Geometrical relations and plethysms in the Homfly skein of the annulus

The oriented framed Homfly skein C of the annulus provides the natural parameter space for the Homfly satellite invariants of a knot. It contains a submodule C+ isomorphic to the algebra of the symmetric functions. We collect and expand formulae relating elements expressed in terms of symmetric functions to Turaev's geometrical basis of C+. We reformulate the formulae of Rosso and Jones for quantum sl(N) invariants of cables in terms of plethysms of symmetric functions, and use the connection between quantum sl(N) invariants and C+ to give a formula for the satellite of a cable as an element of C+. We then analyse the case where a cable is decorated by the pattern which corresponds to a power sum in the symmetric function interpretation of C+ to get direct relations between the Homfly invariants of some diagrams decorated by power sums.Comment: 28 pages, 15 figure

Numerical analysis of the Iosipescu specimen for composite materials

A finite element analysis of the Iosipescu shear tests for unidirectional and cross-ply composites is presented. It is shown that an iterative analysis procedure must be used to model the fixture-specimen kinematics. The correction factors which are needed to compensate for the nonuniformity of stress distribution in calculating shear modulus are shown to be dependent on the material orthotropic ratio and the finite element loading models. Test section strain distributions representative of typical graphite-epoxy specimens are also presented

Review of the literature on individual education plans

Aims and Scope of the Review - this review was carried out under a contract with the New Zealand Ministry of Education, which contained the following requirements: A literature review of national and international developments in the use of the Individual Education Plan (IEP) with schools and families, with particular attention to special education assessment practice(s) and their relationship to the IEP process. The purposes of the review were defined as follows: 1. To undertake a literature review of national and international developments in IEP processes and special education assessment practice to contribute to the Ministry of Education’s current project to review, revise and position the Individual Education Programme (IEP) Guidelines in relation to: the New Zealand Curriculum (Ministry of Education 2007), current assessment practices, effective teaching and learning practices, and engagement and reporting to parents, family and whanau (National Standards). 2. To provide both New Zealand and international research evidence of effective and/or evidence based practice, which, along with the data being collected by the Ministry of Education project team, will ultimately inform the future use of IEPs. The scope of the review was defined as follows: 1. The focus of the review is to be on: students with special needs in all school sector settings, students as learners, not the disability or the diagnosis they present with, the use of IEPs with schools and parents, the role of special education staff and other agencies in the IEP process, and what makes the IEP process effective for schools, students and their families, and what evidence there is of their effectiveness, with particular reference to the educational implications. 2. The literature sourced will include studies from both New Zealand and overseas, and peer reviewed journals and other publications

Thin-film flow in helically wound rectangular channels with small torsion

Laminar gravity-driven thin-film flow down a helically-wound channel of rectangular cross-section with small torsion in which the fluid depth is small is considered. Neglecting the entrance and exit regions we obtain the steady-state solution that is independent of position along the axis of the channel, so that the flow, which comprises a primary flow in the direction of the axis of the channel and a secondary flow in the cross-sectional plane, depends only on position in the two-dimensional cross-section of the channel. A thin-film approximation yields explicit expressions for the fluid velocity and pressure in terms of the free-surface shape, the latter satisfying a non-linear ordinary differential equation that has a simple exact solution in the special case of a channel of rectangular cross-section. The predictions of the thin-film model are shown to be in good agreement with much more computationally intensive solutions of the small-helix-torsion Navier–Stokes equations. The present work has particular relevance to spiral particle separators used in the mineral-processing industry. The validity of an assumption commonly used in modelling flow in spiral separators, namely that the flow in the outer region of the separator cross-section is described by a free vortex, is shown to depend on the problem parameters

Global Optical Control of a Quantum Spin Chain

Quantum processors which combine the long decoherence times of spin qubits together with fast optical manipulation of excitons have recently been the subject of several proposals. I show here that arbitrary single- and entangling two-qubit gates can be performed in a chain of perpetually coupled spin qubits solely by using laser pulses to excite higher lying states. It is also demonstrated that universal quantum computing is possible even if these pulses are applied {\it globally} to a chain; by employing a repeating pattern of four distinct qubit units the need for individual qubit addressing is removed. Some current experimental qubit systems would lend themselves to implementing this idea.Comment: 5 pages, 3 figure

