Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.

The nature and extent of policing alcohol related crime and reducing violence in and around late night entertainment areas

The misuse of alcohol is well documented in Australia and has been associated with disorders and harms that often require police attention. The extent of alcohol-related incidents requiring police attention has been recorded as substantial in some Australian cities (Arro, Crook, & Fenton, 1992; Davey & French, 1995; Ireland & Thommeny, 1993). A significant proportion of harmful drinking occurs in and around licensed premises (Jochelson, 1997; Stockwell, Masters, Phillips, Daly, Gahegan, Midford, & Philp, 1998; Borges, Cherpitel, & Rosovsky, 1998) and most of these incidents are not reported to police (Bryant & Williams, 2000; Lister, Hobbs, Hall, & Winlow, 2000). Alcohol-related incidents have also been found to be concentrated in certain places at certain times (Jochelson, 1997) and therefore manipulating the context in which these incidents occur may provide a means to prevent and reduce the harm associated with alcohol misuse. One of the major objectives of the present program of research was to investigate the occurrence and resource impact of alcohol-related incidents on operational (general duties) policing across a large geographical area. A second objective of the thesis was to examine the characteristics and temporal/spatial dynamics of police attended alcohol incidents in the context of Place Based theories of crime. It was envisaged that this approach would reveal the patterns of the most prevalent offences and demonstrate the relevance of Place Based theories of crime to understanding these patterns. In addition, the role of alcohol, time and place were also explored in order to examine the association between non criminal traffic offences and other types of criminal offences. A final objective of the thesis was to examine the impact of a situational crime prevention strategy that had been initiated to reduce the violence and disorder associated with late-night liquor trading premises. The program of research in this doctorate thesis has been undertaken through the presentation of published papers. The research was conducted in three stages which produced six manuscripts, five of which were submitted to peer reviewed journals and one that was published in a peer reviewed conference proceedings. Stage One included two studies (Studies 1 & 2) both of which involved a cross sectional approach to examine the prevalence and characteristics of alcohol-related incidents requiring police attendance across three large geographical areas that included metropolitan cities, provincial regions and rural areas. Stage Two of the program of research also comprised two cross sectional quantitative studies (Studies 3 & 4) that investigated the temporal and spatial dynamics of the major offence categories attended by operational police in a specific Police District (Gold Coast). Stage Three of the program of research involved two studies (Studies 5 & 6) that assessed the effectiveness of a situational crime prevention strategy. The studies employed a pre-post design to assess the impact on crime, disorder and violence by preventing patrons from entering late-night liquor trading premises between 3 a.m. and 5 a.m. (lockout policy). Although Study Five was solely quantitative in nature, Study Six included both quantitative and qualitative aspects. The approach adopted in Study Six, therefore facilitated not only a quantative comparison of the impact of the lockout policy on different policing areas, but also enabled the processes related to the implementation of the lockout policy to be examined. The thesis reports a program of research involving a common data collection method which then involved a series of studies being conducted to explore different aspects of the data. The data was collected from three sources. Firstly a pilot phase was undertaken to provide participants with training. Secondly a main study period was undertaken immediately following the pilot phase. The first and second sources of data were collected between 29th March 2004 and 2nd May 2004. Thirdly, additional data was collected between the 1st April 2005 and 31st May 2005. Participants in the current program of research were first response operational police officers who completed a modified activity log over a 9 week period (4 week pilot phase & 5 week survey study phase), identifying the type, prevalence and characteristics of alcohol-related incidents that were attended. During the study period police officers attended 31,090 alcohol-related incidents. Studies One and Two revealed that a substantial proportion of current police work involves attendance at alcohol-related incidents (i.e., 25% largely involving young males aged between 17 and 24 years). The most common incidents police attended were vehicle and/or traffic matters, disturbances and offences against property. The major category of offences most likely to involve alcohol included vehicle/traffic matters, disturbances and offences against the person (e.g., common & serious assaults). These events were most likely to occur in the late evenings and early hours of the morning on the weekends, and importantly, usually took longer for police to complete than non alcohol-related incidents. The findings in Studies Three and Four suggest that serious traffic offences, disturbances and offences against the person share similar characteristics and occur in concentrated places at similar times. In addition, it was found that time, place and incident type all have an influence on whether an incident attended by a police officer is alcohol-related. Alcohol-related incidents are more likely to occur in particular locations in the late evenings and early mornings on the weekends. In particular, there was a strong association between the occurrence of alcohol-related disturbances and alcohol-related serious traffic offences in regards to place and time. In general, stealing and property offences were not alcohol-related and occurred in daylight hours during weekdays. The results of Studies Five and Six were mixed. A number of alcohol-related offences requiring police attention were significantly reduced for some policing areas and for some types of offences following the implementation of the lockout policy. However, in some locations the lockout policy appeared to have a negative or minimal impact. Interviews with licensees revealed that although all were initially opposed to the lockout policy as they believed it would have a negative impact on business, most perceived some benefits from its introduction. Some of the benefits included, improved patron safety and the development of better business strategies to increase patron numbers. In conclusion, the overall findings of the six studies highlight the pervasive nature of alcohol across a range of criminal incidents, demonstrating the tremendous impact alcohol-related incidents have on police. The findings also demonstrate the importance of time and place in predicting the occurrence of alcohol-related offences. Although this program of research did not set out to test Place Based theories of crime, these theories were used to inform the interpretation of findings. The findings in the current research program provide evidence for the relevance of Place Based theories of crime to understanding the factors contributing to violence and disorder, and designing relevant crime prevention strategies. For instance, the results in Studies Five and Six provide supportive evidence that this novel lockout initiative can be beneficial for public safety by reducing some types of offences in particular areas in and around late-night liquor trading premises. Finally, intelligent-led policing initiatives based on problem oriented policing, such as the lockout policy examined in this thesis, have potential as a major crime prevention technique to reduce specific types of alcohol-related offences.

