Mathematical modelling of LiFePO4 cathodes

LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. It has been the focus of considerable experimental and theoretical scrutiny in the past decade, resulting in LiFePO4 cathodes that perform well at high discharge rates. This scrutiny has raised several questions about the behaviour of LiFePO4 material during charge and discharge. In contrast to many other battery chemistries that intercalate homogeneously, LiFePO4 can phase-separate into highly and lowly lithiated phases, with intercalation proceeding by advancing an interface between these two phases. The main objective of this thesis is to construct mathematical models of LiFePO4 cathodes that can be validated against experimental discharge curves. This is in an attempt to understand some of the multi-scale dynamics of LiFePO4 cathodes that can be difficult to determine experimentally. The first section of this thesis constructs a three-scale mathematical model of LiFePO4 cathodes that uses a simple Stefan problem (which has been used previously in the literature) to describe the assumed phase-change. LiFePO4 crystals have been observed agglomerating in cathodes to form a porous collection of crystals and this morphology motivates the use of three size-scales in the model. The multi-scale model developed validates well against experimental data and this validated model is then used to examine the role of manufacturing parameters (including the agglomerate radius) on battery performance. The remainder of the thesis is concerned with investigating phase-field models as a replacement for the aforementioned Stefan problem. Phase-field models have recently been used in LiFePO4 and are a far more accurate representation of experimentally observed crystal-scale behaviour. They are based around the Cahn-Hilliard-reaction (CHR) IBVP, a fourth-order PDE with electrochemical (flux) boundary conditions that is very stiff and possesses multiple time and space scales. Numerical solutions to the CHR IBVP can be difficult to compute and hence a least-squares based Finite Volume Method (FVM) is developed for discretising both the full CHR IBVP and the more traditional Cahn-Hilliard IBVP. Phase-field models are subject to two main physicality constraints and the numerical scheme presented performs well under these constraints. This least-squares based FVM is then used to simulate the discharge of individual crystals of LiFePO4 in two dimensions. This discharge is subject to isotropic Li+ diffusion, based on experimental evidence that suggests the normally orthotropic transport of Li+ in LiFePO4 may become more isotropic in the presence of lattice defects. Numerical investigation shows that two-dimensional Li+ transport results in crystals that phase-separate, even at very high discharge rates. This is very different from results shown in the literature, where phase-separation in LiFePO4 crystals is suppressed during discharge with orthotropic Li+ transport. Finally, the three-scale cathodic model used at the beginning of the thesis is modified to simulate modern, high-rate LiFePO4 cathodes. High-rate cathodes typically do not contain (large) agglomerates and therefore a two-scale model is developed. The Stefan problem used previously is also replaced with the phase-field models examined in earlier chapters. The results from this model are then compared with experimental data and fit poorly, though a significant parameter regime could not be investigated numerically. Many-particle effects however, are evident in the simulated discharges, which match the conclusions of recent literature. These effects result in crystals that are subject to local currents very different from the discharge rate applied to the cathode, which impacts the phase-separating behaviour of the crystals and raises questions about the validity of using cathodic-scale experimental measurements in order to determine crystal-scale behaviour.

Modelling the flow of cane constituents through the milling process of a raw sugar factory

