The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.

Multi-objective design optimisation of GFRP sandwich beams

A novel Glass Fibre Reinforced Polymer (GFRP) sandwich panel was developed by an Australian manufacturer for civil engineering applications. This research is motivated by the new applications of GFRP sandwich structures in civil engineering such as slab, beam, girder and sleeper. An optimisation methodology is developed in this work to enhance the design of GFRP sandwich beams. The design of single and glue laminated GFRP sandwich beam were conducted by using numerical optimisation. The numerical multi-objective optimisation considered a design two objectives simultaneously. These objectives are cost and mass. The numerical optimisation uses the Adaptive Range Multi-objective Genetic Algorithm (ARMOGA) and Finite Element (FE) method. Trade-offs between objectives was found during the optimisation process. Multi-objective optimisation shows a core to skin mass ratio equal to 3.68 for the single sandwich beam cross section optimisation and it showed that the optimum core to skin thickness ratio is 11.0.

An accurate numerical scheme for the contraction of a bubble in a Hele-Shaw cell

We report on an accurate numerical scheme for the evolution of an inviscid bubble in radial Hele-Shaw flow, where the nonlinear boundary effects of surface tension and kinetic undercooling are included on the bubble-fluid interface. As well as demonstrating the onset of the Saffman-Taylor instability for growing bubbles, the numerical method is used to show the effect of the boundary conditions on the separation (pinch-off) of a contracting bubble into multiple bubbles, and the existence of multiple possible asymptotic bubble shapes in the extinction limit. The numerical scheme also allows for the accurate computation of bubbles which pinch off very close to the theoretical extinction time, raising the possibility of computing solutions for the evolution of bubbles with non-generic extinction behaviour.

Numerical solution of an optimal control model of dendritic cell treatment of a growing tumour

A new optimal control model of the interactions between a growing tumour and the host immune system along with an immunotherapy treatment strategy is presented. The model is based on an ordinary differential equation model of interactions between the growing tu- mour and the natural killer, cytotoxic T lymphocyte and dendritic cells of the host immune system, extended through the addition of a control function representing the application of a dendritic cell treat- ment to the system. The numerical solution of this model, obtained from a multi species Runge–Kutta forward-backward sweep scheme, is described. We investigate the effects of varying the maximum al- lowed amount of dendritic cell vaccine administered to the system and find that control of the tumour cell population is best effected via a high initial vaccine level, followed by reduced treatment and finally cessation of treatment. We also found that increasing the strength of the dendritic cell vaccine causes an increase in the number of natural killer cells and lymphocytes, which in turn reduces the growth of the tumour.

Thermal performance of load bearing cold-formed steel walls under fire conditions using numerical studies

Cold–formed Light gauge Steel Frame (LSF) wall systems are increasingly used in low-rise and multi-storey buildings and hence their fire safety has become important in the design of buildings. A composite LSF wall panel system was developed recently, where a thin insulation was sandwiched between two plasterboards to improve the fire performance of LSF walls. Many experimental and numerical studies have been undertaken to investigate the fire performance of non-load bearing LSF wall under standard conditions. However, only limited research has been undertaken to investigate the fire performance of load bearing LSF walls under standard and realistic design fire conditions. Therefore in this research, finite element thermal models of both the conventional load bearing LSF wall panels with cavity insulation and the innovative LSF composite wall panel were developed to simulate their thermal behaviour under standard and realistic design fire conditions. Suitable thermal properties were proposed for plasterboards and insulations based on laboratory tests and available literature. The developed models were then validated by comparing their results with available fire test results of load bearing LSF wall. This paper presents the details of the developed finite element models of load bearing LSF wall panels and the thermal analysis results. It shows that finite element models can be used to simulate the thermal behaviour of load bearing LSF walls with varying configurations of insulations and plasterboards. Failure times of load bearing LSF walls were also predicted based on the results from finite element thermal analyses. Finite element analysis results show that the use of cavity insulation was detrimental to the fire rating of LSF walls while the use of external insulation offered superior thermal protection to them. Effects of realistic design fire conditions are also presented in this paper.

Perceptions and expectations for learning and development for older workers within Queensland local government councils : a case study

