Table of contents

The fermion determinant of a chiral two-dimensional (2D) lattice Wilson fermion model with counterterm is considered beyond the perturbation theory. Analytical and numerical values of the counterterm coefficient providing agreement of the lattice and continuum determinants are obtained.

Doubly excited ¹S^e states of helium-like ions (Z=2–10) converging on the N=2, 3 and 4 hydrogenic thresholds are studied by a method of stabilization using correlated Hylleraas-type wavefunctions and a real Hamiltonian. Total energies, kinetic and Coulomb energies and the cosine of the interelectronic angle of the two electrons are calculated. Results obtained show quantitatively the correlation effects in the doubly excited intrashell states and demonstrate how the expectation values of the cosine of the interelectronic angle of the two electrons depend on details of the dynamics.

We study the higher-subshells effect on the direct ionization from inner 1s, 2s, 2p, 3s, 3p subshells of ions charged 5+ and more. The cross-sections analysed are those calculated in the relativistic distorted-wave (RDW) approach. For removal of an electron from a certain nl-subshell of ions, belonging to a sequence of ionization stages, we found approximate scaling of the cross-sections. The scaled cross-sections differ from each other by less than 50%. The difference depends on the number of electrons, N, bound above the nl-subshell undergoing the ionization. With an increase in N the scaled cross-sections decrease for projectiles of near-threshold energy and increase for high-energy (non-relativistic) projectiles. Dependence of the scaled cross-sections on a target ion (its chemical element, charge and level) is weak. For use in applications, we approximated the direct inner-shell ionization cross-sections by a simple formula with nl-dependent coefficients.

This paper studies the dynamics of a self-excited oscillator with two external periodic forces. Both the nonresonant and resonant states of the oscillator are considered. The hysteresis boundaries are derived and the hysteresis domains are defined in terms of the system parameters. Making use of the properties of Hill's equation, we derive the stability conditions of oscillation in the resonant case. Phase portraits are obtained numerically and experimentally. One of the most important contributions of this study is to validate a set of reliable analytical expressions (formulae) describing the system behaviour. These are of great importance for design engineers. The reliability of the analytical formulae is demonstrated by the very good agreement between the results obtained by numerical and experimental analyses.

Front dynamics with time delays in a reaction-diffusion equation with the piecewise linear rate function is studied by considering the response of the self-ordered front to the rapidly varying force. More specifically, the retarding accelerations of the bistable front (BF) joining two states of different stability in the system are examined. Two cases of differently shaped forcing functions are studied. In examining the 'size' of the retardation, namely, the lag time between the propagation velocity of the front and the driving force we approximate the forcing function by the step-like dependence of the flexible steepness. The lag time is found to be sensitive to both the rate (steepness) of the driving force and the characteristic parameters of the rate function. A significant retardation effect occurred when the steepness of the force exceeded the characteristic relaxation rate of the system; the lag time monotonically increases with increasing steepness and approaches the maximal value depending on the relaxation time of the system, when the driving force becomes extremely steep. The influence of delays on the ratchet-like transport of the self-ordered front is studied by considering the response of BF to the periodically oscillating square-pulse force. The average characteristics of the unforced dc motion of BFs are presented. The occurrence of delays, as shown, significantly reduces the unforced dc motion of BF. The ratchet-like transport is highly suppressed if the period of the ac force becomes low compared to the characteristic relaxation time of the system.

A complete eigenvalue spectrum of the parameters is given wherein some higher peak numbers of multipeak electromagnetic solitons in plasma are included. Moreover some interesting scaling laws are obtained for field energy via numerical approaches.

In this paper, the first and second laws of thermodynamics are employed in order to study the inherent irreversibility of a gravity driven non-Newtonian Ostwald-de-Waele power law liquid film along an inclined isothermal plate. Based on some simplified assumptions, the governing equations are obtained and solved analytically. Expressions for fluid velocity, temperature, volumetric entropy generation numbers, irreversibility distribution ratio and the Bejan number (Be) are also determined.