An experiment in mixed compilation/interpretation

One of the classic forms of intermediate representation used for communication between compiler front-ends and back-ends are those based on abstract stack machines. It is possible to compile the stack machine instructions into machine code by means of an interpretive code generator, or to simulate the stack machine at runtime using an interpreter. This paper describes an approach intermediate between these two extremes. The front-end for a commercial Modula 2 compiler was ported to the "industry standard PC", and a partially compiling back-end written. The object code runs with the assistance of an interpreter, but may be linked with libraries which are fully compiled. The intent was to provide a programming environment on the PC which is identical to that of the same compilers on 32-bit UNIX machines. This objective has been met, and the compiler is available to educational institutions as free-ware. The design basis of the new compiler is described, and the performance critically evaluated.

Type Test Elimination using Typeflow Analysis

Programs written in languages of the Oberon family usually contain runtime tests on the dynamic type of variables. In some cases it may be desirable to reduce the number of such tests. Typeflow analysis is a static method of determining bounds on the types that objects may possess at runtime. We show that this analysis is able to reduce the number of tests in certain plausible circumstances. Furthermore, the same analysis is able to detect certain program errors at compile time, which would normally only be detected at program execution. This paper introduces the concepts of typeflow analysis and details its use in the reduction of runtime overhead in Oberon-2.

Temperature variation and emergency hospital admissions for stroke in Brisbane, Australia, 1996-2005

Stroke is a leading cause of disability and death. This study evaluated the association between temperature variation and emergency admissions for stroke in Brisbane, Australia. Daily emergency admissions for stroke, meteorologic and air pollution data were obtained for the period of January 1996 to December 2005. The relative risk of emergency admissions for stroke was estimated with a generalized estimating equations (GEE) model. For primary intracerebral hemorrhage (PIH) emergency admissions, the average daily PIH for the group aged < 65 increased by 15% (95% Confidence Interval (CI): 5, 26%) and 12% (95% CI: 2, 22%) for a 1°C increase in daily maximum temperature and minimum temperature in summer, respectively, after controlling for potential confounding effects of humidity and air pollutants. For ischemic stroke (IS) emergency admissions, the average daily IS for the group aged ≥ 65 decreased by 3% (95% CI: -6, 0%) for a 1°C increase in daily maximum temperature in winter after adjustment for confounding factors. Temperature variation was significantly associated with emergency admissions for stroke, and its impact varied with different type of stroke. Health authorities should pay greater attention to possible increasing emergency care for strokes when temperature changes, in both summer and winter.

Vitamin D and sun protection : the impact of mixed public health messages in Australia

Exposure of the skin to sunlight can cause skin cancer and is also necessary for cutaneous vitamin D production. Media reports have highlighted the purported health benefits of vitamin D. Our aim was to examine attitudes and behaviours related to sun protection and vitamin D. A cross-sectional study of 2,001 residents in Queensland, Australia aged 20-70 years was undertaken. Information collected included: skin cancer risk factors; perceptions about levels of sun exposure required to maintain vitamin D; belief that sun protection increases risk of vitamin D deficiency; intention, and actual change in sun protection practices for adults and children. Multivariate models examined predictors of attitudinal and behavioural change. One-third (32%) believed a fair-skinned adult, and 31% thought a child required at least 30 minutes per day in summer sun to maintain vitamin D levels. Reductions in sun protection were reported by 21% of adults and 14% of children. Factors associated with belief that sun protection may result in not obtaining enough vitamin D included aged ≥ 60 years (OR=1.35, 95% CI 1.09-1.66) and having skin that tanned easily (OR=1.96, 95% CI 1.38-2.78). Participants from low income households, and those who frequently used sun protective clothing were more likely to have reduced sun protection practices (OR=1.33, 95% CI 1.10-1.73 and OR=1.73, 95% CI 1.36-2.20, respectively). This study provides evidence of reductions in sun protection practices in a population living in a high UV environment. There is an urgent need to re-focus messages regarding sun exposure and for continued sun protection practices.

