Numerical solution to the Saffman-Taylor finger problem with kinetic undercooling regularisation

The Saffman-Taylor finger problem is to predict the shape and,in particular, width of a finger of fluid travelling in a Hele-Shaw cell filled with a different, more viscous fluid. In experiments the width is dependent on the speed of propagation of the finger, tending to half the total cell width as the speed increases. To predict this result mathematically, nonlinear effects on the fluid interface must be considered; usually surface tension is included for this purpose. This makes the mathematical problem suffciently diffcult that asymptotic or numerical methods must be used. In this paper we adapt numerical methods used to solve the Saffman-Taylor finger problem with surface tension to instead include the effect of kinetic undercooling, a regularisation effect important in Stefan melting-freezing problems, for which Hele-Shaw flow serves as a leading order approximation when the specific heat of a substance is much smaller than its latent heat. We find the existence of a solution branch where the finger width tends to zero as the propagation speed increases, disagreeing with some aspects of the asymptotic analysis of the same problem. We also find a second solution branch, supporting the idea of a countably infinite number of branches as with the surface tension problem.

Drug diffusion from polymeric delivery devices : a problem with two moving boundaries

An existing model for solvent penetration and drug release from a spherically-shaped polymeric drug delivery device is revisited. The model has two moving boundaries, one that describes the interface between the glassy and rubbery states of polymer, and another that defines the interface between the polymer ball and the pool of solvent. The model is extended so that the nonlinear diffusion coefficient of drug explicitly depends on the concentration of solvent, and the resulting equations are solved numerically using a front-fixing transformation together with a finite difference spatial discretisation and the method of lines. We present evidence that our scheme is much more accurate than a previous scheme. Asymptotic results in the small-time limit are presented, which show how the use of a kinetic law as a boundary condition on the innermost moving boundary dictates qualitative behaviour, the scalings being very different to the similar moving boundary problem that arises from modelling the melting of an ice ball. The implication is that the model considered here exhibits what is referred to as ``non-Fickian'' or Case II diffusion which, together with the initially constant rate of drug release, has certain appeal from a pharmaceutical perspective.

Scaling analysis of unsteady natural convection boundary layer for ramp heating

A scaling analysis for the natural convection boundary layer adjacent to an inclined semi-infinite plate subject to a non-instantaneous heating in the form of an imposed wall temperature which increases linearly up to a prescribed steady value over a prescribed time is reported. The development of the flow from start-up to a steady-state has been described based on scaling analyses and verified by numerical simulations. The analysis reveals that, if the period of temperature growth on the wall is sufficiently long, the boundary layer reaches a quasisteady mode before the growth of the temperature is completed. In this mode the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the imposed wall temperature growth period is sufficiently short, the boundary layer develops differently, but after the wall temperature growth is completed, the boundary layer develops as though the start up had been instantaneous. The steady state values of the boundary layer for both cases are ultimately the same.

An improved boundary layer scaling with ramp heating on a sloping plate

A scaling analysis for the natural convection boundary layer adjacent to an inclined semi-infinite plate subject to a non-instantaneous heating in the form of an imposed wall temperature which increases linearly up to a prescribed steady value over a prescribed time is reported. The development of the boundary layer flow from start-up to a steady-state has been described based on scaling analyses and verified by numerical simulations. The analysis reveals that, if the period of temperature growth on the wall is sufficiently long, the boundary layer reaches a quasi-steady mode before the growth of the temperature is completed. In this mode the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the imposed wall temperature growth period is sufficiently short, the boundary layer develops differently, but after the wall temperature growth is completed, the boundary layer develops as though the startup had been instantaneous. The steady state values of the boundary layer for both cases are ultimately the same.

Breaching the standardised assessment boundary : assessment for learning as a field of exchange

