Repeating patterns : strategies to assist young students to generalise the mathematical structure

This paper focuses on very young students' ability to engage in repeating pattern tasks and identifying strategies that assist them to ascertain the structure of the pattern. It describes results of a study which is part of the Early Years Generalising Project (EYGP) and involves Australian students in Years 1 to 4 (ages 5-10). This paper reports on the results from the early years' cohort (Year 1 and 2 students). Clinical interviews were used to collect data concerning students' ability to determine elements in different positions when two units of a repeating pattern were shown. This meant that students were required to identify the multiplicative structure of the pattern. Results indicate there are particular strategies that assist students to predict these elements, and there appears to be a hierarchy of pattern activities that help students to understand the structure of repeating patterns.

How to achieve maximum charge carrier loading on heteroatom-substituted graphene nanoribbon edges: density functional theory study

The practical number of charge carriers loaded is crucial to the evaluation of the capacity performance of carbon-based electrodes in service, and cannot be easily addressed experimentally. In this paper, we report a density functional theory study of charge carrier adsorption onto zigzag edge-shaped graphene nanoribbons (ZGNRs), both pristine and incorporating edge substitution with boron, nitrogen or oxygen atoms. All edge substitutions are found to be energetically favorable, especially in oxidized environments. The maximal loading of protons onto the substituted ZGNR edges obeys a rule of [8-n-1], where n is the number of valence electrons of the edge-site atom constituting the adsorption site. Hence, a maximum charge loading is achieved with boron substitution. This result correlates in a transparent manner with the electronic structure characteristics of the edge atom. The boron edge atom, characterized by the most empty p band, facilitates more than the other substitutional cases the accommodation of valence electrons transferred from the ribbon, induced by adsorption of protons. This result not only further confirms the possibility of enhancing charge storage performance of carbon-based electrochemical devices through chemical functionalization but also, more importantly, provides the physical rationale for further design strategies.

Charge carrier exchange at chemically modified graphene edges: A density functional theory study

Heteroatom doping on the edge of graphene may serve as an effective way to tune chemical activity of carbon-based electrodes with respect to charge carrier transfer in an aqueous environment. In a step towards developing mechanistic understanding of this phenomenon, we explore herein mechanisms of proton transfer from aqueous solution to pristine and doped graphene edges utilizing density functional theory. Atomic B-, N-, and O- doped edges as well as the native graphene are examined, displaying varying proton affinities and effective interaction ranges with the H3O+ charge carrier. Our study shows that the doped edges characterized by more dispersive orbitals, namely boron and nitrogen, demonstrate more energetically favourable charge carrier exchange compared with oxygen, which features more localized orbitals. Extended calculations are carried out to examine proton transfer from the hydronium ion in the presence of explicit water, with results indicating that the basic mechanistic features of the simpler model are unchanged.

Mathematical modelling of controlled drug release from polymer micro-spheres : incorporating the effects of swelling, diffusion and dissolution via moving boundary problems

