A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

A pilot study utilising cross-age peer tutoring as a method of intervention for anxious adolescents

Anxiety disorders are the most common psychopathology experienced by young people, with up to 18% of adolescents developing an anxiety disorder. The consequences of these disorders, if left untreated, include impaired peer relationships, school absenteeism and self-concept problems. In addition, anxiety disorders may play a causal role in the development of depression in young people, precede eating disorders and predispose adolescents to substance abuse disorders. While the school is often chosen as a place to provide early intervention for this debilitating disorder, the fact that excessive anxiety is often not recognised in school and that young people are reluctant to seek help, makes identifying these adolescents difficult. Even when these young people are identified, there are problems in providing sensitive programs which are not stigmatising to them within a school setting. One method which may engage this adolescent population could be cross-age peer tutoring. This paper reports on a small pilot study using the “Worrybusters” program and a cross-age peer tutoring method to engage the anxious adolescents. These anxious secondary school students planned activities for teacher-referred anxious primary school students for a term in the high school setting and then delivered those activities to the younger students weekly in the next term in the primary school. Although the secondary school students decreased their scores on anxiety self-report measures there were no significant differences for primary school students’ self-reports. However, the primary school parent reports indicated a significant decrease in their child’s anxiety.

Practice as method : the ex/centric fixations project

In the past decade, scholars have proposed a range of terms to describe the relationship between practice and research in the creative arts, including increasingly nuanced definitions of practice-based research, practice-led research and practice-as-research. In this paper, I consider the efficacy of creative practice as method. I use the example of The Ex/Centric Fixations Project – a project in which I have embedded creative practice in a research project, rather than embedding research in a creative project. The Ex/Centric Fixations project investigates the way spectators interpret human experiences – especially human experiences of difference, marginalisation or discrimination – depicted onstage. In particular, it investigates the way postmodern performance writing strategies, and the presence of performing bodied to which the experience depicted can be attached, impacts on interpretations. It is part of a broader research project which examines the performativity of spectatorship, and intervenes in emergent debates about performance, ethics and spectatorship in the context of debate about whether live performance is a privileged site for the emergence of an ethical face-to-face encounter with the Other. Using the metaphor of the Mobius strip, I examines the way practice – as a method, rather than an output – has informed, influenced and problematised the broader research project.

Metal oxide nanofibres membranes assembled by spin-coating method

Ceramic membranes are of particular interest in many industrial processes due to their ability to function under extreme conditions while maintaining their chemical and thermal stability. Major structural deficiencies under conventional fabrication approach are pin-holes and cracks, and the dramatic losses of flux when pore sizes are reduced to enhance selectivity. We overcome these structural deficiencies by constructing hierarchically structured separation layer on a porous substrate using larger titanate nanofibres and smaller boehmite nanofibres. This yields a radical change in membrane texture. The differences in the porous supports have no substantial influences on the texture of resulting membranes. The membranes with top layer of nanofibres coated on different porous supports by spin-coating method have similar size of the filtration pores, which is in a range of 10–100 nm. These membranes are able to effectively filter out species larger than 60 nm at flow rates orders of magnitude greater than conventional membranes. The retention can attain more than 95%, while maintaining a high flux rate about 900 L m-2 h. The calcination after spin-coating creates solid linkages between the fibres and between fibres and substrate, in addition to convert boehmite into -alumina nanofibres. This reveals a new direction in membrane fabrication.

Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

Marx as critical discourse analyst : the genesis of a critical method and its relevance to the critique of global capital.

In this paper we identify elements in Marx´s economic and political writings that are relevant to contemporary critical discourse analysis (CDA). We argue that Marx can be seen to be engaging in a form of discourse analysis. We identify the elements in Marx´s historical materialist method that support such a perspective, and exemplify these in a longitudinal comparison of Marx´s texts.

Radiological aspects of petroleum exploration and production in the sultanate of Oman

This thesis is a study of naturally occurring radioactive materials (NORM) activity concentration, gamma dose rate and radon (222Rn) exhalation from the waste streams of large-scale onshore petroleum operations. Types of activities covered included; sludge recovery from separation tanks, sludge farming, NORM storage, scaling in oil tubulars, scaling in gas production and sedimentation in produced water evaporation ponds. Field work was conducted in the arid desert terrain of an operational oil exploration and production region in the Sultanate of Oman. The main radionuclides found were 226Ra and 210Pb (238U - series), 228Ra and 228Th (232Th - series), and 227Ac (235U - series), along with 40K. All activity concentrations were higher than the ambient soil level and varied over several orders of magnitude. The range of gamma dose rates at a 1 m height above ground for the farm treated sludge had a range of 0.06 0.43 µSv h 1, and an average close to the ambient soil mean of 0.086 ± 0.014 µSv h 1, whereas the untreated sludge gamma dose rates had a range of 0.07 1.78 µSv h 1, and a mean of 0.456 ± 0.303 µSv h 1. The geometric mean of ambient soil 222Rn exhalation rate for area surrounding the sludge was mBq m 2 s 1. Radon exhalation rates reported in oil waste products were all higher than the ambient soil value and varied over three orders of magnitude. This study resulted in some unique findings including: (i) detection of radiotoxic 227Ac in the oil scales and sludge, (ii) need of a new empirical relation between petroleum sludge activity concentrations and gamma dose rates, and (iii) assessment of exhalation of 222Rn from oil sludge. Additionally the study investigated a method to determine oil scale and sludge age by the use of inherent behaviour of radionuclides as 228Ra:226Ra and 228Th:228Ra activity ratios.

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.

