The development of a new N-Line model, which provides a practical tool for simulating regional beach changes induced by short and long-term processes, is described in this thesis. The new N-Line model consists of four main modules that together describe the hydrodynamic and morphological responses. The four constituent modules have been integrated based on a wide range of research including the utility and function of commercial or freeware models. They are RCPWAVE wave module, time-averaged and depth-integrated current module, sediment transport module based on Bailard (1981) and contour change morphological module. Two different time-scales and two staggered grid systems for hydrodynamic and morphological simulations were adopted alternatively. For short-term 2D profile changes, new N-Line model applicability has been examined using data from the laboratory to the field. For ideal beaches, new N-Line can simulate an offshore storm bar generation or an onshore accretion due to high or low energy waves. For SUPERTANK large-scale flume data, the predicted profile matched the measured profile well, especially the bar height and position. For beach profile data from the Gold Coast, storm-induced variations of barred profiles were reasonably modelled. The new N-Line model compared well with other commonly used cross-shore models such as SBEACH and UNIBEST. A new schematisation for a non-monotonic profile and DUNED inclusion were introduced. Sensitivity tests on cross-shore sediment coefficient (Kq), smoothing parameter (??s) and water level fluctuations were performed. For long-term 3D beach changes, the new N-Line model applicability has been tested with various boundary conditions using idealized and real field data. Two periods, 17 and 16 months, of beach changes before and after a major bypass plant commenced operation in 2001 at Letitia Spit were simulated. The profile and shoreline changes were predicted reasonably well. Empirical model parameters were determined after a range of sensitivity and calibration testing. The new N-Line model showed its better performance compared to one-line models. It can handle various boundary conditions, especially bypass conditions. The N-Line model is not only capable of modelling planform variations but also cross-shore profile changes.

The design and management of organised systems, comprised of dynamic interdependent collectives of autonomous agents, is the kind of problem that the discipline of complex systems is intended to address. Nevertheless, conventional model-based applications of complex systems may be of limited utility when the problem is also data-poor and soft. In this case, a quantitative model may be at best meaning-less; at worst harmful. Systems approaches, such as soft systems methodologies, have been developed that provide some guidance in this domain. However, these alternatives do not utilise the exact techniques of complex systems, preferring to abandon mathematical representations altogether. It is the aim of this thesis to advance a “conceptual analysis" approach to complex systems design that exploits deep insights from the mathematics of complex systems, without building explicit models of the underlying system. It is argued that this approach can extend the domain of applicability of the discipline of complex systems into situations where quantitative data is unavailable, and human and social factors are significant. Conceptual analysis of complex systems is inherently multidisciplinary, because it is broader than the foundations of any single conventional discipline. This is reflected in the structure of this thesis, which spans the philosophy, theory and application of complex systems. Part I on systems philosophy develops an understanding of representation, which sheds light on the utility and limitations of models. The history of the systems movement is then surveyed, systemism is distinguished from both individualism and holism, and `system' is defined. Complex systems is contrasted with both early systems theory and contemporary systems approaches. Part II on complex systems theory firstly relates the major theoretical concepts within a rigourous information theoretical framework. They include complexity, edge of chaos, self-organisation, emergence, adaptation, evolution and self refer- entiality. The central systems concept - emergence - is then examined in depth beyond its information theoretic interpretation, leading to a concise definition of emergent properties and emergence. A new framework for understanding emergence in terms of scope, resolution and state yields substantial novel insights. It is shown that emergence is coupled to scope, in contrast to the conventional explanation that relates levels of description. Part III applies the preceding philosophical and theoretical framework to real-world problems in the defence and security arena. In the first example, the theory of multi-scale complexity reveals structural impediments to success for conventional force structures in asymmetric warfare, such as Operation Iraqi Freedom. The second example analyses the capability development process, which is responsible for transforming the security needs of Government into equipment purchasing decisions. The analysis produces practical recommendations for improvements that address the underlying complexity of the problem. Reflections in the conclusion of this thesis focus on the interrelations between philosophy, theory and application. As the individual contributions of this thesis are woven into a single tapestry, they demonstrate the utility of a multidisciplinary approach to complex systems design. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1283989 / Thesis(PhD) -- University of Adelaide, School of Mathematical Sciences, 2007

