Strategies for comparing decimal numbers with the same whole-number part

The strategies employed by 130 Grade 5 Brisbane students in comparing decimal numbers which have the same whole-number part were compared with those identified in similar studies conducted in the USA, France and Israel. Three new strategies were identified. Similar to USA results, the most common comparison errors stemmed from the incorrect whole-number strategy in which length is confused with size. The findings of this present study tend to support Resnick et al.’s (1989) hypothesis that the introduction of decimal-fraction recording before common-fraction recording seems to promote better comparison of decimal numbers.

Construction of multiplicative abstract schema for decimal-number numeration

This paper reports on an intervention study planned to help Year 6 students construct the multiplicative structure underlying decimal-number numeration. Three types of intervention were designed from a numeration model developed from a large study of 173 Year 6 students’ decimal-number knowledge. The study found that students could acquire multiplicative structure as an abstract schema if instruction took account of prior knowledge as informed by the model.

Fractions, reunitisation and the number-line representation

Centre for Mathematics and Science Education, QUT, Brisbane, Australia This paper reports on a study in which Years 6 and 10 students were individually interviewed to determine their ability to unitise and reunitise number lines used to represent mixed numbers and improper fractions. Only 16.7% of the students (all Year 6) were successful on all three tasks and, in general, Year 6 students outperformed Year 8 students. The interviews revealed that the remaining students had incomplete, fragmented or non-existent structural knowledge of mixed numbers and improper fractions, and were unable to unitise or reunitise number lines. The implication for teaching is that instruction should focus on providing students with a variety of fraction representations in order to develop rich and flexible schema for all fraction types (mixed numbers, and proper and improper fractions).

Dynamics of transformation and fragmentation of composite liquid nano-particles

Recent research on particle size distributions and particle concentrations near a busy road cannot be explained by the conventional mechanisms for particle evolution of combustion aerosols. Specifically they appear to be inadequate to explain the experimental observations of particle transformation and the evolution of the total number concentration. This resulted in the development of a new mechanism based on their thermal fragmentation, for the evolution of combustion aerosol nano-particles. A complex and comprehensive pattern of evolution of combustion aerosols, involving particle fragmentation, was then proposed and justified. In that model it was suggested that thermal fragmentation occurs in aggregates of primary particles each of which contains a solid graphite/carbon core surrounded by volatile molecules bonded to the core by strong covalent bonds. Due to the presence of strong covalent bonds between the core and the volatile (frill) molecules, such primary composite particles can be regarded as solid, despite the presence of significant (possibly, dominant) volatile component. Fragmentation occurs when weak van der Waals forces between such primary particles are overcome by their thermal (Brownian) motion. In this work, the accepted concept of thermal fragmentation is advanced to determine whether fragmentation is likely in liquid composite nano-particles. It has been demonstrated that at least at some stages of evolution, combustion aerosols contain a large number of composite liquid particles containing presumably several components such as water, oil, volatile compounds, and minerals. It is possible that such composite liquid particles may also experience thermal fragmentation and thus contribute to, for example, the evolution of the total number concentration as a function of distance from the source. Therefore, the aim of this project is to examine theoretically the possibility of thermal fragmentation of composite liquid nano-particles consisting of immiscible liquid v components. The specific focus is on ternary systems which include two immiscible liquid droplets surrounded by another medium (e.g., air). The analysis shows that three different structures are possible, the complete encapsulation of one liquid by the other, partial encapsulation of the two liquids in a composite particle, and the two droplets separated from each other. The probability of thermal fragmentation of two coagulated liquid droplets is discussed and examined for different volumes of the immiscible fluids in a composite liquid particle and their surface and interfacial tensions through the determination of the Gibbs free energy difference between the coagulated and fragmented states, and comparison of this energy difference with the typical thermal energy kT. The analysis reveals that fragmentation was found to be much more likely for a partially encapsulated particle than a completely encapsulated particle. In particular, it was found that thermal fragmentation was much more likely when the volume ratio of the two liquid droplets that constitute the composite particle are very different. Conversely, when the two liquid droplets are of similar volumes, the probability of thermal fragmentation is small. It is also demonstrated that the Gibbs free energy difference between the coagulated and fragmented states is not the only important factor determining the probability of thermal fragmentation of composite liquid particles. The second essential factor is the actual structure of the composite particle. It is shown that the probability of thermal fragmentation is also strongly dependent on the distance that each of the liquid droplets should travel to reach the fragmented state. In particular, if this distance is larger than the mean free path for the considered droplets in the air, the probability of thermal fragmentation should be negligible. In particular, it follows form here that fragmentation of the composite particle in the state with complete encapsulation is highly unlikely because of the larger distance that the two droplets must travel in order to separate. The analysis of composite liquid particles with the interfacial parameters that are expected in combustion aerosols demonstrates that thermal fragmentation of these vi particles may occur, and this mechanism may play a role in the evolution of combustion aerosols. Conditions for thermal fragmentation to play a significant role (for aerosol particles other than those from motor vehicle exhaust) are determined and examined theoretically. Conditions for spontaneous transformation between the states of composite particles with complete and partial encapsulation are also examined, demonstrating the possibility of such transformation in combustion aerosols. Indeed it was shown that for some typical components found in aerosols that transformation could take place on time scales less than 20 s. The analysis showed that factors that influenced surface and interfacial tension played an important role in this transformation process. It is suggested that such transformation may, for example, result in a delayed evaporation of composite particles with significant water component, leading to observable effects in evolution of combustion aerosols (including possible local humidity maximums near a source, such as a busy road). The obtained results will be important for further development and understanding of aerosol physics and technologies, including combustion aerosols and their evolution near a source.

