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.

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.

Clinical data integration approach using SAS clinical data integration server (CDI) tools

The decisions people make about medical treatments have a great impact on their lives. Health care practitioners, providers and patients often make decisions about medical treatments without complete understanding of the circumstances. The main reason for this is that medical data are available in fragmented, disparate and heterogeneous data silos. Without a centralised data warehouse structure to integrate these data silos, it is highly unlikely and impractical for the users to get all the information required on time to make a correct decision. In this research paper, a clinical data integration approach using SAS Clinical Data Integration Server tools is presented.

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.

Modelling sea water intrusion in coastal aquifers using heterogeneous computing

The objective of this PhD research program is to investigate numerical methods for simulating variably-saturated flow and sea water intrusion in coastal aquifers in a high-performance computing environment. The work is divided into three overlapping tasks: to develop an accurate and stable finite volume discretisation and numerical solution strategy for the variably-saturated flow and salt transport equations; to implement the chosen approach in a high performance computing environment that may have multiple GPUs or CPU cores; and to verify and test the implementation. The geological description of aquifers is often complex, with porous materials possessing highly variable properties, that are best described using unstructured meshes. The finite volume method is a popular method for the solution of the conservation laws that describe sea water intrusion, and is well-suited to unstructured meshes. In this work we apply a control volume-finite element (CV-FE) method to an extension of a recently proposed formulation (Kees and Miller, 2002) for variably saturated groundwater flow. The CV-FE method evaluates fluxes at points where material properties and gradients in pressure and concentration are consistently defined, making it both suitable for heterogeneous media and mass conservative. Using the method of lines, the CV-FE discretisation gives a set of differential algebraic equations (DAEs) amenable to solution using higher-order implicit solvers. Heterogeneous computer systems that use a combination of computational hardware such as CPUs and GPUs, are attractive for scientific computing due to the potential advantages offered by GPUs for accelerating data-parallel operations. We present a C++ library that implements data-parallel methods on both CPU and GPUs. The finite volume discretisation is expressed in terms of these data-parallel operations, which gives an efficient implementation of the nonlinear residual function. This makes the implicit solution of the DAE system possible on the GPU, because the inexact Newton-Krylov method used by the implicit time stepping scheme can approximate the action of a matrix on a vector using residual evaluations. We also propose preconditioning strategies that are amenable to GPU implementation, so that all computationally-intensive aspects of the implicit time stepping scheme are implemented on the GPU. Results are presented that demonstrate the efficiency and accuracy of the proposed numeric methods and formulation. The formulation offers excellent conservation of mass, and higher-order temporal integration increases both numeric efficiency and accuracy of the solutions. Flux limiting produces accurate, oscillation-free solutions on coarse meshes, where much finer meshes are required to obtain solutions with equivalent accuracy using upstream weighting. The computational efficiency of the software is investigated using CPUs and GPUs on a high-performance workstation. The GPU version offers considerable speedup over the CPU version, with one GPU giving speedup factor of 3 over the eight-core CPU implementation.

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.

Integration-segregation decisions under general value functions: "create your own bundle - choose 1, 2, or all 3!",

Whether to keep products segregated (e.g., unbundled) or integrate some or all of them (e.g., bundle) has been a problem of profound interest in areas such as portfolio theory in finance, risk capital allocations in insurance and marketing of consumer products. Such decisions are inherently complex and depend on factors such as the underlying product values and consumer preferences, the latter being frequently described using value functions, also known as utility functions in economics. In this paper, we develop decision rules for multiple products, which we generally call ‘exposure units’ to naturally cover manifold scenarios spanning well beyond ‘products’. Our findings show, e.g. that the celebrated Thaler's principles of mental accounting hold as originally postulated when the values of all exposure units are positive (i.e. all are gains) or all negative (i.e. all are losses). In the case of exposure units with mixed-sign values, decision rules are much more complex and rely on cataloging the Bell number of cases that grow very fast depending on the number of exposure units. Consequently, in the present paper, we provide detailed rules for the integration and segregation decisions in the case up to three exposure units, and partial rules for the arbitrary number of units.

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.