Digital kids, analogue students : a mixed methods study of students' engagement with a school-based Web 2.0 learning innovation

The inquiry documented in this thesis is located at the nexus of technological innovation and traditional schooling. As we enter the second decade of a new century, few would argue against the increasingly urgent need to integrate digital literacies with traditional academic knowledge. Yet, despite substantial investments from governments and businesses, the adoption and diffusion of contemporary digital tools in formal schooling remain sluggish. To date, research on technology adoption in schools tends to take a deficit perspective of schools and teachers, with the lack of resources and teacher ‘technophobia’ most commonly cited as barriers to digital uptake. Corresponding interventions that focus on increasing funding and upskilling teachers, however, have made little difference to adoption trends in the last decade. Empirical evidence that explicates the cultural and pedagogical complexities of innovation diffusion within long-established conventions of mainstream schooling, particularly from the standpoint of students, is wanting. To address this knowledge gap, this thesis inquires into how students evaluate and account for the constraints and affordances of contemporary digital tools when they engage with them as part of their conventional schooling. It documents the attempted integration of a student-led Web 2.0 learning initiative, known as the Student Media Centre (SMC), into the schooling practices of a long-established, high-performing independent senior boys’ school in urban Australia. The study employed an ‘explanatory’ two-phase research design (Creswell, 2003) that combined complementary quantitative and qualitative methods to achieve both breadth of measurement and richness of characterisation. In the initial quantitative phase, a self-reported questionnaire was administered to the senior school student population to determine adoption trends and predictors of SMC usage (N=481). Measurement constructs included individual learning dispositions (learning and performance goals, cognitive playfulness and personal innovativeness), as well as social and technological variables (peer support, perceived usefulness and ease of use). Incremental predictive models of SMC usage were conducted using Classification and Regression Tree (CART) modelling: (i) individual-level predictors, (ii) individual and social predictors, and (iii) individual, social and technological predictors. Peer support emerged as the best predictor of SMC usage. Other salient predictors include perceived ease of use and usefulness, cognitive playfulness and learning goals. On the whole, an overwhelming proportion of students reported low usage levels, low perceived usefulness and a lack of peer support for engaging with the digital learning initiative. The small minority of frequent users reported having high levels of peer support and robust learning goal orientations, rather than being predominantly driven by performance goals. These findings indicate that tensions around social validation, digital learning and academic performance pressures influence students’ engagement with the Web 2.0 learning initiative. The qualitative phase that followed provided insights into these tensions by shifting the analytics from individual attitudes and behaviours to shared social and cultural reasoning practices that explain students’ engagement with the innovation. Six indepth focus groups, comprising 60 students with different levels of SMC usage, were conducted, audio-recorded and transcribed. Textual data were analysed using Membership Categorisation Analysis. Students’ accounts converged around a key proposition. The Web 2.0 learning initiative was useful-in-principle but useless-in-practice. While students endorsed the usefulness of the SMC for enhancing multimodal engagement, extending peer-topeer networks and acquiring real-world skills, they also called attention to a number of constraints that obfuscated the realisation of these design affordances in practice. These constraints were cast in terms of three binary formulations of social and cultural imperatives at play within the school: (i) ‘cool/uncool’, (ii) ‘dominant staff/compliant student’, and (iii) ‘digital learning/academic performance’. The first formulation foregrounds the social stigma of the SMC among peers and its resultant lack of positive network benefits. The second relates to students’ perception of the school culture as authoritarian and punitive with adverse effects on the very student agency required to drive the innovation. The third points to academic performance pressures in a crowded curriculum with tight timelines. Taken together, findings from both phases of the study provide the following key insights. First, students endorsed the learning affordances of contemporary digital tools such as the SMC for enhancing their current schooling practices. For the majority of students, however, these learning affordances were overshadowed by the performative demands of schooling, both social and academic. The student participants saw engagement with the SMC in-school as distinct from, even oppositional to, the conventional social and academic performance indicators of schooling, namely (i) being ‘cool’ (or at least ‘not uncool’), (ii) sufficiently ‘compliant’, and (iii) achieving good academic grades. Their reasoned response therefore, was simply to resist engagement with the digital learning innovation. Second, a small minority of students seemed dispositionally inclined to negotiate the learning affordances and performance constraints of digital learning and traditional schooling more effectively than others. These students were able to engage more frequently and meaningfully with the SMC in school. Their ability to adapt and traverse seemingly incommensurate social and institutional identities and norms is theorised as cultural agility – a dispositional construct that comprises personal innovativeness, cognitive playfulness and learning goals orientation. The logic then is ‘both and’ rather than ‘either or’ for these individuals with a capacity to accommodate both learning and performance in school, whether in terms of digital engagement and academic excellence, or successful brokerage across multiple social identities and institutional affiliations within the school. In sum, this study takes us beyond the familiar terrain of deficit discourses that tend to blame institutional conservatism, lack of resourcing and teacher resistance for low uptake of digital technologies in schools. It does so by providing an empirical base for the development of a ‘third way’ of theorising technological and pedagogical innovation in schools, one which is more informed by students as critical stakeholders and thus more relevant to the lived culture within the school, and its complex relationship to students’ lives outside of school. It is in this relationship that we find an explanation for how these individuals can, at the one time, be digital kids and analogue students.