Controlled drug delivery is a key topic in modern pharmacotherapy, where controlled drug delivery devices are required to prolong the period of release, maintain a constant release rate, or release the drug with a predetermined release profile. In the pharmaceutical industry, the development process of a controlled drug delivery device may be facilitated enormously by the mathematical modelling of drug release mechanisms, directly decreasing the number of necessary experiments. Such mathematical modelling is difficult because several mechanisms are involved during the drug release process. The main drug release mechanisms of a controlled release device are based on the device’s physiochemical properties, and include diffusion, swelling and erosion. In this thesis, four controlled drug delivery models are investigated. These four models selectively involve the solvent penetration into the polymeric device, the swelling of the polymer, the polymer erosion and the drug diffusion out of the device but all share two common key features. The first is that the solvent penetration into the polymer causes the transition of the polymer from a glassy state into a rubbery state. The interface between the two states of the polymer is modelled as a moving boundary and the speed of this interface is governed by a kinetic law. The second feature is that drug diffusion only happens in the rubbery region of the polymer, with a nonlinear diffusion coefficient which is dependent on the concentration of solvent. These models are analysed by using both formal asymptotics and numerical computation, where front-fixing methods and the method of lines with finite difference approximations are used to solve these models numerically. This numerical scheme is conservative, accurate and easily implemented to the moving boundary problems and is thoroughly explained in Section 3.2. From the small time asymptotic analysis in Sections 5.3.1, 6.3.1 and 7.2.1, these models exhibit the non-Fickian behaviour referred to as Case II diffusion, and an initial constant rate of drug release which is appealing to the pharmaceutical industry because this indicates zeroorder release. The numerical results of the models qualitatively confirms the experimental behaviour identified in the literature. The knowledge obtained from investigating these models can help to develop more complex multi-layered drug delivery devices in order to achieve sophisticated drug release profiles. A multi-layer matrix tablet, which consists of a number of polymer layers designed to provide sustainable and constant drug release or bimodal drug release, is also discussed in this research. The moving boundary problem describing the solvent penetration into the polymer also arises in melting and freezing problems which have been modelled as the classical onephase Stefan problem. The classical one-phase Stefan problem has unrealistic singularities existed in the problem at the complete melting time. Hence we investigate the effect of including the kinetic undercooling to the melting problem and this problem is called the one-phase Stefan problem with kinetic undercooling. Interestingly we discover the unrealistic singularities existed in the classical one-phase Stefan problem at the complete melting time are regularised and also find out the small time behaviour of the one-phase Stefan problem with kinetic undercooling is different to the classical one-phase Stefan problem from the small time asymptotic analysis in Section 3.3. In the case of melting very small particles, it is known that surface tension effects are important. The effect of including the surface tension to the melting problem for nanoparticles (no kinetic undercooling) has been investigated in the past, however the one-phase Stefan problem with surface tension exhibits finite-time blow-up. Therefore we investigate the effect of including both the surface tension and kinetic undercooling to the melting problem for nanoparticles and find out the the solution continues to exist until complete melting. The investigation of including kinetic undercooling and surface tension to the melting problems reveals more insight into the regularisations of unphysical singularities in the classical one-phase Stefan problem. This investigation gives a better understanding of melting a particle, and contributes to the current body of knowledge related to melting and freezing due to heat conduction.

Multiple Literacies Theory: Discourse, sensation, resonance and becoming

This thematic issue on education and the politics of becoming focuses on how a Multiple Literacies Theory (MLT) plugs into practice in education. MLT does this by creating an assemblage between discourse, text, resonance and sensations. What does this produce? Becoming AND how one might live are the product of an assemblage (May, 2005; Semetsky, 2003). In this paper, MLT is the approach that explores the connection between educational theory and practice through the lens of an empirical study of multilingual children acquiring multiple writing systems simultaneously. The introduction explicates discourse, text, resonance, sensation and becoming. The second section introduces certain Deleuzian concepts that plug into MLT. The third section serves as an introduction to MLT. The fourth section is devoted to the study by way of a rhizoanalysis. Finally, drawing on the concept of the rhizome, this article exits with potential lines of flight opened by MLT. These are becomings which highlight the significance of this work in terms of transforming not only how literacies are conceptualized, especially in minority language contexts, but also how one might live.

Integrating agency and resource dependence theory : firm profitability, industry regulation, and board task performance

Boards of directors are key governancemechanisms in organizations and fulfill twomain tasks:monitoringmanagers and firm performance, and providing advice and access to resources. In spite of a wealth of researchmuch remains unknown about how boards attend to the two tasks. This study investigates whether organizational (firm profitability) and environmental factors (industry regulation) affect board task performance. The data combine CEOs' responses to a questionnaire, and archival data from a sample of large Italian firms. Findings show that past firm performance is negatively associatedwith board monitoring and advice tasks; greater industry regulation enhances perceived board task performance; board monitoring and advice tasks tend to reinforce each other, despite their theoretical and practical distinction.

