An implicit RBF meshless approach for time fractional diffusion equations

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

The mixed anion mineral parnauite Cu9[(OH)10|SO4|(AsO4)2]•7H2O – a Raman spectroscopic study

The mixed anion mineral parnauite Cu9[(OH)10|SO4|(AsO4)2].7H2O from two localities namely Cap Garonne Mine, Le Pradet, France and Majuba Hill mine, Pershing County, Nevada, USA has been studied by Raman spectroscopy. The Raman spectrum of the French sample is dominated by an intense band at 975 cm-1 assigned to the ν1 (SO4)2- symmetric stretching mode and Raman bands at 1077 and 1097 cm-1 may be attributed to the ν3 (SO4)2- antisymmetric stretching mode. Two Raman bands 1107 and 1126 cm-1 are assigned to carbonate CO32- symmetric stretching bands and confirms the presence of carbonate in the structure of parnauite. The comparatively sharp band for the Pershing County mineral at 976 cm-1 is assigned to the ν1 (SO4)2- symmetric stretching mode and a broad spectral profile centered upon 1097 cm-1 is attributed to the ν3 (SO4)2- antisymmetric stretching mode. Two intense bands for the Pershing County mineral at 851 and 810 cm-1 are assigned to the ν1 (AsO4)3- symmetric stretching and ν3 (AsO4)3- antisymmetric stretching modes. Two Raman bands for the French mineral observed at 725 and 777 cm-1 are attributed to the ν3 (AsO4)3- antisymmetric stretching mode. For the French mineral, a low intensity Raman band is observed at 869 cm-1 and is assigned to the ν1 (AsO4)3- symmetric stretching vibration. Chemical composition of parnauite remains open and the question may be raised is parnauite a solid solution of two or more minerals such as a copper hydroxy-arsenate and a copper hydroxy sulphate.

New variational Bayesian approaches for statistical data mining : with applications to profiling and differentiating habitual consumption behaviour of customers in the wireless telecommunication industry

This thesis investigates profiling and differentiating customers through the use of statistical data mining techniques. The business application of our work centres on examining individuals’ seldomly studied yet critical consumption behaviour over an extensive time period within the context of the wireless telecommunication industry; consumption behaviour (as oppose to purchasing behaviour) is behaviour that has been performed so frequently that it become habitual and involves minimal intentions or decision making. Key variables investigated are the activity initialised timestamp and cell tower location as well as the activity type and usage quantity (e.g., voice call with duration in seconds); and the research focuses are on customers’ spatial and temporal usage behaviour. The main methodological emphasis is on the development of clustering models based on Gaussian mixture models (GMMs) which are fitted with the use of the recently developed variational Bayesian (VB) method. VB is an efficient deterministic alternative to the popular but computationally demandingMarkov chainMonte Carlo (MCMC) methods. The standard VBGMMalgorithm is extended by allowing component splitting such that it is robust to initial parameter choices and can automatically and efficiently determine the number of components. The new algorithm we propose allows more effective modelling of individuals’ highly heterogeneous and spiky spatial usage behaviour, or more generally human mobility patterns; the term spiky describes data patterns with large areas of low probability mixed with small areas of high probability. Customers are then characterised and segmented based on the fitted GMM which corresponds to how each of them uses the products/services spatially in their daily lives; this is essentially their likely lifestyle and occupational traits. Other significant research contributions include fitting GMMs using VB to circular data i.e., the temporal usage behaviour, and developing clustering algorithms suitable for high dimensional data based on the use of VB-GMM.

The role of institutional rural property in diversified investment portfolios in NSW, Australia

The food and fuel crisis experienced in 2006 to 2008 has highlighted the importance of agricultural commodity production throughout developing and developed economies and has placed greater awareness and importance on rural property and rural property markets. These factors have led to an increased interest from major property investment institutions and property companies in the role of rural property in a mixed asset or mixed property investment portfolio. This paper will analyse rural property sales in New South Wales for the period 1990-2008, and will compare total return performance across a number of rural property sectors based on geographic location and land use type. These results show that the inclusion of rural property in an investment portfolio has benefits in relation to return and risk.

