Layers of generality and types of generalization in pattern activities

Pattern generalization is considered one of the prominent routes for in-troducing students to algebra. However, not all generalizations are al-gebraic. In the use of pattern generalization as a route to algebra, we —teachers and educators— thus have to remain vigilant in order not to confound algebraic generalizations with other forms of dealing with the general. But how to distinguish between algebraic and non-algebraic generalizations? On epistemological and semiotic grounds, in this arti-cle I suggest a characterization of algebraic generalizations. This char-acterization helps to bring about a typology of algebraic and arithmetic generalizations. The typology is illustrated with classroom examples.

Performance analysis of a register insertion ring with a variable size buffer

There has been a recent revival of interest in the register insertion (RI) protocol because of its high throughput and low delay characteristics. Several variants of the protocol have been investigated with a view to integrating voice and data applications on a single local area network (LAN). In this paper the performance of an RI ring with a variable size buffer is studied by modelling and simulation. The chief advantage of the proposed scheme is that an efficient but simple bandwidth allocation scheme is easily incorporated. Approximate formulas are derived for queue lengths, queueing times, and total end-to-end transfer delays. The results are compared with previous analyses and with simulation estimates. The effectiveness of the proposed protocol in ensuring fairness of access under conditions of heavy and unequal loading is investigated.

Computational modelling of freeze layers in smelting processes

The use of computational modelling in examining process engineering issues is very powerful. It has been used in the development of the HIsmelt process from its concept. It is desirable to further water-cool the HIsmelt vessel to reduce downtime for replacing refractory. Water-cooled elements close to a metal bath run the risk of failure. This generally occurs when a process perturbation causes the freeze and refractory layers to come away from the water-cooled element, which is then exposed to liquid metal. The element fails as they are unable to remove all the heat. Modelling of the water-cooled element involves modelling the heat transfer, fluid flow, stress and solidification for a localised section of the reaction vessel. The complex interaction between the liquid slag and the refractory applied to the outside of thewater-cooled element is also being examined to model the wear of this layer. The model is being constructed in Physica, a CFD code developed at the University of Greenwich. Modelling of this system has commenced with modelling solidification test cases. These test cases have been used to validate the CFD code’s capability to model the solidification in this system. A model to track the penetration of slag into refractory has also been developed and tested.

DISCOVERY 2010: Spatial and temporal variability in a dynamic polar ecosystem

The Scotia Sea has been a focus of biological- and physical oceanographic study since the Discovery expeditions in the early 1900s. It is a physically energetic region with some of the highest levels of productivity in the Southern Ocean. It is also a region within which there have been greater than average levels of change in upper water column temperature. We describe the results of three cruises transecting the central Scotia Sea from south to north in consecutive years and covering spring, summer and autumn periods. We also report on some community level syntheses using both current-day and historical data from this region. A wide range of parameters were measured during the field campaigns, covering the physical oceanography of the region, air–sea CO2 fluxes, macro- and micronutrient concentrations, the composition and biomass of the nano-, micro- and mesoplankton communities, and the distribution and biomass of Antarctic krill and mesopelagic fish. Process studies examined the effect of iron-stress on the physiology of primary producers, reproduction and egestion in Antarctic krill and the transfer of stable isotopes between trophic layers, from primary consumers up to birds and seals. Community level syntheses included an examination of the biomass-spectra, food-web modelling, spatial analysis of multiple trophic layers and historical species distributions. The spatial analyses in particular identified two distinct community types: a northern warmer water community and a southern cold community, their boundary being broadly consistent with the position of the Southern Antarctic Circumpolar Current Front (SACCF). Temperature and ice cover appeared to be the dominant, over-riding factors in driving this pattern. Extensive phytoplankton blooms were a major feature of the surveys, and were persistent in areas such as South Georgia. In situ and bioassay measurements emphasised the important role of iron inputs as facilitators of these blooms. Based on seasonal DIC deficits, the South Georgia bloom was found to contain the strongest seasonal carbon uptake in the ice-free zone of the Southern Ocean. The surveys also encountered low-production, iron-limited regions, a situation more typical of the wider Southern Ocean. The response of primary and secondary consumers to spatial and temporal heterogeneity in production was complex. Many of the life-cycles of small pelagic organisms showed a close coupling to the seasonal cycle of food availability. For instance, Antarctic krill showed a dependence on early, non-ice-associated blooms to facilitate early reproduction. Strategies to buffer against environmental variability were also examined, such as the prevalence of multiyear life-cycles and variability in energy storage levels. Such traits were seen to influence the way in which Scotia Sea communities were structured, with biomass levels in the larger size classes being higher than in other ocean regions. Seasonal development also altered trophic function, with the trophic level of higher predators increasing through the course of the year as additional predator-prey interactions emerged in the lower trophic levels. Finally, our studies re-emphasised the role that the simple phytoplankton-krill-higher predator food chain plays in this Southern Ocean region, particularly south of the SACCF. To the north, alternative food chains, such as those involving copepods, macrozooplankton and mesopelagic fish, were increasingly important. Continued ocean warming in this region is likely to increase the prevalence of such alternative such food chains with Antarctic krill predicted to move southwards.

SiGe HBTs on Bonded SOI Incorporating Buried Silicide Layers

The performance of silicon bipolar transistors has been significantly improved by the use of ultra narrow base layers of SiGe. To further improve device performance by minimising parasitic resistance and capacitance the authors produced an unique silicon-on-insulator (SOI) substrate incorporating a buried tungsten disilicide layer. This structure forms the basis of a recent submission by Zarlink Semiconductors ( Silvaco, DeMontfort & Queen�s) to DTI for high voltage devices for automotive applications. The Queen�s part of the original EPSRC project was rated as tending to outstanding.

Effect of Rapid Thermal Annealing on the Structure and Magnetic Properties of Chemical Vapour Deposition Cobalt Layers

Future read heads in hard disc storage require high conformal coatings of metal magnetic layers over high aspect ratio profiles. This paper describes pioneering work on the use of MOCVD for the deposition of cobalt layers. While pure cobalt layers could be deposited at 400C their magnetic properties are poor. It was found that the magnetic properties of the layers could be significantly enhanced with an optimised rapid thermal anneal. This work was sponsored by Seagate Technology and led to a follow up PhD studentship on the co-deposition of cobalt and iron by MOCVD.

Hydrogen bonding and collective proton modes in clusters and periodic layers of squaric acid: A density functional study

Hydrogen bonding in clusters and extended layers of squaric acid molecules has been investigated by density functional computations. Equilibrium geometries, harmonic vibrational frequencies, and energy barriers for proton transfer along hydrogen bonds have been determined using the Car-Parrinello method. The results provide crucial parameters for a first principles modeling of the potential energy surface, and highlight the role of collective modes in the low-energy proton dynamics. The importance of quantum effects in condensed squaric acid systems has been investigated, and shown to be negligible for the lowest-energy collective proton modes. This information provides a quantitative basis for improved atomistic models of the order-disorder and displacive transitions undergone by squaric acid crystals as a function of temperature and pressure. (C) 2001 American Institute of Physics.