Table of contents

The electron diffusion induced by a two-dimensional electrostatic turbulence, in a sheared slab approximation of the toroidal magnetic geometry, is studied firstly using the decorrelation trajectory method (DCT), secondly by direct numerical simulation. The former semi-analytical method allows us to go beyond the Corrsin approximation, thus allowing for a non-classical analysis of the particle trapping phenomenon. The DCT results are compared to the transport properties of the electrons obtained by numerical simulations assuming an isotropic spectrum of electrostatic drift type turbulence that is Gaussian for small wavevectors and power-law k⁻³ for large wavevectors. The 'radial' and the 'poloidal' running and asymptotic diffusion coefficients of thermal electrons are obtained for physically relevant parameter values. The existence of enhanced diffusion in the poloidal direction is observed in the presence of magnetic shear. The agreement between the semi-analytical method and the purely numerical method is pointed out.

The 2p^2 1D^e resonance state of the helium atom embedded in model plasma environments is calculated using CI-type basis functions. The plasma effects have been taken care of by using the screened Coulomb potential obtained from the Debye model. The stabilization method has been used to extract resonance parameters. The resonance energy and width for the lowest ¹D^e resonance for different screening parameters are reported.

Matter wave interference effects in the macrodomain for charged particles in a magnetic field are reported for different scatterer positions between the electron gun and collector plate. The results obtained serve to validate and establish the important premises of the formalism that it is the scattering, (inter alia off the grid wires in this case) which generates the transition amplitude waves resulting in the novel quantum effects observed on the macro-scale associated with the transition amplitude wave. The variation of the position of origin of the grid-generated transition amplitude wave then leads to the variation of interference characteristics accordingly in the plate and grid currents. A Fourier decomposition of the interference peaks reveal also the presence of harmonics which are a manifestation of the Landau level structure. A rich class of quantum phenomena are thus discovered in the simple dynamical system of charged particles in a magnetic field in the ostensibly classical domain of operation, with the transition amplitude wave generated as a consequence of scattering being the new element of quantum description on the macro-scale.

We have found that two 'asymptotic' aspects α and β of an asymptotic iteration method for the Dirac equation satisfy nonlinear Riccati equations simultaneously and are reciprocal to each other. By these two properties, we have an insight into this method and reveal why this method can give solutions to the Dirac equation. Furthermore, using the new iteration termination condition expressed by equation (15), instead of solving the differential equations directly, we have found exact eigenvalues as well as exact wavefunctions of the Dirac equation with two dimensional Coulomb potential.

New exact solutions with an arbitrary function for the (n+1)-dimensional double sinh-Gordon equation are studied by means of auxiliary solutions of the cubic nonlinear Klein–Gordon (CNKG) fields. By a proper selection of the arbitrary function and the appropriate solutions of the CNKG systems, new wave solutions including periodic–kink like waves, periodic–solitoffs and periodic waves are obtained explicitly.

The solutions of trigonometric Scarf potential, PT/non-PT symmetric and non-Hermitian q-deformed hyperbolic Scarf and Manning–Rosen potentials are obtained by solving the Schrödinger equation. The Nikiforov–Uvarov method is used to obtain the real energy spectra and corresponding eigenfunctions.

Fully relativistic calculations on the energies and electric dipole rates of x-ray multiplets arising from states of 2p^q, 2s2p^q and 2s² 2p^q configurations of variously ionized neon with q ranging from 6 to 1 have been performed. The calculations have been carried out using multi-configuration Dirac–Fock wavefunctions with the inclusion of Breit interaction, quantum electrodynamics contributions and finite nuclear mass and size corrections. An attempt has been made to take into account the dominant contributions to correlation effects. Using a scaling procedure on the already available relativistic radial matrix elements for a single vacancy in the K shell, the Auger rates have been calculated. The numerical results for the x-ray and Auger transitions of double vacancy states of neon ionized to different degrees in the L shell have been compared with other available theoretical and experimental values. Due to the influence of both relativity and configuration interaction, the configuration average x-ray rates obtained from individual multiplet rates were seen to substantially differ from non-relativistic rates for many transitions.

The time-fractional diffusion-wave equation is considered. The time-fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∊ (0,2]. The fractional derivative is described in the Caputo sense. This paper presents the analytical solutions of the fractional diffusion equations by an Adomian decomposition method. By using initial conditions, the explicit solutions of the equations have been presented in the closed form and then their numerical solutions have been represented graphically. Four examples are presented to show the application of the present technique. The present method performs extremely well in terms of efficiency and simplicity.

Transport through a molecule sandwiched between two metallic electrodes and coupled with a mesoscopic ring that threads a magnetic flux ϕ is studied. An analytic approach for electron transport through the molecular bridge system is presented. The electronic transport properties are discussed in two aspects: (i) the presence of an external magnetic field and (ii) the strength of the molecule to electrodes coupling.

Electrostatic ion-temperature-gradient (ITG) driven drift waves are investigated by using Brangskii's model for the ions and Boltzmann distribution for the electrons in a dust-contaminated plasma with equilibrium density, temperature, and magnetic field gradients. Within the local approximation, we are able to recover the coupled ion-acoustic drift-waves in an inhomogeneous magnetic field and the Rudakov–Sagdeev (R–S) ITG instability in the presence of dust-charge fluctuations. It has been shown that the dust charging is always dissipative and the growth rate of various modes are damped. Furthermore, we also derive an expression for the anomalous ion-energy flux and transport coefficient in the presence of nonthermal fluctuations. The present investigation should be helpful in identifying the features of low-frequency turbulence and associated cross-field ion-energy transport in magnetically confined dust-contaminated tokamak plasmas.