Mathematical modelling of LiFePO4 cathodes

LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. It has been the focus of considerable experimental and theoretical scrutiny in the past decade, resulting in LiFePO4 cathodes that perform well at high discharge rates. This scrutiny has raised several questions about the behaviour of LiFePO4 material during charge and discharge. In contrast to many other battery chemistries that intercalate homogeneously, LiFePO4 can phase-separate into highly and lowly lithiated phases, with intercalation proceeding by advancing an interface between these two phases. The main objective of this thesis is to construct mathematical models of LiFePO4 cathodes that can be validated against experimental discharge curves. This is in an attempt to understand some of the multi-scale dynamics of LiFePO4 cathodes that can be difficult to determine experimentally. The first section of this thesis constructs a three-scale mathematical model of LiFePO4 cathodes that uses a simple Stefan problem (which has been used previously in the literature) to describe the assumed phase-change. LiFePO4 crystals have been observed agglomerating in cathodes to form a porous collection of crystals and this morphology motivates the use of three size-scales in the model. The multi-scale model developed validates well against experimental data and this validated model is then used to examine the role of manufacturing parameters (including the agglomerate radius) on battery performance. The remainder of the thesis is concerned with investigating phase-field models as a replacement for the aforementioned Stefan problem. Phase-field models have recently been used in LiFePO4 and are a far more accurate representation of experimentally observed crystal-scale behaviour. They are based around the Cahn-Hilliard-reaction (CHR) IBVP, a fourth-order PDE with electrochemical (flux) boundary conditions that is very stiff and possesses multiple time and space scales. Numerical solutions to the CHR IBVP can be difficult to compute and hence a least-squares based Finite Volume Method (FVM) is developed for discretising both the full CHR IBVP and the more traditional Cahn-Hilliard IBVP. Phase-field models are subject to two main physicality constraints and the numerical scheme presented performs well under these constraints. This least-squares based FVM is then used to simulate the discharge of individual crystals of LiFePO4 in two dimensions. This discharge is subject to isotropic Li+ diffusion, based on experimental evidence that suggests the normally orthotropic transport of Li+ in LiFePO4 may become more isotropic in the presence of lattice defects. Numerical investigation shows that two-dimensional Li+ transport results in crystals that phase-separate, even at very high discharge rates. This is very different from results shown in the literature, where phase-separation in LiFePO4 crystals is suppressed during discharge with orthotropic Li+ transport. Finally, the three-scale cathodic model used at the beginning of the thesis is modified to simulate modern, high-rate LiFePO4 cathodes. High-rate cathodes typically do not contain (large) agglomerates and therefore a two-scale model is developed. The Stefan problem used previously is also replaced with the phase-field models examined in earlier chapters. The results from this model are then compared with experimental data and fit poorly, though a significant parameter regime could not be investigated numerically. Many-particle effects however, are evident in the simulated discharges, which match the conclusions of recent literature. These effects result in crystals that are subject to local currents very different from the discharge rate applied to the cathode, which impacts the phase-separating behaviour of the crystals and raises questions about the validity of using cathodic-scale experimental measurements in order to determine crystal-scale behaviour.

A Design Theory for Context-Aware Information Systems

This research studies information systems that adapt to the context in which they are used and provides recommendations on how the design of such systems can be improved. This thesis covers the problem of context-awareness via two case studies in the insurance and transportation industries. The study highlights shortcomings in the understanding of the relationship between information systems and context. Furthermore, it presents a new, theory-informed approach to design, and provides guidance for system developers seeking to implement context-aware information systems.

Implementing the self-management threshold learning outcome in Australian legal curricula : insights from self-determination theory

In 2010, six Threshold Learning Outcomes (TLOs) for law were developed by the Australian Learning and Teaching Council's Discipline Scholars: Law. The final of these outcomes, TLO 6, concerns self-management. This thesis examines strategies for implementing self-management in Australian legal education by first contextualising the development of TLO 6 in light of other relevant national and international developments in higher education, and secondly, analysing this learning outcome through the lens of Self-Determination Theory (SDT), an influential branch of educational psychology. It is argued that the central concept of autonomous self-regulation in SDT provides insights into factors that are relevant to law students’ capacities for long-term self-management, which is reinforced by analysis of the literature on law students’ distress. Accordingly, curriculum design that supports students’ autonomy may simultaneously promote students’ self-management capacities. The discussion of theoretical and practical perspectives on autonomy supportive curriculum design in this thesis thus illuminates potential pedagogical approaches for the implementation of TLO 6 in Australian legal curricula.

