Table of contents

The bound state energy eigenvalues and the corresponding wave functions of the "deformed" Rosen-Morse and modified Rosen-Morse potentials have been obtained by the Nikiforov-Uvarov method (Büyükkiliç et al 1997 Theor. Chim Acta.98 192). The "deformed hyperbolic functions" that were introduced for the first time by Arai (1991 J. Math. Anal. Appl.158 63) have been used. The energy eigenvalues of these "deformed hyperbolic molecular potentials" bring up the criteria for the shape invariance of the potentials according to the deformation parameter q, as well as bringing a bound for the value of the parameter.

We study the coupled Einstein–Euler–Lagrange equations for non-stationary domain walls. Solutions to these equations are exhibited to be self-consistent with the choice of the energy-momentum tensor of the form T_t^t = T_x^x = T_y^y and T_z^z = 0. It is found that domain walls are usually non-static and the scalar field potential depends on the metric coefficients.

Traffic on a one-lane freeway with two species of vehicles is investigated using the asymmetric exclusion model with open boundaries. The vehicles are filed from their probability of jam, the fast vehicle can overtake the slow one. Using numerical simulations, densities and currents of vehicles are calculated on one hand, as a function of the position in the road and in the other hand as a function of the rate of vehicles entry. The effects of the moving rate P₂₀ of the slow vehicles and the jumping rate Δt on the (α, β) phase diagram are examined. A passage from first to second order transition occurs by decreasing the jumping rate and/or decreasing the moving rate of the slow vehicles.

The expansion of moments technique for generating short-time expansions for the moments associated with the probability density p(x, t) is used to solve the diffusion-convection-reaction equations. The obtained results are compared with those found by other theories such as Lie group theory and operator technique.

A previously proposed and tested (1996 Phys. Rev. Lett.76 102; 1996 Phys. Rev. Lett.77 2029) van der Waals density functional is applied to van der Waals complexes. Dynamic polarizabilities, α(iu), and dispersion coefficients, C₆, are obtained with a useful accuracy and at a low computational cost using ground-state electron densities as input. We compare results for C₆ for small and medium-sized molecules with existing results obtained using more cumbersome methods. The computational simplicity of the functional opens up the possibility to treat large systems of real interest within different fields of physics, chemistry and biology. This is illustrated by the application to C₆₀. We present results for the static polarizability α₀ and the dispersion coefficient C₆ for two such molecules.

We report theoretical transition probabilities for all allowed transitions between the lowest configurations in Ag II (4d¹⁰, 4d⁹5s and 4d⁹5p) and lifetimes of all 4d⁹5p levels. The method of superposition-of-configurations, in fully ab initio form, was employed. Our results are in particularly good agreement with previous experimental and theoretical work (Biémont E et al 1997 J. Phys. B: At. Mol. Opt. Phys.30 2067). Possible astrophysical applications are briefly discussed.

Spectra of rare earth elements emitted from ultra short pulse laser produced plasma were recorded using simultaneously high and low resolution, spectrometers. A study of the broad band emission of the Δn = 1 transitions in highly ionized Ba and Sm plasma showed that this band is completely unresolved. The spectra were analyzed using the LTE based on super-transition array (STA) model. The theory reconstructs the entire Ba spectrum using a single temperature and density, whereas for Sm the discrepancies between the theory and experiment are not reconcilable. The agreement in the Ba case is attributed to the fact that BaF₂ target is transparent to the laser's prepulse effects, producing a homogeneous dense plasma, whereas for Sm the dilute plasma created by the prepulse is far from LTE. The obtained results posses a significant implication to the applicability of the STA model, in particular for calculations of opacities and conversion of laser light to x-rays.

The spectra of lanthanum and cerium were photographed on a 10.7 m grazing incidence spectrograph in the 80 Å–500 Å region using a triggered spark source. The La XIII and Ce XIV spectra were investigated. Earlier analysis of La XIII was confirmed and seven additional lines were classified in this spectrum. In the Ce XIV spectrum the ground state 4d⁹²D separation was found to be 28401 cm^-1 and seventeen levels were established in the 4d⁸5p configuration. Nineteen lines were classified in this spectrum. Least squared fitted (LSF) and relativistic Hartree Fock (HFR) calculations were carried out to interpret the spectra.

A new operator approach to the solution of the non-relativistic Schrödinger equation for few-body quantum systems with pair-wise interaction is presented. The problem is solved on the basis of the sequential account of configurations (SAC) method proposed. The wave-function of a few-body system determined with allowance for the configuration interaction (CI-wavefunction) is expressed in terms of the one-configuration wavefunctions with use of the configuration mixing operator _(±) introduced in the paper. The examination is carried out with an example of a few-electron atomic system. An analytical expression for the _(±)-operator has been represented and an integral equation for the CI-wavefunction has been obtained. It is shown that: (I) the correlation interaction inside an isolated configuration does not destroy the independent particle approximation; (ii) in the framework of the present approach the self-action is excluded. The present approach has enabled to receive an analytical expression for the _(±)-operator without applying the non-physical procedure of 'switching-on' the interconfiguration interaction.

