Quantum manifestations of scattering orbits in the scaled spectrum of a non-hydrogenic atom in crossed fields

Evidence for scattering closed orbits for the Rydberg electron of the singly excited helium atom in crossed electric and magnetic fields at constant scaled energy and constant scaled electric field strength has been found through a quantum calculation of the photo-excitation spectrum. A particular 3D scattering orbit in a mixed regular and chaotic region has been investigated and the hydrogenic 3D closed orbits composing it identified. To the best of our knowledge, this letter reports the first quantum calculation of the scaled spectrum of a non- hydrogenic atom in crossed fields.

Quantum manifestations of closed orbits in the photoexcitation scaled spectrum of the hydrogen atom in crossed fields

The scaled photoexcitation spectrum of the hydrogen atom in crossed electric and magnetic fields has been obtained by means of accurate quantum mechanical calculation using a new algorithm. Closed orbits in the corresponding classical system have also been obtained, using a new, efficient and practical searching procedure. Two new classes of closed orbit have been identified. Fourier transforming each photoexcitation quantum spectrum to yield a plot against scaled action has allowed direct comparison between peaks in such plots and the scaled action values of closed orbits, Excellent agreement has been found with all peaks assigned.

The closed orbits and the photo-excitation scaled spectrum of the hydrogen atom in crossed fields

In a recent Letter to the Editor (J Rao, D Delande and K T Taylor 2001 J. Phys. B: At. Mol. Opt. Phys. 34 L391-9) we made a brief first report of our quantal and classical calculations for the hydrogen atom in crossed electric and magnetic fields at constant scaled energy and constant scaled electric field strength. A principal point of that communication was our statement that each and every peak in the Fourier transform of the scaled quantum photo-excitation spectrum for scaled energy value epsilon = -0.586 538 871028 43 and scaled electric value (f) over tilde = 0.068 537 846 207 618 71 could be identified with a scaled action value of a found and mapped-out closed orbit up to a scaled action of 20. In this follow-up paper, besides presenting full details of our quantum and classical methods, we set out the scaled action values of all 317 closed orbits involved, together with the geometries of many.

Near-field distribution of optical transmission of periodic subwavelength holes in a metal film

Optical transmission of a two-dimensional array of subwavelength holes in a metal film has been numerically studied using a differential method. Transmission spectra have been calculated showing a significant increase of the transmission in certain spectral ranges corresponding to the excitation of the surface polariton Bloch waves on a metal surface with a periodic hole structure. Under the enhanced transmission conditions, the near-field distribution of the transmitted light reveals an intensity enhancement greater than 2 orders of magnitude in localized (similar to 40 nm) spots resulting from the interference of the surface polaritons Bragg scattered by the holes in an array.

Muscle-specific variations in use-dependent crossed-facilitation of corticospinal pathways mediated by transcranial direct current (DC) stimulation

The tendency for contractions of muscles in the upper limb to give rise to increases in the excitability of corticospinal projections to the homologous muscles of the opposite limb is well known. Although the suppression of this tendency is integral to tasks of daily living, its exploitation may prove to be critical in the rehabilitation of acquired hemiplegias. Transcranial direct current (DC) stimulation induces changes in cortical excitability that outlast the period of application. We present evidence that changes in the reactivity of the corticospinal pathway induced by DC stimulation of the motor cortex interact systematically with those brought about by contraction of the muscles of the ipsilateral limb. During the application of flexion torques (up to 50% of maximum) applied at the left wrist, motor evoked potentials (MEPs) were evoked in the quiescent muscles of the right arm by magnetic stimulation of the left motor cortex (M1). The MEPs were obtained prior to and following 10 min of anodal, cathodal or sham DC stimulation of left M1. Cathodal stimulation counteracted increases in the crossed-facilitation of projections to the (right) wrist flexors that otherwise occurred as a result of repeated flexion contractions at the left wrist. In addition, cathodal stimulation markedly decreased the excitability of corticospinal projections to the wrist extensors of the right limb. Thus changes in corticospinal excitability induced by DC stimulation can be shaped (i.e. differentiated by muscle group) by focal contractions of muscles in the limb ipsilateral to the site of stimulation. (C) 2008 Elsevier Ireland Ltd. All rights reserved.

Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.

Quality factor assessment of subwavelength resonant cavities at FIR frequencies

Subwavelength resonators at FIR are presented and studied. The structures consist of 1D cavities formed between a metallized (silver) surface and a metamaterial surface comprising a periodic array of silver patches on a silver-backed silicon substrate. The concept derives from recent discoveries of artificial magnetic conductors (AMC). By studying the currents excited on the metamaterial surface by a normally incident plane wave, the nature of the emerging resonant phenomena and the physical mechanism underlying the AMC operation are investigated. Full wave simulations, based on finite element method and time-domain transmission line modelling technique, have been carried out to demonstrate the effective AMC boundary condition and prove the possibilities for subwavelength cavities. The quality factor of the resonant cavities is assessed as a function of the cavity profile. It is demonstrated that the quality factor drops to about 1/8 of the half-wavelength value for lambda/8 resonant cavity.

High-gain subwavelength resonant cavity antennas based on metamaterial ground planes

Planar metarnaterial Surfaces with negative reflection phase values are proposed as ground planes in a high-gain resonant cavity antenna configuration. The antenna is formed by the metarnaterial ground plane (MGP) and a superimposed metallodielectric electromagnetic band gap (MEBG) array that acts as a partially reflective surface (PRS). A single dipole positioned between the PRS and the ground IS utilised as the excitation. Ray analysis is employed to describe the functioning of the antennas and to qualitatively predict the effect of the MGP oil the antenna performance. By employing MGPs with negative reflection phase values, the planar antenna profile is reduced to subwavelength values (less than lambda/6) whilst maintaining high directivity. Full-wave simulations have been carried out with commercially available software (Microstripes (TM)). The effect of the finite PRS size on the antenna radiation performance (directivity and sidelobe level) is studied. A prototype has been fabricated and tested experimentally in order to validate the predictions.

Novel loading tests on full-scale tapered member portal frames

This paper presents the experimental results of loading tests on two 18m span tapered member portal frames designed to BS 5950. Deflection test results for vertical, lateral and combined loading cases are compared with the predictions given by elastic analysis to BS 5950 and shown to be favourable. The predicted ultimate capacities and modes of failure, which were by lateral-torsional buckling of the columns, were also found to agree with the experimental behaviour. It was found that the method of modelling the tapered members as a series of prismatic elements gave good comparison with test results.