bifurcations diagram containing four types of the spiral motion induced by different frequencies of pacing: rigidly rotating, inward-petal meandering, resonant drift, and outward-petal meandering spiral. Simulation shows that the spiral resonantly drifts when the frequency of pacing is close to that of the spiral rotation. We also find that the speed and direction of the drift can be efficiently controlled by means of the strength and phase of the local pacing, which is consistent with analytical results based on the framework of the weak deformation approximation.

X-ray photoelectron spectroscopy (XPS), magnetization and magnetic susceptibility of Mn1−x Alx (x = 0.0, 0.2, 0.4, 0.5, 0.6, 0.7) alloys are reported. X-ray diffraction measurements showed that all investigated samples have the same crystallographic structure as the parent compound (AuCu3-structure type). The alloys are disordered for x ≤ 0.5, but become almost crystallographically ordered for higher Al concentration. This change in the crystallographic order is reflected both in the magnetization and Curie temperature values. The exchange interaction is ferromagnetic between the pairs of the near-neighbour Mn-Ni and Ni-Ni magnetic moments and antiferromagnetic for Mn-Mn pairs. The last one is present only in the disordered alloys, which leads to smaller values of the magnetization of these alloys in comparison with the ordered ones. The Mn magnetic moment has the fully ordered value of 3.2 μB in all investigated alloys. The decrease of the Ni magnetic moment as the Al concentration increases may be explained by the hybridization of the Ni 3d and Al 3sp states, which leads to a partial filling of the Ni 3d band. The magnetic susceptibility measurements pointed out the existence of spin fluctuations on Ni sites.

The dissociated core structure of dislocation in two-dimensional triangular lattice is determined by the variational method within lattice theory. The dissociation effect leads to a narrower core width of partial dislocations than the compact one. The equilibrium separation between two partial dislocations is not very sensitive to the intrinsic stacking fault energy and there exists deviation from the intrinsic stacking fault energy criterion in the continuous elastic theory of dislocation. The relationship between the equilibrium separation and intrinsic stacking fault energy is analogous in lattice theory and the Peierls-Nabarro model. But the equilibrium separation obtained in lattice theory is wider than that obtained in the Peierls-Nabarro model for the same intrinsic stacking fault energy.

The structural changes within the Silver iodide (AgI) and Copper iodide (CuI) induced by pressure have been investigated using an effective interaction potential. CuI and AgI in their parent zinc blende (ZnS) to rock salt (NaCl) through an intermediate structure have been reported. The calculated values for the phase transition pressures and associate volume collapses are generally in good agreement with measured data.

The polycrystalline Bi8Fe6Ti3O27 compound was prepared by a high-temperature solid-state reaction technique. Preliminary structural analysis by X-ray diffraction (XRD) confirms the formation of a single-phase compound in an orthorhombic crystal system at room temperature. The elemental content of the compound was analyzed by EDAX microanalysis. Microstructural analysis by scanning electron microscopy (SEM) shows that the compound has well defined grains, which are distributed uniformly throughout the surface of the pellet sample. Detailed studies of temperature-dependent dielectric response at various frequencies show dielectric anomalies at 380, 389 and 403°C for 10 kHz, 100 kHz, and 1 MHz respectively. The hysteresis loop observed by applying an electric field of 12 kV/cm on the poled sample with smaller remanent polarization supports the existence of ferroelectricity in this material. The value of d33 of the compound was found to be 19 pC/N.

Functional oligoperoxide surfactants and coordinating oligoperoxide metal complexes were studied as modifiers of glass flat plates to provide the localization of radical forming sites and other functional fragments in adsorbed polymeric layers of a nanoscale thickness. Both the kinetics of the coating formation and properties of the nanolayers witness the dependence of the packing density of oligoperoxide molecules in the coatings on the oligoperoxide natures, concentrations and conditions of the sorption modification. The availability of definite amount of peroxide groups in formed nanolayer provides the possibility of controlled radical graft polymerization initiated from modified surface leading to reliable surface protection, functionality and targeted surface hydrophilic-hydrophobic properties.

