The Auslander-Gorenstein property for Z-algebras

We provide a framework for part of the homological theory of Z-algebras and their generalizations, directed towards analogues of the Auslander-Gorenstein condition and the associated double Ext spectral sequence that are useful for enveloping algebras of Lie algebras and related rings. As an application, we prove the equidimensionality of the characteristic variety of an irreducible representation of the Z-algebra, and for related representations over quantum symplectic resolutions. In the special case of Cherednik algebras of type A, this answers a question raised by the authors.Comment: 31 page

Simulating a dual beam combiner at SUSI for narrow-angle astrometry

The Sydney University Stellar Interferometer (SUSI) has two beam combiners, i.e. the Precision Astronomical Visible Observations (PAVO) and the Microarcsecond University of Sydney Companion Astrometry (MUSCA). The primary beam combiner, PAVO, can be operated independently and is typically used to measure properties of binary stars of less than 50 milliarc- sec (mas) separation and the angular diameters of single stars. On the other hand, MUSCA was recently installed and must be used in tandem with the for- mer. It is dedicated for microarcsecond precision narrow-angle astrometry of close binary stars. The performance evaluation and development of the data reduction pipeline for the new setup was assisted by an in-house computer simulation tool developed for this and related purposes. This paper describes the framework of the simulation tool, simulations carried out to evaluate the performance of each beam combiner and the expected astrometric precision of the dual beam combiner setup, both at SUSI and possible future sites.Comment: 28 pages, 23 figures, accepted for publication in Experimental Astronomy. The final publication is available at http://link.springer.co

A low cost scheme for high precision dual-wavelength laser metrology

A novel method capable of delivering relative optical path length metrology with nanometer precision is demonstrated. Unlike conventional dual-wavelength metrology which employs heterodyne detection, the method developed in this work utilizes direct detection of interference fringes of two He-Ne lasers as well as a less precise stepper motor open-loop position control system to perform its measurement. Although the method may be applicable to a variety of circumstances, the specific application where this metrology is essential is in an astrometric optical long baseline stellar interferometer dedicated to precise measurement of stellar positions. In our example application of this metrology to a narrow-angle astrometric interferometer, measurement of nanometer precision could be achieved without frequency-stabilized lasers although the use of such lasers would extend the range of optical path length the metrology can accurately measure. Implementation of the method requires very little additional optics or electronics, thus minimizing cost and effort of implementation. Furthermore, the optical path traversed by the metrology lasers is identical with that of the starlight or science beams, even down to using the same photodetectors, thereby minimizing the non-common-path between metrology and science channels.Comment: 17 pages, 4 figures, accepted for publication in Applied Optic

Effect of Riffle Height and Spacing of a Sluice Board on Placer Gold Recovery

Sluicing is the preferred mineral processing technique for the treatment of placer gold-bearing alluvium for small scale and artisanal miners in Ghana because sluice board is perceived to be the most cost effective device. However, there are differences in approaches from design to operation.  In this work, about 50 kg of ore was obtained from “Peace School” small scale mining site near the University of Mines and Technology, Tarkwa. It was processed to determine the effects of riffle height and spacing on gold recovery. It was confirmed that, in order to trap a greater percentage of gold particles, the height of the riffle ought to be higher than the suspension height of the gold. The suspension heights of the gold particles of the various operational regimes of the sluice board at superficial velocities of 0.5 m/s, 1.0 m/s, 1.5 m/s and 2.0 m/ were   0.9 cm, 1.2 cm, 1.5 cm and 2.9 cm respectively. Analysis of concentrates showed that, 85.4% of gold was recovered during sluicing at approximately 1.0 cm riffle height.  The lowest recovery was recorded at 0.5 cm riffle height. Gold recovery was also affected by riffles spacing.  For the indicated speeds and the riffle heights the necessary spacing should not be more than 20 cm. The peak recovery was obtained at a riffle height of 1.0 cm but dropped after 20.0 cm spacing. Keywords: Sluice Board, Riffle Height, Gold, Rifle Spacing

Methodology for environmental assessment of agri-environment schemes: the Agri Environmental Footprint Index

End of project reportAgri-environment schemes pay farmers for the provision of environmental services. Such schemes tend to have multiple measures that deliver multiple environmental objectives, and there is a lack of consistent methodology with which to measure the environmental benefits of such schemes. Funded by EU FP6, the Agri-Environment Footprint project (www.footprint.rdg.ac.uk) aimed to address this challenge, and this report provides results from selected components of the project.European Unio

Spontaneous soliton formation and modulational instability in Bose-Einstein condensates

The dynamics of an elongated attractive Bose-Einstein condensate in an axisymmetric harmonic trap is studied. It is shown that density fringes caused by self-interference of the condensate order parameter seed modulational instability. The latter has novel features in contradistinction to the usual homogeneous case known from nonlinear fiber optics. Several open questions in the interpretation of the recent creation of the first matter-wave bright soliton train [Strecker {\it et al.} Nature {\bf 417} 150 (2002)] are addressed. It is shown that primary transverse collapse, followed by secondary collapse induced by soliton--soliton interactions, produce bursts of hot atoms at different time scales.Comment: 4 pages, 3 figures. Phys. Rev. Lett. in pres