Distribution of black nodes at various levels in a linear quadtree

The distribution of black leaf nodes at each level of a linear quadtree is of significant interest in the context of estimation of time and space complexities of linear quadtree based algorithms. The maximum number of black nodes of a given level that can be fitted in a square grid of size 2n × 2n can readily be estimated from the ratio of areas. We show that the actual value of the maximum number of nodes of a level is much less than the maximum obtained from the ratio of the areas. This is due to the fact that the number of nodes possible at a level k, 0≤k≤n − 1, should consider the sum of areas occupied by the actual number of nodes present at levels k + 1, k + 2, …, n − 1.

Effects of fish density distribution and effort distribution on catchability

The effects of fish density distribution and effort distribution on the overall catchability coefficient are examined. Emphasis is also on how aggregation and effort distribution interact to affect overall catch rate [catch per unit effort (cpue)]. In particular, it is proposed to evaluate three indices, the catchability index, the knowledge parameter, and the aggregation index, to describe the effectiveness of targeting and the effects on overall catchability in the stock area. Analytical expressions are provided so that these indices can easily be calculated. The average of the cpue calculated from small units where fishing is random is a better index for measuring the stock abundance. The overall cpue, the ratio of lumped catch and effort, together with the average cpue, can be used to assess the effectiveness of targeting. The proposed methods are applied to the commercial catch and effort data from the Australian northern prawn fishery. The indices are obtained assuming a power law for the effort distribution as an approximation of targeting during the fishing operation. Targeting increased catchability in some areas by 10%, which may have important implications on management advice.

Distribution of phosphorus and oxygen between liquid steel and basic oxygen steelmaking slag

The efficiency of dephosphorisation is governed by the thermodynamic behaviour of phosphorus and oxygen in molten metal, and P2O5 and FeO in slag. The equilibrium distribution of phosphorus and oxygen, for a wide range of chemical compositions simulating the evolution of slag composition during a typical BOF blow, has been experimentally determined. A mathematical model for estimation of the activity coefficients, as a function of the chemical composition, was also attempted.

Spatial and temporal distribution of tropical phytoplankton species and biomass in the Gulf of Carpenteria, Australia

The biomass and species composition of tropical phytoplankton in Albatross Bay, Gulf of Carpentaria, northern Australia, were examined monthly for 6 yr (1986 to 1992). Chlorophyll a (chl a) concentrations were highest (2 to 5.7 mu g l(-1)) in the wet season at inshore sites, usually coinciding with low salinities (30 to 33 ppt) and high temperatures (29 to 32 degrees C). At the offshore sites chi a concentrations were lower (0.2 to 2 mu g l(-1)) and did not vary seasonally. Nitrate and phosphate concentrations were generally low (0 to 3.68 mu M and 0.09 to 3 mu M for nitrate and phosphate respectively), whereas silicate was present in concentrations in the range 0.19 to 13 mu M. The phytoplankton community was dominated by diatoms, particularly at the inshore sites, as determined by a combination of microscopic and high-performance liquid chromatography (HPLC) pigment analyses. At the offshore sites the proportion of green flagellates increased. The cyanobacterium genus Trichodesmium and the diatom genera Chaetoceros, Rhizosolenia, Bacteriastrum and Thalassionema dominated the phytoplankton caught in 37 mu m mesh nets; however, in contrast to many other coastal areas studied worldwide there was no distinct species succession of the diatoms and only Trichodesmium showed seasonal changes in abundance. This reflects a stable phytoplankton community in waters without pulses of physical and chemical disturbances. These results are discussed in the context of the commercial prawn fishery in the Gulf of Carpentaria and the possible effect of phytoplankton on prawn larval growth and survival.

Five new species of Aptenocanthon Matthews (Coleoptera: Scarabaeidae: Scarabaeinae) from tropical Australia, with notes on distribution

Five new species of the flightless scarabaeine genus Aptenocanthon Matthews are described from northern Australia: jimara sp. nov. from the Northern Territory; kabura sp. nov., wollumbin sp. nov., winyur sp. nov. and speewah sp. nov. from mountains in the wet tropics of northern Queensland. A key is given to the eight species in the genus. A. jimara is the first record of the genus away from the east coast. Biology and distribution are discussed.

Distribution of barnacle epizoites of the crab Portunus pelagicus in the Moreton Bay region, eastern Australia

The parasites of some decapod crustaceans are known to cause sterilisation of their hosts, and can thus have an important impact on the population dynamics of infested species. Blue swimmer crabs (Portunus pelagicus) collected in three areas around Moreton Bay, Australia were examined for the presence of epizoic barnacles in their branchial chambers and on their carapace. Of the 952 crabs inspected 92% were infested with Octolasmis spp. The mean number of barnacles (predominantly Octolasmis warwickii) per carapace and gill chamber (mainly O. angulata) were 2.35 and 71.1, respectively. Barnacle infestation of gills was found to differ significantly by area, season and sex with the deeper offshore areas exhibiting the highest number of barnacles. The distribution within the hosts showed barnacles were more likely to be distributed in areas closer to the inhalant aperture. Highest abundances were found on the proximal surface of the hypobranchial side of gills 3, 4 and 5. Host moult stage and parasitism by Sacculina granifera were also found to affect the abundance of epizoic barnacles in some areas.

