Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

Basin analysis and economic geology of the Northern Mount Isa Basin

The Mount Isa Basin is a new concept used to describe the area of Palaeo- to Mesoproterozoic rocks south of the Murphy Inlier and inappropriately described presently as the Mount Isa Inlier. The new basin concept presented in this thesis allows for the characterisation of basin-wide structural deformation, correlation of mineralisation with particular lithostratigraphic and seismic stratigraphic packages, and the recognition of areas with petroleum exploration potential. The northern depositional margin of the Mount Isa Basin is the metamorphic, intrusive and volcanic complex here referred to as the Murphy Inlier (not the "Murphy Tectonic Ridge"). The eastern, southern and western boundaries of the basin are obscured by younger basins (Carpentaria, Eromanga and Georgina Basins). The Murphy Inlier rocks comprise the seismic basement to the Mount Isa Basin sequence. Evidence for the continuity of the Mount Isa Basin with the McArthur Basin to the northwest and the Willyama Block (Basin) at Broken Hill to the south is presented. These areas combined with several other areas of similar age are believed to have comprised the Carpentarian Superbasin (new term). The application of seismic exploration within Authority to Prospect (ATP) 423P at the northern margin of the basin was critical to the recognition and definition of the Mount Isa Basin. The Mount Isa Basin is structurally analogous to the Palaeozoic Arkoma Basin of Illinois and Arkansas in southern USA but, as with all basins it contains unique characteristics, a function of its individual development history. The Mount Isa Basin evolved in a manner similar to many well described, Phanerozoic plate tectonic driven basins. A full Wilson Cycle is recognised and a plate tectonic model proposed. The northern Mount Isa Basin is defined as the Proterozoic basin area northwest of the Mount Gordon Fault. Deposition in the northern Mount Isa Basin began with a rift sequence of volcaniclastic sediments followed by a passive margin drift phase comprising mostly carbonate rocks. Following the rift and drift phases, major north-south compression produced east-west thrusting in the south of the basin inverting the older sequences. This compression produced an asymmetric epi- or intra-cratonic clastic dominated peripheral foreland basin provenanced in the south and thinning markedly to a stable platform area (the Murphy Inlier) in the north. The fmal major deformation comprised east-west compression producing north-south aligned faults that are particularly prominent at Mount Isa. Potential field studies of the northern Mount Isa Basin, principally using magnetic data (and to a lesser extent gravity data, satellite images and aerial photographs) exhibit remarkable correlation with the reflection seismic data. The potential field data contributed significantly to the unravelling of the northern Mount Isa Basin architecture and deformation. Structurally, the Mount Isa Basin consists of three distinct regions. From the north to the south they are the Bowthorn Block, the Riversleigh Fold Zone and the Cloncurry Orogen (new names). The Bowthom Block, which is located between the Elizabeth Creek Thrust Zone and the Murphy Inlier, consists of an asymmetric wedge of volcanic, carbonate and clastic rocks. It ranges from over 10 000 m stratigraphic thickness in the south to less than 2000 min the north. The Bowthorn Block is relatively undeformed: however, it contains a series of reverse faults trending east-west that are interpreted from seismic data to be down-to-the-north normal faults that have been reactivated as thrusts. The Riversleigh Fold Zone is a folded and faulted region south of the Bowthorn Block, comprising much of the area formerly referred to as the Lawn Hill Platform. The Cloncurry Orogen consists of the area and sequences equivalent to the former Mount Isa Orogen. The name Cloncurry Orogen clearly distinguishes this area from the wider concept of the Mount Isa Basin. The South Nicholson Group and its probable correlatives, the Pilpah Sandstone and Quamby Conglomerate, comprise a later phase of now largely eroded deposits within the Mount Isa Basin. The name South Nicholson Basin is now outmoded as this terminology only applied to the South Nicholson Group unlike the original broader definition in Brown et al. (1968). Cored slimhole stratigraphic and mineral wells drilled by Amoco, Esso, Elf Aquitaine and Carpentaria Exploration prior to 1986, penetrated much of the stratigraphy and intersected both minor oil and gas shows plus excellent potential source rocks. The raw data were reinterpreted and augmented with seismic stratigraphy and source rock data from resampled mineral and petroleum stratigraphic exploration wells for this study. Since 1986, Comalco Aluminium Limited, as operator of a joint venture with Monument Resources Australia Limited and Bridge Oil Limited, recorded approximately 1000 km of reflection seismic data within the basin and drilled one conventional stratigraphic petroleum well, Beamesbrook-1. This work was the first reflection seismic and first conventional petroleum test of the northern Mount Isa Basin. When incorporated into the newly developed foreland basin and maturity models, a grass roots petroleum exploration play was recognised and this led to the present thesis. The Mount Isa Basin was seen to contain excellent source rocks coupled with potential reservoirs and all of the other essential aspects of a conventional petroleum exploration play. This play, although high risk, was commensurate with the enormous and totally untested petroleum potential of the basin. The basin was assessed for hydrocarbons in 1992 with three conventional exploration wells, Desert Creek-1, Argyle Creek-1 and Egilabria-1. These wells also tested and confrrmed the proposed basin model. No commercially viable oil or gas was encountered although evidence of its former existence was found. In addition to the petroleum exploration, indeed as a consequence of it, the association of the extensive base metal and other mineralisation in the Mount Isa Basin with hydrocarbons could not be overlooked. A comprehensive analysis of the available data suggests a link between the migration and possible generation or destruction of hydrocarbons and metal bearing fluids. Consequently, base metal exploration based on hydrocarbon exploration concepts is probably. the most effective technique in such basins. The metal-hydrocarbon-sedimentary basin-plate tectonic association (analogous to Phanerozoic models) is a compelling outcome of this work on the Palaeo- to Mesoproterozoic Mount lsa Basin. Petroleum within the Bowthom Block was apparently destroyed by hot brines that produced many ore deposits elsewhere in the basin.

