Convergence of partial-wave expansions for energies, scattering amplitudes and positron annihilation rates

We use many-body theory to find the asymptotic behaviour of second-order correlation corrections to the energies and positron annihilation rates in many- electron systems with respect to the angular momenta l of the single-particle orbitals included. The energy corrections decrease as 1/(l+1/2)4, in agreement with the result of Schwartz, whereas the positron annihilation rate has a slower 1/(l+1/2)2 convergence rate. We illustrate these results by numerical calculations of the energies of Ne and Kr and by examining results from extensive con?guration-interaction calculations of PsH binding and annihilation.

A Review of Numerical Modelling of Wave Energy Converter Arrays

Large-scale commercial exploitation of wave energy is certain to require the deployment of wave energy converters (WECs) in arrays, creating ‘WEC farms’. An understanding of the hydrodynamic interactions in such arrays is essential for determining optimum layouts of WECs, as well as calculating the area of ocean that the farms will require. It is equally important to consider the potential impact of wave farms on the local and distal wave climates and coastal processes; a poor understanding of the resulting environmental impact may hamper progress, as it would make planning consents more difficult to obtain. It is therefore clear that an understanding the interactions between WECs within a farm is vital for the continued development of the wave energy industry.To support WEC farm design, a range of different numerical models have been developed, with both wave phase-resolving and wave phase-averaging models now available. Phase-resolving methods are primarily based on potential flow models and include semi-analytical techniques, boundary element methods and methods involving the mild-slope equations. Phase-averaging methods are all based around spectral wave models, with supra-grid and sub-grid wave farm models available as alternative implementations.The aims, underlying principles, strengths, weaknesses and obtained results of the main numerical methods currently used for modelling wave energy converter arrays are described in this paper, using a common framework. This allows a qualitative comparative analysis of the different methods to be performed at the end of the paper. This includes consideration of the conditions under which the models may be applied, the output of the models and the relationship between array size and computational effort. Guidance for developers is also presented on the most suitable numerical method to use for given aspects of WEC farm design. For instance, certain models are more suitable for studying near-field effects, whilst others are preferable for investigating far-field effects of the WEC farms. Furthermore, the analysis presented in this paper identifies areas in which the numerical modelling of WEC arrays is relatively weak and thus highlights those in which future developments are required.

Development of sampling methods for Raman analysis of solid dosage forms of therapeutic and illicit drugs

The results of a study aimed at determining the most important experimental parameters for automated, quantitative analysis of solid dosage form pharmaceuticals (seized and model 'ecstasy' tablets) are reported. Data obtained with a macro-Raman spectrometer were complemented by micro-Raman measurements, which gave information on particle size and provided excellent data for developing statistical models of the sampling errors associated with collecting data as a series of grid points on the tablets' surface. Spectra recorded at single points on the surface of seized MDMA-caffeine-lactose tablets with a Raman microscope (lambda(ex) = 785 nm, 3 mum diameter spot) were typically dominated by one or other of the three components, consistent with Raman mapping data which showed the drug and caffeine microcrystals were ca 40 mum in diameter. Spectra collected with a microscope from eight points on a 200 mum grid were combined and in the resultant spectra the average value of the Raman band intensity ratio used to quantify the MDMA: caffeine ratio, mu(r), was 1.19 with an unacceptably high standard deviation, sigma(r), of 1.20. In contrast, with a conventional macro-Raman system (150 mum spot diameter), combined eight grid point data gave mu(r) = 1.47 with sigma(r) = 0.16. A simple statistical model which could be used to predict sigma(r) under the various conditions used was developed. The model showed that the decrease in sigma(r) on moving to a 150 mum spot was too large to be due entirely to the increased spot diameter but was consistent with the increased sampling volume that arose from a combination of the larger spot size and depth of focus in the macroscopic system. With the macro-Raman system, combining 64 grid points (0.5 mm spacing and 1-2 s accumulation per point) to give a single averaged spectrum for a tablet was found to be a practical balance between minimizing sampling errors and keeping overhead times at an acceptable level. The effectiveness of this sampling strategy was also tested by quantitative analysis of a set of model ecstasy tablets prepared from MDEA-sorbitol (0-30% by mass MDEA). A simple univariate calibration model of averaged 64 point data had R-2 = 0.998 and an r.m.s. standard error of prediction of 1.1% whereas data obtained by sampling just four points on the same tablet showed deviations from the calibration of up to 5%.

Comparison of elicitation methods for moral and affective beliefs in the theory of planned behaviour

Although the theory of planned behaviour (TPB) has been applied successfully in the area of food choice, it has been criticized for its pure utilitarian approach to the factors determining behaviour. Despite the increase in predictive power of the model with added components such as affective attitude and moral and ethical concerns, in most studies the elicitation process still only addresses people's utilitarian beliefs about the behaviour with little attention paid to other aspects. This study compares the traditional method of elicitation of advantages and disadvantages with two other methods (word association and open-ended) in the elicitations of beliefs, attitudes and moral concerns in relation to the consumption of organic foods. Results show the traditional method to be best for eliciting cognitive beliefs, open-ended emotion task for eliciting emotional beliefs and open-ended beliefs task best for moral concerns. The advantages and disadvantages of each method are discussed.

Measurement of Quenching Coefficients and Developement of Calibration Methods for Quantitative Spectroscopy of Plasma at Elevated Pressures

Measurements of collisional de-excitation (quenching) coefficients required for the interpretation of emission and fluorescence spectroscopic measurements are reported. Particular attention is turned on argon transitions which are of interest for actinometric determinations of atomic ground state populations and on fluorescence lines originating from excited atoms and noble gases in connection with two-photon excitation (TALIF) of atomic radicals. A novel method is described which allows to infer quenching coefficients for collisions with molecular hydrogen of noble gas states in the energy range up to 24 eV. The excitation is performed in these experiments by collisions of energetic electrons in the sheath of an RF excited hydrogen plasma during the field reversal phase which lasts about 10 ns. We describe in addition a calibration method - including quenching effects - for the determination by TALIF of absolute atomic radical densities of hydrogen, nitrogen and oxygen using two-photon resonances in noble gases close by the resonances of the species mentioned. The paper closes with first ideas on a novel technique to bypass quenching effects in TALIF by introducing an additional, controllable loss by photoionization that will allow quenching-free determination of absolute atomic densities with prevalent nanosecond laser systems in situations where collisional de-excitation dominates over spontaneous emission.