Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Analysis of the microbial community structure and function of a laboratory scale enhanced biological phosphorus removal reactor

A laboratory scale sequencing batch reactor (SBR) operating for enhanced biological phosphorus removal (EBPR) and fed with a mixture of volatile fatty acids (VFAs) showed stable and efficient EBPR capacity over a four-year-period. Phosphorus (P), poly-beta-hydroxyalkanoate (PHA) and glycogen cycling consistent with classical anaerobic/aerobic EBPR were demonstrated with the order of anaerobic VFA uptake being propionate, acetate then butyrate. The SBR was operated without pH control and 63.67+/-13.86 mg P l(-1) was released anaerobically. The P% of the sludge fluctuated between 6% and 10% over the operating period (average of 8.04+/-1.31%). Four main morphological types of floc-forming bacteria were observed in the sludge during one year of in-tensive microscopic observation. Two of them were mainly responsible for anaerobic/aerobic P and PHA transformations. Fluorescence in situ hybridization (FISH) and post-FISH chemical staining for intracellular polyphosphate and PHA were used to determine that 'Candidatus Accumulibacter phosphatis' was the most abundant polyphosphate accumulating organism (PAO), forming large clusters of coccobacilli (1.0-1.5 mum) and comprising 53% of the sludge bacteria. Also by these methods, large coccobacillus-shaped gammaproteobacteria (2.5-3.5 mum) from a recently described novel cluster were glycogen-accumulating organisms (GAOs) comprising 13% of the bacteria. Tetrad-forming organisms (TFOs) consistent with the 'G bacterium' morphotype were alphaproteobacteria , but not Amaricoccus spp., and comprised 25% of all bacteria. According to chemical staining, TFOs were occasionally able to store PHA anaerobically and utilize it aerobically.

Glycogen-accumulating organisms in laboratory-scale and full scale wastewater treatment processes

Laboratory-scale sequencing batch reactors (SBRs) as models for wastewater treatment processes were used to identify glycogen-accumulating organisms (GAOs), which are thought to be responsible for the deterioration of enhanced biological phosphorus removal (EBPR). The SBRs (called Q and T), operated under alternating anaerobic-aerobic conditions typical for EBPR, generated mixed microbial communities (sludges) demonstrating the GAO phenotype. Intracellular glycogen and poly-beta-hydroxyalkanoate (PHA) transformations typical of efficient EBPR occurred but polyphosphate was not bioaccumulated and the sludges contained 1.8% P (sludge Q) and 1.5% P (sludge T). 16S rDNA clone libraries were prepared from DNA extracted from the Q and T sludges. Clone inserts were grouped into operational taxonomic units (OTUs) by restriction fragment length polymorphism banding profiles. OTU representatives were sequenced and phylogenetically analysed. The Q sludge library comprised four OTUs and all six determined sequences were 99.7% identical, forming a cluster in the gamma-Proteobacteria radiation. The T sludge library comprised eight OTUs and the majority of clones were Acidobacteria subphylum 4 (49% of the library) and candidate phylum OPU (39% of the library). One OTU (two clones, of which one was sequenced) was in the gamma-Proteobacteria radiation with 95% sequence identity to the Q sludge clones. Oligonucleotide probes (called GAOQ431 and GAOQ989) were designed from the gamma-Proteobacteria clone sequences for use in fluorescence in situ hybridization (FISH); 92 % of the Q sludge bacteria and 28 % of the T sludge bacteria bound these probes in FISH. FISH and post-FISH chemical staining for PHA were used to determine that bacteria from a novel gamma-Proteobacteria cluster were phenotypically GAOs in one laboratory-scale SBR and two fullscale wastewater treatment plants. It is suggested that the GAOs from the novel cluster in the gamma-Proteobacteria radiation be named 'Candidatus Competibacter phosphatis'.