The introduction of the Australian curriculum, the use of standardised testing (e.g. NAPLAN) and the My School website are couched in a context of accountability. This circumstance has stimulated and in some cases renewed a range of boundaries in Australian Education. The consequences that arise from standardised testing have accentuated the boundaries produced by social reproduction in education which has led to an increase in the numbers of students disengaging from mainstream education and applying for enrolment at the Edmund Rice Education Australia Flexible Learning Centre Network (EREAFLCN). Boundaries are created for many young people who are denied access to credentials and certification as a result of being excluded from or in some way disengaging from standardised education and testing. Young people who participate at the EREAFLCN arrive with a variety of forms of cultural capital that are not valued in current education and employment fields. This is not to say that these young people’s different forms of cultural capital have no value, but rather that such funds of knowledge, repertoires and cultural capital are not valued by the majority of powerful agents in educational and employment fields. How then can the qualitative value of traditionally unorthodox - yet often intricate, ingenious, and astute - versions of cultural capital evident in the habitus of many young people be made to count, be recognised, be valuated? Can a process of educational assessment be a field of capital exchange and a space which breaches boundaries through a valuating process? This paper reports on the development of an innovative approach to assessment in an alternative education institution designed for the re-engagement of ‘at risk’ youth who have left formal schooling. A case study approach has been used to document the engagement of six young people, with an educational approach described as assessment for learning as a field of exchange across two sites in the EREAFLCN. In order to capture the broad range of students’ cultural and social capital, an electronic portfolio system (EPS) is under trial. The model draws on categories from sociological models of capital and reconceptualises the eportfolio as a sociocultural zone of learning and development. Results from the trial show a general tendency towards engagement with the EPS and potential for the attainment of socially valued cultural capital in the form of school credentials. In this way restrictive boundaries can be breached and a more equitable outcome achieved for many young Australians.

“A problem of versions” : laying down the law in the school playground

Purpose This chapter investigates an episode where a supervising teacher on playground duty asks two boys to each give an account of their actions over an incident that had just occurred on some climbing equipment in the playground. Methodology This paper employs an ethnomethodological approach using conversation analysis. The data are taken from a corpus of video recorded interactions of children, aged 7-9 years, and the teacher, in school playgrounds during the lunch recess. Findings The findings show the ways that children work up accounts of their playground practices when asked by the teacher. The teacher initially provided interactional space for each child to give their version of the events. Ultimately, the teacher’s version of how to act in the playground became the sanctioned one. The children and the teacher formulated particular social orders of behavior in the playground through multi-modal devices, direct reported speech and scripts. Such public displays of talk work as socialization practices that frame teacher-sanctioned morally appropriate actions in the playground. Value of paper This chapter shows the pervasiveness of the teacher’s social order, as she presented an institutional social order of how to interact in the playground, showing clearly the disjunction of adult-child orders between the teacher and children.

The creative citizen : understanding the value of design education programs in the knowledge economy

The knowledge economy relies on the diffusion and use of knowledge as well as its creation (Houghton and Sheenan, 2000). The future success of economic activity will depend on the capacity of organisations to transform by increasing their flexibility. In particular, this transformation is dependant on a decentralised, networked and multi-skilled workforce. To help organisations transition, new strategies and structures for education are required. Education systems need to concentrate less on specialist skills and more on the development of people with broad-based problem solving skills that are adaptable, with social and inter-personal communication skills necessary for networking and communication. This paper presents the findings of a ‘Knowledge Economy Market Development Mapping Study’ conducted to identify the value of design education programs from primary through to tertiary level in Queensland, Australia. The relationship of these programs to the development of the capacities mentioned above is explored. The study includes the collection of qualitative and quantitative data consisting of a literature review, focus groups and survey. Recommendations for the future development of design education programs in Queensland, Australia are proposed, and future research opportunities are presented and discussed.

Efficient solution of multiple cracks in great number using eigen COD boundary integral equations with iteration procedure

A newly developed computational approach is proposed in the paper for the analysis of multiple crack problems based on the eigen crack opening displacement (COD) boundary integral equations. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix to determine all the unknown CODs step by step. To deal with the interactions among cracks for multiple crack problems, all cracks in the problem are divided into two groups, namely the adjacent group and the far-field group, according to the distance to the current crack in consideration. The adjacent group contains cracks with relatively small distances but strong effects to the current crack, while the others, the cracks of far-field group are composed of those with relatively large distances. Correspondingly, the eigen COD of the current crack is computed in two parts. The first part is computed by using the fictitious tractions of adjacent cracks via the local Eshelby matrix derived from the traction boundary integral equations in discretized form, while the second part is computed by using those of far-field cracks so that the high computational efficiency can be achieved in the proposed approach. The numerical results of the proposed approach are compared not only with those using the dual boundary integral equations (D-BIE) and the BIE with numerical Green's functions (NGF) but also with those of the analytical solutions in literature. The effectiveness and the efficiency of the proposed approach is verified. Numerical examples are provided for the stress intensity factors of cracks, up to several thousands in number, in both the finite and infinite plates.