A spatially explicit multi-competitor coexistence model of penaeid (shrimp) distribution on the Australian Great Barrier Reef

A spatially explicit multi-competitor coexistence model was developed for meta-populations of prawns (shrimp) occupying habitat patches across the Great Barrier Reef, where dispersal was localised and dispersal rates varied between species. Prawns were modelled as individuals moving to and from patches or cells according to pre-set decision rules. The landscape was simulated as a matrix of cells with each cell having a spatially explicit survival index for each species. Mixed species prawn assemblages moved over this simplified spatially explicit landscape. A low level of chronic random environmental disturbance was assumed (cyclone and tropical storm damage) with additional acute spatially confined disturbance due to commercial trawling, modelled as an increase in mortality affecting inter-specific competition. The general form of the results was for increased disturbance to favour good-colonising "generalist" species at the expense of good-competitor "specialists". Increasing fishing mortality (local patch extinctions) combined with poor colonising ability resulted in low equilibrium abundance for even the best competitor, while in the same circumstances the poorest competitor but best coloniser could have the highest equilibrium abundance. This mimics the switch from high-value prawn species to lower-value prawn species as trawl effort increases, reflected in historic catch and effort logbook data and reported anecdotaly from the north Queensland trawl fleet. To match the observed distribution and behaviour of prawn assemblages, a combination inter-species competition, a spatially explicit landscape, and a defined pattern of disturbance (trawling) was required. Modelling this combination could simulate not only general trends in spatial distribution of each of prawn species but also localised concentrations observed in the survey data

Low-density koala (Phascolarctos cinereus) populations in the mulgalands of south-west Queensland. II. Distribution and diet

This study used faecal pellets to investigate the broadscale distribution and diet of koalas in the mulgalands biogeographic region of south-west Queensland. Koala distribution was determined by conducting faecal pellet searches within a 30-cm radius of the base of eucalypts on 149 belt transects, located using a multi-scaled stratified sampling design. Cuticular analysis of pellets collected ffom 22 of these sites was conducted to identify the dietary composition of koalas within the region. Our data suggest that koala distribution is concentrated in the northern and more easterly regions of the study area, and appears to be strongly linked with annual rainfall. Over 50% of our koala records were obtained from non-riverine communities, indicating that koalas in the study area are not primarily restricted to riverine communities, as bas frequently been suggested. Cuticular analysis indicates that more than 90% of koala diet within the region consists of five eucalypt species. Our data highlights the importance of residual Tertiary landforms to koala conservation in the region.

Distribution and abundance of white grubs (Coleoptera: Scarabaeidae) on groundnut in southern India

Scarab species associated with groundnuts were surveyed in Andhra Pradesh, Karnataka and Tamil Nadu, southern India, between 1995 and 2001. Scarab adults were collected from trees on which they were feeding and/or mating, and larvae (white grubs) from groundnut fields. Holotrichia species, especially H. reynaudi and H. serrata were the major species associated with groundnut. H. reynaudi predominated in the central Deccan area, while H. serrata was most abundant in areas to the south and west. A new, undescribed, Holotrichia species near H. consanguinea was collected south and south-west of Hyderabad in mixed populations with H. reynaudi. However, the full extent of this new species’ distribution remains uncertain. H. rufoflava was rarely associated with groundnut, but was common as an adult at some locations. Other genera encountered during surveys were Anomala, Adoretus, Schizonycha, Autoserica. In survey data, densities of Holotrichia larvae and ‘all other white grubs’ were both very highly correlated with % of damaged groundnut plants. These correlations in combination with concurrent observations of plant damage establish a causal link between white grubs and plant damage and death in southern Indian groundnut. Ranking of preferred host trees for adults were developed from field observations for four Holotrichia species and Schizonycha spp. and will assist grower-initiated surveys of pest occurrence. In combination with insecticide efficacy data published elsewhere, the survey provides the basis for an environmentally friendly and economically viable pest-management system for white grubs on groundnut in southern India.

