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.

Labour rights as human rights : workers' safety at work in Australian-based supply chains

The increase of buyer-driven supply chains, outsourcing and other forms of non-traditional employment has resulted in challenges for labour market regulation. One business model which has created substantial regulatory challenges is supply chains. The supply chain model involves retailers purchasing products from brand corporations who then outsource the manufacturing of the work to traders who contract with factories or outworkers who actually manufacture the clothing and textiles. This business model results in time and cost pressures being pushed down the supply chain which has resulted in sweatshops where workers systematically have their labour rights violated. Literally millions of workers work in dangerous workplaces where thousands are killed or permanently disabled every year. This thesis has analysed possible regulatory responses to provide workers a right to safety and health in supply chains which provide products for Australian retailers. This thesis will use a human rights standard to determine whether Australia is discharging its human rights obligations in its approach to combating domestic and foreign labour abuses. It is beyond this thesis to analyse Occupational Health and Safety (OHS) laws in every jurisdiction. Accordingly, this thesis will focus upon Australian domestic laws and laws in one of Australia’s major trading partners, the Peoples’ Republic of China (China). It is hypothesised that Australia is currently breaching its human rights obligations through failing to adequately regulate employees’ safety at work in Australian-based supply chains. To prove this hypothesis, this thesis will adopt a three- phase approach to analysing Australia’s regulatory responses. Phase 1 will identify the standard by which Australia’s regulatory approach to employees’ health and safety in supply chains can be judged. This phase will focus on analysing how workers’ rights to safety as a human right imposes a moral obligation on Australia to take reasonablely practicable steps regulate Australian-based supply chains. This will form a human rights standard against which Australia’s conduct can be judged. Phase 2 focuses upon the current regulatory environment. If existing regulatory vehicles adequately protect the health and safety of employees, then Australia will have discharged its obligations through simply maintaining the status quo. Australia currently regulates OHS through a combination of ‘hard law’ and ‘soft law’ regulatory vehicles. The first part of phase 2 analyses the effectiveness of traditional OHS laws in Australia and in China. The final part of phase 2 then analyses the effectiveness of the major soft law vehicle ‘Corporate Social Responsibility’ (CSR). The fact that employees are working in unsafe working conditions does not mean Australia is breaching its human rights obligations. Australia is only required to take reasonably practicable steps to ensure human rights are realized. Phase 3 identifies four regulatory vehicles to determine whether they would assist Australia in discharging its human rights obligations. Phase 3 then analyses whether Australia could unilaterally introduce supply chain regulation to regulate domestic and extraterritorial supply chains. Phase 3 also analyses three public international law regulatory vehicles. This chapter considers the ability of the United Nations Global Compact, the ILO’s Better Factory Project and a bilateral agreement to improve the detection and enforcement of workers’ right to safety and health.

Advanced analysis of steel frame structures comprising non-compact sections

During the past decade, a significant amount of research has been conducted internationally with the aim of developing, implementing, and verifying "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures. Application of these methods permits comprehensive assessment of the actual failure modes and ultimate strengths of structural systems in practical design situations, without resort to simplified elastic methods of analysis and semi-empirical specification equations. Advanced analysis has the potential to extend the creativity of structural engineers and simplify the design process, while ensuring greater economy and more uniform safety with respect to the ultimate limit state. The application of advanced analysis methods has previously been restricted to steel frames comprising only members with compact cross-sections that are not subject to the effects of local buckling. This precluded the use of advanced analysis from the design of steel frames comprising a significant proportion of the most commonly used Australian sections, which are non-compact and subject to the effects of local buckling. This thesis contains a detailed description of research conducted over the past three years in an attempt to extend the scope of advanced analysis by developing methods that include the effects of local buckling in a non-linear analysis formulation, suitable for practical design of steel frames comprising non-compact sections. Two alternative concentrated plasticity formulations are presented in this thesis: the refined plastic hinge method and the pseudo plastic zone method. Both methods implicitly account for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the methods for the analysis of steel frames comprising non-compact sections has been established by comparison with a comprehensive range of analytical benchmark frame solutions. Both the refined plastic hinge and pseudo plastic zone methods are more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations. For example, the pseudo plastic zone method predicts the ultimate strength of the analytical benchmark frames with an average conservative error of less than one percent, and has an acceptable maximum unconservati_ve error of less than five percent. The pseudo plastic zone model can allow the design capacity to be increased by up to 30 percent for simple frames, mainly due to the consideration of inelastic redistribution. The benefits may be even more significant for complex frames with significant redundancy, which provides greater scope for inelastic redistribution. The analytical benchmark frame solutions were obtained using a distributed plasticity shell finite element model. A detailed description of this model and the results of all the 120 benchmark analyses are provided. The model explicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. Its accuracy was verified by comparison with a variety of analytical solutions and the results of three large-scale experimental tests of steel frames comprising non-compact sections. A description of the experimental method and test results is also provided.

