Table of contents

The method of unrestricted transition arrays successfully applied for the interpretation of spectra of high temperature plasmas is grounded on usage of explicit expressions for the main global characteristics of spectra. However, in the relativistic approximation only the expressions for the first two such characteristics—average energy and variance—were known, and calculated taking into account Coulomb and spin–orbit interactions as well as restricting the transition operator by the electric dipole operator. In this study, we present the expressions for the first three global characteristics in the relativistic Dirac–Breit approximation. As an example of their application the asymmetry of spectra for various ions of tungsten is investigated.

For this study, calculations of circular polarization of electromagnetic emission are made. The emission is a result of coalescence of two types of turbulent pulsations with close and essentially different frequencies. The case of emission propagation along the magnetic field is considered. It is shown that the polarization corresponds mainly to the extraordinary wave.

The properties of the charged particle in a certain varying magnetic field are outlined. A realization of the creation and annihilation operators for the wavefunctions is studied. It is shown that these operators satisfy the commutation relation of an SU(1,1) group. The closed analytical expressions for the matrix elements of different function ρ and ρ(d/dρ) are evaluated.

A study of azimuthal angle void probability of produced pions has been carried out in relativistic and ultra relativistic nucleus–nucleus interactions (³²S–AgBr interactions at 200 A GeV, ¹⁶O–AgBr interactions at 60 A GeV , ²⁴Mg–AgBr interactions at 4.5 A GeV and ¹²C–AgBr interactions at 4.5 A GeV). The study reveals a very interesting observation-void probability showing scaling behaviour at significantly lower energy (²⁴Mg–AgBr interactions at 4.5 A GeV and ¹²C–AgBr interactions at 4.5 A GeV) whereas the behaviour is not so pronounced at higher energy in ¹⁶O–AgBr interactions at 60 A GeV and the data do not reveal scaling behaviour at all in case of ³²S–AgBr interactions at 200 A GeV.

The morphological features of initial ionospheric scintillations on 3.925 GHz beacon signal from geostationary satellite Intelsat (701) at Suva (Lat., 18.08° S, Long., 178.3° E, Geom. Lat., 22.1° S), Fiji, a low latitude station in the South Pacific region have been studied during the period of December 2003 to June 2004. Scintillations were, in general, sparse, of which activity was more pronounced in the daytime. Scintillation occurrence was less in general, showing a peak value of about 2.5% at 09 h LT and a secondary peak of about 2% at around 16 h LT. Scintillations were weak (S₄ index ⩽ 0.25) and occurred mostly in patches of short duration of 2–5 min. It is reported here that weak and short duration scintillations with more daytime occurrence are mainly due to (i) the higher frequency beacon signal used, (ii) the recording station being situated off the equatorial ionisation anomaly belt, and (iii) the period of observation falling in the low solar activity phase of the current solar cycle.

Considering a saturation laser model with cross-correlated additive and multiplicative noises, we derive the stationary probability distribution function P_st(I), the stationary intensity correlation function C(s) and the associated relaxation time T_c by virtute of the Novikov theorem and Stratonovich's decoupling ansatz. Based on numerical computation, we discuss the effects of the correlation strength λ, the cross-correlation time τ, and the noises intensity. The correlation strength λ attenuates the probability distribution and increases the intensity fluctuation of the laser system. The correlation strength λ and the noise intensity D and Q speed up the relaxation of the system from an arbitrary state to the steady state and enhance the stability of the laser intensity output. For the case of negative correlation (λ < 0), the cross-correlation τ enhances the probability distribution, decreases the intensity fluctuation, slows down the relaxation of the system from an arbitrary state to the steady state, and decreases the stability of the laser intensity output; by contrast, the effects of the cross-correlation time τ on P_st(x), C(s), and T_c are entirely opposite for (λ > 0).

The acceleration mechanism of electrons in the presence of a strong axial magnetic field and Gaussian laser pulse is investigated by solving the dynamical equations numerically using a 2D relativistic code for particle acceleration. In the presence of a guide magnetic field, a large amplitude plasma wave of finite transverse extent and large phase velocity resonantly accelerates electrons when the Doppler shifted wave frequency equals electron–cyclotron frequency. After the electrons have gained high axial velocity, they may gain energy from the wave via Cerenkov resonance. The amplitude of the plasma wave increases when the strength of the magnetic field increases and hence the electron energy increases further.

We propose a new exactly solvable potential which consists of the modified Kratzer potential plus a new ring-shaped potential βctg²θ/r². The exact solutions of the bound states of the Schrödinger equation for this potential are presented analytically by using the Nikiforov–Uvarov method, which is based on solving the second-order linear differential equation by reducing to a generalized equation of hypergeometric type. The wavefunctions of the radial and angular parts are taken on the form of the generalized Laguerre polynomials and the total energy of the system is different from the modified Kratzer potential because of the contribution of the angular part.