Current literature warns organisations about a global ageing phenomenon. Workplace ageing is causing a diminishing work pool which has consequences for a sustainable workforce in the future. This phenomenon continues to impact on local government councils in Australia. Australia has one of the world’s most rapidly ageing populations, and there is evidence that Australian local government councils are already resulting in an unsustainable workforce. Consequently, this research program investigated the role of older workers in the Queensland local government workplace in enabling them to extend their working lives towards transitional employment and a sustainable workforce in the future. Transitional Employment is intended as a strategy for enabling individuals to have greater control over their employment options and their employability during the period leading to their final exit from the workforce. There was no evidence of corporate support for older workers in Queensland local government councils other than tokenistic government campaigns encouraging organisations to "better value their older workers". (Queensland Government, 2007d, p.6). TE is investigated as a possible intervention for older workers in the future. The international and national literature review reflected a range of matters impacting on current older workers in the workforce and barriers preventing them from accessing services towards extending their employment beyond the traditional retirement age (60 years) as defined by the Australian Government; an age when individuals can access their superannuation. Learning and development services were identified as one of those barriers. There was little evidence of investment in or consistent approaches to supporting older workers by organisations. Learning and development services appeared at best to be ad hoc, reactive to corporate productivity and outputs with little recognition of the ageing phenomenon (OECD, 2006, p.23) and looming skills and labour shortages (ALGA, 2006, p. 19). Themes from the literature review led to the establishment of three key research questions: 1. What are the current local government workforce issues impacting on skills and labour retention? 2. What are perceptions about the current workplace environment? And, 3. What are the expectations about learning and development towards extending employability of older workers within the local government sector? The research questions were explored by utilising three qualitative empirical studies, using some numerical data for reporting and comparative analysis. Empirical Study One investigated common themes for accessing transitional employment and comprised two phases. A literature review and Study One data analysis enabled the construction of an initial Transitional Employment Model which includes most frequent themes. Empirical Study Two comprised focus groups to further consider those themes. This led to identification of issues impacting the most on access to learning and development by older workers and towards a revised TEM. Findings presented majority support for transitional employment as a strategy for supporting older workers to work beyond their traditional retirement age. Those findings are presented as significant issues impacting on access to transitional employment within the final 3-dimensionsal TEM. The model is intended as a guide for responding to an ageing workforce by local government councils in the future. This study argued for increased and improved corporate support, particularly for learning and development services for older workers. Such support will enable older workers to maintain their employability and extend their working lives; a sustainable workforce in the future.

Final-state effects in neutron Compton scattering measurements on zirconium deuteride and beryllium

We report inelastic neutron scattering measurements of the neutron Compton profile, J(y), for Be and for D in polycrystalline ZrD2 over a range of momentum transfers, q between 27 and 178 °A−1. The measurements were performed using the inverse geometry spectrometer eVS which is situated at the UK pulsed spallation neutron source ISIS. We have investigated deviations from impulse approximation (IA) scattering which are generically referred to as final state effects (FSEs) using a method described by Sears. This method allows both the magnitude and the q dependence of the FSE to be studied. Analysis of the measured data was compared with analysis of numerical simulations based on the harmonic approximation and good agreement was found for both ZrD2 and Be. Finally we have shown how (∇2V), where V is the interatomic potential, can be extracted from the antisymmetric component of J(y).

Numerical solutions for thin film flow down the outside and inside of a vertical cylinder

We consider a model for thin film flow down the outside and inside of a vertical cylinder. Our focus is to study the effect that the curvature of the cylinder has on the gravity-driven instability of the advancing contact line and to simulate the resulting fingering patterns that form due to this instability. The governing partial differential equation is fourth order with a nonlinear degenerate diffusion term that represents the stabilising effect of surface tension. We present numerical solutions obtained by implementing an efficient alternating direction implicit scheme. When compared to the problem of flow down a vertical plane, we find that increasing substrate curvature tends to increase the fingering instability for flow down the outside of the cylinder, whereas flow down the inside of the cylinder substrate curvature has the opposite effect. Further, we demonstrate the existence of nontrivial travelling wave solutions which describe fingering patterns that propagate down the inside of a cylinder at constant speed without changing form. These solutions are perfectly analogous to those found previously for thin film flow down an inclined plane.

Hydrogeological framework, conceptual and numerical groundwater flow model of Laidley Creek catchment, Queensland, Australia

This thesis studies the water resources of Laidley Creek catchment within the Lockyer Valley where groundwater is used for intensive irrigation of crops. A holistic approach was used to consider groundwater within the total water cycle. The project mapped the geology, measured stream flows and groundwater levels, and analysed the chemistry of the waters. These data were integrated within a catchment-wide conceptual model, including historic and rainfall records. From this a numerical simulation was produced to test data validity and develop predictions of behaviour, which can support management decisions, particularly in times of variable climate.

Robust scale initialization for long-range stereo visual odometry

Achieving a robust, accurately scaled pose estimate in long-range stereo presents significant challenges. For large scene depths, triangulation from a single stereo pair is inadequate and noisy. Additionally, vibration and flexible rigs in airborne applications mean accurate calibrations are often compromised. This paper presents a technique for accurately initializing a long-range stereo VO algorithm at large scene depth, with accurate scale, without explicitly computing structure from rigidly fixed camera pairs. By performing a monocular pose estimate over a window of frames from a single camera, followed by adding the secondary camera frames in a modified bundle adjustment, an accurate, metrically scaled pose estimate can be found. To achieve this the scale of the stereo pair is included in the optimization as an additional parameter. Results are presented both on simulated and field gathered data from a fixed-wing UAV flying at significant altitude, where the epipolar geometry is inaccurate due to structural deformation and triangulation from a single pair is insufficient. Comparisons are made with more conventional VO techniques where the scale is not explicitly optimized, and demonstrated over repeated trials to indicate robustness.

