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Publication Open Access An extension to the theory of steady selective withdrawal for a two layer fluid(Lincoln University. Applied Computing, Mathematics and Statistics Group., 2000-05) Wood, Ian R; Choo, KennethMost reservoirs contain stratified fluid and selective withdrawal is used to obtain water of the desired properties. Initially we review the case with an infinite upper layer with a sharp interface. When the total discharge is specified, then the ratio of the discharge from each layer is determined by the criteria of smoothness at the virtual control (i.e. the critical point). At this point, the long wave velocity on the interface is zero. For the case when the upper layer depth is large, we show that the control is in the valve and the virtual control (which determines the ratio of the discharge in each layer) moves further from the source as the total discharge increases. When there is a finite upper layer, a portion of the flow is in the duct and a portion of the flow is in the free surface. We derive the criteria for the virtual control in the free surface flow and show that the duct control occurs first. If we then assume that the flow is not over-specified, we determine the necessary conditions for a smooth transition between the duct and the free surface flow. This enables us to determine the minimum ratio of the upper layer depth to the lower layer depth for the steady duct solution to be valid. This contrasts with the conclusions of Bryant and Wood (1976).Publication Open Access Solute dispersion by 1D stepped velocity fluctuations(Lincoln University. Applied Computing, Mathematics and Statistics Group., 2003) Verwoerd, W; Kulasiri, DonThe effect of fluctuations in the drift velocity on dispersion by a porous medium is investigated. An analytical model is developed which represents the effect of a single discrete step in the velocity of a 1 dimensional flow as a multiplicative factor that modifies the underlying linear growth in solute variance predicted by the standard advection-dispersion equation. The algebraic structure of the model identifies two variable combinations ∆ and α that characterize the step and the rate of stochastic dispersion respectively, in terms of which a simple formula for the downstream effect of the step on dispersion is obtained. This formalism is next applied to a sequence of 3 steps representing a velocity fluctuation, and it is shown that while kinetic compression effects cancel out across such a fluctuation, the stochastic dispersion increases for any plausible combination of ∆ and α. This implies that a dispersion enhancement factor ƒ is associated with a fluctuation, and a simple formula is obtained for this in terms of variables that describe the fluctuation length and amplitude. Moreover, the algebra leads to the definition of a natural length scale Λ related to the Peelet number of the flow. Repeated application of this formula is used to find the cumulative dispersion enhancement by a sequence of identical fluctuations, leading to an expression for dispersivity as a function of the distance traversed by a solute plume. Key features of the model are that the dispersivity behaves differently for traversal lengths above and below Λ, and that above this transition it is proportional to a fractional power of the traversal length. These features are in agreement with experimental observation of scale-dependent dispersivity, but quantitatively the observed growth in dispersivity over several orders of magnitude is not obtained for any reasonable choice of parameter values.Publication Open Access Scale-dependent dispersivity: a velocity fluctuation model(Applied Management and Computing Division, 2003-08) Verwoerd, Wynand S.In the previous paper, (03/2001) it was shown that the cumulative effect of multiple one-dimensional velocity fluctuations can explain qualitative features of the observed scale dependent dispersivity in natural aquifers, but not the magnitude of the effect. It is plausible that in real systems the enhancement of dispersion caused by a single fluctuation may be larger than that derived for the 1 dimensional stepped fluctuation, because for example there are additional enhancement mechanisms in 2 and 3 dimensional systems. However this paper shows that to achieve the observed magnitude, it is not enough to increase the size of enhancement factor but in addition the rate at which the effect of a single fluctuation changes with fluctuation length and with position along the fluctuation sequence need to be modified. Several variations are explored. Simple assumptions are shown to lead to dispersivity formulas in terms of purely algebraic power laws, while more elaborate assumptions yield expressions that are still analytic but contain non-elementary functions. In either case it is possible to find the required variation of the dispersivity over 3 or more orders of magnitude and with curve shapes that are consistent with historical observations. Moreover, this is achieved with plausible parameter values, leading for example to the conjecture that in the observed systems the porous medium could not have been homogeneous on a scale of more than centimeters. The model presented is schematic in the sense that it contains some detail assumptions not derived from first principles, but is believed to capture the essentials of the mechanism that causes scale dependent dispersivity. It sets some boundaries for viable detail models, but within those boundaries the final predictions are not very sensitive to the detail assumptions. A key merit of the treatment is that it identifies crucial variables that need to be measured or controlled in experimental studies.Publication Open Access Determination of fat content in retail ready meat samples using image