Planck pre-launch status: Expected LFI polarisation capability

We present a system-level description of the Low Frequency Instrument (LFI) considered as a differencing polarimeter, and evaluate its expected performance. The LFI is one of the two instruments on board the ESA Planck mission to study the cosmic microwave background. It consists of a set of 22 radiometers sensitive to linear polarisation, arranged in orthogonally-oriented pairs connected to 11 feed horns operating at 30, 44 and 70 GHz. In our analysis, the generic Jones and Mueller-matrix formulations for polarimetry are adapted to the special case of the LFI. Laboratory measurements of flight components are combined with optical simulations of the telescope to investigate the values and uncertainties in the system parameters affecting polarisation response. Methods of correcting residual systematic errors are also briefly discussed. The LFI has beam-integrated polarisation efficiency >99% for all detectors, with uncertainties below 0.1%. Indirect assessment of polarisation position angles suggests that uncertainties are generally less than 0°.5, and this will be checked in flight using observations of the Crab nebula. Leakage of total intensity into the polarisation signal is generally well below the thermal noise level except for bright Galactic emission, where the dominant effect is likely to be spectral-dependent terms due to bandpass mismatch between the two detectors behind each feed, contributing typically 1–3% leakage of foreground total intensity. Comparable leakage from compact features occurs due to beam mismatch, but this averages to < 5 × 10^(-4) for large-scale emission. An inevitable feature of the LFI design is that the two components of the linear polarisation are recovered from elliptical beams which differ substantially in orientation. This distorts the recovered polarisation and its angular power spectrum, and several methods are being developed to correct the effect, both in the power spectrum and in the sky maps. The LFI will return a high-quality measurement of the CMB polarisation, limited mainly by thermal noise. To meet our aspiration of measuring polarisation at the 1% level, further analysis of flight and ground data is required. We are still researching the most effective techniques for correcting subtle artefacts in polarisation; in particular the correction of bandpass mismatch effects is a formidable challenge, as it requires multi-band analysis to estimate the spectral indices that control the leakage

Review of the Supply of and Demand for Further Education in Scotland

These documents provide are an Executive Summary and Full Report of the background to, methodology for, and overall conclusions and recommendations of a review of the supply of and demand for Further Education (FE) provision in Scottish Further Education colleges in 2000. The review was commissioned by the Scottish Further Education Funding Council (SFEFC), and carried out between November 1999 and June 2000 by a team of researchers drawn from the Scottish Further Education Unit (SFEU), the Centre for Research in Lifelong Learning, Glasgow Caledonian University/University of Stirling, and the Applied Statistics Group, Napier University

Criteria for reachability of quantum states

We address the question of which quantum states can be inter-converted under the action of a time-dependent Hamiltonian. In particular, we consider the problem applied to mixed states, and investigate the difference between pure and mixed-state controllability introduced in previous work. We provide a complete characterization of the eigenvalue spectrum for which the state is controllable under the action of the symplectic group. We also address the problem of which states can be prepared if the dynamical Lie group is not sufficiently large to allow the system to be controllable.Comment: 14 pages, IoP LaTeX, first author has moved to Cambridge university ([email protected]

Persistence of low wind speed conditions and implications for wind power variability

As the penetration of wind generation increases on power systems throughout the world, the effects of wind variability on power systems are of increasing concern. This study focuses on sustained occurrences of low wind speeds over durations ranging from 1 h to 20 days. Such events have major implications for the variability of energy yields from wind farms. This, in turn, influences the accuracy of wind resource assessment. The frequency analysis techniques commonly used to study wind variability cannot represent the autocorrelation properties of wind speeds and thus provide no information on the probabilities of occurrence of such sustained, low wind events. We present two complementary methods for assessing wind variability, runs analysis and intensity–duration–frequency analysis, both with emphasis on characterising the occurrence of continuous, extended periods (up to several days) of low wind speeds. Multi-annual time series of hourly wind speeds from meteorological stations in Ireland are analysed with both techniques. Sustained 20-day periods corresponding to extremely low levels of wind generation are found to have return periods of around 10 years in coastal areas. Persistent, widespread low wind speed conditions across the entire country are found to occur only rarely

Sizing battery energy storage systems: using multi-objective optimisation to overcome the investment scale problem of annual worth

The financial objective, when sizing a Battery Energy Storage System (BESS) for installation in a microgrid, is to maximise the difference between discounted BESS benefits and discounted BESS costs. This may be described as maximising Annual Worth (AW). However, one drawback of sizing microgrid BESS using AW is that the scale of investment is not taken into consideration. This can lead to unrealistic BESS sizes. This paper presents two multi-objective optimisation (MOO) models to account for the scale of investment required in sizing BESS. The first model, Paired Comparison, utilises two objective functions: Daily Worth (DW), which maximises daily benefit cost differences a BESS installation provides a microgrid; and Daily Cost (DC), which minimises the daily cost of a BESS installation. The second model, called Rating Method, uses the objective functions DW and Daily Benefit-Cost Ratio (DBCR), the latter of which maximises the relative measure of BESS benefit and BESS cost. Both models are solved for a test microgrid system under three different scenarios using Compromise Programming (CP). For system designers who rank objective functions by importance, the Rating Method is the appropriate approach, whereas system designers who rank objective functions by absolute values should use Paired Comparison

Limits of control for quantum systems: kinematical bounds on the optimization of observables and the question of dynamical realizability

In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for non-dissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We summarize our previous results on kinematical bounds and show that these bounds are dynamically realizable for completely controllable systems. Moreover, we establish improved bounds for certain partially controllable systems. Finally, the question of dynamical realizability of the bounds for arbitary partially controllable systems is shown to depend on the accessible sets of the associated control system on the unitary group U(N) and the results of a few control computations are discussed briefly.Comment: 5 pages, orginal June 30, 2000, revised September 28, 200

Review of the Supply of and Demand for Further Education in Scotland

These documents provide are an Executive Summary and Full Report of the background to, methodology for, and overall conclusions and recommendations of a review of the supply of and demand for Further Education (FE) provision in Scottish Further Education colleges in 2000. The review was commissioned by the Scottish Further Education Funding Council (SFEFC), and carried out between November 1999 and June 2000 by a team of researchers drawn from the Scottish Further Education Unit (SFEU), the Centre for Research in Lifelong Learning, Glasgow Caledonian University/University of Stirling, and the Applied Statistics Group, Napier University

Degrees of controllability for quantum systems and applications to atomic systems

Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions are discussed. The results are applied to determine the degree of controllability for various atomic systems with degenerate energy levels and transition frequencies.Comment: 20 pages, IoP LaTeX, revised and expanded versio

Orbits of quantum states and geometry of Bloch vectors for NN-level systems

Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a stratification with strata given by unitary orbit manifolds, which can be identified with flag manifolds. The results are applied to study the geometry of the coherence vector for n-level quantum systems. It is shown that the unitary orbits can be naturally identified with spheres in R^{n^2-1} only for n=2. In higher dimensions the coherence vector only defines a non-surjective embedding into a closed ball. A detailed analysis of the three-level case is presented. Finally, a refined stratification in terms of symplectic orbits is considered.Comment: 15 pages LaTeX, 3 figures, reformatted, slightly modified version, corrected eq.(3), to appear in J. Physics