Compliance with international financial reporting standards (IFRS) and the value relevance of accounting information in emerging stock markets : evidence from Kuwait

Since the 1960s, the value relevance of accounting information has been an important topic in accounting research. The value relevance research provides evidence as to whether accounting numbers relate to corporate value in a predicted manner (Beaver, 2002). Such research is not only important for investors but also provides useful insights into accounting reporting effectiveness for standard setters and other users. Both the quality of accounting standards used and the effectiveness associated with implementing these standards are fundamental prerequisites for high value relevance (Hellstrom, 2006). However, while the literature comprehensively documents the value relevance of accounting information in developed markets, little attention has been given to emerging markets where the quality of accounting standards and their enforcement are questionable. Moreover, there is currently no known research that explores the association between level of compliance with International Financial Reporting Standards (IFRS) and the value relevance of accounting information. Motivated by the lack of research on the value relevance of accounting information in emerging markets and the unique institutional setting in Kuwait, this study has three objectives. First, it investigates the extent of compliance with IFRS with respect to firms listed on the Kuwait Stock Exchange (KSE). Second, it examines the value relevance of accounting information produced by KSE-listed firms over the 1995 to 2006 period. The third objective links the first two and explores the association between the level of compliance with IFRS and the value relevance of accounting information to market participants. Since it is among the first countries to adopt IFRS, Kuwait provides an ideal setting in which to explore these objectives. In addition, the Kuwaiti accounting environment provides an interesting regulatory context in which each KSE-listed firm is required to appoint at least two external auditors from separate auditing firms. Based on the research objectives, five research questions (RQs) are addressed. RQ1 and RQ2 aim to determine the extent to which KSE-listed firms comply with IFRS and factors contributing to variations in compliance levels. These factors include firm attributes (firm age, leverage, size, profitability, liquidity), the number of brand name (Big-4) auditing firms auditing a firm’s financial statements, and industry categorization. RQ3 and RQ4 address the value relevance of IFRS-based financial statements to investors. RQ5 addresses whether the level of compliance with IFRS contributes to the value relevance of accounting information provided to investors. Based on the potential improvement in value relevance from adopting and complying with IFRS, it is predicted that the higher the level of compliance with IFRS, the greater the value relevance of book values and earnings. The research design of the study consists of two parts. First, in accordance with prior disclosure research, the level of compliance with mandatory IFRS is examined using a disclosure index. Second, the value relevance of financial statement information, specifically, earnings and book value, is examined empirically using two valuation models: price and returns models. The combined empirical evidence that results from the application of both models provides comprehensive insights into value relevance of accounting information in an emerging market setting. Consistent with expectations, the results show the average level of compliance with IFRS mandatory disclosures for all KSE-listed firms in 2006 was 72.6 percent; thus, indicating KSE-listed firms generally did not fully comply with all requirements. Significant variations in the extent of compliance are observed among firms and across accounting standards. As predicted, older, highly leveraged, larger, and profitable KSE-listed firms are more likely to comply with IFRS required disclosures. Interestingly, significant differences in the level of compliance are observed across the three possible auditor combinations of two Big-4, two non-Big 4, and mixed audit firm types. The results for the price and returns models provide evidence that earnings and book values are significant factors in the valuation of KSE-listed firms during the 1995 to 2006 period. However, the results show that the value relevance of earnings and book values decreased significantly during that period, suggesting that investors rely less on financial statements, possibly due to the increase in the available non-financial statement sources. Notwithstanding this decline, a significant association is observed between the level of compliance with IFRS and the value relevance of earnings and book value to KSE investors. The findings make several important contributions. First, they raise concerns about the effectiveness of the regulatory body that oversees compliance with IFRS in Kuwait. Second, they challenge the effectiveness of the two-auditor requirement in promoting compliance with regulations as well as the associated cost-benefit of this requirement for firms. Third, they provide the first known empirical evidence linking the level of IFRS compliance with the value relevance of financial statement information. Finally, the findings are relevant for standard setters and for their current review of KSE regulations. In particular, they highlight the importance of establishing and maintaining adequate monitoring and enforcement mechanisms to ensure compliance with accounting standards. In addition, the finding that stricter compliance with IFRS improves the value relevance of accounting information highlights the importance of full compliance with IFRS and not just mere adoption.