Supplement : Efficient weak second-order stochastic Runge-Kutta methods for non-commutative Stratonvich stochastic differential equations

This paper gives a modification of a class of stochastic Runge–Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

We consider time-space fractional reaction diffusion equations in two dimensions. This equation is obtained from the standard reaction diffusion equation by replacing the first order time derivative with the Caputo fractional derivative, and the second order space derivatives with the fractional Laplacian. Using the matrix transfer technique proposed by Ilic, Liu, Turner and Anh [Fract. Calc. Appl. Anal., 9:333--349, 2006] and the numerical solution strategy used by Yang, Turner, Liu, and Ilic [SIAM J. Scientific Computing, 33:1159--1180, 2011], the solution of the time-space fractional reaction diffusion equations in two dimensions can be written in terms of a matrix function vector product $f(A)b$ at each time step, where $A$ is an approximate matrix representation of the standard Laplacian. We use the finite volume method over unstructured triangular meshes to generate the matrix $A$, which is therefore non-symmetric. However, the standard Lanczos method for approximating $f(A)b$ requires that $A$ is symmetric. We propose a simple and novel transformation in which the standard Lanczos method is still applicable to find $f(A)b$, despite the loss of symmetry. Numerical results are presented to verify the accuracy and efficiency of our newly proposed numerical solution strategy.

Investigation of phenol degradation : True reaction kinetics on fixed film titanium dioxide photocatalyst

This study of photocatalytic oxidation of phenol over titanium dioxide films presents a method for the evaluation of true reaction kinetics. A flat plate reactor was designed for the specific purpose of investigating the influence of various reaction parameters, specifically photocatalytic film thickness, solution flow rate (1–8 l min−1), phenol concentration (20, 40 and 80 ppm), and irradiation intensity (70.6, 57.9, 37.1and 20.4 W m−2), in order to further understand their impact on the reaction kinetics. Special attention was given to the mass transfer phenomena and the influence of film thickness. The kinetics of phenol degradation were investigated with different irradiation levels and initial pollutant concentration. Photocatalytic degradation experiments were performed to evaluate the influence of mass transfer on the reaction and, in addition, the benzoic acid method was applied for the evaluation of mass transfer coefficient. For this study the reactor was modelled as a batch-recycle reactor. A system of equations that accounts for irradiation, mass transfer and reaction rate was developed to describe the photocatalytic process, to fit the experimental data and to obtain kinetic parameters. The rate of phenol photocatalytic oxidation was described by a Langmuir–Hinshelwood type law that included competitive adsorption and degradation of phenol and its by-products. The by-products were modelled through their additive effect on the solution total organic carbon.

Structural and thermal performance of cold-formed steel stud wall systems under fire conditions