We present a new improvement to the Alekseev inverse scattering method. This improved inverse scattering method is extended to a double form, followed by the generation of some new solutions of the double-complex Kinnersley equations. As the double-complex function method contains the Kramer-Neugebauer substitution and analytic continuation, a pair of real gravitation soliton solutions of the Einstein’s field equations can be obtained from a double N-soliton solution. In the case of the flat Minkowski space background solution, the general formulas of the new solutions are presented.

The Einstein field equations for the Friedmann universe reduce to a system of three first-order equations for the space-like components and a constraint from the temporal component. We analyse the system from the viewpoints of symmetry and singularity analyses. The solutions of particular relevance to Cosmology are highlighted.

The mobility of electrons in vertical transport in GaAs/Ga1−y AlyAs barrier structures was investigated using geometric magnetoresistance measurements in the dark. The samples studied had Ga1−y AlyAs (0 ≤ y ≤ 0:26) linearly graded barriers between the n+-GaAs contacts and the Ga0:74Al0:26As central barrier, which contain N w (=0, 2, 4, 7 and 10) n-doped GaAs quantum wells. The mobility was determined as functions of (i) temperature (80–290 K) at low applied voltage (0.01–0.1 V) and (ii) applied voltage (0.005–1.6 V) at selected temperatures in the range 3.5–290 K. The experimental results for the temperature dependence of low-field mobility suggest that space-charge scattering is dominant in the samples with N w=0 and 2, whereas ionized impurity scattering is dominant in the samples with N w=4, 7 and 10. The effect of polar optical phonon scattering on the mobility becomes significant in all barrier structures at temperatures above about 200 K. The difference between the measured mobility and the calculated total mobility in the samples with N w=4, 7 and 10, observed above 200 K, is attributed to the reflection of electrons from well-barrier interfaces in the quantum wells and interface roughness scattering. The rapid decrease of mobility with applied voltage at high voltages is explained by intervalley scattering of hot electrons.

The charge form factor of the 6Li nucleus is considered on the basis of its cluster structure. The charge density of 6Li is presented as a superposition of two terms. One of them is a folded density and the second one is a sum of the 4He and deuteron densities. Using the available experimental data for 4He and deuteron charge form factors, a satisfactory agreement of the calculations within the suggested scheme is obtained with the experimental data for the charge form factor of 6Li, including those in the region of large transferred momenta.

In the paper calculation of the moments of inertia for nuclei from the region 87 ≤ Z ≤ 100 and 130 ≤ N ≤ 156 was made in dependence on the angular momentum of their rotational states. The experimental values of the moments of inertia were calculated for rotational energy of the classic rotor in its quantum form, with the use of a simple formula. The moment of inertia term appearing in the formula was treated as a variable. The calculations were carried out on the basis of experimental data for the energies of the rotational levels for 51 bands built on ground states for even-even nuclei and for nuclei with odd mass number A. In addition, 30 rotational bands built on excited states were also analysed in the investigated region in case of even-even nuclei. For many bands and nuclei the considered dependence of the moment of inertia on angular momentum has been found in the analytical form by fitting polynomials to the experimental data. It turned out that obtained results for the moments of inertia made it possible to describe the energies of rotational levels with a relative deviation not greater or only slightly greater than 1%. In general, in the case of 12 bands of ground level the maximum relative deviation of obtained level energies is smaller than 1%.

The even-even Selenium isotopes in the A∼80 mass region and the general features of its structure have been investigated within the framework of the interacting boson model-2. The neutron proton version of the model has been applied to the Se (A=74 to 80) isotopes with emphasis on the description of the 01+, 21+, 02+, 22+ and 41+ states. The energy levels, B(E2)and B(M1)electromagnetic transition probabilities were calculated. The results of these calculations were compared with previous experimental results and were shown to be in good agreement.