Applicable in arterial mechanics, Bose gases of impenetrable bosons and Bose–Einstein condensates, a variable-coefficient Korteweg–de Vries (vcKdV) equation is investigated in this paper with symbolic computation. Based on the Ablowitz–Kaup–Newell–Segur system, the Lax pair and auto-Bäcklund transformation are constructed. Furthermore, the nonlinear superposition formula and an infinite number of conservation laws for the vcKdV equation are also derived. Special attention is paid to the analytic one- and two-solitonic solutions with their physical properties and possible applications discussed.

The paper investigates the robust synchronization for two identical uncertain chaotic systems with different parameters perturbation and external disturbances. Based on Lyapunov stability theory, linear matrix inequality (LMI) techniques and adaptive techniques, a novel controller is proposed. With the resulting controller, global asymptotical synchronization between two identical uncertain chaotic systems is achieved. Finally, a Lorenz system is given as an example to verify the effectiveness of the proposed controller.

We study the nonlinear response of a system with cubic and quartic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The method of multiple scales is used to derive a second-order equation governing the components of the response of the system near its natural frequency. In this equation, the amplitude of the excitation, which is a function of time, appears as parametric excitation. The result of the perturbation analysis was used to study the response of the system to constant amplitude and harmonically modulated excitations. For harmonically modulated excitations, various resonances occur and these were shown to correspond to external combination resonances. Two coupled first-order ordinary differential equations describe the evolution of the amplitude and phase. The evolution equations are used to determine the steady-state motion and representative frequency-response curves are presented for each resonance. The stability of the steady-state solution is investigated. The response amplitude has a multivalued curve and symmetric single value curve for the variation of the amplitude with the detuning parameter σ and the coefficient of external excitation f respectively. The response amplitude is not affected and has the same magnitude for decreasing values of the damping factor μ. The response amplitude loses stability for increasing values of the coefficient of cubic term α.

In this study, the (n, p) reaction cross-sections of some target nuclei in the rare-earth elements have been investigated for an incident energy range of 8–24 MeV. In these calculations, the geometry-dependent hybrid model and the cascade exciton model including the effects of pre-equilibrium have been used. The full exciton model has also been used to investigate the pre-equilibrium direct effects. All calculated results have been compared with experimental data. In addition, the ratios of experimental (n, p) cross-sections to calculated cross-sections using empirical and semi-empirical formulae have been calculated.

The bound state solutions of the s-wave radial Schrödinger equation with Manning–Rosen potential are presented exactly by the standard method. It is found that the solutions can be expressed by the generalized hypergeometric functions ₂F₁(a, b; c; z). The intractable normalized wavefunctions are derived. We also study the special case for α=0 and find that this potential will reduce to the Hulthén potential.

In this paper, with the help of q-deformed hyperbolic functions, we successfully obtain a new variable separation solution for the (2+1)-dimensional Kortweg-de Vries (KdV) equation. Based on the variable separation solution and by selecting appropriate functions, new types of interactions between special solitons, such as bell-like compacton, peakon-like compacton and compacton-like semi-foldon, are investigated.

We study some characteristics of a model for networks called the semi-bipartite networks. This model is constructed from two parts. In the first part which is called the centre of the network all nodes are connected together. The nodes of the second part (peripheral nodes) are not connected to each other, but there are some links between them and the nodes of the centre (central nodes). We show that such a network has a high clustering coefficient and a short average path length. In this model these two characteristics of the network are independent of the size of the network directly, but it depends on the fraction of central nodes. In this model the average path length has an upper bound and the clustering coefficient has a lower bound regardless of the size of the network.

In this paper, the higher-dimensional complex nonlinear Klein–Gordon equation is investigated. We firstly use a transformation to separate this equation into a nonlinear ordinary differential equation (ODE) and a set of partial differential equations (PDE). And then, we solve these two families of equations, respectively. Finally many types of solutions of the higher-dimensional complex nonlinear Klein–Gordon equation are obtained, and when N⩾2, these solutions contain two arbitrary functions which lead to abundant structures.

Hidden satellites due to Coster–Kronig transitions have a characteristic threshold energy in their appearance and hence can be identified by looking at spectra at either side of the threshold. To investigate the hidden satellites, we measured Lβ_2,3,15 spectra of Ir, Pt and Au below and above the L₁ edge. The measured spectra were normalized using Lβ₁ spectra. The existence of hidden satellites was confirmed by observing the differences between the normalized spectra above and below the L₁ edge.

The Tm³⁺:5NaF-9YF₃ single crystals were grown by Czochralski pulling technique after purification of the starting materials. The obtained crystals are of good optical quality. Optical absorption of this material is investigated. The Judd–Ofelt (JO) analysis was applied to the room temperature absorption intensities of Tm³⁺ ions to determine the so-called JO intensity parameters and the transition strengths. These JO parameters are used to calculate the radiative transition probabilities, the radiation lifetimes and the branching ratios. The results obtained indicate that Tm³⁺:5NaF-9YF₃ may be considered as a laser active material.