Theoretical investigation of mechanisms of formation and interaction of nanoparticles

In this thesis an investigation into theoretical models for formation and interaction of nanoparticles is presented. The work presented includes a literature review of current models followed by a series of five chapters of original research. This thesis has been submitted in partial fulfilment of the requirements for the degree of doctor of philosophy by publication and therefore each of the five chapters consist of a peer-reviewed journal article. The thesis is then concluded with a discussion of what has been achieved during the PhD candidature, the potential applications for this research and ways in which the research could be extended in the future. In this thesis we explore stochastic models pertaining to the interaction and evolution mechanisms of nanoparticles. In particular, we explore in depth the stochastic evaporation of molecules due to thermal activation and its ultimate effect on nanoparticles sizes and concentrations. Secondly, we analyse the thermal vibrations of nanoparticles suspended in a fluid and subject to standing oscillating drag forces (as would occur in a standing sound wave) and finally on lattice surfaces in the presence of high heat gradients. We have described in this thesis a number of new models for the description of multicompartment networks joined by a multiple, stochastically evaporating, links. The primary motivation for this work is in the description of thermal fragmentation in which multiple molecules holding parts of a carbonaceous nanoparticle may evaporate. Ultimately, these models predict the rate at which the network or aggregate fragments into smaller networks/aggregates and with what aggregate size distribution. The models are highly analytic and describe the fragmentation of a link holding multiple bonds using Markov processes that best describe different physical situations and these processes have been analysed using a number of mathematical methods. The fragmentation of the network/aggregate is then predicted using combinatorial arguments. Whilst there is some scepticism in the scientific community pertaining to the proposed mechanism of thermal fragmentation,we have presented compelling evidence in this thesis supporting the currently proposed mechanism and shown that our models can accurately match experimental results. This was achieved using a realistic simulation of the fragmentation of the fractal carbonaceous aggregate structure using our models. Furthermore, in this thesis a method of manipulation using acoustic standing waves is investigated. In our investigation we analysed the effect of frequency and particle size on the ability for the particle to be manipulated by means of a standing acoustic wave. In our results, we report the existence of a critical frequency for a particular particle size. This frequency is inversely proportional to the Stokes time of the particle in the fluid. We also find that for large frequencies the subtle Brownian motion of even larger particles plays a significant role in the efficacy of the manipulation. This is due to the decreasing size of the boundary layer between acoustic nodes. Our model utilises a multiple time scale approach to calculating the long term effects of the standing acoustic field on the particles that are interacting with the sound. These effects are then combined with the effects of Brownian motion in order to obtain a complete mathematical description of the particle dynamics in such acoustic fields. Finally, in this thesis, we develop a numerical routine for the description of "thermal tweezers". Currently, the technique of thermal tweezers is predominantly theoretical however there has been a handful of successful experiments which demonstrate the effect it practise. Thermal tweezers is the name given to the way in which particles can be easily manipulated on a lattice surface by careful selection of a heat distribution over the surface. Typically, the theoretical simulations of the effect can be rather time consuming with supercomputer facilities processing data over days or even weeks. Our alternative numerical method for the simulation of particle distributions pertaining to the thermal tweezers effect use the Fokker-Planck equation to derive a quick numerical method for the calculation of the effective diffusion constant as a result of the lattice and the temperature. We then use this diffusion constant and solve the diffusion equation numerically using the finite volume method. This saves the algorithm from calculating many individual particle trajectories since it is describes the flow of the probability distribution of particles in a continuous manner. The alternative method that is outlined in this thesis can produce a larger quantity of accurate results on a household PC in a matter of hours which is much better than was previously achieveable.

A modified particle filter for simultaneous robot localization and landmark tracking in an indoor environment

This paper presents the implementation of a modified particle filter for vision-based simultaneous localization and mapping of an autonomous robot in a structured indoor environment. Through this method, artificial landmarks such as multi-coloured cylinders can be tracked with a camera mounted on the robot, and the position of the robot can be estimated at the same time. Experimental results in simulation and in real environments show that this approach has advantages over the extended Kalman filter with ambiguous data association and various levels of odometric noise.