Exact nonlinear coherent vortex solutions, in the form of dipolar like configuration, are derived in a two-dimensional (2D) electrostatic interchange turbulence model. The vortex structure incorporates effects due to nonlinear diamagnetic interactions that are associated with the finite Larmour radius (FLR) of the magnetized ions. Numerical simulations indicate that the propagating dipole vortex is a long-lived, spatially well-localized coherent structure of the interchange mode that persists for several eddy turn-over times. Collisional as well as weak diamagnetic interactions have stabilizing effects on these structures.

In the rotation equation of the angle θ between the molecular axis and the laser polarization direction, the dependence of laser-induced polarizability on the molecular internuclear distance R is considered. The effect of the R dependence of laser-induced polarizability on molecular dynamic alignment in an intense femtosecond laser field is investigated with 20 and 100 fs laser pulses for N₂ molecules and with 60 and 100 fs laser pulses for Br₂ molecules at intensities of 5×10¹⁴ W cm⁻² and 5×10¹⁵ W cm⁻². This effect exists and only occurs during the dissociative process after the molecule is ionized. It enhances the degrees of molecular dynamic alignment and is more significant in reorienting the angular distributions of molecules towards the laser polarization direction in the conditions of high laser intensity and short pulse length. Compared with the N₂ molecule, the effect of the R dependence of laser-induced polarizability on molecular dynamic alignment for Br₂ is stronger. The reasons are presented and discussed.

Fifty seven new electron levels of odd parity in neutral praseodymium are presented. These have been found on the basis of an analysis of hitherto unclassified spectral lines with the method of laser-induced fluorescence (LIF). For all the levels the hyperfine magnetic dipole interaction constants A have been determined.

A condition associated with the plasma boundary or other charged interface is reviewed. It is pointed out that in comparing theories and simulations of such interfaces, in order to avoid conflicting results it should be ascertained that the systems under consideration are thermodynamically equivalent. For the plasma–wall interface in equilibrium, the rate of change of the surface-charge density with respect to the surface potential must be positive.

Nonlinear electron plasma oscillations in a cold-plasma have been studied numerically using one-dimensional (1D) Vlasov–Poisson equations. It is shown that both ion motion and the relativistic effect of electron motion can lead to phase mixing phenomena even if a plasma oscillation is at a moderate amplitude. When its amplitude is relatively small, the phase mixing is mainly caused by the ion motion. When its amplitude is large, the relativistic effect of electrons is dominant. The nonlinear process caused by the relativistic effect depends significantly upon the phase velocity of the plasma oscillation, while that caused by the ion motion depends weakly upon its phase velocity.

Birefringence phenomena stemming from vacuum polarization are revisited in the framework of coherent scattering. Based on photon–photon scattering, our analysis brings out the direct connection between this process and vacuum birefringence. We show how this procedure can be extended to the Kerr and the Cotton–Mouton birefringences in vacuum, thus providing a unified treatment of various polarization schemes, including those involving static fields.

An intense short pulse laser propagating through a gas jet comprised of clusters, quickly converts the clusters into plasma balls and causes oscillations of the electron cloud in the direction of the electric field of the laser. In each wave period, electrons spend a significant amount of their time outside the clusters, leaving behind a net positive charge and the clusters undergo Coulomb explosion and expand. During the expansion when the cluster electrons plasma frequency equals times the laser frequency, , the electron quiver velocity is resonantly enhanced. The nonlinear electron response gives rise to the generation of a third-harmonic. At a typical laser intensity of I_L ≈ 10¹⁵ W cm⁻² at 1 μm wavelength, the normalized third-harmonic amplitude of the pump wave in a deuterium cluster of radius 100 Å, and density ∼10¹⁴ cm⁻³, turns out to be 1.7×10⁻³.

The properties of the plasma–wall transition layer in the presence of a radio-frequency (rf) electric field are studied theoretically and numerically. When the electrostatic potential is positive at the wall compared to the potential in the bulk plasma, the positive ions are repelled from the wall by the potential, while the electrons are repelled by the ponderomotive force of the rf field. The result is that the plasma is almost completely evacuated at the wall, and is efficiently confined.