Mathematical modelling of tumour growth and interaction with host tissue and the immune system

In this thesis, three mathematical models describing the growth of solid tumour incorporating the host tissue and the immune system response are developed and investigated. The initial model describes the dynamics of the growing tumour and immune response before being extended in the second model by introducing a time-varying dendritic cell-based treatment strategy. Finally, in the third model, we present a mathematical model of a growing tumour using a hybrid cellular automata. These models can provide information to pre-experimental work to assist in designing more effective and efficient laboratory experiments related to tumour growth and interactions with the immune system and immunotherapy.

Adsorption and dissociation of ammonia borane outside and inside single-walled carbon nanotubes : A density functional theory study

Amonia borane (AB) has been identified as a potential candidate highcapacity hydrogen storage material. This work probes the adsorption and dissociation of AB inside and outside single-walled carbon nanotubes (SWCNTs) within the framework of density functional theory. The dissociation barriers of AB have been calculated and compared with that of the isolated AB molecule. On the basis of the present calculations, no notable improvement results from SWCNT confinement; on the contrary, the dissociation barrier slightly increases with respect to isolated AB.

A density functional theory study on CO2 capture and activation by graphene-like boron nitride with boron vacancy

First principle calculations for a hexagonal (graphene-like) boron nitride (g-BN) monolayer sheet in the presence of a boron-atom vacancy show promising properties for capture and activation of carbon dioxide. CO2 is found to decompose to produce an oxygen molecule via an intermediate chemisorption state on the defect g-BN sheet. The three stationary states and two transition states in the reaction pathway are confirmed by minimum energy pathway search and frequency analysis. The values computed for the two energy barriers involved in this catalytic reaction after enthalpy correction indicate that the catalytic reaction should proceed readily at room temperature.

A density functional theory study of CO2 and N2 adsorption on aluminium nitride single walled nanotubes

Strong binding of isolated carbon dioxide (CO2) on aluminium nitride (AlN) single walled nanotubes is verified using two different functionals. Two optimized configurations corresponding to physisorption and chemisorption are linked by a low energy barrier, such that the chemisorbed state is accessible and thermodynamically favored at low temperatures. In contrast, N2 is found only to form a physisorbed complex with the AlN nanotube, suggesting the potential application of aluminium nitride based materials for CO2 fixation. The effect of nanotube diameter on gas adsorption properties is also discussed. The diameter is found to have an important effect on the chemisorption of CO2, but has little effect on the physisorption of either CO2 or N2.

Adsorption of carbon dioxide and nitrogen on single-layer aluminum nitride nanostructures studied by density functional theory

The adsorption of carbon dioxide and nitrogen molecules on aluminum nitride (AlN) nanostructures has been explored using first-principle computational methods. Optimized configurations corresponding to physisorption and, subsequentially, chemisorption of CO2 are identified, in contrast to N2, for which only a physisorption structure is found. Transition-state searches imply a low energy barrier between the physisorption and chemisorption states for CO2 such that the latter is accessible and thermodynamically favored at room temperature. The effective binding energy of the optimized chemisorption structure is apparently larger than those for other CO2 adsorptive materials, suggesting the potential for application of aluminum nitride nanostructures for carbon dioxide capture and storage.

The effect of Fe doping on adsorption of CO2/N2within carbon nanotubes : a density functional theory study with dispersion corrections

An ab initio density functional theory (DFT) study with correction for dispersive interactions was performed to study the adsorption of N2 and CO2 inside an (8, 8) single-walled carbon nanotube. We find that the approach of combining DFT and van der Waals correction is very effective for describing the long-range interaction between N2/CO2 and the carbon nanotube (CNT). Surprisingly, exohedral doping of an Fe atom onto the CNT surface will only affect the adsorption energy of the quadrupolar CO2 molecule inside the CNT (20–30%), and not that of molecular N2. Our results suggest the feasibility of enhancement of CO2/N2 separation in CNT-based membranes by using exohedral doping of metal atoms.