This thesis reports on an investigation to develop an advanced and comprehensive milling process model of the raw sugar factory. Although the new model can be applied to both, the four-roller and six-roller milling units, it is primarily developed for the six-roller mills which are widely used in the Australian sugar industry. The approach taken was to gain an understanding of the previous milling process simulation model "MILSIM" developed at the University of Queensland nearly four decades ago. Although the MILSIM model was widely adopted in the Australian sugar industry for simulating the milling process it did have some incorrect assumptions. The study aimed to eliminate all the incorrect assumptions of the previous model and develop an advanced model that represents the milling process correctly and tracks the flow of other cane components in the milling process which have not been considered in the previous models. The development of the milling process model was done is three stages. Firstly, an enhanced milling unit extraction model (MILEX) was developed to access the mill performance parameters and predict the extraction performance of the milling process. New definitions for the milling performance parameters were developed and a complete milling train along with the juice screen was modelled. The MILEX model was validated with factory data and the variation in the mill performance parameters was observed and studied. Some case studies were undertaken to study the effect of fibre in juice streams, juice in cush return and imbibition% fibre on extraction performance of the milling process. It was concluded from the study that the empirical relations developed for the mill performance parameters in the MILSIM model were not applicable to the new model. New empirical relations have to be developed before the model is applied with confidence. Secondly, a soluble and insoluble solids model was developed using modelling theory and experimental data to track the flow of sucrose (pol), reducing sugars (glucose and fructose), soluble ash, true fibre and mud solids entering the milling train through the cane supply and their distribution in juice and bagasse streams.. The soluble impurities and mud solids in cane affect the performance of the milling train and further processing of juice and bagasse. New mill performance parameters were developed in the model to track the flow of cane components. The developed model is the first of its kind and provides some additional insight regarding the flow of soluble and insoluble cane components and the factors affecting their distribution in juice and bagasse. The model proved to be a good extension to the MILEX model to study the overall performance of the milling train. Thirdly, the developed models were incorporated in a proprietary software package "SysCAD’ for advanced operational efficiency and for availability in the ‘whole of factory’ model. The MILEX model was developed in SysCAD software to represent a single milling unit. Eventually the entire milling train and the juice screen were developed in SysCAD using series of different controllers and features of the software. The models developed in SysCAD can be run from macro enabled excel file and reports can be generated in excel sheets. The flexibility of the software, ease of use and other advantages are described broadly in the relevant chapter. The MILEX model is developed in static mode and dynamic mode. The application of the dynamic mode of the model is still under progress.

Modelling bluetooth and fusing with loops

The invited presentation was delivered at Queensland Department of Main Roads, Brisbane Australia, 17th June 2013

Empirical modelling of the relationship between bus and car speeds on signalised urban networks

Vehicle speed is an important attribute for the utility of a transport mode. The speed relationship between multiple modes of transport is of interest to the traffic planners and operators. This paper quantifies the relationship between bus speed and average car speed by integrating Bluetooth data and Transit Signal Priority data from the urban network in Brisbane, Australia. The method proposed in this paper is the first of its kind to relate bus speed and average car speed by integrating multi-source traffic data in a corridor-based method. Three transferable regression models relating not-in-service bus; in-service bus during peak; and in-service bus during off peak periods with average car are proposed. The models are cross-validated and the interrelationships are significant

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.

Modelling users' contextual querying behaviour for web image searching

The rapid growth of visual information on Web has led to immense interest in multimedia information retrieval (MIR). While advancement in MIR systems has achieved some success in specific domains, particularly the content-based approaches, general Web users still struggle to find the images they want. Despite the success in content-based object recognition or concept extraction, the major problem in current Web image searching remains in the querying process. Since most online users only express their needs in semantic terms or objects, systems that utilize visual features (e.g., color or texture) to search images create a semantic gap which hinders general users from fully expressing their needs. In addition, query-by-example (QBE) retrieval imposes extra obstacles for exploratory search because users may not always have the representative image at hand or in mind when starting a search (i.e. the page zero problem). As a result, the majority of current online image search engines (e.g., Google, Yahoo, and Flickr) still primarily use textual queries to search. The problem with query-based retrieval systems is that they only capture users’ information need in terms of formal queries;; the implicit and abstract parts of users’ information needs are inevitably overlooked. Hence, users often struggle to formulate queries that best represent their needs, and some compromises have to be made. Studies of Web search logs suggest that multimedia searches are more difficult than textual Web searches, and Web image searching is the most difficult compared to video or audio searches. Hence, online users need to put in more effort when searching multimedia contents, especially for image searches. Most interactions in Web image searching occur during query reformulation. While log analysis provides intriguing views on how the majority of users search, their search needs or motivations are ultimately neglected. User studies on image searching have attempted to understand users’ search contexts in terms of users’ background (e.g., knowledge, profession, motivation for search and task types) and the search outcomes (e.g., use of retrieved images, search performance). However, these studies typically focused on particular domains with a selective group of professional users. General users’ Web image searching contexts and behaviors are little understood although they represent the majority of online image searching activities nowadays. We argue that only by understanding Web image users’ contexts can the current Web search engines further improve their usefulness and provide more efficient searches. In order to understand users’ search contexts, a user study was conducted based on university students’ Web image searching in News, Travel, and commercial Product domains. The three search domains were deliberately chosen to reflect image users’ interests in people, time, event, location, and objects. We investigated participants’ Web image searching behavior, with the focus on query reformulation and search strategies. Participants’ search contexts such as their search background, motivation for search, and search outcomes were gathered by questionnaires. The searching activity was recorded with participants’ think aloud data for analyzing significant search patterns. The relationships between participants’ search contexts and corresponding search strategies were discovered by Grounded Theory approach. Our key findings include the following aspects: - Effects of users' interactive intents on query reformulation patterns and search strategies - Effects of task domain on task specificity and task difficulty, as well as on some specific searching behaviors - Effects of searching experience on result expansion strategies A contextual image searching model was constructed based on these findings. The model helped us understand Web image searching from user perspective, and introduced a context-aware searching paradigm for current retrieval systems. A query recommendation tool was also developed to demonstrate how users’ query reformulation contexts can potentially contribute to more efficient searching.