The influence of phosphate glass electrode in the configuration of resistive plate chamber has been studied using GEANT3.21 Monte Carlo code. Bakelite electrodes were replaced by phosphate glass electrodes, as these glass materials have low bulk resistivity, are portable and easy to handle. These types of RPCs in their compact form of all materials are suitable for high rate background environment. We find that these new types of RPCs give little higher response to γ-rays and e+/e− particles, both for single-and double gap RPCs. The results of simulation are discussed.

We have studied the formation of the molecular ion Rb2+ and the atomic ion Rb+. These are created in laser excited rubidium vapor at the first resonance, 5s–5p and 5p-nl transitions. A theoretical model is applied to this interaction to explain the time evolution and the laser-power dependence of the population density of Rb+ and Rb2+. A set of rate equations which describe: the temporal variation of the population density of the excited states; the atomic ion density; and the electron density, were solved numerically under the experimental conditions of Barbier and Cheret. In their experiment the Rb concentration was 1×1013cm−3 and the laser power was taken to be 50–500 mW at vapor temperature = 450 K. The results showed that the main processes for producing Rb2+ are associative ionization and Hornbeck-Molnar ionization. The calculations have also showed that, the atomic ions Rb+ are formed through the Penning Ionization (PI) and photoionization processes. Moreover, a reasonable agreement between the experimental results and our calculations for the ion currents of the Rb+ and Rb2+ is obtained.

Noise can induce an inverse period-doubling transition and chaos. The effects of noise on each periodic orbit of three different period sequences are investigated for the logistic map. It is found that the dynamical behavior of each orbit, induced by an uncorrelated Gaussian white noise, is different in the mergence transition. For an orbit of the period-six sequence, the maximum of the probability density in the presence of noise is greater than that in the absence of noise. It is also found that, under the same intensity of noise, the effects of uncorrelated Gaussian white noise and exponentially correlated colored (Gaussian) noise on the period-four sequence are different.

In our work we propose a novel method of analysis of photorefractive transport equations. The method based on a perturbative approach can be used in the case of two wave mixing and four wave mixing geometry, i.e. for the samples illuminated by interference patterns. Presented approach can be employed for a broad range of material and experimental parameters, particularly for arbitrary depth of light modulation pattern. The approximate analytical solution is compared with results of numerical calculations and a good agreement practically in every case was found.

We study nonlinear interactions between discrete optical solitons that propagate in different regimes of diffraction, and the nonlinear scattering of dispersive waves by local optical potentials. It is well known in optics that when linear coherent waves meet, they interfere without interactions. Linear waves also scatter through local optical structures not exchanging any power with the guided modes of these structures. As a focusing Kerr nonlinearity is present, such linearly-inhibited phenomena can exist. Our studies are performed in silica and AlGaAs nonlinear waveguides, excited by ultra-short pulses in the near infrared.

The main methods describing polarization of electromagnetic waves in weakly anisotropic inhomogeneous media are reviewed: the quasi-isotropic approximation (QIA) of geometrical optics method that deals with coupled equations for electromagnetic field components, and the Stokes vector formalism (SVF), dealing with Stokes vector components, which are quadratic in electromagnetic field intensity. The equation for the Stokes vector evolution is shown to be derived directly from QIA, whereas the inverse cannot be true. Derivation of SVF from QIA establishes a deep unity of these two approaches, which happen to be equivalent up to total phase. It is pointed out that in contrast to QIA, the Stokes vector cannot be applied for a polarization analysis of the superposition of coherent electromagnetic beams. Additionally, the ability of QIA to describe a normal modes conversion in inhomogeneous media is emphasized.

We investigate the transverse second-harmonic generation in as grown strontium barium niobate (SBN) crystals with a random structure of anti-parallel ferroelectric domains. We consider both, single and counter-propagating pulse geometries. We investigate polarization properties of the second harmonic signal and discuss applications of this process for short pulses characterization.

Orientational nonlinearity is the major mechanism of nonlinear optical phenomena observed in liquidcrystalline phase while it does not appear to such extent in any other materials. It is caused by distortion of initial molecular arrangement of an anisotropic medium induced by optical field. Deformation of the anisotropic structure means spatial changes of refractive index of the medium. This effect has been studied in earnest since the 1980s as its application became more apparent. In this paper, some results of experimental examination of molecular reorientation in nematics by optical field are presented, which are not explained in frame of existing Oseen-Frank model and Erickson-Leslie continuous theory. Possible reasons of this discordance are considered and a way of explanation is suggested.

