Combined R-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrodinger equation: The one-electron case

In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron’s coordinates separated over two regions; that is, regions I and II. In region I the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wave function. In region II a grid representation of the wave function is considered and propagation in space and time is obtained through the finite-difference method. With this, a combination of basis set and grid methods is put forward for tackling multiregion time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multielectron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely, that beyond a certain distance (encompassing region I) a single ejected electron is distinguishable from the other electrons of the multielectron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.

Techniques for multiple-set synchronous islanding control

Power system islanding can improve the continuity of power supply. Synchronous islanded operation enables the islanded system to remain in phase with the main power system while not electrically connected, so avoiding out-of-synchronism re-closure. Specific consideration is required for the multiple-set scenario. In this paper a suitable island management system is proposed, with the emphasis being on maximum island flexibility by allowing passive islanding transitions to occur, facilitated by intelligent control. These transitions include: island detection, identification, fragmentation, merging and return-to-mains. It can be challenging to detect these transitions while maintaining syn-chronous islanded operation. The performance of this control system in the presence of a variable wind power in-feed is also examined. A Mathworks SimPowerSystems simulation is used to investigate the performance of the island management system. The benefit and requirements for energy storage, com-munications and distribution system protection for this application are considered.

Relativistic laser pulse compression in plasmas with a linear axial density gradient

The self-compression of a relativistic Gaussian laser pulse propagating in a non-uniform plasma is investigated. A linear density inhomogeneity (density ramp) is assumed in the axial direction. The nonlinear Schrodinger equation is first solved within a one-dimensional geometry by using the paraxial formalism to demonstrate the occurrence of longitudinal pulse compression and the associated increase in intensity. Both longitudinal and transverse self-compression in plasma is examined for a finite extent Gaussian laser pulse. A pair of appropriate trial functions, for the beam width parameter (in space) and the pulse width parameter (in time) are defined and the corresponding equations of space and time evolution are derived. A numerical investigation shows that inhomogeneity in the plasma can further boost the compression mechanism and localize the pulse intensity, in comparison with a homogeneous plasma. A 100 fs pulse is compressed in an inhomogeneous plasma medium by more than ten times. Our findings indicate the possibility for the generation of particularly intense and short pulses, with relevance to the future development of tabletop high-power ultrashort laser pulse based particle acceleration devices and associated high harmonic generation. An extension of the model is proposed to investigate relativistic laser pulse compression in magnetized plasmas.

Electromagnetic pulse compression and energy localization in quantum plasmas

The evolution of the intensity of a relativistic laser beam propagating through a dense quantum plasma is investigated, by considering different plasma regimes. A cold quantum fluid plasma and then a thermal quantum description(s) is (are) adopted, in comparison with the classical case of reference. Considering a Gaussian beam cross-section, we investigate both the longitudinal compression and lateral/longitudinal localization of the intensity of a finite-radius electromagnetic pulse. By employing a quantum plasma fluid model in combination with Maxwell's equations, we rely on earlier results on the quantum dielectric response, to model beam-plasma interaction. We present an extensive parametric investigation of the dependence of the longitudinal pulse compression mechanism on the electron density in cold quantum plasmas, and also study the role of the Fermi temperature in thermal quantum plasmas. Our numerical results show pulse localization through a series of successive compression cycles, as the pulse propagates through the plasma. A pulse of 100 fs propagating through cold quantum plasma is compressed to a temporal size of approximate to 1.35 attosecond and a spatial size of approximate to 1.08 10(-3) cm. Incorporating Fermi pressure via a thermal quantum plasma model is shown to enhance localization effects. A 100 fs pulse propagating through quantum plasma with a Fermi temperature of 350 K is compressed to a temporal size of approximate to 0.6 attosecond and a spatial size of approximate to 2.4 10(-3) cm. (c) 2010 Elsevier B.V. All rights reserved.

On the set of hypercyclic vectors for the differentiation

Let D be the differentiation operator Df = f' acting on the Fréchet space H of all entire functions in one variable with the standard (compact-open) topology. It is known since the 1950’s that the set H(D) of hypercyclic vectors for the operator D is non-empty. We treat two questions raised by Aron, Conejero, Peris and Seoane-Sepúlveda whether the set H(D) contains (up to the zero function) a non-trivial subalgebra of H or an infinite-dimensional closed linear subspace of H. In the present article both questions are answered affirmatively.

Design of quantum-dot cellular automata circuits using cut-set retiming

As a potential alternative to CMOS technology, QCA provides an interesting paradigm in both communication and computation. However, QCAs unique four-phase clocking scheme and timing constraints present serious timing issues for interconnection and feedback. In this work, a cut-set retiming design procedure is proposed to resolve these QCA timing issues. The proposed design procedure can accommodate QCAs unique characteristics by performing delay-transfer and time-scaling to reallocate the existing delays so as to achieve efficient clocking zone assignment. Cut-set retiming makes it possible to effectively design relatively complex QCA circuits that include feedback. It utilizes the similar characteristics of synchronization, deep pipelines and local interconnections common to both QCA and systolic architectures. As a case study, a systolic Montgomery modular multiplier is designed to illustrate the procedure. Furthermore, a nonsystolic architecture, an S27 benchmark circuit, is designed and compared with previous designs. The comparison shows that the cut-set retiming method achieves a more efficient design, with a reduction of 22%, 44%, and 46% in terms of cell count, area, and latency, respectively.

Deformation of titanium alloy Ti-6Al-4V under dynamic compression

Deformation localisation is the main reason for material failure in cold forging of titanium alloys and is thus closely related to the production yield of cold forging. In the study of the influence of process parameters on dynamic compression, considering material constitutive behaviour, physical parameters and process parameters, a numerical dynamic compression model for titanium alloys has been constructed. By adjusting the process parameters, the severity of strain localisation and stress state in the localised zone can be controlled thus enhancing the compression performance of titanium alloys.

Relationship between microstructure and deformation behaviour during dynamic compression in Ti-3Al-5Mo-5V alloy

The relationship between microstructure and deformation and damage behaviour during dynamic compression in Ti-3Al-5Mo-5V alloy has been studied using several experimental techniques, including optical microscopy, scanning electron microscopy and microhardness measurements. It was found that the deformation behaviour during dynamic compression was closely related to deformation parameters. After dynamic deformation, the deformation shear band that formed in the titanium alloy had microhardness similar to that of the matrix. However, the microhardness of the white shear band was much higher than the matrix microhardness. The effects of deformation parameters, including deformation rate and deformation degree, on deformation localisation were investigated. Based on the results from the present work, the microstructure and deformation processing parameters can be optimised. In addition, treatment methods after dynamic compression were explored to restore alloy properties. Using post-deformation heat treatment, the microstructure and property inhomogeneity caused by shear bands could be largely removed.