Cold-formed steel stud walls are a major component of Light Steel Framing (LSF) building systems used in commercial, industrial and residential buildings. In the conventional LSF stud wall systems, thin steel studs are protected from fire by placing one or two layers of plasterboard on both sides with or without cavity insulation. However, there is very limited data about the structural and thermal performance of stud wall systems while past research showed contradicting results, for example, about the benefits of cavity insulation. This research was therefore conducted to improve the knowledge and understanding of the structural and thermal performance of cold-formed steel stud wall systems (both load bearing and non-load bearing) under fire conditions and to develop new improved stud wall systems including reliable and simple methods to predict their fire resistance rating. Full scale fire tests of cold-formed steel stud wall systems formed the basis of this research. This research proposed an innovative LSF stud wall system in which a composite panel made of two plasterboards with insulation between them was used to improve the fire rating. Hence fire tests included both conventional steel stud walls with and without the use of cavity insulation and the new composite panel system. A propane fired gas furnace was specially designed and constructed first. The furnace was designed to deliver heat in accordance with the standard time temperature curve as proposed by AS 1530.4 (SA, 2005). A compression loading frame capable of loading the individual studs of a full scale steel stud wall system was also designed and built for the load-bearing tests. Fire tests included comprehensive time-temperature measurements across the thickness and along the length of all the specimens using K type thermocouples. They also included the measurements of load-deformation characteristics of stud walls until failure. The first phase of fire tests included 15 small scale fire tests of gypsum plasterboards, and composite panels using different types of insulating material of varying thickness and density. Fire performance of single and multiple layers of gypsum plasterboards was assessed including the effect of interfaces between adjacent plasterboards on the thermal performance. Effects of insulations such as glass fibre, rock fibre and cellulose fibre were also determined while the tests provided important data relating to the temperature at which the fall off of external plasterboards occurred. In the second phase, nine small scale non-load bearing wall specimens were tested to investigate the thermal performance of conventional and innovative steel stud wall systems. Effects of single and multiple layers of plasterboards with and without vertical joints were investigated. The new composite panels were seen to offer greater thermal protection to the studs in comparison to the conventional panels. In the third phase of fire tests, nine full scale load bearing wall specimens were tested to study the thermal and structural performance of the load bearing wall assemblies. A full scale test was also conducted at ambient temperature. These tests showed that the use of cavity insulation led to inferior fire performance of walls, and provided good explanations and supporting research data to overcome the incorrect industry assumptions about cavity insulation. They demonstrated that the use of insulation externally in a composite panel enhanced the thermal and structural performance of stud walls and increased their fire resistance rating significantly. Hence this research recommends the use of the new composite panel system for cold-formed LSF walls. This research also included steady state tensile tests at ambient and elevated temperatures to address the lack of reliable mechanical properties for high grade cold-formed steels at elevated temperatures. Suitable predictive equations were developed for calculating the yield strength and elastic modulus at elevated temperatures. In summary, this research has developed comprehensive experimental thermal and structural performance data for both the conventional and the proposed non-load bearing and load bearing stud wall systems under fire conditions. Idealized hot flange temperature profiles have been developed for non-insulated, cavity insulated and externally insulated load bearing wall models along with suitable equations for predicting their failure times. A graphical method has also been proposed to predict the failure times (fire rating) of non-load bearing and load bearing walls under different load ratios. The results from this research are useful to both fire researchers and engineers working in this field. Most importantly, this research has significantly improved the knowledge and understanding of cold-formed LSF walls under fire conditions, and developed an innovative LSF wall system with increased fire rating. It has clearly demonstrated the detrimental effects of using cavity insulation, and has paved the way for Australian building industries to develop new wall panels with increased fire rating for commercial applications worldwide.

Bilski v Kappos : The United States Supreme Court delivers mixed views on patenting non-physical inventions and business methods

The United States Supreme Court has handed down a once in a generation patent law decision that will have important ramifications for the patentability of non-physical methods, both internationally and in Australia. In Bilski v Kappos, the Supreme Court considered whether an invention must either be tied to a machine or apparatus, or transform an article into a different state or thing to be patentable. It also considered for the first time whether business methods are patentable subject matter. The decision will be of particular interest to practitioners who followed the litigation in Grant v Commissioner of Patents, a Federal Court decision in which a Brisbane-based inventor was denied a patent over a method of protecting an asset from the claims of creditors.

Velocity-jump models with crowding effects

Velocity jump processes are discrete random walk models that have many applications including the study of biological and ecological collective motion. In particular, velocity jump models are often used to represent a type of persistent motion, known as a “run and tumble”, which is exhibited by some isolated bacteria cells. All previous velocity jump processes are non-interacting, which means that crowding effects and agent-to-agent interactions are neglected. By neglecting these agent-to-agent interactions, traditional velocity jump models are only applicable to very dilute systems. Our work is motivated by the fact that many applications in cell biology, such as wound healing, cancer invasion and development, often involve tissues that are densely packed with cells where cell-to-cell contact and crowding effects can be important. To describe these kinds of high cell density problems using a velocity jump process we introduce three different classes of crowding interactions into a one-dimensional model. Simulation data and averaging arguments lead to a suite of continuum descriptions of the interacting velocity jump processes. We show that the resulting systems of hyperbolic partial differential equations predict the mean behavior of the stochastic simulations very well.