analysis(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2003-08) Chandraratne, Meegalla R.; Samarasinghe, Sandhya; Kulasiri, Gamalathge D.; Isherwood, Peter; Bekhit, A. E. D.; Bickerstaffe, RoyAs a result of constantly growing consumer expectations for meat quality, the meat industry is placing more and more emphasis on quality assurance issues. Fat content in meat influences some important meat quality parameters and meat marketability. Visible fat includes marbling (intramuscular) and intermuscular fat. Chemical analysis is currently used to determine the fat percentage in meat. However, this is a tedious, expensive and time-consuming method. Some measurements, like the number, size distribution and spatial distribution of marbling, are totally impossible by chemical analysis. For the meat industry, it is very useful to have an accurate, reliable, cost effective, fast and nondestructive technique to determine the fat content. Computer vision has enormous potential for evaluating meat quality because image processing and analysis techniques can quantitatively and consistently characterize complex geometric, colour and textural properties. The objectives of the present study were: a) to apply image processing techniques to quantify fat content of beef and lamb steaks; b) to develop a relationship between the chemical fat content and the fat content measured by image analysis.Publication Open Access Constrained visualization using the Shepard Interpolation Family(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2003-12) Brodlie, K. W.; Asim, M. R.; Unsworth, KeithThis paper discusses the problem of visualizing data where there are underlying constraints that must be preserved. For example, we may know that the data is inherently positive. We show how the Modified Quadratic Shepard method, which interpolates scattered data of any dimensionality, can be constrained to preserve positivity. We do this by forcing the quadratic basis functions to be positive. The method can be extended to handle other types of contraints, including lower bound of 0 and upper bound of 1, as occurs with fractional data. A further extension allows general range restrictions, creating an interpolant that lies between any two specified functions as the lower and upper bounds.Publication Open Access Cellular lines: an introduction(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2003) Geer, P.; McLaughlin, H.; Unsworth, KeithThis paper provides a definition of a cellular line in a cellular array. It also presents a way of determining whether or not a cell set is a cellular line. Brief statements about existence, uniqueness, and properties of cellular lines are included.Publication Open Access An investigation of differences in mature and younger student's use of a computer-based learning package(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2002-12) Abell, Walter L.; Gilmore, Helen M.; McLennan, Theresa J.; Sedcole, John R.Older or ""mature"" students are becoming a larger proportion of the student population in tertiary education. This study looked at the difference between mature and younger students' use of, and attitudes towards, a Computer Based Learning (CBL) package used in a first year Economics class. Surveys, interviews and automatic recording of package use were used to gather data. It was found that the mature students made significantly more use of the package than the younger students. Other interesting results included the pattern of use and the way the two groups viewed the package. The results have implications for the provision of CBL material for both groups.Publication Open Access Exploration of behaviour of a stochastic transport model using computational experiments(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2002-04) Rajanayaka, Channa N.; Kulasiri, DonFickian assumptions are used in deriving the advection-dispersion equation which models the solute transport in porous media. The hydrodynamic dispersion coefficient defined as a result of these assumptions has been found to be scale dependent. Kulasiri and Verwoerd [1999] developed a stochastic computational model for solute transport in saturated porous media without using Fickian assumptions. The model consists of two main parameters; correlation length and variance, and the velocity of solute was assumed as a fundamental stochastic variable. In this paper, the stochastic model was investigated to understand its behaviour. As the statistical nature of the model changes with the parameters, the computational solution of the model was explored in relation to the parameters. The variance is found to be the dominant parameter, however, there is a correlation between two parameters and they influence the stochasticity of the flow in a complex manner. We hypothesised that the variance is inversely proportional to the pore size and the correlation length represents the geometry of flow. The computational results of different scales show that the hypotheses are reasonable. The model illustrates that it could capture the scale dependence of dispersivity and mimic the advection-dispersion equation in more deterministic situations.Publication Open Access A hybrid artificial neural networks approach to solve the inverse problem in advection-dispersion models(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2002-04) Rajanayaka, Channa N.; Samarasinghe, Sandhya; Kulasiri, D.Publication Open Access Scale dependent solute dispersion in porous media(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2003-01) Rajanayaka, Channa N.; Kulasiri, DonScale dependency of solute dispersion in porous media is one of the major striking issues in simulating larger scale aquifers. There are numerous studies dedicated to development of the simulation models that represent heterogeneous real world aquifers. In this paper we investigated the ability of a stochastic