Motivations for eWOM exchanges in an online community : self-development, problem solving support, relaxation

Electronic word-of-mouth (eWOM) has gained significant attention from academics and practitioners since it has become an important source of consumers’ product information, which can influence consumer purchase intentions (Cheung & Lee, 2012). eWOM exchanges exist in two types of online communities: online communities of practice and online communities of interest. A few prior studies in online communities of interest have examined members’ motivations for product knowledge exchange (Hung & Li, 2007; Ma & Agarwal, 2007). However, there is a lack of understanding of member motivations for exchanging social bonds and enjoyment in addition to exchanging knowledge pertaining to products in the community. It is important to have an initial comprehension of motivation as an antecedent of these three eWOM exchanges so as to be able to determine the driving factors that lead members to generate eWOM communication. Thus, the research problem "What are the driving factors for members to exchange eWOM in an online community?" was justified for investigation. The purpose of this study was to examine different member motivations for exchanging three types of eWOM. Resource exchange theory and theory on consumer motivation and behavior were applied to develop a conceptual framework for this study. This study focused on an online beauty community since there is an increasing trend of consumers turning to online beauty resources so as to exchange useful beauty product information (SheSpot, 2011). As this study examined consumer motivation in an online beauty community, a web-based survey was the most effective and efficient way to gain responses from beauty community members and these members were appropriate samples from which to draw a conclusion about the whole population. Multiple regression analysis was used to test the relationships between member motivations and eWOM exchanges. It was found that members have different motivations for exchanging knowledge, social bonds, and enjoyment related to products: self-development, problem solving support, and relaxation, respectively. This study makes three theoretical contributions. First, this study identifies the influence of self-development motivation on knowledge exchange in an online community of interest, just as this motivation has previously been found in online communities of practice. This study highlights that members of the two different types of online communities share similar goals of knowledge exchange, despite the two communities evincing different attributes (e.g., member characteristics and tasks’ objectives). Further, this study will assist researchers to understand other motivations identified by prior research in online communities of practice since such motivations may be applicable to online communities of interest. Second, this study offers a new perspective on member motivation for social bonding. This study indicates that in addition to social support from friends and family, consumers are motivated to build social bonds with members in an online community of interest since they are an important source of problem solving support in regard to products. Finally, this study extends the body of knowledge pertaining to member motivation for enjoyment exchange. This study provides a basis for researchers to understand that members in an online community of interest value experiential aspects of enjoyable consumption activities, and thus based on group norms, members have a mutual desire for relaxation from enjoyment exchange. The major practical contribution is that this study provides an important guideline for marketing managers to develop different marketing strategies based on member motivations for exchanging three types of eWOM in an online community of interest, such as an online beauty community. This will potentially help marketing managers increase online traffic and revenue, and thus bring success to the community. Although, this study contributes to the literature by highlighting three distinctive member motivations for eWOM exchanges in an online community of interest, there are some possible research limitations. First, this study was conducted in an online beauty community in Australia. Hence, further research should replicate this study in other industries and nations so as to give the findings greater generalisability. Next, online beauty community members are female skewed. Thus, future research should examine whether similar patterns of motivations would emerge in other online communities that tend to be populated by males (e.g., communities focused on football). Further, a web-based survey has its limitations in terms of self-selection and self-reporting (Bhatnagar & Ghose, 2004). Therefore, further studies should test the framework by employing different research methods in order to overcome these weaknesses.

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.

Integration-segregation decisions under general value functions: "create your own bundle - choose 1, 2, or all 3!",

Whether to keep products segregated (e.g., unbundled) or integrate some or all of them (e.g., bundle) has been a problem of profound interest in areas such as portfolio theory in finance, risk capital allocations in insurance and marketing of consumer products. Such decisions are inherently complex and depend on factors such as the underlying product values and consumer preferences, the latter being frequently described using value functions, also known as utility functions in economics. In this paper, we develop decision rules for multiple products, which we generally call ‘exposure units’ to naturally cover manifold scenarios spanning well beyond ‘products’. Our findings show, e.g. that the celebrated Thaler's principles of mental accounting hold as originally postulated when the values of all exposure units are positive (i.e. all are gains) or all negative (i.e. all are losses). In the case of exposure units with mixed-sign values, decision rules are much more complex and rely on cataloging the Bell number of cases that grow very fast depending on the number of exposure units. Consequently, in the present paper, we provide detailed rules for the integration and segregation decisions in the case up to three exposure units, and partial rules for the arbitrary number of units.