Efficiency of knowledge integration in enterprise systems implementation

Recent literature has emphasized the pivotal role of knowledge integration in Enterprise Systems (ES) success. This research-in-progress paper, building upon Knowledge Based Theory of the firm (KBT), examines the efficiency of knowledge integration in the context of ES implementation and identifies the factors contributing to its enhancement. The proposed model in this paper suggests that the efficiency of knowledge integration in an ES implementation process depends upon the level of common knowledge and the level of coordination in the ES adopting organization. It further suggests that the level of common knowledge can be enhanced by proper training, improving ES users’intrinsic and extrinsic motivations and business process modeling and the level of coordination can be improved by articulating a clear unified organizational goal for the ES adoption in the organization, forming a competent ES team, enhancing interdepartmental communication and the cross-functionality in the organization structure.

Integration of Saudi Arabia’s conservative Islamic culture in sustainable housing design

The cities of Saudi Arabia have perhaps the largest growth rates of cities in the Middle East, such that it has become a cause in shortage of housing for mid and low-income families, as is the case in other developing countries. Even when housing is found, it is not sustainable nor is it providing the cultural needs of those families. The aim of this paper is to integrate the unique conservative Islamic Saudi culture into the design of sustainable housing. This paper is part of a preliminary study of an on-going PhD thesis, which utilises a semistructured interview of a panel of nine experts in collecting the data. The interviews consisted of ten questions ranging from general questions such as stating their expertise and work position to more specific question such as listing the critical success factors and/or barriers for applying sustainability to housing in Saudi Arabia. Since the participants were selected according to their experience, the answers to the interview questions were satisfactory where the generation of the survey questions for the second stage in the PhD thesis took place after analysing the participant’s answers to the interview questions. This paper recommends design requirements for accommodating the conservative Islamic Saudi Culture in low cost sustainable houses. Such requirements include achieving privacy through the use of various types of traditional Saudi architectural elements, such as the method of decorative screening of windows, called Mashrabiya, and having an inner courtyard where the house looks inward rather than outward. Other requirements include educating firms on how to design sustainable housing, educating the public on the advantages of sustainable housing and implementing new laws that enforce the utilisation of sustainable methods to housing construction. This paper contributes towards the body of knowledge by proposing initial findings on how to integrate the conservative Islamic culture of Saudi Arabia into the design of a sustainable house specifically for mid and low-income families. This contribution can be implemented on developing countries in the region that are faced with housing shortage for mid and low-income families.

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.

From strategic design to design integration

Within a growing awareness of design as central to the strategic success and the sustained competitive advantage of firms, this paper examines how companies pursue design driven innovation (Verganti, 2008, 2009) and respond to design led innovation initiatives (Matthews & Bucolo 2013). Specifically, this paper reports the findings of a collaborative research project where CEO sponsored senior managers from five multi-national organisations, met regularly over a twelve-month period, to discuss their progress on applying a design led approach in their firms. This longitudinal research project traced the process and progress of change instigated by the senior management representatives, as well as the deeper investigation of the barriers and challenges to re-frame design more strategically in their organisation. Data were collected through workshops and interviews throughout the twelve-month period, regarding the firms’ journeys and also the barriers and challenges firms faced in order to become design led. The findings present a novel set of implications for both designers and management scholars. This paper seeks to contribute to research and practice by investigating the processes and outcomes of a design led innovation program and to propose implications for practice for designers and management.

The effect of polystyrene sodium sulfonate grafting on polyethylene terephthalate artificial ligaments on in vitro mineralisation and in vivo bone tissue integration

This study investigates the impact of polystyrene sodium sulfonate (PolyNaSS) grafting onto the osseo-integration of a polyethylene terephthalate artificial ligament (Ligament Advanced Reinforcement System, LARS™) used for Anterior Cruciate Ligament (ACL). The performance of grafted and non-grafted ligaments was assessed in vitro by culturing human osteoblasts under osteogenic induction and this demonstrated that the surface modification was capable of up-regulating the secretion of ALP and induced higher level of mineralisation as measured 6 weeks post-seeding by Micro-Computed Tomography. Grafted and non-grafted LARS™ were subsequently implanted in an ovine model for ACL reconstruction and the ligament-to-bone interface was evaluated by histology and biomechanical testings 3 and 12 months post-implantation. The grafted ligaments exhibited more frequent direct ligament-to-bone contact and bone formation in the core of the ligament at the later time point than the non-grafted specimens, the grafting also significantly reduced the fibrous encapsulation of the ligament 12 months post-implantation. However, this improved osseo-integration was not translated into a significant increase in the biomechanical pull-out loads. These results provide evidences that PolyNaSS grafting improved the osseo-integration of the artificial ligament within the bone tunnels. This might positively influence the outcome of the surgical reconstructions, as higher ligament stability is believed to limit micro-movement and therefore permits earlier and enhanced healing.