Customer equity management : the impact of strategy drivers and customer data management on customer equity outcomes

This research contributes to the field of customer equity by examining how important the strategy drivers of consumption and customer data management are in contributing to the value of the customer asset. A mixed methods approach focused on one sector: the Australian accommodation hotels. From this research, a deeper understanding of how to theorise, conceptualise and practice customer equity management has been achieved.

Modelling busway station dwell time using smart cards

Dwell time at the busway station has a significant effect on bus capacity and delay. Dwell time has conventionally been estimated using models developed on the basis of field survey data. However field survey is resource and cost intensive, so dwell time estimation based on limited observations can be somewhat inaccurate. Most public transport systems are now equipped with Automatic Passenger Count (APC) and/or Automatic Fare Collection (AFC) systems. AFC in particular reduces on-board ticketing time, driver’s work load and ultimately reduces bus dwell time. AFC systems can record all passenger transactions providing transit agencies with access to vast quantities of data. AFC data provides transaction timestamps, however this information differs from dwell time because passengers may tag on or tag off at times other than when doors open and close. This research effort contended that models could be developed to reliably estimate dwell time distributions when measured distributions of transaction times are known. Development of the models required calibration and validation using field survey data of actual dwell times, and an appreciation of another component of transaction time being bus time in queue. This research develops models for a peak period and off peak period at a busway station on the South East Busway (SEB) in Brisbane, Australia.

Measurement, modelling and capacity analysis for novel, fixed multi-user single-antenna MIMO-OFDM system, in rural environments

High-speed broadband internet access is widely recognised as a catalyst to social and economic development. However, the provision of broadband Internet services with the existing solutions to rural population, scattered over an extensive geographical area, remains both an economic and technical challenge. As a feasible solution, the Commonwealth Scientific and Industrial Research Organization (CSIRO) proposed a highly spectrally efficient, innovative and cost-effective fixed wireless broadband access technology, which uses analogue TV frequency spectrum and Multi-User MIMO (MUMIMO) technology with Orthogonal-Frequency-Division-Multiplexing (OFDM). MIMO systems have emerged as a promising solution for the increasing demand of higher data rates, better quality of service, and higher network capacity. However, the performance of MIMO systems can be significantly affected by different types of propagation environments e.g., indoor, outdoor urban, or outdoor rural and operating frequencies. For instance, large spectral efficiencies associated with MIMO systems, which assume a rich scattering environment in urban environments, may not be valid for all propagation environments, such as outdoor rural environments, due to the presence of less scatterer densities. Since this is the first time a MU-MIMO-OFDM fixed broadband wireless access solution is deployed in a rural environment, questions from both theoretical and practical standpoints arise; For example, what capacity gains are available for the proposed solution under realistic rural propagation conditions?. Currently, no comprehensive channel measurement and capacity analysis results are available for MU-MIMO-OFDM fixed broadband wireless access systems which employ large scale multiple antennas at the Access Point (AP) and analogue TV frequency spectrum in rural environments. Moreover, according to the literature, no deterministic MU-MIMO channel models exist that define rural wireless channels by accounting for terrain effects. This thesis fills the aforementioned knowledge gaps with channel measurements, channel modeling and comprehensive capacity analysis for MU-MIMO-OFDM fixed wireless broadband access systems in rural environments. For the first time, channel measurements were conducted in a rural farmland near Smithton, Tasmania using CSIRO's broadband wireless access solution. A novel deterministic MU-MIMO-OFDM channel model, which can be used for accurate performance prediction of rural MUMIMO channels with dominant Line-of-Sight (LoS) paths, was developed under this research. Results show that the proposed solution can achieve 43.7 bits/s/Hz at a Signal-to- Noise Ratio (SNR) of 20 dB in rural environments. Based on channel measurement results, this thesis verifies that the deterministic channel model accurately predicts channel capacity in rural environments with a Root Mean Square (RMS) error of 0.18 bits/s/Hz. Moreover, this study presents a comprehensive capacity analysis of rural MU-MIMOOFDM channels using experimental, simulated and theoretical models. Based on the validated deterministic model, further investigations on channel capacity and the eects of capacity variation, with different user distribution angles (θ) around the AP, were analysed. For instance, when SNR = 20dB, the capacity increases from 15.5 bits/s/Hz to 43.7 bits/s/Hz as θ increases from 10° to 360°. Strategies to mitigate these capacity degradation effects are also presented by employing a suitable user grouping method. Outcomes of this thesis have already been used by CSIRO scientists to determine optimum user distribution angles around the AP, and are of great significance for researchers and MU-MUMO-OFDM system developers to understand the advantages and potential capacity gains of MU-MIMO systems in rural environments. Also, results of this study are useful to further improve the performance of MU-MIMO-OFDM systems in rural environments. Ultimately, this knowledge contribution will be useful in delivering efficient, cost-effective high-speed wireless broadband systems that are tailor-made for rural environments, thus, improving the quality of life and economic prosperity of rural populations.