Using the relativistic quantum stationary Hamilton–Jacobi equation within the framework of the equivalence postulate, and grounding oneself on both relativistic and quantum Lagrangians, we construct a Lagrangian of a relativistic quantum system in one dimension and derive a third order equation of motion representing a first integral of the relativistic quantum Newton's law. Then, we plot the relativistic quantum trajectories of a particle moving under constant and linear potentials. We establish the existence of nodes and link them to the de Broglie wavelength.

We establish the quantum stationary Hamilton–Jacobi equation in 3D and its solutions for three symmetrical potentials: Cartesian symmetry potential, spherical symmetry potential and cylindrical symmetry potential.

We study relationships between the dipole excitation and the ground state ms radius of a two-body system in the case of local potentials. We recall the inequality obtained long ago by Bertlmann and Martin, and discuss correction factors transforming the inequality in an approximate expression. Connecting the correction factor to the contribution of the lowest dipole state to the sum rule, we get a lower bound to the ms radius. Inverting the relationships yields a bound for the square of the dipole transition matrix element, and thus a bound to the lowest dipole state transition rate.

It is shown that Chandrasekhar gives some misleading comments concerning his method to derive the pulsation equation for relativistic stars. Strictly following his procedure and approximations, we find that this equation should contain an extra term which destroys the beauty and simplicity of the pulsation equation. However, using a better approximation, we find that just this extra term cancels, and the nice original version of the pulsation equation is correct after all.

In this paper, the energy eigenvalues and the corresponding eigenfunctions are calculated for the Kratzer potential. Then we obtain the ladder operators for the one-dimensional (1D) and 3D Kratzer potential. Finally, we show that these operators satisfy the SU(2) commutation relation.

The phase transition properties of a ferroelectric superlattice with two alternating layers A and B described by a transverse spin-1/2 Ising model have been investigated using the effective field theory within a probability distribution technique that accounts for the self spin correlation functions. The Curie temperature T_c, polarization and susceptibility have been obtained. The effects of the transverse field and the ferroelectric and antiferroelectric interfacial coupling strength between two ferroelectric materials are discussed. They relate to the physical properties of antiferroelectric/ferroelectric superlattices.

Resistive plate chambers (RPCs) are gaseous parallel-plate detectors with good spatial and time resolution, which makes them very useful in high energy physics and astrophysics experiments. In the present study, glass plates are utilized as the electrodes in the construction of RPCs, these kinds of glass-RPCs are being used in many ongoing high energy physics experiments. In this paper, for the first time Monte Carlo simulation of 2 mm gas gap RPCs with glass electrodes have been performed with GEANT4 standard and low-energy packages. Gamma ray propagation through these RPCs with two types of sources, is discussed. We report measurements of the response of a glass RPC for gamma rays of energy in the range 0.1–1000.0 MeV. As expected glass electrode RPCs give higher sensitivity results than bakelite plates RPCs. The obtained results show a good agreement between GEANT4 standard and low-energy packages (showing ∼99% agreement for both low and high energy gamma rays). The evaluated results are applied to both endcap and barrel areas of CMS regions. According to these results, a hit rate of about 100, 50 and 30 Hz cm⁻² is calculated using GEANT4 standard electromagnetic package for a 20×20 cm² glass RPC in the ME1, ME2, and ME4 regions respectively. While for the same gamma source and GEANT4 package, a hit rate of about 0.46 and 1.40 Hz cm⁻² was computed for the MB1 and MB4 stations respectively. Similar characteristics of hit rates have been observed for the GEANT4 low electromagnetic package.

We have investigated the melting behaviour of Au_N  (N=12–14) clusters by means of molecular dynamics simulation on the basis of the Voter–Chen version of the embedded-atom method. The melting behaviour of the clusters is described in terms of short-time average temperatures and atomic coordination numbers of the clusters. Results have shown that during the melting process, the phase changes occur as a collective and simultaneous motion of all the atoms in a very short-time interval. Furthermore the Au₁₄ cluster presents a two-stage melting behaviour which is different from those of the Au₁₂ and Au₁₃ clusters. The isomer sampling probabilities are obtained from the thermal quenching of the molten clusters, and their energy-spectrum widths are investigated. The results of the isomer forming probabilities showed that the global minimum structures of these clusters are not always the most probable ones to be formed in the experiments.

A recent paper by the author proposes that the phenomenon of inertia may be explained if the four metrical coefficients in the Minkowskian line element were to change as a consequence of acceleration. A certain scale factor multiplying the four metrical coefficients was found, which depends solely on velocity. This dynamic scale factor, which is [1−(v/c)²)], models inertia as a gravitational-type phenomenon. With this metric the geodesic of general relativity is an identity, and all accelerating trajectories are geodesics. This paper shows that the same scale factor also agrees with special relativity, but offers a new perspective. A new kind of dynamic process involving four-dimensional scale transition is proposed.