A brief overview of recent theoretical results in the area of three-dimensional dissipative optical solitons is given. A systematic analysis demonstrates the existence and stability of both fundamental (spinless) and spinning three-dimensional dissipative solitons in both normal and anomalous group-velocity regimes. Direct numerical simulations of the evolution of stationary solitons of the three-dimensional cubic-quintic Ginzburg-Landau equation show full agreement with the predictions based on computation of the instability eigenvalues from the linearized equations for small perturbations. It is shown that the diffusivity in the transverse plane is necessary for the stability of vortex solitons against azimuthal perturbations, while fundamental (zero-vorticity) solitons may be stable in the absence of diffusivity. It has also been found that, at values of the nonlinear gain above the upper border of the soliton existence domain, the three-dimensional dissipative solitons either develop intrinsic pulsations or start to expand in the temporal (longitudinal) direction keeping their structure in the transverse spatial plane.

A mode-selective directional coupler based on titanium in-diffused channel waveguides in lithium niobate is investigated. This coupler may be utilized as a key part of an add-drop multiplexer for dense wavelength division multiplexing in optical network nodes. The proposed coupler is based on evanescent coupling of the fundamental mode of a single-mode channel to the first higher mode of a parallel bi-modal waveguide. Our experimental results show that a compact directional coupler with coupling efficiencies larger than 90%, large bandwidth around 1550 nm, and with negligible polarization dependence can be realized using electro-optic lithium niobate substrates.

We overview our recent theoretical results on spatio-spectral control, diffraction management, and broadband all-optical switching of polychromatic light in periodically curved one and two dimensional arrays of coupled optical waveguides. In particular, we show that polychromatic light beams and patterns produced by white-light and supercontinuum sources can experience wavelength-independent normal, anomalous, or zero diffraction in specially designed structures. We also demonstrate that in the nonlinear regime, it is possible to achieve broadband all-optical switching of polychromatic light in a directional waveguide coupler with special bending of the waveguide axes. Our results suggest novel opportunities for creation of all-optical logical gates and switches which can operate in a very broad frequency region, e.g., covering the entire visible spectrum.

The method of paraxial complex geometrical optics (CGO) is presented, which describes Gaussian beam diffraction in arbitrary smoothly inhomogeneous media, including lens-like waveguides. By way of an example, the known analytical solution for Gaussian beam diffraction in free space is presented. Paraxial CGO reduces the problem of Gaussian beam diffraction in inhomogeneous media to the system of the first order ordinary differential equations, which can be readily solved numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous media as compared to the numerical methods of wave optics. For the paraxial on-axis Gaussian beam propagation in lens-like waveguide, we compare CGO solutions with numerical results for finite differences beam propagation method (FD-BPM). The CGO method is shown to provide 50-times higher rate of calculation then FD-BPM at comparable accuracy. Besides, paraxial eikonal-based complex geometrical optics is generalized for nonlinear Kerr type medium. This paper presents CGO analytical solutions for cylindrically symmetric Gaussian beam in Kerr type nonlinear medium and effective numerical solutions for the self-focusing effect of Gaussian beam with elliptic cross section. Both analytical and numerical solutions are shown to be in a good agreement with previous results, obtained by other methods.

We have investigated the nonlinear propagation of light in photonic crystal fibers filled with nematic liquid crystals. We analyzed a configuration with a periodic modulation of the refractive index corresponding to a matrix of waveguides. Matrices of coupled waveguides allow observing a variety of new phenomena both for low power light beam propagation and with an existence of nonlinear effects. The opportunity for the creation of solitary waves caused by the interplay between diffraction and nonlinear effects in these kinds of fibers is investigated. At low power the propagating light beam spreads as it couples to more and more waveguides. When the intensity is increased the light modifies the refractive index distribution, inducing a defect in the periodic structure. The creation of such a defect can lead to a situation in which the light becomes self-localized and its diffractive broadening is eliminated. Eventually, in the case of positive Kerr-type nonlinearity, a discrete soliton can be created. In the case of negative nonlinearity the refractive index decreases with the optical power and can lead to bandgap shifting. The incident beam, with a frequency initially within the bandgap, is then turned outside the bandgap resulting in the changing of the propagation effect for the discrete diffraction effect. As a consequence the delocalization of the light can be observed.