We investigate reaction-diffusion models for populations whose members undergo two specific processes: dispersal and settling. Systems of this type occur throughout biological science, in contexts ranging from ecology to cell biology.Here we consider three distinct applications, namely: / • animal translocation, / • the invasion of a domain by precursor and differentiated cells, and / • the development of tissue-engineered cartilage. / Mathematical modelling of these systems provides an understanding of the population-level patterns that emerge from the behaviour of individuals. / A multi-species reaction-diffusion model is developed and analysed for each of the three applications. We present numerical results, which are illuminated through analytical results derived for simplified or limiting cases. For these special cases, results are obtained using analytical techniques including perturbation analysis, travelling wave analysis and phase plane methods. These analytic results provide a more complete understanding of system behaviour than numerical results alone. Emphasis is placed on connecting modelling results with experimental observations. / The first application considered is animal translocations. Translocations are widely used to reintroduce threatened species to areas where they have disappeared. A variety of different dispersal and settling mechanisms are considered, and results compared. The model is applied to a case study of a double translocation of the Maud Island frog, Leiopelma pakeka. Results suggest that settling occurs at a constant rate, with repulsion playing a significantrole in dispersal. This research demonstrates that mathematical modelling of translocations is useful in suggesting design and monitoring strategies for future translocations, and as an aid in understanding observed behaviour. / The second application we investigate is the invasion of a domain by cells that migrate, proliferate and differentiate. The model is applicable to neural crest cell invasion in the developing enteric (intestinal) nervous system, but is presented in general terms and is of broader applicability. Regions of the parameter space are characterised according to existence, shape and speed of travelling wave solutions. Our observations may be used in conjunction with experimental results to identify key parameters determining the invasion speed for a particular biological system. Furthermore, these results may assist experimentalists in identifying the resource that is limiting proliferation of precursor cells. / As a third application, we propose a model for the development of cartilage around a single chondrocyte. The limited ability of cartilage to repair when damaged has led to the investigation of tissue engineering as a method for reconstructing cartilage. As in healthy cartilage, the model predicts a balance between synthesis, transport, binding and decay of matrix components. Our observations could explain differences observed experimentally between various scaffold media. Modelling results are also used to predict the minimum chondrocyte seeding density required to produce functional cartilage. / In summary, we develop reaction-diffusion models for dispersing and settling populations for three biological applications. Numerical and analytical results provide an understanding of population-level behaviour. This thesis demonstrates that mathematical modelling of biological systems can further understanding of biological systems and help to answer questions posed by experimental research.

There are numerous techniques for improving the mixing of fuel and oxidant species. However, many of these methods cannot be applied to combustion systems due to material limitations. A means of mixing the reacting species without physically invading the flow stream is therefore desired. In this work, induced electromagnetic forces known as Lorentz forces are considered as a means of enhancing the combustion of co-flowing reactant streams. To evaluate the effect of various parameters on the mixing process, a non-dimensional description is derived and used to develop a numerical model. Numerical experiments are performed based on a three level Box-Behnken design in which the dimensionless Lorentz force parameter, Reynolds number, and Euler number are varied. The Lorentz force parameter has a large effect on the mixing process. The Reynolds number has a minor effect on mixing, and the Euler number has a negligible effect. Confirmation of these results through experimental work is needed. Approaches that could be used to verify these results experimentally are outlined, and the construction and testing of a burner suitable for further experiments on Lorentz mixing is described. / Graduation date: 1997

The main purpose of this research is to provide the commercial seafood industry of the Pacific Northwest information on preferences of restaurateurs, retailers, and wholesalers for whole albacore, low-value added albacore products (chunks, medallions, and steaks), albacore loins, and high-value added albacore products (hot smoked and lox). All of these products were categorized as non-traditional market forms of albacore products, except whole albacore. The empirical analysis was based on self explicated and conjoint analysis. The demand models for albacore products were estimated using weighted least squares. Profitability equations for albacore products were estimated using a two-limit Tobit model. From the self explicated section, it was found that the attributes of price, flavor, blood spots/bruising, and bleeding of whole albacore were considered highly important by respondents. From the conjoint analysis section, it was found that, as expected a priori, price had a statistical significant effect on the demand and profitability models for all albacore products. Other variables, such as location of the firm, type of firm, experience with tuna species, and ranking of albacore had statistical significant effects on the demand and profitability equations. Wholesalers, restaurateurs, and retailers agreed that quality is a major concern and will influence their preferences when purchasing albacore can products. Overall, the findings from this research provide guidance to the commercial seafood industry of the Pacific Northwest to enhance the markets for albacore products. / Graduation date: 1997