Hamstring strain injuries : factors that lead to injury and re-injury

Hamstring strain injuries (HSIs) are common in a number of sports and incidence rates have not declined in recent times. Additionally, the high rate of recurrent injuries suggests that our current understanding of HSI and re-injury risk is incomplete. Whilst the multifactoral nature of HSIs is agreed upon by many, often individual risk factors and/or causes of injury are examined in isolation. This review aims to bring together the causes, risk factors and interventions associated with HSIs to better understand why HSIs are so prevalent. Running is often identified as the primary activity type for HSIs and given the high eccentric forces and moderate muscle strain placed on the hamstrings during running these factors are considered to be part of the aetiology of HSIs. However, the exact causes of HSIs remain unknown and whilst eccentric contraction and muscle strain purportedly play a role, accumulated muscle damage and/or a single injurious event may also contribute. Potentially, all of these factors interact to varying degrees depending on the injurious activity type (i.e. running, kicking). Furthermore, anatomical factors, such as the biarticular organization, the dual innervations of biceps femoris (BF), fibre type distribution, muscle architecture and the degree of anterior pelvic tilt, have all been implicated. Each of these variables impact upon HSI risk via a number of different mechanisms that include increasing hamstring muscle strain and altering the susceptibility of the hamstrings to muscle damage. Reported risk factors for HSIs include age, previous injury, ethnicity, strength imbalances, flexibility and fatigue. Of these, little is known, definitively, about why previous injury increases the risk of future HSIs. Nevertheless, interventions put in place to reduce the incidence of HSIs by addressing modifiable risk factors have focused primarily on increasing eccentric strength, correcting strength imbalances and improving flexibility. The response to these intervention programmes has been mixed with varied levels of success reported. A conceptual framework is presented suggesting that neuromuscular inhibition following HSIs may impede the rehabilitation process and subsequently lead to maladaptation of hamstring muscle structure and function, including preferentially eccentric weakness, atrophy of the previously injured muscles and alterations in the angle of peak knee flexor torque. This remains an area for future research and practitioners need to remain aware of the multifactoral nature of HSIs if injury rates are to decline.

Tracking employees' twists and turns : describing a mixed methods approach to assessing change in the psychological contract

The psychological contract is a key analytical device utilised by both academics and practitioners to conceptualise and explore the dynamics of the employment relationship. However, despite the recognised import of the construct, some authors suggest that its empirical investigation has fallen into a 'methodological rut' [Conway & Briner, 2005, p. 89] and is neglecting to assess key tenets of the concept, such as its temporal and dynamic nature. This paper describes the research design of a longitudinal, mixed methods study which draws upon the strengths of both qualitative and quantitative modes of inquiry in order to explore the development of, and changes in, the psychological contract. Underpinned by a critical realist philosophy, the paper seeks to offer a research design suitable for exploring the process of change not only within the psychological contract domain, but also for similar constructs in the human resource management and broader organisational behaviour fields.

Formation mechanisms of secondary organic aerosols in relation to laser printer emissions