Spatio-temporal modelling of ultrafine particle number concentration

This thesis developed semi-parametric regression models for estimating the spatio-temporal distribution of outdoor airborne ultrafine particle number concentration (PNC). The models developed incorporate multivariate penalised splines and random walks and autoregressive errors in order to estimate non-linear functions of space, time and other covariates. The models were applied to data from the "Ultrafine Particles from Traffic Emissions and Child" project in Brisbane, Australia, and to longitudinal measurements of air quality in Helsinki, Finland. The spline and random walk aspects of the models reveal how the daily trend in PNC changes over the year in Helsinki and the similarities and differences in the daily and weekly trends across multiple primary schools in Brisbane. Midday peaks in PNC in Brisbane locations are attributed to new particle formation events at the Port of Brisbane and Brisbane Airport.

Towards modelling web search behaviour : integrating users’ cognitive styles

With the rapid growth of information on the Web, the study of information searching has let to an increased interest. Information behaviour (IB) researchers and information systems (IS) developers are continuously exploring user - Web search interactions to understand and to help users to provide assistance with their information searching. In attempting to develop models of IB, several studies have identified various factors that govern user's information searching and information retrieval (IR), such as age, gender, prior knowledge and task complexity. However, how users' contextual factors, such as cognitive styles, affect Web search interactions has not been clearly explained by the current models of Web Searching and IR. This study explores the influence of users' cognitive styles on their Web search behaviour. The main goal of the study is to enhance Web search models with a better understanding of how these cognitive styles affect Web searching. Modelling Web search behaviour with a greater understanding of user's cognitive styles can help information science researchers and IS designers to bridge the semantic gap between the user and the IS. To achieve the aims of the study, a user study with 50 participants was conducted. The study adopted a mixed method approach incorporating several data collection strategies to gather a range of qualitative and quantitative data. The study utilised pre-search and post-search questionnaires to collect the participants' demographic information and their level of satisfaction about the search interactions. Riding's (1991) Cognitive Style Analysis (CSA) test was used to assess the participants' cognitive styles. Participants completed three predesigned search tasks and the whole user - web search interactions, including thinkaloud, were captured using a monitoring program. Data analysis involved several qualitative and quantitative techniques: the quantitative data gave raise to detailed findings about users' Web searching and cognitive styles, the qualitative data enriched the findings with illustrative examples. The study results provide valuable insights into Web searching behaviour among different cognitive style users. The findings of the study extend our understanding of Web search behaviour and how users search information on the Web. Three key study findings emerged: • Users' Web search behaviour was demonstrated through information searching strategies, Web navigation styles, query reformulation behaviour and information processing approaches while performing Web searches. The manner in which these Web search patterns were demonstrated varied among the users with different cognitive style groups. • Users' cognitive styles influenced their information searching strategies, query reformulation behaviour, Web navigational styles and information processing approaches. Users with particular cognitive styles followed certain Web search patterns. • Fundamental relationships were evident between users' cognitive styles and their Web search behaviours; and these relationships can be illustrated through modelling Web search behaviour. Two models that depict the associations between Web search interactions, user characteristics and users' cognitive styles were developed. These models provide a greater understanding of Web search behaviour from the user perspective, particularly how users' cognitive styles influence their Web search behaviour. The significance of this research is twofold: it will provide insights for information science researchers, information system designers, academics, educators, trainers and librarians who want to better understand how users with different cognitive styles perform information searching on the Web; at the same time, it will provide assistance and support to the users. The major outcomes of this study are 1) a comprehensive analysis of how users search the Web; 2) extensive discussion on the implications of the models developed in this study for future work; and 3) a theoretical framework to bridge high-level search models and cognitive models.