Time-domain models were developed to predict the response of a tethered buoy subject to hydrodynamic loadings. A coupled analysis of the interaction of a buoy and its mooring is included and three-dimensional response is assumed. External loadings include hydrodynamic forces, tethers tensions, wind loadings and the weight of both cable and buoy. System nonlinearities include, large rotational and translational motions, and non-conservative fluid loadings. The mooring problem is formulated as a nonlinear two-point-boundary-value-problem. The problem is then converted to a combine initial-value and boundary-value problem to a discrete boundary-value problem at particular time, using a Newmark-like difference formula. At each instant in time the nonlinear boundary-value problem is solved by direct integration and using a successive iterative algorithm, such that boundary conditions are always satisfied. Buoy equations of motion are derived by both a small angle assumption and a large angle assumption. The small angle formulation uses the Eulerian angle for rotational coordinates. Coupling between the buoy and cable is performed by adopting the buoy equations of motion as boundary conditions at one end for the mooring problem. The rotational coordinates for the large angle formulation are represented by Euler parameters. The large angle formulation is solved by a predictor-corrector type of time integration of buoy motions constrained by tether forces. Coupling between the buoy and moorings is then enforced through matching of the velocity of the tether attachment points on the buoy with velocity of the tether ends; the velocities of tether attachment points serve as boundary conditions for the various mooring cables attached. Multiple time steps are used to account for different sizes of integration time step required for stability of solution in the buoy and tether. Numerical examples are provided to contrast the validity and capability of the formulations and solution techniques. Responses of three types of buoy (sphere, spar and disc) are predicted by the present models and compared to results obtained by experiments. Application of the present model to solve a multi-leg/multi-point mooring system is also provided. / Graduation date: 1996

In this paper a partial least squares (PLS) approach to dynamic modelling with latent variables is proposed. Let Y be a matrix of manifest variables and H the matrix of the corresponding latent variables. And let H = BH+ε be a structural PLS model with a coefficient matrix B. Then this model can be made a dynamic one by substituting for B a matrix F = B + CL containing the lag operator L. Then the structural dynamic model H = FH+ε is formally estimated like an ordinary PLS model. In an exploratory way the model can be used for forecasting purposes. The procedure is being programmed in ISP.

The main topic of this thesis is how to combine model outputs from deterministic models with measurements from monitoring stations for air pollutants or other meteorological variables. We consider two different approaches to address this particular problem. The first approach is by using the Bayesian Melding (BM) model proposed by Fuentes and Raftery (2005). We successfully implement this model and conduct several simulation studies to examine the performance of this model in different scenarios. We also apply the melding model to the ozone data to show the importance of using the Bayesian melding model to calibrate the model outputs. That is, to adjust the model outputs for the prediction of measurements. Due to the Bayesian framework of the melding model, we can extend it to incorporate other components such as ensemble models, reversible jump MCMC for variable selection. However, the BM model is purely a spatial model and we generally have to deal with space-time dataset in practice. The deficiency of the BM approach leads us to a second approach, an alternative to the BM model, which is a linear mixed model (different from most linear mixed models, the random effects being spatially correlated) with temporally and spatially correlated residuals. We assume the spatial and temporal correlation are separable and use an AR process to model the temporal correlation. We also develop a multivariate version of this model. Both the melding model and linear mixed model are Bayesian hierarchical models, which can better estimate the uncertainties of the estimates and predictions.

A mathematical model of Limiting Dilution Analysis for two limiting parameters is presented and investigated. Limiting Dilution Analysis is a microbiological cell assay developed for immunological application. In the given case we deal with the interaction between B lymphocytes, macrophage derived factor and T-independent antigens. The state of the art is that quantitative statements are only possible if one cell type (in general the B cells) is limiting and all others are in excess present. The basis for this thesis is a set of experiments in which B cells and macrophage derived factor are limiting and all other involved cells and factors are in saturating amounts present. It is shown that so far presented suggestions on modeling Limiting Dilution Analysis for two limiting cell-types are not suitable for this problem. Further, a mathematical model based on data is presented and interpreted in immunological terms with the help of a set of partial differential equations. The basis for the interpretation of the model are changes in affinity and saturation effects, both not incorporated in the so far presented models of the assay. In particular the relevance of mathematical interpretation of this process for the identification of new concepts as the saturation effects is stressed. The model of partial differential equations is highly non-linear but offers the possibility of interpreting the highly interrelated processes apart from each other. / Graduation date: 1994

We consider two risk-averse financial agents who negotiate the price of an illiquid indivisible contingent claim in an incomplete semimartingale market environment. Under the assumption that the agents are exponential utility maximizers with non-traded random endowments, we provide necessary and sufficient conditions for the negotiation to be successful, i.e., for the trade to occur. We, also, study the asymptotic case where the size of the claim is small compared to the random endowments and give a full characterization in this case. We, then, study a partial-equilibrium problem for a bundle of divisible claims and establish its existence and uniqueness. A number of technical results on conditional indifference prices are provided. Finally, we generalize the notion of partial-equilibrium pricing in the case where the agents' risk preferences are modelled by convex capital requirements. / text