Energy levels, oscillator strengths and transition probabilities for transitions among the fine-structure levels of the terms belonging to the 3s²3p², 3s3p³, 3s²3p3d, 3p⁴, 3s²3p4s, 3s²3p4p, 3s²3p4d and 3s²3p4f configurations of Ca VII are calculated using extensive configuration-interaction (CI) wavefunctions obtained with the CIV3 (configuration interaction version 3) computer code of Hibbert. The relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian which consists of the non-relativistic term plus the one-body mass correction, Darwin term, and spin–orbit, spin–other–orbit, and spin–spin operators. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made, so that the energy splittings are as close as possible to the experimental values. The energy splitting of 70 fine-structure levels, oscillator strengths and transition probabilities for electric-dipole-allowed and intercombination transitions and, also the lifetimes of fine-structure levels are presented and compared with available experimental and other theoretical results. Our calculated fine-structure energies, including their ordering, show excellent agreement (better than 0.5%) with the available experimental results. In this calculation, we also predict new data for several levels where no other theoretical and experimental results are available.

The acceleration of electrons by the self-generated quasi-static magnetic field in the interaction of n laser pulses with a plasma is investigated. The relativistic dynamics of a single electron is followed numerically. It is found that the electron can be much more effectively accelerated by n laser pulses, each with amplitude a₀ and having a fixed frequency difference from the preceding one, than by a single pulse with amplitude na₀. The large enhancement of acceleration can be attributed to stochastic-like resonance between the electron motion at the beat-frequencies of lasers and at the cyclotron motion frequency.

We have studied nonlinear quantum optical effects in a doubly driven four-level atomic system in a homogeneously broadened regime. On application of two strong fields the system can be made to display double electromagnetically induced transparency (EIT) because of constructive quantum interference giving rise to nonlinear absorption at three-photon resonance condition. This fact may be used to obtain other phenomena like the effect of photon switching in a pulsed regime and large cross phase modulation (XPM) effect. We also show that the behaviour of spatial modulation of transparency of the weak probe beam in a three-level system interacted with a strong standing wave pump field can be dramatically changed in our four-level ladder type system. Here, strong coupling field acting on the uppermost transition is represented by a standing wave whereas strong pump and weak probe fields acting successively on the lower transitions are represented by travelling waves. The effect of double EIT on nonlinear light generation based on the four-wave-mixing (FWM) technique is also investigated. We have examined that the four wave mixing efficiency can be effectively controlled by varying the strength of the pump field.

A numerical investigation is presented to show the existence, formation and possible realization of large amplitude solitary potentials in a charge varying dusty plasma with two-temperature trapped ions. These nonlinear localized structures are self-consistent solutions of the Vlasov equation representing saturated states of a four-stream unstable collisionless dusty plasma. The saturation is provided by an interplay between ion trapping and dust charging. It is found that under certain conditions the effect of dust charge variation can be quite important. In particular, it may be noted that the dust charge variation leads to an additional enlargement of the nonlinear localized structure and provides an alternate physical mechanism causing anomalous dissipation.

Semiclassical approximations for tunnelling processes usually involve complex trajectories or complex times. In this paper, we use a previously derived approximation involving only real trajectories propagating in real time to describe the scattering of a Gaussian wavepacket by a finite square potential barrier. We show that the approximation describes both tunnelling and interferences very accurately in the limit of small Planck's constant. We use these results to estimate the tunnelling time of the wavepacket and find that, for high energies, the barrier slows down the wavepacket but that it speeds it up at energies comparable to the barrier height.

The present paper reports a computational investigation of the geometry and electronic structure as well as the migration of a hydrogen impurity in the cubic SrTiO₃ crystal. The study is done using an approach based on the Hartree–Fock theory and developed for periodic systems. It is found that the H impurity forms the so-called OH group at the equilibrium. Analysis of electron density within the defective region implies the enhancement in covalent chemical bonding. A possible defect migration has been also investigated.

A sufficient criterion for synchronizing two identical non-autonomous chaotic systems coupled by sinusoidal state error feedback control is firstly derived in the form of a matrix inequality by the Lyapunov direct method. The matrix inequality is then simplified into some algebraic inequalities based on the Gerschgorin disc theorem. In order to obtain simpler algebraic criteria, the state variables are restricted in a sub-region. The property that similar matrices have the same eigenvalues is further applied to obtain more flexible synchronization criteria. Numerical examples are simulated to show that complete chaos synchronization can be achieved under these criteria by three practical non-autonomous chaotic systems: the Mathieu–Duffing equation of two dimensions, a gyrostat system of three dimensions and a loudspeaker system of four dimensions.

By using the basic concepts of the supersymmetric quantum mechanics formalism and the functional analysis method, we solve approximately the Dirac equation for the arbitrary pseudo-orbital angular momentum number and obtain the bound state solutions for the nuclei in the relativistic empirical potential as a diatomic molecular model. All of the analyses are prepared under the conditions of the exact pseudospin symmetry and the associated two-component spinor wavefunctions of the Dirac equation are obtained approximately.