solute transport model (SSTM) of capturing the scale dependency. Initially, flow profiles were visually compared for different flow lengths. Then a stochastic inverse method was used to estimate the corresponding dispersion coefficient (D) for each parameter combination of the stochastic model. The results reveal that SSTM is capable of simulating the scale effect of solute dispersion, and to some extent, they agree with the past literature. Dispersivity increases with the smaller flow lengths, and the rate of increase decreases and tends to reach an asymptotic value for larger scales for similar parameters of SSTM.Publication Open Access Dynamic modelling of pest control using a pesticide(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2003-08) Verwoerd, Wynand; Nguyen, LKA general differential equation model of the temporal evolution of a pest population density when subjected to control measures using a pesticide, is investigated. The model is based on logistic growth combined with population dispersal described by diffusion, and pesticide action is characterised by its LD90 toxicity measure and a consumption limited by a saturation pesticide density. Solutions are found for a number of assumed scenarios concerning the initial pest distribution and pesticide application strategy. Criteria are established for pesticide toxicity and application density to ensure eradication, and the efficiency of the strategies investigated are compared with regard to total pesticide consumption. It is shown that rather general conclusions can be reached, such as that it is inevitable that a pesticide residue is left after full eradication has been accomplished.Publication Open Access Study of fracture properties of wood using high-speed video imaging and neural networks(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2002-04) Samarasinghe, Sandhya; Kulasiri, D.In this study, the Duration of Load (DOL) for crack initiation and propagation, crack speed, and load carrying capacity were investigated for three Rates of Loading (ROL) and four sizes of notched wood beams using high-speed video imaging and neural networks. For the smallest ROL, there was a distinct volume effect on DOL to initiation which was almost inhibited at the largest ROL. The DOL for crack propagation for all volumes appeared to be random. The crack propagation was a wave phenomenon with positive and negative speeds that varied with the rate of loading. The study showed that the crack initiation load, peak load, and their respective gross stresses were independent of ROL but were nonlinealry correlated with volume and the smallest volume maintained the highest stress. The stresses followed the Weibull's weakest link theory. Artificial Neural Networks (ANN) revealed meaningful trends for the combined effect of physical and geometric variables on the loads and stresses. Fracture toughness was insensitive to ROL and realtively constant for the three larger volumes. However, the smallest size produced the largest fracture toughness, which was explained by a neural network model that showed that the width had the greatest influence on fracture toughness highlighting plane stress conditions. The study showed the usefulness of ANN for analyzing interaction among many variables affecting wood fracture behaviour and their potential to become reliable predictors of load carrying capacity including maximum load and stress and fracture toughness under the uncertain influence of these variables.Publication Open Access On modelling drying of porous materials: analytical solutions to coupled partial differential equations governing heat and moisture transfer(Lincoln University. Applied Computing, Mathematics and Statistics Group., 2002-04) Kulasiri, Don; Koloszar, Jozsef; Woodhead, Ian M.Luikov theory of heat and mass transfer provides a framework to model drying of porous materials. The coupled partial differential equations governing the moisture and heat transfer can be solved using numerical techniques, and in this paper, we solve them analytically in a setting suitable for industrial drying situations. We discuss the nature of the solutions using the property values of pine wood. It is shown that the temperature gradients playa significant role in deciding the moisture profiles within the material when thickness is large, and the models based only on moisture potential gradients may not be sufficient to explain the drying phenomena in moist porous materials.Publication Open Access Solute dispersion in porous flow with a constant velocity gradient(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2002-04) Verwoerd, Wynand S.; Kulasiri, D.In a previous paper, we have shown that stepwise changes in the macroscopic flow velocity of a carrier fluid through a porous medium, substantially affects the dispersion of solutes that it carries. This paper extends the work to the case of a continuously changing flow velocity. The stochastic model used to describe pore deflection of the flow path, is reduced by the use of Dynkin' s formula to the formulation of a deterministic differential equation. An exact solution is found for the case of a flow velocity that varies linearly with position, and the resulting integral equation for the solute probability distribution is also solved exactly. This is applied to the case of a solute concentration plume represented by an initially Gaussian concentration peak. The modulated Gaussian that is calculated shows that the time evolution of the plume differs fundamentally from that predicted by the standard diffusive model. Implications of this conclusion for modelling dispersion in a variable flow velocity are further explored.Publication Open Access From conceptual model to end user implementation(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2001-10) Churcher, Clare; McLennan, Theresa; McKinnon, Alan