Quantum Mechanics of Semantic Space

Presentation about information modelling and artificial intelligence, semantic structure, cognitive processing and quantum theory.

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.

Flood fatalities in contemporary Australia (1997-2008) : disaster medicine

Objective: Flood is the most common natural disaster in Australia and causes more loss of life than any other disaster. This article describes the incidence and causes of deaths directly associated with floods in contemporary Australia. ---------- Methods: The present study compiled a database of flood fatalities in Australia in the period of 1997–2008 inclusive. The data were derived from newspapers and historic accounts, as well as government and scientific reports. Assembled data include the date and location of fatalities, age and gender of victims and the circumstances of the death. ---------- Results: At least 73 persons died as a direct result of floods in Australia in the period of 1997–2008. The largest number of fatalities occurred in New South Wales and Queensland. Most fatalities occurred during February, and among men (71.2%). People between the ages of 10 and 29 and those over 70 years are overrepresented among those drowned. There is no evident decline in the number of deaths over time. 48.5% fatalities related to motor vehicle use. 26.5% fatalities occurred as a result of inappropriate or high-risk behaviour during floods. ---------- Conclusion: In modern developed countries with adequate emergency response systems and extensive resources, deaths that occur in floods are almost all eminently preventable. Over 90% of the deaths are caused by attempts to ford flooded waterways or inappropriate situational conduct. Knowledge of the leading causes of flood fatalities should inform public awareness programmes and public safety police enforcement activities.

Productions of space : civic participation of young people at university

Civic participation of young people around the world is routinely described in deficit terms, as they are labelled apathetic, devoid of political knowledge, disengaged from the community and self-absorbed (Andolina, 2002; Weller, 2006). This paper argues that the connectivity of time, space and social values (Lefebvre, 1991; Soja, 1996) are integral to understanding the performances of young people as civic subjects. Today’s youth negotiate unstable social, economic and environmental conditions, new technologies and new forms of community. Loyalty, citizenship and notions of belonging take on new meanings in these changing global conditions. Using the socio-spatial theories of Lefebvre and Foucault, and the tools of critical discourse analysis, this paper argues that the chronotope, or time/space relationship of universities, produces student citizens who, in resistance to a complex global society, create a cocooned space which focuses on moral and spiritual values that can be enacted on a personal level.

The Space Day at QUT

The Space Day has been running at QUT for about a decade. The Space Day started out as a single lecture on the stars delivered to a group of high school students from Brisbane State High School (BSHS), just across the river from QUT and therefore convenient for the school to visit. I was contacted by Victor James of St. Laurence’s College (SLC), Brisbane asking if he could bring a group of boys to QUT for a lecture similar to that delivered to BSHS. However, for SLC a hands-on laboratory session was added to the lecture and thus the Space Day was born. For the Space Day we have concentrated on year 7 – 10 students. Subsequently, many other schools from Brisbane and further afield in Queensland have attended a Space Day.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by a Caputo fractional derivative, and the second order space derivative by a symmetric fractional derivative. First, a method of separating variables expresses the analytical solution of the TSS-FDE in terms of the Mittag--Leffler function. Second, we propose two numerical methods to approximate the Caputo time fractional derivative: the finite difference method; and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPE-NST), which involve the Caputo time fractional derivative (CTFD) of order α ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ ∈ (1, 2). Approximating the CTFD and RSFD using the L1-algorithm and shifted Grunwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.