Hydrolytic kinetic resolution of terminal mono- and bis-epoxides in the synthesis of insect pheromones: routes to (-)-(R)- and (+)-(S)-10-methyldodecyl acetate, (-)-(R)-10-methyl-2-tridecanone, (-)-(R)-(Z)-undec-6-en-2-ol (Nostrenol), (-)-(1R,7R)-1,7-dime

Hydrolytic kinetic resolution (HKR) of functionalised epoxides using (salen)Co(OAc) complexes provides enantiomerically enriched epoxides and diols, which have been transformed into important insect sex pheromones. In this general approach, (-)-(R)- and (+)-(S)-10-methyldodecyl acetates from the smaller tea tortrix moth were obtained, as was (-)-(R)-10-methyltridecan-2-one from the southern corn rootworm. The (S)-epoxide obtained from undec-1-en-6-yne was transformed to (-)-(R)-(Z)-undec-6-en-2-ol (Nostrenol) from ant-lions. HKR of appropriate bisepoxides was also investigated, and transformations of the resulting bisepoxides and epoxydiols provided (-)-(1R,7R)-1,7-dimethylnonylpropanoate from corn rootworms, (-)-(6R,12R)-6,12-dimethylpentadecan-2-one from the female banded cucumber beetle, and (-)-(2S,11S)-2,11-diacetoxytridecane and (+)-(2S,12S)-2,12-diacetoxytridecane from female pea-midges. (C) 2002 Elsevier Science Ltd. All rights reserved.

A formal model of real-time program compilation

Program compilation can be formally defined as a sequence of equivalence-preserving transformations, or refinements, from high-level language programs to assembler code, Recent models also incorporate timing properties, but the resulting formalisms are intimidatingly complex. Here we take advantage of a new, simple model of real-time refinement, based on predicate transformer semantics, to present a straightforward compilation formalism that incorporates real-time constraints. (C) 2002 Elsevier Science B.V. All rights reserved.

Transformation processes, pathways, and possible sources of distinctive polychlorinated dibenzo-p-dioxin signatures in sink environments

In recent years, studies on environmental samples with unusual dibenzo-p-dioxin (PCDD) congener profiles were reported from a range of countries. These profiles, characterized by a dominance of octachlorinated dibenzodioxin (OCDD) and relatively low in dibenzofuran (PCDF) concentrations, could not be attributed to known sources or formation processes. In the present study, the processes that result in these unusual profiles were assessed using the concentrations and isomer signatures of PCDDs from dated estuarine sediment cores in Queensland, Australia. Increases in relative concentrations of lower chlorinated PODS and a relative decrease of OCDD were correlated with time of sediment deposition. Preferred lateral, anaerobic dechlorination of OCDD represents a likely pathway for these changes. In Queensland sediments, these transformations result in a distinct dominance of isomers fully chlorinated in the 1,4,6,9-positions (1,4-patterns), and similar 1,4-patterns were observed in sediments from elsewhere. Consequently, these environmental samples may not reflect the signatures of the original source, and a reevaluation of source inputs was undertaken. Natural formation of PCDDs, which has previously been suggested, is discussed; however, based on the present results and literature comparisons, we propose an alternative scenario. This scenario hypothesizes that an anthropogenic PCDD precursor input (e.g. pentachlorophenol) results in the contamination. These results and hypothesis imply further investigations are warrented into possible anthropogenic sources in areas where natural PCDD formation has been suggested.

The martensitic transformation in ceramics - its role in transformation toughening

This paper reviews the current knowledge and understanding of martensitic transformations in ceramics - the tetragonal to monoclinic transformation in zirconia in particular. This martensitic transformation is the key to transformation toughening in zirconia ceramics. A very considerable body of experimental data on the characteristics of this transformation is now available. In addition, theoretical predictions can be made using the phenomenological theory of martensitic transformations. As the paper will illustrate, the phenomenological theory is capable of explaining all the reported microstructural and crystallographic features of the transformation in zirconia and in some other ceramic systems. Hence the theory, supported by experiment, can be used with considerable confidence to provide the quantitative data that is essential for developing a credible, comprehensive understanding of the transformation toughening process. A critical feature in transformation toughening is the shape strain that accompanies the transformation. This shape strain, or nucleation strain, determines whether or not the stress-induced martensitic transformation can occur at the tip of a potentially dangerous crack. If transformation does take place, then it is the net transformation strain left behind in the transformed region that provides toughening by hindering crack growth. The fracture mechanics based models for transformation toughening, therefore, depend on having a full understanding of the characteristics of the martensitic transformation and, in particular, on being able to specify both these strains. A review of the development of the models for transformation toughening shows that their refinement and improvement over the last couple of decades has been largely a result of the inclusion of more of the characteristics of the stress-induced martensitic transformation. The paper advances an improved model for the stress-induced martensitic transformation and the strains resulting from the transformation. This model, which separates the nucleation strain from the subsequent net transformation strain, is shown to be superior to any of the constitutive models currently available. (C) 2002 Elsevier Science Ltd. All rights reserved.