Effects of particle size distribution in the response of model granular materials in multi-ring shear

Rail track undergoes complex loading patterns under moving traffic conditions compared to roads due to its continued and discontinued multi-layered structure, including rail, sleepers, ballast layer, sub-ballast layer, and subgrade. Particle size distributions (PSDs) of ballast, subballast, and subgrade layers can be critical in cyclic plastic deformation of rail track under moving traffic on frequent track degradation of rail tracks, especially at bridge transition zones. Conventional test approaches: static shear and cyclic single-point load tests are however unable to replicate actual loading patterns of moving train. Multi-ring shear apparatus; a new type of torsional simple shear apparatus, which can reproduce moving traffic conditions, was used in this study to investigate influence of particle size distribution of rail track layers on cyclic plastic deformation. Three particle size distributions, using glass beads were examined under different loading patterns: cyclic sin-gle-point load, and cyclic moving wheel load to evaluate cyclic plastic deformation of rail track under different loading methods. The results of these tests suggest that particle size distributions of rail track structural layers have significant impacts on cyclic plastic deformation under moving train load. Further, the limitations in con-ventional test methods used in laboratories to estimate the plastic deformation of rail track materials lead to underestimate the plastic deformation of rail tracks.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

Development of innovative robust stability enhancement algorithms for distribution systems containing distributed generators

This project was a step forward in improving the voltage profile of traditional low voltage distribution networks with high photovoltaic generation or high peak demand. As a practical and economical solution, the developed methods use a Dynamic Voltage Restorer or DVR, which is a series voltage compensator, for continuous and communication-less power quality enhancement. The placement of DVR in the network is optimised in order to minimise its power rating and cost. In addition, new approaches were developed for grid synchronisation and control of DVR which are integrated with the voltage quality improvement algorithm for stable operation.

Distribution and eradication of an exotic tephritid fruit fly in Australia: Relevance of invasion theory

Data from the eradication of the incursion of Bactrocera papayae Drew and Hancock (Dipt.: Tephritidae) in Australia (1995-1998) are used to assess the significance of various aspects of invasion theory, including the influence of towns on establishment, influence of propagule pressure on the pattern of establishment, and the existence of source-sink dynamics. Because there were no sentinel traps in place, considerable spread had occurred before the eradication campaign started. The distribution of fly density around the epicentre in the town of Cairns and a transect along the main traffic routes to the north and south fitted a Cauchy model with a tail having the same slope as a power model with an exponent of -2.4 extending to 160 km. The Cauchy model indicated that 50% of the flies on the transect would have occurred within 3.2 km of the epicentre, 90% within 13.2 km, and 99% within 60 km. The two major satellites at Mareeba (35 km from the epicentre in Cairns) and Mossman (65 km) were not used for the transect data and had respectively 15 and 30 times the density predicted by the model. The proportion of traps that caught flies (a measure of site occupancy) fell with distance from the epicentre. B. papayae was trapped consistently on only three of the 16 rainforest transects that were surveyed and these were relatively close to urban areas where eradication efforts were intense. Despite there being no eradication effort in the rainforest, the trends to extinction were similar to those in adjacent areas. The strategy of initially concentrating eradication efforts on the core and major satellites while maintaining a quarantine barrier at the airport and the boundaries of the infested area appears to be the key to the containment and rapid eradication of the incursion.

Constitutive modeling of shape memory alloy wire with non-local rate kinetics

A constitutive modeling approach for shape memory alloy (SMA) wire by taking into account the microstructural phase inhomogeneity and the associated solid-solid phase transformation kinetics is reported in this paper. The approach is applicable to general thermomechanical loading. Characterization of various scales in the non-local rate sensitive kinetics is the main focus of this paper. Design of SMA materials and actuators not only involve an optimal exploitation of the hysteresis loops during loading-unloading, but also accounts for fatigue and training cycle identifications. For a successful design of SMA integrated actuator systems, it is essential to include the microstructural inhomogeneity effects and the loading rate dependence of the martensitic evolution, since these factors play predominant role in fatigue. In the proposed formulation, the evolution of new phase is assumed according to Weibull distribution. Fourier transformation and finite difference methods are applied to arrive at the analytical form of two important scaling parameters. The ratio of these scaling parameters is of the order of 10(6) for stress-free temperature-induced transformation and 10(4) for stress-induced transformation. These scaling parameters are used in order to study the effect of microstructural variation on the thermo-mechanical force and interface driving force. It is observed that the interface driving force is significant during the evolution. Increase in the slopes of the transformation start and end regions in the stress-strain hysteresis loop is observed for mechanical loading with higher rates.

Application of Maclaurin Series in Structural Analysis

In the simple theory of flexure of beams, the slope, bending moment, shearing force, load and other quantities are functions of a derivative of y with respect to x. It is shown that the elastic curve of a transversely loaded beam can be represented by the Maclaurin series. Substitution of the values of the derivatives gives a direct solution of beam problems. In this paper the method is applied to derive the Theorem or three moments and slope deflection equations. The method is extended to the solution of a rigid portal frame. Finally the method is applied to deduce results on which the moment distribution method of analyzing rigid frames is based.