Electron spin coherence in metallofullerenes: Y, Sc and La@C82

Endohedral fullerenes encapsulating a spin-active atom or ion within a carbon cage offer a route to self-assembled arrays such as spin chains. In the case of metallofullerenes the charge transfer between the atom and the fullerene cage has been thought to limit the electron spin phase coherence time (T2) to the order of a few microseconds. We study electron spin relaxation in several species of metallofullerene as a function of temperature and solvent environment, yielding a maximum T2 in deuterated o-terphenyl greater than 200 microseconds for Y, Sc and La@C82. The mechanisms governing relaxation (T1, T2) arise from metal-cage vibrational modes, spin-orbit coupling and the nuclear spin environment. The T2 times are over 2 orders of magnitude longer than previously reported and consequently make metallofullerenes of interest in areas such as spin-labelling, spintronics and quantum computing.Comment: 5 pages, 4 figure

Measuring errors in single qubit rotations by pulsed electron paramagnetic resonance

The ability to measure and reduce systematic errors in single-qubit logic gates is crucial when evaluating quantum computing implementations. We describe pulsed electron paramagnetic resonance (EPR) sequences that can be used to measure precisely even small systematic errors in rotations of electron-spin-based qubits. Using these sequences we obtain values for errors in rotation angle and axis for single-qubit rotations using a commercial EPR spectrometer. We conclude that errors in qubit operations by pulsed EPR are not limiting factors in the implementation of electron-spin based quantum computers

A Study of the Reionization History of Intergalactic Helium with FUSE and VLT

We obtained high-resolution VLT and FUSE spectra of the quasar HE2347-4342 to study the properties of the intergalactic medium between redshifts z=2.0-2.9. The high-quality optical spectrum allows us to identify approximately 850 HeII absorption components with column densities between N~5X10^11 and $ 10^18 cm^-2. The reprocessed FUSE spectrum extends the wavelength coverage of the HeII absorption down to an observed wavelength of 920 A. Approximately 1400 HeII absorption components are identified, including 917 HeII Ly-alpha systems and some of their HeII Ly-beta, Ly-gamma, and Ly-delta counterparts. The ionization structure of HeII is complex, with approximately 90 components that are not detected in the hydrogen spectrum. These components may represent the effect of soft ionizing sources. The ratio Eta=N(HeII)/N(HI) varies approximately from unity to more than a thousand, with a median value of 62 and a distribution consistent with the intrinsic spectral indices of quasars. This suggests that the dominant ionizing field is from the accumulated quasar radiation, with contributions from other soft sources such as star-forming regions and obscured AGN, which do not ionize helium. We find an evolution in Eta toward smaller values at lower redshift, with the gradual disappearance of soft components. At redshifts z>2.7, the large but finite increase in the HeII opacity, Tau=5+/-1, suggests that we are viewing the end stages of a reionization process that began at an earlier epoch. Fits of the absorption profiles of unblended lines indicate comparable velocities between hydrogen and He^+ ions. At hydrogen column densities N<3X10^12 cm^-2 the number of forest lines shows a significant deficit relative to a power law, and becomes negligible below N=10^11 cm^-2.Comment: 40 pages, 10 Postscript figures, uses Aastex.sty The Astrophysical Journal, in pres

Numerical Prediction and Wind Tunnel Experiment for a Pitching Unmanned Combat Air Vehicle

The low-speed flowfield for a generic unmanned combat air vehicle (UCAV) is investigated both experimentally and numerically. A wind tunnel experiment was conducted with the Boeing 1301 UCAV at a variety of angles of attack up to 70 degrees, both statically and with various frequencies of pitch oscillation (0.5, 1.0, and 2.0 Hz). In addition, pitching was performed about three longitudinal locations on the configuration (the nose, 35% MAC, and the tail). Solutions to the unsteady, laminar, compressible Navier–Stokes equations were obtained on an unstructured mesh to match results from the static and dynamic experiments. The computational results are compared with experimental results for both static and pitching cases. Details about the flowfield, including vortex formation and interaction, are shown and discussed, including the non-linear aerodynamic characteristics of the vehicle

High Fidelity Single Qubit Operations using Pulsed EPR

Systematic errors in spin rotation operations using simple RF pulses place severe limitations on the usefulness of the pulsed magnetic resonance methods in quantum computing applications. In particular, the fidelity of quantum logic operations performed on electron spin qubits falls well below the threshold for the application of quantum algorithms. Using three independent techniques, we demonstrate the use of composite pulses to improve this fidelity by several orders of magnitude. The observed high-fidelity operations are limited by pulse phase errors, but nevertheless fall within the limits required for the application of quantum error correction.Comment: 4 pages, 3 figures To appear in Phys. Rev. Let