Fate of N-15-labelled nitrate in a wet summer under different residue management regimes in young hoop pine plantations

A field study was conducted to investigate the fate of N-15-labelled nitrate applied at 20 kg N ha(-1) in a wet summer to microplots installed in areas under different residue management regimes in second-rotation hoop pine (Araucaria cunninghamii) plantations aged 1-3 years in south-east Queensland, Australia. PVC microplots of 235 mm diameter and 300 mm long were driven into 250 mm soil. There were three replications of each of eight treatments. These were areas just under and between 1-year-old windrows (ca. 2-3 m in width) of harvesting residues spaced 15 m apart, and with and without incorporated foliage residues (20 t DM ha(-1)); the areas just under and between 2- or 3-year-old windrows spaced 10 m apart. Only 7-29% of the added N-15 was recovered from the top 750 mm of the soil profile with the leaching loss estimated to be 70-86% over the 34-day period. The N-15 loss via denitrification was 3.7-6.3% by directly measuring the N-15 gases emitted. The microplots with the incorporated residues at the 1-year-old site had the highest N-15 loss (6.3%) as compared with the other treatments. The N-15 mass balance method together with the use of bromide (Br) tracer applied at 100 kg Br ha(-1) failed to obtain a reliable estimate of the denitrification loss. The microplots at the 1-year-old site had higher N-15 immobilisation rate (7.5-24.7%) compared with those at 2- and 3-year-old sites (2.1-3.6%). Incorporating the residues resulted in an increase in N-15 immobilisation rate (24.5-24.7%) compared with the control without the incorporated residues (8.4-14.3%). These findings suggest that climatic conditions played important roles in controlling the N-15 transformations in the wet summer season and that the residue management regimes could also significantly influence the N-15 transformations. Most of the N-15 loss occurred through leaching, but a considerable amount of the N-15 was lost through denitrification. Bromide proved to be an unsuitable tracer for monitoring the N-15 leaching and movement under the wet summer conditions. (C) 2002 Elsevier Science B.V. All rights reserved.

Rural lines of flight: Telecommunications and post-metro dreaming

Information and communications technologies hold a prominent place in the cultural imagination of many people living outside the Australian metropolis, especially recent émigrés. A vision of a wired pastoral conjures up the possibilities of city work, connections and pleasures accompanying the flight to the country. Such aspirations have given a twist to one of the great topos of Australian post-invasion communications history, communications ameliorating the perceived isolation in the bush. This article examines important changes to rural telecommunications in the 1990s coinciding with post-metro dreaming and digital convergence, namely the rise of local telecommunications. Neo-Foucauldian accounts of citizenship hold some promise for explaining the criss-cross of tangled lines of flight in regional communications in the twenty-first century: emergent subjectivities, utopian digital modes of becoming, new politics of infrastructure, reconfigured relationships among state, market and citizen.

An overview of APSIM, a model designed for farming systems simulation

The Agricultural Production Systems Simulator (APSIM) is a modular modelling framework that has been developed by the Agricultural Production Systems Research Unit in Australia. APSIM was developed to simulate biophysical process in farming systems, in particular where there is interest in the economic and ecological outcomes of management practice in the face of climatic risk. The paper outlines APSIM's structure and provides details of the concepts behind the different plant, soil and management modules. These modules include a diverse range of crops, pastures and trees, soil processes including water balance, N and P transformations, soil pH, erosion and a full range of management controls. Reports of APSIM testing in a diverse range of systems and environments are summarised. An example of model performance in a long-term cropping systems trial is provided. APSIM has been used in a broad range of applications, including support for on-farm decision making, farming systems design for production or resource management objectives, assessment of the value of seasonal climate forecasting, analysis of supply chain issues in agribusiness activities, development of waste management guidelines, risk assessment for government policy making and as a guide to research and education activity. An extensive citation list for these model testing and application studies is provided. Crown Copyright (C) 2002 Published by Elsevier Science B.V. All rights reserved.