Artificial grain boundary Josephson junctions : properties and applications

Engineered grain boundary Josephson junctions in YBaCuO were formed on bicrystal Y-ZrO2 substrates. Laser deposited films were patterned into micron size microbridges. The authors obsd. a pronounced correlation between superconducting transport properties of grain boundary junctions and the misorientation angle θ between the two halves of the bicrystal. The crit. Josephson current Ic decreased about four orders of magnitude as θ was increased from 0 to 45 degrees. Clear microwave and magnetic field responses were obsd. at 77 K. At this temp., crit. current times normal resistance products, IcRn, of up to 1 mV were measured for low angle grain boundaries, and Shapiro steps were obsd. up to that voltage. DC SQUIDs were fabricated, and best performance at 77 K was obtained for θ = 32° with a 4-μm strip width. To utilize the higher IcRn value of a lower θ, submicron junctions have to be developed. [on SciFinder(R)]

A 3D virtual medical imaging suite : bridging the academic-clinical training boundary

Aims The Medical Imaging Training Immersive Environment (MITIE) system is a recently developed virtual reality (VR) platform that allows students to practice a range of medical imaging techniques. The aim of this pilot study was to harvest user feedback about the educational value of the application and inform future pedagogical development. This presentation explores the use of this technology for skills training and blurring the boundaries between academic learning and clinical skills training. Background MITIE is a 3D VR environment that allows students to manipulate a patient and radiographic equipment in order to produce a VR-generated image for comparison with a gold standard. As with VR initiatives in other health disciplines (1-6) the software mimics clinical practice as much as possible and uses 3D technology to enhance immersion and realism. The software was developed by the Medical Imaging Course Team at a provider University with funding from a Health Workforce Australia “Simulated Learning Environments” grant. Methods Over 80 students undertaking the Bachelor of Medical Imaging Course were randomised to receive practical experience with either MITIE or radiographic equipment in the medical radiation laboratory. Student feedback about the educational value of the software was collected and performance with an assessed setup was measured for both groups for comparison. Ethical approval for the project was provided by the university ethics panel. Results This presentation provides qualitative analysis of student perceptions relating to satisfaction, usability and educational value as well as comparative quantitative performance data. Students reported high levels of satisfaction and both feedback and assessment results confirmed the application’s significance as a pre-clinical training tool. There was a clear emerging theme that MITIE could be a useful learning tool that students could access to consolidate their clinical learning, either during their academic timetables or their clinical placement. Conclusion Student feedback and performance data indicate that MITIE has a valuable role to play in the clinical skills training for medical imaging students both in the academic and the clinical environment. Future work will establish a framework for an appropriate supporting pedagogy that can cross the boundary between the two environments. This project was possible due to funding made available by Health Workforce Australia.

Leadership in problem-oriented policing

Purpose – The purpose of this paper is to explore the role of leadership in problem-oriented policing (POP). Design/methodology/approach – This paper uses interrupted time series models to isolate the impact on crime trends of a transformational leader's efforts to spearhead the implementation of a program of POP, called the problem solving model (PSM), in a southern state in Australia. Findings – This paper finds that the PSM led directly to an impact on overall crime, with a significant reduction in crimes per 100,000 persons per year after the introduction of the PSM. The majority of the overall crime drop attributable to implementation of POP was driven by reductions in property crime. It was noted that the leadership influence of the PSM was not effective in reducing all types of crime. Crimes against the person where not affected by the introduction of the PSM and public nuisance crimes largely followed the forecasted, upward trajectory. Practical implications – The driver behind the PSM was Commissioner Hyde and the success of the PSM is largely attributable to his strong commitment to transformational leadership and a top-down approach to implementation. These qualities encapsulate the original ideas behind POP that Goldstein (1979, 2003), back in 1979, highlighted as critical for the success of future POP programs. Social implications – Reducing crime is an important part of creating safe communities and improving quality of life for all citizens. This research shows that successful implementation of the PSM within South Australia under the strong leadership of Commissioner Hyde was a major factor in reducing property crime and overall crime rates. Originality/value – This paper is valuable because it demonstrates the link between strong leadership in policing, the commissioner's vision for POP and how his vision then translated into widespread adoption of POP. The study empirically shows that the statewide adoption of POP led to significant reductions in crime, particularly property crime.

Eigenstrain boundary integral equations with local Eshelby matrix for stress analysis of ellipsoidal particles

Aiming at the large scale numerical simulation of particle reinforced materials, the concept of local Eshelby matrix has been introduced into the computational model of the eigenstrain boundary integral equation (BIE) to solve the problem of interactions among particles. The local Eshelby matrix can be considered as an extension of the concepts of Eshelby tensor and the equivalent inclusion in numerical form. Taking the subdomain boundary element method as the control, three-dimensional stress analyses are carried out for some ellipsoidal particles in full space with the proposed computational model. Through the numerical examples, it is verified not only the correctness and feasibility but also the high efficiency of the present model with the corresponding solution procedure, showing the potential of solving the problem of large scale numerical simulation of particle reinforced materials.