Port of Brisbane stormwater quality : stage 2 development of a port specific water quality model

Background: The quality of stormwater runoff from ports is significant as it can be an important source of pollution to the marine environment. This is also a significant issue for the Port of Brisbane as it is located in an area of high environmental values. Therefore, it is imperative to develop an in-depth understanding of stormwater runoff quality to ensure that appropriate strategies are in place for quality improvement, where necessary. To this end, the Port of Brisbane Corporation aimed to develop a port specific stormwater model for the Fisherman Islands facility. The need has to be considered in the context of the proposed future developments of the Port area. ----------------- The Project: The research project is an outcome of the collaborative Partnership between the Port of Brisbane Corporation (POBC) and Queensland University of Technology (QUT). A key feature of this Partnership is that it seeks to undertake research to assist the Port in strengthening the environmental custodianship of the Port area through ‘cutting edge’ research and its translation into practical application. ------------------ The project was separated into two stages. The first stage developed a quantitative understanding of the generation potential of pollutant loads in the existing land uses. This knowledge was then used as input for the stormwater quality model developed in the subsequent stage. The aim is to expand this model across the yet to be developed port expansion area. This is in order to predict pollutant loads associated with stormwater flows from this area with the longer term objective of contributing to the development of ecological risk mitigation strategies for future expansion scenarios. ----------------- Study approach: Stage 1 of the overall study confirmed that Port land uses are unique in terms of the anthropogenic activities occurring on them. This uniqueness in land use results in distinctive stormwater quality characteristics different to other conventional urban land uses. Therefore, it was not scientifically valid to consider the Port as belonging to a single land use category or to consider as being similar to any typical urban land use. The approach adopted in this study was very different to conventional modelling studies where modelling parameters are developed using calibration. The field investigations undertaken in Stage 1 of the overall study helped to create fundamental knowledge on pollutant build-up and wash-off in different Port land uses. This knowledge was then used in computer modelling so that the specific characteristics of pollutant build-up and wash-off can be replicated. This meant that no calibration processes were involved due to the use of measured parameters for build-up and wash-off. ---------------- Conclusions: Stage 2 of the study was primarily undertaken using the SWMM stormwater quality model. It is a physically based model which replicates natural processes as closely as possible. The time step used and catchment variability considered was adequate to accommodate the temporal and spatial variability of input parameters and the parameters used in the modelling reflect the true nature of rainfall-runoff and pollutant processes to the best of currently available knowledge. In this study, the initial loss values adopted for the impervious surfaces are relatively high compared to values noted in research literature. However, given the scientifically valid approach used for the field investigations, it is appropriate to adopt the initial losses derived from this study for future modelling of Port land uses. The relatively high initial losses will reduce the runoff volume generated as well as the frequency of runoff events significantly. Apart from initial losses, most of the other parameters used in SWMM modelling are generic to most modelling studies. Development of parameters for MUSIC model source nodes was one of the primary objectives of this study. MUSIC, uses the mean and standard deviation of pollutant parameters based on a normal distribution. However, based on the values generated in this study, the variation of Event Mean Concentrations (EMCs) for Port land uses within the given investigation period does not fit a normal distribution. This is possibly due to the fact that only one specific location was considered, namely the Port of Brisbane unlike in the case of the MUSIC model where a range of areas with different geographic and climatic conditions were investigated. Consequently, the assumptions used in MUSIC are not totally applicable for the analysis of water quality in Port land uses. Therefore, in using the parameters included in this report for MUSIC modelling, it is important to note that it may result in under or over estimations of annual pollutant loads. It is recommended that the annual pollutant load values given in the report should be used as a guide to assess the accuracy of the modelling outcomes. A step by step guide for using the knowledge generated from this study for MUSIC modelling is given in Table 4.6. ------------------ Recommendations: The following recommendations are provided to further strengthen the cutting edge nature of the work undertaken: * It is important to further validate the approach recommended for stormwater quality modelling at the Port. Validation will require data collection in relation to rainfall, runoff and water quality from the selected Port land uses. Additionally, the recommended modelling approach could be applied to a soon-to-be-developed area to assess ‘before’ and ‘after’ scenarios. * In the modelling study, TSS was adopted as the surrogate parameter for other pollutants. This approach was based on other urban water quality research undertaken at QUT. The validity of this approach should be further assessed for Port land uses. * The adoption of TSS as a surrogate parameter for other pollutants and the confirmation that the <150 m particle size range was predominant in suspended solids for pollutant wash-off gives rise to a number of important considerations. The ability of the existing structural stormwater mitigation measures to remove the <150 m particle size range need to be assessed. The feasibility of introducing source control measures as opposed to end-of-pipe measures for stormwater quality improvement may also need to be considered.

Greenhouse Gas Emissions Calculator for Grain and Biofuel Farming Systems

Greenhouse gas markets, where invisible gases are traded, must seem like black boxes to most people. Farmers can make money on these markets, such as the Chicago Climate Exchange, by installing methane capture technologies in animal-based systems, no-till farming, establishing grasslands, and planting trees.

A study of environmental and management drivers of non-co2 greenhouse gas emissions in Australian agro-ecosystems

Australian climate, soils and agricultural management practices are significantly different from those of the northern hemisphere nations. Consequently, experimental data on greenhouse gas production from European and North American agricultural soils and its interpretation are unlikely to be directly applicable to Australian systems.