Rating for sustainable subdivision neighbourhood design (RSSND) : case of Bangkok metropolitan region (BMR), Thailand an eco-efficiency modelling approach

Bangkok Metropolitan Region (BMR) is the centre for various major activities in Thailand including political, industry, agriculture, and commerce. Consequently, the BMR is the highest and most densely populated area in Thailand. Thus, the demand for houses in the BMR is also the largest, especially in subdivision developments. For these reasons, the subdivision development in the BMR has increased substantially in the past 20 years and generated large numbers of subdivision developments (AREA, 2009; Kridakorn Na Ayutthaya & Tochaiwat, 2010). However, this dramatic growth of subdivision development has caused several problems including unsustainable development, especially for subdivision neighbourhoods, in the BMR. There have been rating tools that encourage the sustainability of neighbourhood design in subdivision development, but they still have practical problems. Such rating tools do not cover the scale of the development entirely; and they concentrate more on the social and environmental conservation aspects, which have not been totally accepted by the developers (Boonprakub, 2011; Tongcumpou & Harvey, 1994). These factors strongly confirm the need for an appropriate rating tool for sustainable subdivision neighbourhood design in the BMR. To improve level of acceptance from all stakeholders in subdivision developments industry, the new rating tool should be developed based on an approach that unites the social, environmental, and economic approaches, such as eco-efficiency principle. Eco-efficiency is the sustainability indicator introduced by the World Business Council for Sustainable Development (WBCSD) since 1992. The eco-efficiency is defined as the ratio of the product or service value according to its environmental impact (Lehni & Pepper, 2000; Sorvari et al., 2009). Eco-efficiency indicator is concerned to the business, while simultaneously, is concerned with to social and the environment impact. This study aims to develop a new rating tool named "Rating for sustainable subdivision neighbourhood design (RSSND)". The RSSND methodology is developed by a combination of literature reviews, field surveys, the eco-efficiency model development, trial-and-error technique, and the tool validation process. All required data has been collected by the field surveys from July to November 2010. The ecoefficiency model is a combination of three different mathematical models; the neighbourhood property price (NPP) model, the neighbourhood development cost (NDC) model, and the neighbourhood occupancy cost (NOC) model which are attributable to the neighbourhood subdivision design. The NPP model is formulated by hedonic price model approach, while the NDC model and NOC model are formulated by the multiple regression analysis approach. The trial-and-error technique is adopted for simplifying the complex mathematic eco-efficiency model to a user-friendly rating tool format. Credibility of the RSSND has been validated by using both rated and non-rated of eight subdivisions. It is expected to meet the requirements of all stakeholders which support the social activities of the residents, maintain the environmental condition of the development and surrounding areas, and meet the economic requirements of the developers.

A Bayesian network approach to modelling temporal behaviour of Lyngbya majuscula bloom initiation