Pharmacological consequence of the A118G μ opioid receptor polymorphism on morphine-and fentanyl-mediated modulation of Ca2+ channels in humanized mouse sensory neurons

Background: The most common functional single nucleotide polymorphism of the human OPRM1 gene, A118G, has been shown to be associated with interindividual differences in opioid analgesic requirements, particularly with morphine, in patients with acute postoperative pain. The purpose of this study was to examine whether this polymorphism would modulate the morphine and fentanyl pharmacological profile of sensory neurons isolated from a humanized mouse model homozygous for either the 118A or 118G allele. Methods: The coupling of wild-type and mutant μ opioid receptors to voltage-gated Ca channels after exposure to either ligand was examined by employing the whole cell variant of the patch-clamp technique in acutely dissociated trigeminal ganglion neurons. Morphine-mediated antinociception was measured in mice carrying either the 118AA or 118GG allele. RESULTS:: The biophysical parameters (cell size, current density, and peak current amplitude potential) measured from both groups of sensory neurons were not significantly different. In 118GG neurons, morphine was approximately fivefold less potent and 26% less efficacious than that observed in 118AA neurons. On the other hand, the potency and efficacy of fentanyl were similar for both groups of neurons. Morphine-mediated analgesia in 118GG mice was significantly reduced compared with the 118AA mice. Conclusions: This study provides evidence to suggest that the diminished clinical effect observed with morphine in 118G carriers results from an alteration of the receptor's pharmacology in sensory neurons. In addition, the impaired analgesic response with morphine may explain why carriers of this receptor variant have an increased susceptibility to become addicted to opioids. © 2011 the American Society of Anesthesiologists, Inc. Lippincott Williams & Wilkins. Anesthesiology.

Safety enhancement of operator protection systems on self-propelled mining equipment

In the long term, with development of skill, knowledge, exposure and confidence within the engineering profession, rigorous analysis techniques have the potential to become a reliable and far more comprehensive method for design and verification of the structural adequacy of OPS, write Nimal J Perera, David P Thambiratnam and Brian Clark. This paper explores the potential to enhance operator safety of self-propelled mechanical plant subjected to roll over and impact of falling objects using the non-linear and dynamic response simulation capabilities of analytical processes to supplement quasi-static testing methods prescribed in International and Australian Codes of Practice for bolt on Operator Protection Systems (OPS) that are post fitted. The paper is based on research work carried out by the authors at the Queensland University of Technology (QUT) over a period of three years by instrumentation of prototype tests, scale model tests in the laboratory and rigorous analysis using validated Finite Element (FE) Models. The FE codes used were ABAQUS for implicit analysis and LSDYNA for explicit analysis. The rigorous analysis and dynamic simulation technique described in the paper can be used to investigate the structural response due to accident scenarios such as multiple roll over, impact of multiple objects and combinations of such events and thereby enhance the safety and performance of Roll Over and Falling Object Protection Systems (ROPS and FOPS). The analytical techniques are based on sound engineering principles and well established practice for investigation of dynamic impact on all self propelled vehicles. They are used for many other similar applications where experimental techniques are not feasible.

