Virtual fencing applications : Implementing and testing an automated cattle control system

Managing livestock movement in extensive systems has environmental and production benefits. Currently permanent wire fencing is used to control cattle; this is both expensive and inflexible. Cattle are known to respond to auditory and visual cues and we investigated whether these can be used to manipulate their behaviour. Twenty-five Belmont Red steers with a mean live weight of 270kg were each randomly assigned to one of five treatments. Treatments consisted of a combination of cues (audio, tactile and visual stimuli) and consequence (electrical stimulation). The treatments were electrical stimulation alone, audio plus electrical stimulation, vibration plus electrical stimulation, light plus electrical stimulation and electrified electric fence (6kV) plus electrical stimulation. Cue stimuli were administered for 3s followed immediately by electrical stimulation (consequence) of 1kV for 1s. The experiment tested the operational efficacy of an on-animal control or virtual fencing system. A collar-halter device was designed to carry the electronics, batteries and equipment providing the stimuli, including audio, vibration, light and electrical of a prototype virtual fencing device. Cattle were allowed to travel along a 40m alley to a group of peers and feed while their rate of travel and response to the stimuli were recorded. The prototype virtual fencing system was successful in modifying the behaviour of the cattle. The rate of travel of cattle along the alley demonstrated the large variability in behavioural response associated with tactile, visual and audible cues. The experiment demonstrated virtual fencing has potential for controlling cattle in extensive grazing systems. However, larger numbers of cattle need to be tested to derive a better understanding of the behavioural variance. Further controlled experimental work is also necessary to quantify the interaction between cues, consequences and cattle learning.

Design of a Web interface for anatomical images

Interactive documents for use with the World Wide Web have been developed for viewing multi-dimensional radiographic and visual images of human anatomy, derived from the Visible Human Project. Emphasis has been placed on user-controlled features and selections. The purpose was to develop an interface which was independent of host operating system and browser software which would allow viewing of information by multiple users. The interfaces were implemented using HyperText Markup Language (HTML) forms, C programming language and Perl scripting language. Images were pre-processed using ANALYZE and stored on a Web server in CompuServe GIF format. Viewing options were included in the document design, such as interactive thresholding and two-dimensional slice direction. The interface is an example of what may be achieved using the World Wide Web. Key applications envisaged for such software include education, research and accessing of information through internal databases and simultaneous sharing of images by remote computers by health personnel for diagnostic purposes.

An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

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.