E.For a number of reasons many users are responsible for the implementation and maintenance of their own databases. While they may have the technical skills to set up data repositories, many end users lack the analysis skills to design a conceptual model which accurately reflects the subtleties and complexities of their requirements. In this paper we discuss why it is important for end users to obtain help in developing a full conceptual model of their data. We propose a number of ways to capture the most essential aspects of the model to produce a simplified design that an end user can be reasonably confident of implementing and using accurately. We discuss how the simplifications may impact on the final application. Our simplification methods are illustrated with an example of a scientific database and we also show how to represent the simplified model in both a database and a spreadsheet.Publication Open Access The effects of variable flow velocity on contaminant dispersion in porous flow(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2001-07) Verwoerd, Wynand S.; Kulasiri, D.The diffusion-like behaviour of contaminant dispersion that underlies the commonly used advection-dispersion equation (ADE), has been shown by the authors to follow rigorously from a model that uses stochastic displacements to represent porous flow in a homogenous medium. This paper extends the model, as in a realistic aquifer the velocity will vary due to flow geometry and inhomogeneity of the medium. An integral formulation of the solute mass conservation law involving the probability distribution of fluid elements is presented. This is first applied to several numerical examples involving transmission of a gaussian contaminant plume through discrete velocity steps. A net increase in dispersion is found even when the average velocity is maintained. This is the result of the interaction of kinematic effects and dispersion. Some results from an analytical calculation are also presented, which show that the effects of a velocity step decay away from the step location. This leads to an expression for a scaling length, and the conclusion that dispersion is only sensitive to velocity fluctuations on a similar length scale as that of the dispersion itself.Publication Open Access Investigation of a stochastic inverse method to estimate parameters in groundwater models(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2001-07) Rajanayaka, Channa N.; Kulasiri, DonNatural systems are heterogeneous and they contain noise due to random inputs, irregular varying coefficients and fluctuations in boundary conditions. In this paper, we model the behaviour of natural systems using stochastic differential equations, present a parameter estimation procedure for such models in a general setting, and extend it to simple groundwater models. The applications to groundwater models are within the context of one dimensional solute transport problem to estimate parameters for two governing equations, one consisting of a single parameter and other of two parameters. The results of this inverse methodology are reliable in the presence of noise. However, the investigation of solute transport parameter estimates shows an inverse relationship to the noise level. The main advantage of the estimation methodology presented here is its direct dependence on field observations of state variables of natural systems in the presence of uncertainty.Publication Open Access Discrete lines and ant algorithms(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2001-03) Geer, P.; McLaughlin, H. W.; Unsworth, KeithThis is a report on work in progress. The focus is on the design of an algorithm used to construct discrete lines. It is intended that this is the first step in applying models of complex adaptive systems to more complex geometric constructs. We construct discrete lines using agents (virtual ants) The agents are given very few rules, and otherwise move freely. With this design we allow a particular line to emerge from the movement of the agents rather than model the line first and then display it.Publication Open Access Cache visualization techniques for exploring the performance of a distributed system(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2000-12) McKinnon, Alan E.; Cochrane, Mike; Churcher, Clare; Jarquin, RogerThe cache management of a distributed system has a significant effect on the performance of an application. This paper presents some exploratory visualizations of cache data from an object-oriented distributed processing system. The visualizations are aimed at helping a developer understand the operation of the cache and how that affects the performance of an application.Publication Open Access A decision support system for determining newspaper press layout configurations(Lincoln University. Applied Computing, Mathematics and Statistics Group, 2000-12) Prachuabmoh, Parames; Churcher, Clare; McKinnon, Alan E.In recent years, the demand for colour in newspaper production has increased considerably as newspaper readers and advertisers expect more extensive use of colour in the illustration of papers. A newspaper printing press consists of many different physical components. The way that these are set up, a newspaper press layout configuration, determines the attributes of the newspaper: paper size, number of sections, section sizes, and the position of colour pages. The number of possible newspaper press layout configurations is very large and to determine a press layout configuration to match a specific newspaper requirement is a very complex procedure. This report summarises how the newspaper layout configuration affects the attributes of a newspaper and describes two applications Threading and Layout, which have been developed as decision support tools to generate all possible newspaper layout configurations.