We present calculations of the quasi-steady state gain coefficient for the 4p⁵4d ¹P–4p⁵5p 1/2[1/2]₀ transition in Kr-like Y IV, Zr V, Nb VI and Mo VII ions. Gain coefficients which can lead to FUV-VUV (~260 to 60 nm) lasing are found in all ions. Large gain coefficients are found for each ion at temperatures in excess of the ion's equilibrium temperature; realizing lasing in these systems will require a transient excitation mechanism. The density at which the maximal gain coefficient obtains increases for increasing ionization state. The 4p⁵5s 1/2[1/2]₁–4p⁵5p 1/2[1/2]₀ and 4p⁵5s 3/2[3/2]₁– 4p⁵5p 1/2[1/2]₀ transitions also show population inversion and modest gain coefficients. Attractive features of these ions as potential lasents are the large ratio between the energy of the lasing transition and the excitation energy of the upper level of the lasing transition as well as the ease with which they are produced in a low temperature, table-top scale plasma source.

Using molecular mechanics, we study the development of turbulence in a dense gas. The gas is taken to be water vapor molecules at 150°C. To assure high density, we limit molecular motions to within a fixed, closed boundary. This leads naturally to a cavity problem. Primary vortices are generated in the cavity for wallspeeds V = -24 -120, -600 Å/ps. Turbulent flow is generated with wallspeed V = -3000 Å/ps. The mechanisms for primary vortex generation are clearly delineated, as are those for turbulent flow. In addition, the onset of turbulence is determined to within acceptable experimental error to be V = -2065 Å/ps.

The problem of the multicharged ion generation in the sources based on the electron cyclotron resonance phenomenon is discussed. Such important peculiarities as the existence of three electron groups and the closeness of the electron cyclotron resonance surface in magnetic fields of "minimum B" type are taken into consideration. The degree of electrical neutrality of plasma and the depth of a potential well for ions of different charge states are estimated. Consideration is given to conditions necessary for a negative potential well formation in the core plasma. It is shown that the effective temperatures as well as the life times of ions with different charges are distinct and moreover, they are functions of the ion charge state distribution.

The rotational and potential currents, induced by a test charged particle moving through a rarefied plasma, are investigated. The problem of current neutralization is discussed.

Theoretical analysis of electron heating in microwave gas discharge sustained by surface cyclotron waves (SCW) is presented. A discharge chamber with planar geometry immersed into a steady magnetic field that is oriented perpendicularly to the plasma interface is considered. The plasma is assumed to be bounded by a planar dielectric sheath. The SCW are the eigenmodes of this structure. Their eigenfrequencies belong to the ranges between the harmonics of the electron cyclotron frequency. SCW propagate across the external steady magnetic field. Plasma particle motion is examined using a kinetic approach. A model of particle mirror reflection from the interface of the plasma is utilized. Spatial distribution of the SCW electromagnetic fields, SCW power flow and their energy absorption by plasma particles under both collisional and collisionless regimes are studied analytically. The presented results can be interesting for plasma technologies on processing of solids.

By employing Braginskii transport equations for electrons, we derive a system of nonlinear equations which govern the dynamics of low-frequency short–wavelength electromagnetic waves in the presence of equilibrium density, temperature and magnetic field gradients. New electron-temperature-gradient driven electromagnetic drift–wave instabilities are shown to exist. Anomalous electron energy transport caused by nonthermal electromagnetic fluctuations is also derived. Furthermore, possible stationary solutions of the nonlinear system are obtained in the form of spatially bounded dipolar as well as chain of vortices. The results of our investigations should be helpful to understand the wave phenomena in space and laboratory plasmas.

The excitation of surface plasmon-polariton waves propagating across an external magnetic field (Voigt geometry) in a semiconductor-metal structure by means of the attenuated total reflection method is investigated. The phase matching conditions for the surface waves excitation in the Kretchmann configuration are derived and analyzed. The effect of different nonlinearities on the excitation of the surface waves is studied as well.

We calculate the fractal dimensions of a set of 97 proteins selected from four different structural classes and establish their relationship with the local and global folding of the tertiary structure of these proteins.

In this paper we deal with electromagnetic radiation arising due to variation of the dipole moment of a ferroelectric pattern as a result of its temperature change. It is also shown here that, when the pattern is heated up with a powerful electromagnetic pulse, the total radiated energy is inversely related to the pulse duration τ_p (at the same heating power). The radiation spectrum has its maximum at the frequencies of the order of τ_p^-1 and exponentially abates if the frequency exceeds τ_p^-1. The results of experimental investigation of radio-frequency radiation from ferroelectric crystals when they are heated with pulse laser radiation of nanosecond duration are touched upon below. A numerical calculation of the magnetic component of the radio wavefield has been performed for a laser pulse of a particular shape. A comparison between the experimental results and the theory prediction is also available here.

We use the exact correlation function of the density of energy levels in a magnetic field to evaluate persistent currents in mesoscopic metals. We also analyze the perturbation theory limit of the correlation function vis-a-vis the perturbation theory limit of the orbital response.