In this paper we discuss the joint propagation of a periodically modulated field and a pulse of different frequency in an optical fiber. The pulse experiences the action of an index lattice induced via cross-phase modulation by the periodic field. We predict effects of discreteness to show up both in the temporal and in the spatial domain. For large walk-off between the two fields one should observe Bloch oscillations in frequency space, where discrete diffraction is expected to occur for equal velocities of both waves.

This paper analyzes the second harmonic generation (SHG) efficiency of light with partial temporal coherence due to depolarization effects in birefringent media. It discusses relations between SHG efficiency fading, light source spectrum, crystal birefringence, and phase matching conditions. The efficiency of SHG pumped by the partially coherent light beam that may depolarize light in nonlinear birefringent crystal is also analyzed. The basic theory of SHG with its modification for partially coherent light with depolarization and some numerical calculations of the SHG process are described.

The effect of adsorbed Sn as a surfactant on Ge diffusion on a Si(111) surface has been studied by Low Energy Electron Diffraction and Auger Electron Spectroscopy. The experimental dependence of Ge diffusion coefficients on the Si(111) surface versus temperature in the presence of adsorbed Sn atoms has been measured in the range from 300 to 650°C. It has been shown that at a Sn coverage of about 1 monolayer the mobility of Ge atoms increases by several orders of magnitude.

Single crystalline ZnO film is grown on GaN/sapphire (0001) substrate by molecular beam epitaxy. Ga2O3 is introduced into the ZnO/GaN heterostructure intentionally by oxygen-plasma pre-exposure on the GaN surface prior to ZnO growth. The crystalline orientation and interfacial microstructure are characterized by X-ray diffraction and transmission electron microscopy. X-ray diffraction analysis shows strong c-axis preferred orientation of the ZnO film. Cross-sectional transmission electron microscope images reveal that an additional phase is formed at the interface of ZnO/GaN. Through a comparison of diffraction patterns, we confirm that the interface layer is monoclinic Ga2O3 and the main epitaxial relationship should be $$ (0001)_{ZnO} \parallel (001)_{Ga_2 O_3 } \parallel (0001)_{GaN} $$ and $$ [2 - 1 - 10]_{ZnO} \parallel [010]_{Ga_2 O_3 } \parallel [2 - 1 - 10]_{GaN} $$.

Using a pulsed laser deposition (PLD) process on a ZnO target in an oxygen atmosphere, thin films of this material have been deposited on Si(111) substrates. An Nd: YAG pulsed laser with a wavelength of 1064 nm was used as the laser source. The influences of the deposition temperature, laser energy, annealing temperature and focus lens position on the crystallinity of ZnO films were analyzed by X-ray diffraction. The results show that the ZnO thin films obtained at the deposition temperature of 400°C and the laser energy of 250 mJ have the best crystalline quality in our experimental conditions. The ZnO thin films fabricated at substrate temperature 400°C were annealed at the temperatures from 400°C to 800°C in an atmosphere of N2. The results show that crystalline quality has been improved by annealing, the optimum temperature being 600°C. The position of the focusing lens has a strong influence on pulsed laser deposition of the ZnO thin films and the optimum position is 59.5 cm from the target surface for optics with a focal length of 70 cm.

A new approximate analytical technique to address for non-linear problems, namely Optimal Homotopy Asymptotic Method (OHAM) is proposed and has been applied to thin film flow of a fourth grade fluid down a vertical cylinder. This approach however, does not depend upon any small/large parameters in comparison to other perturbation method. This method provides a convenient way to control the convergence of approximation series and allows adjustment of convergence regions where necessary. The series solution has been developed and the recurrence relations are given explicitly. The results reveal that the proposed method is very accurate, effective and easy to use.