A retrospective cohort investigation of active range of motion within one week of open reduction and internal fixation of distal radius fractures

Distal radius fractures stabilized by open reduction internal fixation (ORIF) have become increasingly common. There is currently no consensus on the optimal time to commence range of motion (ROM) exercises post-ORIF. A retrospective cohort review was conducted over a five-year period to compare wrist and forearm range of motion outcomes and number of therapy sessions between patients who commenced active ROM exercises within the first seven days and from day eight onward following ORIF of distal radius fractures. One hundred and twenty-one patient cases were identified. Clinical data, active ROM at initial and discharge therapy assessments, fracture type, surgical approaches, and number of therapy sessions attended were recorded. One hundred and seven (88.4%) cases had complete datasets. The early active ROM group (n = 37) commenced ROM a mean (SD) of 4.27 (1.8) days post-ORIF. The comparator group (n = 70) commenced ROM exercises 24.3 (13.6) days post-ORIF. No significant differences were identified between groups in ROM at initial or discharge assessments, or therapy sessions attended. The results from this study indicate that patients who commenced active ROM exercises an average of 24 days after surgery achieved comparable ROM outcomes with similar number of therapy sessions to those who commenced ROM exercises within the first week.

Numerical simulation of anomalous diffusion with application to medical imaging

The first objective of this project is to develop new efficient numerical methods and supporting error and convergence analysis for solving fractional partial differential equations to study anomalous diffusion in biological tissue such as the human brain. The second objective is to develop a new efficient fractional differential-based approach for texture enhancement in image processing. The results of the thesis highlight that the fractional order analysis captured important features of nuclear magnetic resonance (NMR) relaxation and can be used to improve the quality of medical imaging.

Very sensitive fiber Bragg grating accelerometer using transverse forces with an easy over-range protection and low cross axial sensitivity

The first fiber Bragg grating (FBG) accelerometer using direct transverse forces is demonstrated by fixing the FBG by its two ends and placing a transversely moving inertial object at its middle. It is very sensitive because a lightly stretched FBG is more sensitive to transverse forces than axial forces. Its resonant frequency and static sensitivity are analyzed by the classic spring-mass theory, assuming the axial force changes little. The experiments show that the theory can be modified for cases where the assumption does not hold. The resonant frequency can be modified by a linear relationship experimentally achieved, and the static sensitivity by an alternative method proposed. The principles of the over-range protection and low cross axial sensitivity are achieved by limiting the movement of the FBG and were validated experimentally. The sensitivities 1.333 and 0.634 nm/g were experimentally achieved by 5.29 and 2.83 gram inertial objects at 10 Hz from 0.1 to 0.4 g (g = 9.8 m/s 2), respectively, and their resonant frequencies were around 25 Hz. Their theoretical static sensitivities and resonant frequencies found by the modifications are 1.188 nm/g and 26.81 Hz for the 5.29 gram one and 0.784 nm/g and 29.04 Hz for the 2.83 gram one, respectively.

Laboratory measurement of hydraulic conductivity functions of two unsaturated sandy soils during drying and wetting processes

The importance of applying unsaturated soil mechanics to geotechnical engineering design has been well understood. However, the consumption of time and the necessity for a specific laboratory testing apparatus when measuring unsaturated soil properties have limited the application of unsaturated soil mechanics theories in practice. Although methods for predicting unsaturated soil properties have been developed, the verification of these methods for a wide range of soil types is required in order to increase the confidence of practicing engineers in using these methods. In this study, a new permeameter was developed to measure the hydraulic conductivity of unsaturated soils using the steady-state method and directly measured suction (negative pore-water pressure) values. The apparatus is instrumented with two tensiometers for the direct measurement of suction during the tests. The apparatus can be used to obtain the hydraulic conductivity function of sandy soil over a low suction range (0-10 kPa). Firstly, the repeatability of the unsaturated hydraulic conductivity measurement, using the new permeameter, was verified by conducting tests on two identical sandy soil specimens and obtaining similar results. The hydraulic conductivity functions of the two sandy soils were then measured during the drying and wetting processes of the soils. A significant hysteresis was observed when the hydraulic conductivity was plotted against the suction. However, the hysteresis effects were not apparent when the conductivity was plotted against the volumetric water content. Furthermore, the measured unsaturated hydraulic conductivity functions were compared with predictions using three different predictive methods that are widely incorporated into numerical software. The results suggest that these predictive methods are capable of capturing the measured behavior with reasonable agreement.

Simulation of retrofitted unreinforced concrete masonry unit walls under blast loading

This paper describes an investigation into the effectiveness of using spray-on nano-particle reinforced polymer and aluminium foam as new types of retrofit material to prevent the breaching and collapse of unreinforced concrete masonry walls subjected to blast over a whole range of dynamic and impulsive regimes. Material models from the LSDYNA material library were used to model the behaviors of each of the materials and its interface for retrofitted and unretrofitted masonry walls. Available test data were used to validate the numerical models. Using the validated LS-DYNA numerical models, the pressure-impulse diagrams for retrofitted concrete masonry walls were constructed. The efficiency of using these retrofits to strengthen the unreinforced concrete masonry unit (CMU) walls under various pressures and impulses was investigated using pressure-impulse diagrams. Comparisons were made to find the most efficient retrofits for masonry walls against blasts.