Lyngbya majuscula is a cyanobacterium (blue-green algae) occurring naturally in tropical and subtropical coastal areas worldwide. Deception Bay, in Northern Moreton Bay, Queensland, has a history of Lyngbya blooms, and forms a case study for this investigation. The South East Queensland (SEQ) Healthy Waterways Partnership, collaboration between government, industry, research and the community, was formed to address issues affecting the health of the river catchments and waterways of South East Queensland. The Partnership coordinated the Lyngbya Research and Management Program (2005-2007) which culminated in a Coastal Algal Blooms (CAB) Action Plan for harmful and nuisance algal blooms, such as Lyngbya majuscula. This first phase of the project was predominantly of a scientific nature and also facilitated the collection of additional data to better understand Lyngbya blooms. The second phase of this project, SEQ Healthy Waterways Strategy 2007-2012, is now underway to implement the CAB Action Plan and as such is more management focussed. As part of the first phase of the project, a Science model for the initiation of a Lyngbya bloom was built using Bayesian Networks (BN). The structure of the Science Bayesian Network was built by the Lyngbya Science Working Group (LSWG) which was drawn from diverse disciplines. The BN was then quantified with annual data and expert knowledge. Scenario testing confirmed the expected temporal nature of bloom initiation and it was recommended that the next version of the BN be extended to take this into account. Elicitation for this BN thus occurred at three levels: design, quantification and verification. The first level involved construction of the conceptual model itself, definition of the nodes within the model and identification of sources of information to quantify the nodes. The second level included elicitation of expert opinion and representation of this information in a form suitable for inclusion in the BN. The third and final level concerned the specification of scenarios used to verify the model. The second phase of the project provides the opportunity to update the network with the newly collected detailed data obtained during the previous phase of the project. Specifically the temporal nature of Lyngbya blooms is of interest. Management efforts need to be directed to the most vulnerable periods to bloom initiation in the Bay. To model the temporal aspects of Lyngbya we are using Object Oriented Bayesian networks (OOBN) to create ‘time slices’ for each of the periods of interest during the summer. OOBNs provide a framework to simplify knowledge representation and facilitate reuse of nodes and network fragments. An OOBN is more hierarchical than a traditional BN with any sub-network able to contain other sub-networks. Connectivity between OOBNs is an important feature and allows information flow between the time slices. This study demonstrates more sophisticated use of expert information within Bayesian networks, which combine expert knowledge with data (categorized using expert-defined thresholds) within an expert-defined model structure. Based on the results from the verification process the experts are able to target areas requiring greater precision and those exhibiting temporal behaviour. The time slices incorporate the data for that time period for each of the temporal nodes (instead of using the annual data from the previous static Science BN) and include lag effects to allow the effect from one time slice to flow to the next time slice. We demonstrate a concurrent steady increase in the probability of initiation of a Lyngbya bloom and conclude that the inclusion of temporal aspects in the BN model is consistent with the perceptions of Lyngbya behaviour held by the stakeholders. This extended model provides a more accurate representation of the increased risk of algal blooms in the summer months and show that the opinions elicited to inform a static BN can be readily extended to a dynamic OOBN, providing more comprehensive information for decision makers.

Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies

Background The expansion of cell colonies is driven by a delicate balance of several mechanisms including cell motility, cell-to-cell adhesion and cell proliferation. New approaches that can be used to independently identify and quantify the role of each mechanism will help us understand how each mechanism contributes to the expansion process. Standard mathematical modelling approaches to describe such cell colony expansion typically neglect cell-to-cell adhesion, despite the fact that cell-to-cell adhesion is thought to play an important role. Results We use a combined experimental and mathematical modelling approach to determine the cell diffusivity, D, cell-to-cell adhesion strength, q, and cell proliferation rate, ?, in an expanding colony of MM127 melanoma cells. Using a circular barrier assay, we extract several types of experimental data and use a mathematical model to independently estimate D, q and ?. In our first set of experiments, we suppress cell proliferation and analyse three different types of data to estimate D and q. We find that standard types of data, such as the area enclosed by the leading edge of the expanding colony and more detailed cell density profiles throughout the expanding colony, does not provide sufficient information to uniquely identify D and q. We find that additional data relating to the degree of cell-to-cell clustering is required to provide independent estimates of q, and in turn D. In our second set of experiments, where proliferation is not suppressed, we use data describing temporal changes in cell density to determine the cell proliferation rate. In summary, we find that our experiments are best described using the range D = 161 - 243 ?m2 hour-1, q = 0.3 - 0.5 (low to moderate strength) and ? = 0.0305 - 0.0398 hour-1, and with these parameters we can accurately predict the temporal variations in the spatial extent and cell density profile throughout the expanding melanoma cell colony. Conclusions Our systematic approach to identify the cell diffusivity, cell-to-cell adhesion strength and cell proliferation rate highlights the importance of integrating multiple types of data to accurately quantify the factors influencing the spatial expansion of melanoma cell colonies.

Mathematical modelling of counter flow v-grove solar air collector

Double-pass counter flow v-grove collector is considered one of the most efficient solar air-collectors. In this design of the collector, the inlet air initially flows at the top part of the collector and changes direction once it reaches the end of the collector and flows below the collector to the outlet. A mathematical model is developed for this type of collector and simulation is carried out using MATLAB programme. The simulation results were verified with three distinguished research results and it was found that the simulation has the ability to predict the performance of the air collector accurately as proven by the comparison of experimental data with simulation. The difference between the predicted and experimental results is, at maximum, approximately 7% which is within the acceptable limit considering some uncertainties in the input parameter values to allow comparison. A parametric study was performed and it was found that solar radiation, inlet air temperature, flow rate and length have a significant effect on the efficiency of the air collector. Additionally, the results are compared with single flow V-groove collector.