Due to their large surface area, complex chemical composition and high alveolar deposition rate, ultrafine particles (UFPs) (< 0.1 ìm) pose a significant risk to human health and their toxicological effects have been acknowledged by the World Health Organisation. Since people spend most of their time indoors, there is a growing concern about the UFPs present in some indoor environments. Recent studies have shown that office machines, in particular laser printers, are a significant indoor source of UFPs. The majority of printer-generated UFPs are organic carbon and it is unlikely that these particles are emitted directly from the printer or its supplies (such as paper and toner powder). Thus, it was hypothesised that these UFPs are secondary organic aerosols (SOA). Considering the widespread use of printers and human exposure to these particles, understanding the processes involved in particle formation is of critical importance. However, few studies have investigated the nature (e.g. volatility, hygroscopicity, composition, size distribution and mixing state) and formation mechanisms of these particles. In order to address this gap in scientific knowledge, a comprehensive study including state-of-art instrumental methods was conducted to characterise the real-time emissions from modern commercial laser printers, including particles, volatile organic compounds (VOCs) and ozone (O3). The morphology, elemental composition, volatility and hygroscopicity of generated particles were also examined. The large set of experimental results was analysed and interpreted to provide insight into: (1) Emissions profiles of laser printers: The results showed that UFPs dominated the number concentrations of generated particles, with a quasi unimodal size distribution observed for all tests. These particles were volatile, non-hygroscopic and mixed both externally and internally. Particle microanalysis indicated that semi-volatile organic compounds occupied the dominant fraction of these particles, with only trace quantities of particles containing Ca and Fe. Furthermore, almost all laser printers tested in this study emitted measurable concentrations of VOCs and O3. A positive correlation between submicron particles and O3 concentrations, as well as a contrasting negative correlation between submicron particles and total VOC concentrations were observed during printing for all tests. These results proved that UFPs generated from laser printers are mainly SOAs. (2) Sources and precursors of generated particles: In order to identify the possible particle sources, particle formation potentials of both the printer components (e.g. fuser roller and lubricant oil) and supplies (e.g. paper and toner powder) were investigated using furnace tests. The VOCs emitted during the experiments were sampled and identified to provide information about particle precursors. The results suggested that all of the tested materials had the potential to generate particles upon heating. Nine unsaturated VOCs were identified from the emissions produced by paper and toner, which may contribute to the formation of UFPs through oxidation reactions with ozone. (3) Factors influencing the particle emission: The factors influencing particle emissions were also investigated by comparing two popular laser printers, one showing particle emissions three orders of magnitude higher than the other. The effects of toner coverage, printing history, type of paper and toner, and working temperature of the fuser roller on particle number emissions were examined. The results showed that the temperature of the fuser roller was a key factor driving the emission of particles. Based on the results for 30 different types of laser printers, a systematic positive correlation was observed between temperature and particle number emissions for printers that used the same heating technology and had a similar structure and fuser material. It was also found that temperature fluctuations were associated with intense bursts of particles and therefore, they may have impact on the particle emissions. Furthermore, the results indicated that the type of paper and toner powder contributed to particle emissions, while no apparent relationship was observed between toner coverage and levels of submicron particles. (4) Mechanisms of SOA formation, growth and ageing: The overall hypothesis that UFPs are formed by reactions with the VOCs and O3 emitted from laser printers was examined. The results proved this hypothesis and suggested that O3 may also play a role in particle ageing. In addition, knowledge about the mixing state of generated particles was utilised to explore the detailed processes of particle formation for different printing scenarios, including warm-up, normal printing, and printing without toner. The results indicated that polymerisation may have occurred on the surface of the generated particles to produce thermoplastic polymers, which may account for the expandable characteristics of some particles. Furthermore, toner and other particle residues on the idling belt from previous print jobs were a very clear contributing factor in the formation of laser printer-emitted particles. In summary, this study not only improves scientific understanding of the nature of printer-generated particles, but also provides significant insight into the formation and ageing mechanisms of SOAs in the indoor environment. The outcomes will also be beneficial to governments, industry and individuals.

New percentage body fat prediction equations for Japanese females

Anthropometry is a simple and cost-efficient method for the assessment of body composition. However prediction equations to estimate body composition using anthropometry should be ‘population-specific’. Most popular body composition prediction equations for Japanese females were proposed more than 40 years ago and there is some concern regarding their usefulness in Japanese females living today. The aim of this study was to compare percentage body fat (%BF) estimated from anthropometry and dual energy x-ray absorptiometry (DXA) to examine the applicability of commonly used prediction equations in young Japanese females. Body composition of 139 Japanese females aged between 18 and 27 years of age (BMI range: 15.1–29.1 kg/m2) was measured using whole-body DXA (Lunar DPX-LIQ) scans. From anthropometric measurements %BF was estimated using four equations developed from Japanese females. The results showed that the traditionally employed prediction equations for anthropometry significantly (p<0.01) underestimate %BF of young Japanese females and therefore are not valid for the precise estimation of body composition. New %BF prediction equations were proposed from the DXA and anthropometry results. Application of the proposed equations may assist in more accurate assessment of body fatness in Japanese females living today.

Mixed convection laminar flow along a horizontal plate subject to streamwise sinusoidal surface temperature

Mixed convection of a two-dimensional laminar incompressible flow along a horizontal flat plate with streamwise sinusoidal surface temperature has been numerically investigated for different values of Rayleigh number and Reynolds number for constant values of Prandtl number, amplitude and frequency of periodic temperature. The numerical scheme is based on the finite element method adapted to rectangular non-uniform mesh elements by a non-linear parametric solution algorithm. The fluid considered in this study is air. The results are obtained for the Rayleigh number and Reynolds number ranging from 102 to 104 and 1 to 100, respectively, with constant physical properties for the fluid medium considered. Velocity and temperature profiles, streamlines, isotherms, and average Nusselt numbers are presented to observe the effect of the investigating parameters on fluid flow and heat transfer characteristics. The present results show that the convective phenomena are greatly influenced by the variation of Rayleigh numbers and Reynolds number.