The excitation of ³²S to energies from 24 to 37 MeV followed by its decay to ²⁸Si has been brought about by the two-step alpha transfer reaction ²⁸Si(⁶Li,d)³²S*→α+²⁸Si. A sudden perishing of the decay to the ²⁸Si ground state occurs at 31 MeV of excitation. At about the same energy an increase in the decay to the first excited 2⁺ state is observed. The yields of ²⁸Si in its ground state or excited to the 2₁⁺ and 4₁⁺ state prohibit strong fluctuations. This supports the assumption of the existence of states at high excitation in ³²S. The results are based on d–α coincidences, which were found to exhibit a strong forward–backward correlation.

Liquid–liquid phase transition in liquid Al₂O₃·2SiO₂ (AS2) has been studied at 4200 K in a model containing 3025 particles under periodic boundary conditions with Born–Mayer type pair potentials via molecular dynamics (MD) simulation. Structure and dynamics of models at densities ranging from 2.60 to 4.20 g cm⁻³ at a temperature of 4200 K have been analysed in detail through the partial radial distribution functions (PRDF), coordination number distribution, bond-angle distribution, interatomic distances and diffusion constant. We found clear evidence of transition from a tetrahedral to an octahedral network structure in the model upon compression, like that observed in simple oxide systems. Moreover, the transition is accompanied by an anomalous diffusion of components in the system.

It is demonstrated how all the mechanical equations of classical electromagnetism (CEM) may be derived from only Coulomb's inverse square force law, special relativity and Hamilton's principle. The instantaneous nature of the Coulomb force in the centre-of-mass frame of two interacting charged objects, mediated by the exchange of space-like virtual photons, is predicted by quantum electrodynamics (QED). The interaction Lagrangian of QED is shown to be identical, in the appropriate limit, to the potential energy term in the Lorentz-invariant Lagrangian of CEM. A comparison is made with the Feynman–Wheeler action-at-a-distance formulation of CEM.

We report in this paper a detailed analysis of modulational instability of a plane wave solution of discrete dissipative structures. A generalized Ablowitz–Ladik (AL) equation with a cubic and quintic nonlinearity is then considered, and analysed via the full linear stability analysis of the nonlinear plane wave solution. We derive analytical expressions for the domain of existence as well as the gain of modulational instability of moving plane waves. In particular, we find that discreteness drastically modifies the stability condition as well as the quintic nonlinearity. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model. The generation of pulse trains with high repetition rate predicted by analytical study is then exhibited.

This paper presents an analytical study of the simultaneous principal parametric resonances of two coupled Duffing equations with time delay state feedback. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. The method of multiple scales is used to determine a set of ordinary differential equations governing the modulation of the amplitudes and phases of the two modes. The first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the frequency–response curves. We analyse the effect of time delay and the other different parameters on these oscillations. The stability of the fixed points is examined by using the variational method. Numerical solutions are carried out and graphical representations of the results are presented and discussed. Increasing in the time delay τ given decreasing and increasing in the regions of definition and stability respectively and the first mode has decreased magnitudes. The multivalued solutions disappear when decreasing the coefficients of cubic nonlinearities of the second mode α₃ and the detuning parameter σ₂ respectively. Both modes shift to the left for increasing linear feedback gain v₁ and the coefficient of parametric excitation f₁ respectively.

It is shown that the modification of experiments where the dust acoustic waves were detected allows one to measure the strength of the grain attraction at large distances between the grains. Such detection is important for establishing experimentally the mechanism of plasma crystal formation.

This is my first December Editorial since the start of the partnership between the Royal Swedish Academy and Institute of Physics Publishing and I am delighted to announce that the year has been a great success.

We have seen a 40% increase in submissions and a substantial increase in numbers of readers. We have published many strong papers by some excellent authors including P K Shukla, J Tennyson and A Kilic. I am also pleased to report that the Physica Scripta Impact Factor increased by over 50% to 1.24.

In 2007 we will be continuing our relationship and we aim to improve transparency for authors with the help of the Author Services homepage. The Topical Issue programme will continue although in a different format. While we are no longer producing CDs, subscribers will have full access to the material online via the journal homepage, which will enable increased search capabilities across the journal content. The full archive since 1970 will also be available during 2007.

It only remains for me to thank all contributors, editors, referees and readers. I look forward to 2007 and another successful year for the journal.

Roger WäpplingEditor-in-Chief