We construct explicit Darboux transformations of arbitrary order for a class of generalized, linear Schrödinger equations. Our construction contains the well-known Darboux transformations for Schrödinger equations with position-dependent mass, Schrödinger equations coupled to a vector potential and Schrödinger equations for weighted energy.

A string action which is essentially a Willmore functional is presented and studied. This action determines the physics of a surface in Euclidean three space which can be used to model classical string configurations. By varying this action an equation of motion for the mean curvature of the surface is obtained which is shown to govern certain classical string configurations. Several classes of classical solutions for this equation are discussed from the symmetry group point of view and an application is presented.

In this paper we present two results. First, we derive the most general group of infinitesimal transformations for the Schrödinger Equation of the general time-dependent Harmonic Oscillator in an electric field. The infinitesimal generators and the commutation rules of this group are presented and the group structure is identified. From here it is easy to construct a set of unitary operators that transform the general Hamiltonian to a much simpler form. The relationship between squeezing and dynamical symmetries is also stressed. The second result concerns the application of these group transformations to obtain solutions of the Schrödinger equation in a time-dependent potential. These solutions are believed to be useful for describing particles confined in boxes with moving boundaries. The motion of the walls is indeed governed by the time-dependent frequency function. The applications of these results to non-rigid quantum dots and tunnelling through fluctuating barriers is also discussed, both in the presence and in the absence of a time-dependent electric field. The differences and similarities between both cases are pointed out.

A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form $$ V(r,\theta ) = \tfrac{1} {8}\kappa r_e^2 \left( {\tfrac{r} {{r_e }} - \tfrac{{r_e }} {r}} \right)^2 + \tfrac{{\beta cos^2 \theta }} {{r^2 sin^2 \theta }} $$. The energy eigenvalues and eigenfunctions of the bound-states for the Schrödinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions.

Making an ansatz to the wave function, the exact solutions of the D-dimensional radial Schrödinger equation with some molecular potentials, such as pseudoharmonic and modified Kratzer, are obtained. Restrictions on the parameters of the given potential, δ and ν are also given, where η depends on a linear combination of the angular momentum quantum number ℓ and the spatial dimensions D and δ is a parameter in the ansatz to the wave function. On inserting D = 3, we find that the bound state eigensolutions recover their standard analytical forms in literature.

The analytic mean-field approach (AMFP) was applied to study the thermodynamic properties of Zirconium (Zr). The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived. The formalism for the case of the Morse potential is used in this work. The four potential parameters are determined by fitting the molar volume of the three phases of Zr. The calculated molar volume of α, β and ω Zr are in fairly good agreement with the available experimental data. The results presented in this paper verify that the AMFP is a useful approach to study the thermodynamic properties of Zr. Furthermore, we predict the variation of the relationship of free energy and internal energy versus the molar volume at various temperatures and the dependence of the bulk modulus, the thermal expansion coefficient and the heat capacity on temperature at zero pressure of α, β and ω Zr.

The centripetal and Coriolis accelerations experienced by a cart traveling over a rotating turntable are usually calculated proceeding from the known kinematics of the problem. Respective forces can be regarded as due to the entrainment of the cart in the moving solid environs. We extend the approach to the general case of a particle entrained in the flow of the surrounding medium. The expression for the driving force on the particle obtained from the kinematics of the entrainment prescribed appears to be isomorphic to the Lorentz and Coulomb force on a positive electric charge. The inverse direction of the electromagnetic force on a negative charge implies that a growing applied flow induces the upstream motion of the particle. A possible microscopic mechanism for it may be the Magnus force dynamics of a kink in a vortex tangle. The loop on a straight vortex filament can be taken as a model of the electron, the loop with a cavitation models the positron. The Lorentz force is concerned with the Coriolis acceleration. The Coulomb interaction is due to the centripetal or centrifugal force that arises in the turbophoresis of the kink in the perturbation field generated in the medium by the center of pressure.