Generation in context : an exploratory method for musical enquiry

This paper discusses a method, Generation in Context, for interrogating theories of music analysis and music perception. Given an analytic theory, the method consists of creating a generative process that implements the theory in reverse. Instead of using the theory to create analyses from scores, the theory is used to generate scores from analyses. Subjective evaluation of the quality of the musical output provides a mechanism for testing the theory in a contextually robust fashion. The method is exploratory, meaning that in addition to testing extant theories it provides a general mechanism for generating new theoretical insights. We outline our initial explorations in the use of generative processes for music research, and we discuss how generative processes provide evidence as to the veracity of theories about how music is experienced, with insights into how these theories may be improved and, concurrently, provide new techniques for music creation. We conclude that Generation in Context will help reveal new perspectives on our understanding of music.

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

Modelling water droplet movement on a leaf surface

The central aim for the research undertaken in this PhD thesis is the development of a model for simulating water droplet movement on a leaf surface and to compare the model behavior with experimental observations. A series of five papers has been presented to explain systematically the way in which this droplet modelling work has been realised. Knowing the path of the droplet on the leaf surface is important for understanding how a droplet of water, pesticide, or nutrient will be absorbed through the leaf surface. An important aspect of the research is the generation of a leaf surface representation that acts as the foundation of the droplet model. Initially a laser scanner is used to capture the surface characteristics for two types of leaves in the form of a large scattered data set. After the identification of the leaf surface boundary, a set of internal points is chosen over which a triangulation of the surface is constructed. We present a novel hybrid approach for leaf surface fitting on this triangulation that combines Clough-Tocher (CT) and radial basis function (RBF) methods to achieve a surface with a continuously turning normal. The accuracy of the hybrid technique is assessed using numerical experimentation. The hybrid CT-RBF method is shown to give good representations of Frangipani and Anthurium leaves. Such leaf models facilitate an understanding of plant development and permit the modelling of the interaction of plants with their environment. The motion of a droplet traversing this virtual leaf surface is affected by various forces including gravity, friction and resistance between the surface and the droplet. The innovation of our model is the use of thin-film theory in the context of droplet movement to determine the thickness of the droplet as it moves on the surface. Experimental verification shows that the droplet model captures reality quite well and produces realistic droplet motion on the leaf surface. Most importantly, we observed that the simulated droplet motion follows the contours of the surface and spreads as a thin film. In the future, the model may be applied to determine the path of a droplet of pesticide along a leaf surface before it falls from or comes to a standstill on the surface. It will also be used to study the paths of many droplets of water or pesticide moving and colliding on the surface.

Characterisation of soils with the use of instrumental techniques : a multivariate forensic study

The value of soil evidence in the forensic discipline is well known. However, it would be advantageous if an in-situ method was available that could record responses from tyre or shoe impressions in ground soil at the crime scene. The development of optical fibres and emerging portable NIR instruments has unveiled a potential methodology which could permit such a proposal. The NIR spectral region contains rich chemical information in the form of overtone and combination bands of the fundamental infrared absorptions and low-energy electronic transitions. This region has in the past, been perceived as being too complex for interpretation and consequently was scarcely utilized. The application of NIR in the forensic discipline is virtually non-existent creating a vacancy for research in this area. NIR spectroscopy has great potential in the forensic discipline as it is simple, nondestructive and capable of rapidly providing information relating to chemical composition. The objective of this study is to investigate the ability of NIR spectroscopy combined with Chemometrics to discriminate between individual soils. A further objective is to apply the NIR process to a simulated forensic scenario where soil transfer occurs. NIR spectra were recorded from twenty-seven soils sampled from the Logan region in South-East Queensland, Australia. A series of three high quartz soils were mixed with three different kaolinites in varying ratios and NIR spectra collected. Spectra were also collected from six soils as the temperature of the soils was ramped from room temperature up to 6000C. Finally, a forensic scenario was simulated where the transferral of ground soil to shoe soles was investigated. Chemometrics methods such as the commonly known Principal Component Analysis (PCA), the less well known fuzzy clustering (FC) and ranking by means of multicriteria decision making (MCDM) methodology were employed to interpret the spectral results. All soils were characterised using Inductively Coupled Plasma Optical Emission Spectroscopy and X-Ray Diffractometry. Results were promising revealing NIR combined with Chemometrics is capable of discriminating between the various soils. Peak assignments were established by comparing the spectra of known minerals with the spectra collected from the soil samples. The temperature dependent NIR analysis confirmed the assignments of the absorptions due to adsorbed and molecular bound water. The relative intensities of the identified NIR absorptions reflected the quantitative XRD and ICP characterisation results. PCA and FC analysis of the raw soils in the initial NIR investigation revealed that the soils were primarily distinguished on the basis of their relative quartz and kaolinte contents, and to a lesser extent on the horizon from which they originated. Furthermore, PCA could distinguish between the three kaolinites used in the study, suggesting that the NIR spectral region was sensitive enough to contain information describing variation within kaolinite itself. The forensic scenario simulation PCA successfully discriminated between the ‘Backyard Soil’ and ‘Melcann® Sand’, as well as the two sampling methods employed. Further PCA exploration revealed that it was possible to distinguish between the various shoes used in the simulation. In addition, it was possible to establish association between specific sampling sites on the shoe with the corresponding site remaining in the impression. The forensic application revealed some limitations of the process relating to moisture content and homogeneity of the soil. These limitations can both be overcome by simple sampling practices and maintaining the original integrity of the soil. The results from the forensic scenario simulation proved that the concept shows great promise in the forensic discipline.