The ergonomics of interfacing a human operator with the control

This workshop provides an ergonomic framework and design rules for the design of automotive controls, considering anthropometric design, physiologic design, biomechanic design and information design.

Intuitionistic fuzzy Choquet integral operator-based approach for black-start decision-making

Determining the optimal of black-start strategies is very important for speeding the restoration speed of a power system after a global blackout. Most existing black-start decision-making methods are based on the assumption that all indexes are independent of each other, and little attention has been paid to the group decision-making method which is more reliable. Given this background, the intuitionistic fuzzy set and further intuitionistic fuzzy Choquet integral operator are presented, and a black-start decision-making method based on this integral operator is presented. Compared to existing methods, the proposed algorithm cannot only deal with the relevance among the indexes, but also overcome some shortcomings of the existing methods. Finally, an example is used to demonstrate the proposed method. © 2012 The Institution of Engineering and Technology.

Othering the Malay in Malaysia : a planned consequence of politics?

This paper examines the rise in the politicisation of Islam in Malaysia and links it to the othering of the Malaysian Malay. It is my argument that both were “conquering” tools of Malaysia’s “Father of Modernisation”, Mahathir Mohamad, devised to win the support of the Malay Muslim majority in Malaysia. The many awards bestowed on Mahathir obscure the fact that he was instrumental in the systematic erosion of the power and roles of state institutions, especially at the Federal government level. This includes the significant loss of the independence of the Malaysian judiciary. Whilst per capita income in Malaysia may well have increased eight times under his 22-year leadership, this paper asks why is it that the majority of the Malays remain the largest number among the poor and the more disenfranchised of ethnicities in the country? Why have Malay and Muslim women suffered such a rapid decreasing ability to access justice? This paper examines existing research on the social and political changes Malaysia has experienced with Islamisation and under Mahathir’s rule, as well as studies on Malayness, Malay nationalism and Muslim Malay identity formation. The paper elaborates the othering of a majority people, the Malays in Malaysia, and how this othering has brought forth a fast-growing political power in the name of a supremacist Islam, a puritanical Sunni and Malay Islam. Specific events in the rise and rule of Mahathir as Malaysia’s then Prime Minister are reviewed, such as the banning of The Malay Dilemma, and the split in the United Malays National Organisation (UMNO) in 1987. Also examined is the varying emphasis between Muslim and race, and how during Mahathir’s rule, that strong misogynist and patriarchal attitudes took hold in Malay Muslim consciousness, a colonising consciousness that is othering the perceived cultural and genetic “impurities” within the Malay.

A securities market operator's use of the "please explain" price query and its impact on compliance

Market operators in New Zealand and Australia, such as the New Zealand Exchange (NZX) and the Australian Securities Exchange (ASX), have the regulatory power in their listing rules to issue queries to their market participants to explain unusual fluctuations in trading price and/or volume in the market. The operator will issue a price query where it believes that the market has not been fully informed as to price relevant information. Responsive regulation theory has informed much of the regulatory debate in securities laws in the region. Price queries map onto the lower level of the enforcement pyramid envisaged by responsive regulation and are one strategy that a market operator can use in communicating its compliance expectations to its stakeholders. The issue of a price query may be a precursor to more severe enforcement activities. The aim of this study is to investigate whether increased use of price queries by the securities market operator in New Zealand corresponded with an increase in disclosure frequency by all participating companies. The study finds that an increased use of price queries did correspond with an increase in disclosure frequency. A possible explanation for this finding is that price queries are an effective means of appealing to the factors that motivate corporations, and the individuals who control them, to comply with the law and regulatory requirements. This finding will have implications for both the NZX and the ASX as well as for regulators and policy makers generally.