We apply the Asymptotic Iteration Method to obtain the bound-state energy spectrum for the d-dimensional Klein-Gordon equation with scalar S(r) and vector potentials V(r). When S(r) and V(r) are both Coulombic, we obtain all the exact solutions; when the potentials are both of Kratzer type, we obtain all the exact solutions for S(r) = V(r); if S(r) > V(r) we obtain exact solutions under certain constraints on the potential parameters: in this case, a possible general solution is found in terms of a monic polynomial, whose coefficients form a set of elementary symmetric polynomials.

The electronic energy-band structure, density of states (DOS), and optical properties of AgBO3 in the paraelectric cubic phase have been studied by using density functional theory within the local density approximation for exchange-correlation for the first time. The band structure shows a band gap of 1.533 eV (AgNbO3)and 1.537 eV (AgTaO3)at (M-⌈)point in the Brillouin zone. The optical spectra of AgBO3 in the photon energy range up to 30 eV are investigated under the scissor approximation. The real and imaginary parts of the dielectric function and — thus the optical constants such as reflectivity, absorption coefficient, electron energy-loss function, refractive index, and extinction coefficient — are calculated. We have also made some comparisons with related experimental and theoretical data that is available.

In a first stage, the paper deals with the derivation and the solution of the equation of the probability density function of a stochastic system driven simultaneously by a fractional Gaussian white noise and a fractional Poissonian white noise both of the same order. The key is the Taylor’s series of fractional order f(x + h) = E α(hαDx α)f(x) where E α() denotes the Mittag-Leffler function, and D x α is the so-called modified Riemann-Liouville fractional derivative which removes the effects of the non-zero initial value of the function under consideration. The corresponding fractional linear partial differential equation is solved by using a suitable extension of the Lagrange’s technique involving an auxiliary set of fractional differential equations. As an example, one considers a half-oscillator of fractional order driven by a fractional Poissonian noise.

Among all the theories proposed to explain the “anomalous” perihelion precession of Mercury’s orbit first announced in 1859 by Le Verrier, the general theory of relativity proposed by Einstein in November 1915 alone could calculate Mercury’s “anomalous” precession with the precision demanded by observational accuracy. Since Mercury’s precession was a directly derived result of the full general theory, it was viewed by Einstein as the most critical test of general relativity from amongst the three tests he proposed. With the advent of the space age, the level of observational accuracy has improved further and it is now possible to detect this precession for other planetary orbits of the solar system — viz., Venus and the Earth. This conclusively proved that the phenomenon of “anomalous” perihelion precession of planetary orbits is a relativistic effect. Our previous papers presented the mathematical model and the computed value of the relativistic perihelion precession of Mercury’s orbit using an alternate relativistic gravitational model, which is a remodeled form of Einstein’s relativity theories, and which retained only experimentally proven principles. In addition this model has the benefit of data from almost a century of relativity experimentation, including those that have become possible with the advent of the space age. Using this model, we present in this paper the computed values of the relativistic precession of Venus and the Earth, which compare well with the predictions of general relativity and are also in agreement with the observed values within the range of uncertainty.

Direct Numerical Simulation (DNS) of decaying isotropic 3D magnetohydrodynamic (MHD) turbulence based on the 10243-modes in a periodic box is used to study the statistical properties of turbulence. In this paper, the presence of intermittency in MHD turbulence is investigated through the analysis of the Probability Distribution Function (PDF) for Elsässer fields and total energy fluctuations. We observe that the PDFs of the Elsässer fields fluctuations display a strong non-Gaussian behavior at small scale, which can be ascribed to multifractality feature, while the PDFs of the total energy fluctuations have the same shape over all observed scales and are monofractal. The PDFs have stretched exponential tail and satisfy the function P(|δX|) ∼ exp(−A|δX|μ). Numerically, we extract the exponent μ and find that it is constant for monofractal behavior as the length scale varies. To check the notion of self-similarity in the respective fluctuation, we apply the compensated structure functions.