Determining a set of surrogate parameters to evaluate urban stormwater quality

This thesis details methodology to estimate urban stormwater quality based on a set of easy to measure physico-chemical parameters. These parameters can be used as surrogate parameters to estimate other key water quality parameters. The key pollutants considered in this study are nitrogen compounds, phosphorus compounds and solids. The use of surrogate parameter relationships to evaluate urban stormwater quality will reduce the cost of monitoring and so that scientists will have added capability to generate a large amount of data for more rigorous analysis of key urban stormwater quality processes, namely, pollutant build-up and wash-off. This in turn will assist in the development of more stringent stormwater quality mitigation strategies. The research methodology was based on a series of field investigations, laboratory testing and data analysis. Field investigations were conducted to collect pollutant build-up and wash-off samples from residential roads and roof surfaces. Past research has identified that these impervious surfaces are the primary pollutant sources to urban stormwater runoff. A specially designed vacuum system and rainfall simulator were used in the collection of pollutant build-up and wash-off samples. The collected samples were tested for a range of physico-chemical parameters. Data analysis was conducted using both univariate and multivariate data analysis techniques. Analysis of build-up samples showed that pollutant loads accumulated on road surfaces are higher compared to the pollutant loads on roof surfaces. Furthermore, it was found that the fraction of solids smaller than 150 ìm is the most polluted particle size fraction in solids build-up on both roads and roof surfaces. The analysis of wash-off data confirmed that the simulated wash-off process adopted for this research agrees well with the general understanding of the wash-off process on urban impervious surfaces. The observed pollutant concentrations in wash-off from road surfaces were different to pollutant concentrations in wash-off from roof surfaces. Therefore, firstly, the identification of surrogate parameters was undertaken separately for roads and roof surfaces. Secondly, a common set of surrogate parameter relationships were identified for both surfaces together to evaluate urban stormwater quality. Surrogate parameters were identified for nitrogen, phosphorus and solids separately. Electrical conductivity (EC), total organic carbon (TOC), dissolved organic carbon (DOC), total suspended solids (TSS), total dissolved solids (TDS), total solids (TS) and turbidity (TTU) were selected as the relatively easy to measure parameters. Consequently, surrogate parameters for nitrogen and phosphorus were identified from the set of easy to measure parameters for both road surfaces and roof surfaces. Additionally, surrogate parameters for TSS, TDS and TS which are key indicators of solids were obtained from EC and TTU which can be direct field measurements. The regression relationships which were developed for surrogate parameters and key parameter of interest were of a similar format for road and roof surfaces, namely it was in the form of simple linear regression equations. The identified relationships for road surfaces were DTN-TDS:DOC, TP-TS:TOC, TSS-TTU, TDS-EC and TSTTU: EC. The identified relationships for roof surfaces were DTN-TDS and TSTTU: EC. Some of the relationships developed had a higher confidence interval whilst others had a relatively low confidence interval. The relationships obtained for DTN-TDS, DTN-DOC, TP-TS and TS-EC for road surfaces demonstrated good near site portability potential. Currently, best management practices are focussed on providing treatment measures for stormwater runoff at catchment outlets where separation of road and roof runoff is not found. In this context, it is important to find a common set of surrogate parameter relationships for road surfaces and roof surfaces to evaluate urban stormwater quality. Consequently DTN-TDS, TS-EC and TS-TTU relationships were identified as the common relationships which are capable of providing measurements of DTN and TS irrespective of the surface type.

Closed-form design equations for decoupling networks of small arrays

Small element spacing in compact arrays results in strong mutual coupling between the array elements. A decoupling network consisting of reactive cross-coupling elements can alleviate problems associated with the coupling. Closed-form design equations for the decoupling networks of symmetrical arrays with two or three elements are presented.