Bubble extinction in Hele-Shaw flow with surface tension and kinetic undercooling regularisation

We perform an analytic and numerical study of an inviscid contracting bubble in a two-dimensional Hele-Shaw cell, where the effects of both surface tension and kinetic undercooling on the moving bubble boundary are not neglected. In contrast to expanding bubbles, in which both boundary effects regularise the ill-posedness arising from the viscous (Saffman-Taylor) instability, we show that in contracting bubbles the two boundary effects are in competition, with surface tension stabilising the boundary, and kinetic undercooling destabilising it. This competition leads to interesting bifurcation behaviour in the asymptotic shape of the bubble in the limit it approaches extinction. In this limit, the boundary may tend to become either circular, or approach a line or "slit" of zero thickness, depending on the initial condition and the value of a nondimensional surface tension parameter. We show that over a critical range of surface tension values, both these asymptotic shapes are stable. In this regime there exists a third, unstable branch of limiting self-similar bubble shapes, with an asymptotic aspect ratio (dependent on the surface tension) between zero and one. We support our asymptotic analysis with a numerical scheme that utilises the applicability of complex variable theory to Hele-Shaw flow.

Adaptive dynamic path re-planning RRT algorithms with game theory for UAVs

The main aim of this paper is to describe an adaptive re-planning algorithm based on a RRT and Game Theory to produce an efficient collision free obstacle adaptive Mission Path Planner for Search and Rescue (SAR) missions. This will provide UAV autopilots and flight computers with the capability to autonomously avoid static obstacles and No Fly Zones (NFZs) through dynamic adaptive path replanning. The methods and algorithms produce optimal collision free paths and can be integrated on a decision aid tool and UAV autopilots.

Intellectual Property and Development : Theory and Practice

The book examines the correlation between Intellectual Property Law – notably copyright – on the one hand and social and economic development on the other. The main focus of the initial overview is on historical, legal, economic and cultural aspects. Building on that, the work subsequently investigates how intellectual property systems have to be designed in order to foster social and economic growth in developing countries and puts forward theoretical and practical solutions that should be considered and implemented by policy makers, legal experts and the Word Intellectual Property Organization (WIPO).

Contextual models and the non-Newtonian paradigm

Biological systems exhibit a wide range of contextual effects, and this often makes it difficult to construct valid mathematical models of their behaviour. In particular, mathematical paradigms built upon the successes of Newtonian physics make assumptions about the nature of biological systems that are unlikely to hold true. After discussing two of the key assumptions underlying the Newtonian paradigm, we discuss two key aspects of the formalism that extended it, Quantum Theory (QT). We draw attention to the similarities between biological and quantum systems, motivating the development of a similar formalism that can be applied to the modelling of biological processes.

Organic and acquisitive growth : re-examining, testing and extending Penrose’s growth theory

The Theory of the Growth of The Firm by Edith Penrose, first published in 1959, is a seminal contribution to the field of management. Penrose's intention was to create a theory of firm growth which was logically consistent and empirically tractable (Buckley and Casson, 2007). Much attention, however, has been focused on her unintended contribution to the resource-based view (henceforth RBV) (e.g. Kor and Mahoney, 2004; Lockett and Thompson, 2004) rather than her firm growth theory. We feel that this is unfortunate because despite a rapidly growing body of empirical work, conceptual advancement in growth studies has been limited (Davidsson and Wiklund, 2000; Davidsson et ai., 2006; Delmar, 1997; Storey, 1994). The growth literature frequently references Penrose's work, but little explicit testing of her ideas has been undertaken. This is surprising given that Penrose's work remains the most comprehensive theory of growth to date. One explanation is that she did not formality present her arguments, favouring verbal exposition over formalized models (Lockett, 2005; Lockett and Thompson, 2004). However, the central propositions and conclusions of her theory can be operationalized and empirically tested.

Reconnection : a contemporary development in cultural landscape theory contributing to rehabilitation strategies for Australian open-cut coal mining landscapes

A value-shift began to influence global political thinking in the late 20th century, characterised by recognition of the need for environmentally, socially and culturally sustainable resource development. This shift entailed a move away from thinking of ‘nature’ and ‘culture’ as separate entities – the former existing to serve the latter – toward the possibility of embracing the intrinsic worth of the nonhuman world. Cultural landscape theory recognises ‘nature’ as at once both ‘natural’, and a ‘cultural’ construct. As such, it may offer a framework through which to progress in the quest for ‘sustainable development’. This study makes a contribution to this quest by asking whether contemporary developments in cultural landscape theory can contribute to rehabilitation strategies for Australian open-cut coal mining landscapes. The answer is ‘yes’. To answer the research question, a flexible, ‘emergent’ methodological approach has been used, resulting in the following outcomes. A thematic historical overview of landscape values and resource development in Australia post-1788, and a review of cultural landscape theory literature, contribute to the formation of a new theoretical framework: Reconnecting the Interrupted Landscape. This framework establishes a positive answer to the research question. It also suggests a method of application within the Australian open-cut coal mining landscape, a highly visible exemplar of the resource development landscape. This method is speculatively tested against the rehabilitation strategy of an operating open-cut coal mine, concluding with positive recommendations to the industry, and to government.

Insulin and the insulin-like growth factor system : a novel theory for hyperinsulinemic laminitis pathogenesis

Research into hyperinsulinemic laminitis has progressed significantly in recent years with the use of the prolonged-euglycemic, hyperinsulinemic clamp (p-EHC). Previous investigations of laminitis pathophysiology have focused on digital vascular dysfunction, inflammation, altered glucose metabolism within the lamellae, and lamellar basement membrane breakdown by metalloproteinases. The etiopathogenesis of laminitis occurring in association with hyperinsulinemia is yet to be fully characterized, but it may not involve these mechanisms. Insulin stimulates cellular proliferation and can also affect other body systems, such as the insulin-like growth factor (IGF) system. Insulin-like growth factor-1 (IGF-1) is structurally homologous to insulin and, like insulin, binds with strong affinity to a specific tyrosine kinase receptor on the cell surface to produce its effects, which include promoting cell proliferation. Receptors for IGF-1 (IGF-1R) are present in the lamellar epidermis. An alternative theory for the pathogenesis of hyperinsulinemic laminitis is that uncontrolled cell proliferation, mediated through both the insulin receptor (InsR) and IGF-1R, leads to lengthening, weakening, and failure of the lamellae. An analysis of the proliferative activity of lamellar epidermal cells during the developmental and acute phases of hyperinsulinemic laminitis, and lamellar gene expression of the InsR and IGF-1R was undertaken.

Methane activation on Fe4 cluster : a density functional theory study

We report a comprehensive theoretical study on reaction of methane by Fe4 cluster. This Letter gains insight into the mechanism of the reaction and indicate the Fe4 cluster has strong catalytic effect on the activation reaction of methane. In detail, the results show the cleavage of the first C–H bond is both an energetically and kinetically favourable process and the breaking of the second C–H is the rate-determining step. Moreover, our Letter demonstrates that the different cluster size of iron can not only determine the catalytic activity of methane but also control the product selectivity.

Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

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.