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Mathematical modelling of riots and protests is now becoming a powerful tool in providing a better understanding of dynamics of social unrest with the eventual goal to ensure a sustainable development of the human society. Currently, however, most of the existing studies in the considered research area are based on either non-spatial or spatially implicit models, whereas in a large number of cases dynamics of social protests clearly exhibit spatial heterogeneity. To bridge the existing gap, here we explore spatial-temporal patterns of social protests using a reaction-diffusion modelling framework. Our model variables are: the number of protesters and the cumulative amount of damage made as an outcome of the protest. The system has been studied analytically as well as by means of extensive numerical simulation in one dimensional and two-dimensional space. We show that the proposed model exhibits a variety of dynamical regimes including stationary patterns with round hot spots as well as complex labyrinthine-like structures. The system also predicts the various types propagating waves of protests with regular and irregular fronts as well as a patchy spread, where protests spread in space via irregular motion and interaction of separate patches of high numbers of protestors without formation of any continuous front, the number of protestors between patches being nearly zero. We reveal the structure of the model's parameter space, identifying the range of key parameters for which particular dynamical regimes are possible. Along with reaction-diffusion model, considering continuous space, we also consider the model of protests on discrete networks of different nature. We find that Turing instability can lead to pattern formation on networks, which opens up an exciting possibility to explore it as a generation mechanism in a large number of social unrest contexts. The networkbased model also shows a variety of non-Turing patterns including both stationary and non-stationary complex dynamics, where different nodes behave differently. Finally, we consider a realistic network to model the yellow vests movement in France.

Microglia, a type of glial cell, perform many tasks while interacting with neurons, astrocytes, and oligodendrocytes. Despite moderate advances in the characterisation of microglia in laboratory rodents, very little information is known about the physiology of microglia in the human brain. This is a challenging task and consequently this thesis attempts to advance knowledge of microglia function through mathematical modelling. Microglia restructure their intracellular actin cytoskeleton to enable motility; this requires a complex molecular cascade involving a set of ionic channels, membrane-coupled receptors, and cytosolic components. In this research, we develop a theoretical foundation for studying P2-mediated calcium and PI3K/Akt signalling in human microglial cells. Firstly, a detailed mathematical model is built for the dynamics of human P2XRs in microglia. Subsequently, experimental whole-cell currents are used to derive the P2X-mediated electrophysiology of human microglia (sodium and calcium dynamics, and membrane potential). Secondly, microglial-directed motility involves a complex family of intracellular signalling pathways that are mainly controlled by P2Y-mediated cytosolic calcium (Ca2+) signalling and activation of the PI3K/Akt pathway. This thesis addresses the development of mathematical models for these two complex aspects of microglial functions and investigates the interconnecting role of PI3K pathway to Ca2+. Our predictions reveal new quantitative insights into how P2Rs regulate ionic concentrations in terms of physiological interactions and transient responses. Simulation results show that kink-like, intricate Ca2+ responses mediated by P2XRs arise from a complex cooperative activation of both P2XRs, and ionic extruders and pumps. More importantly, the proposed model supports our hypothesis that calcium influx via P2YR and P2XR can explain the experimentally observed twin peaks in the phosphorylated Akt. To the best of our knowledge, this is the first biophysical model that aims to predict complicated Akt and P2-mediated Ca2+ responses in microglia. The biophysical models provide direction for new fundamental experimental research.

Whilst biodegradable plastics may be beneficial in overcoming plastic leakage, current usage practices do not take advantage of their biodegradability, with most ending up in landfills. Using biodegradable plastics for packaging films would suit their properties, and composting biodegradable films may be a better end-of-life scenario than recycling due to the inefficiency of film recycling and, in particular, multilayer film recycling. This thesis aims to investigate whether biodegradable films can be used for high-barrier multilayer packaging in modified atmosphere packaging (MAP) of meat products and whether they would provide an environmental benefit. This thesis sets out to 1) find the permeability requirements for a biodegradable film to work for this application, 2) investigate biodegradable films with the permeability requirement and other properties required of a packaging film, 3) analyse the environmental impacts of the proposed biodegradable film, specifically, global warming potential and non-renewable energy use, 4) investigate the real-life compostability of the materials used in the proposed film and the impact of the materials on the compost. A new mathematical model was created to calculate the maximum carbon dioxide permeability that would not shorten the shelf-life of the product. Pseudomonas spp. was used as a signifier of shelf-life as this type of spoilage bacteria is particularly sensitive to headspace carbon dioxide concentration. This was validated against 15 studies from the literature which were performed under varying conditions. A typical MAP meat product would require a permeability of 1.7 x10-6 m3 m-2 hr-1 atm-1. Using response surface methodology, the results were used to develop an equation to calculate the required permeability for different conditions. This is the first study to create a mathematical model centred on calculating the carbon dioxide permeability requirements for MAP of meat. In the next chapter, a biodegradable multilayer film was manufactured with a high barrier inner layer, butenediol vinyl alcohol (BVOH), and a biodegradable tie layer. There were two independent variables: 1) the outer layer material type (polylactic acid, polyhydroxyalkanoate (PHA), polybutylene succinate, and polybutylene adipate terephthalate), 2) BVOH thickness relative to the overall film thickness. The properties investigated were tensile strength, puncture strength, heat seal strength, permeability, peel strength, contact angle, and biodegradability. Since the films are intended for use with wet foods, mechanical properties and permeability were tested under high relative humidity. The best candidate for permeability was the film with PHA as the outer layer. The BVOH thickness had minimal impact on the films. This was the first study on the use of BVOH as a barrier layer. The environmental impact of the PHA/BVOH multilayer film was then compared to a conventional low-density polyethylene/ethylene vinyl alcohol film using life cycle analysis. Since the global warming potential (GWP) of meat is significantly higher than the packaging it comes in, a fair comparison would be one where the food waste could be assumed to be the same. So, the functional unit was based on film thickness required to maintain shelf-life, calculated using the model from Chapter 3. The biodegradable packaging emitted 2.3 times the GWP of the conventional film. However, if waste products and better farming practices were incorporated, the biodegradable film could have a GWP 92% lower than that of conventional films. This is a novel method of calculating the functional unit and the first to investigate the life cycle of BVOH. To explore end-of-life characteristics, the biodegradation of a common type of the material composing most of the desired film, polyhydroxybutyrate (PHB), was investigated, in comparison to high-density polyethylene. This was carried out at an industrial composting site, over the two main stages of the composting process: pasteurisation, and stabilisation phases. The degree of biodegradation of the materials was investigated using thermal gravimetric analysis and differential scanning calorimetry. The biofilm development on the polymers and the impact of the materials on the compost microbiome were both analysed using PacBio sequencing. This is a novel study investigating in situ composting conditions and the effect of bioplastics on the microbiome of the compost. Results showed that as the microbiome in the compost changes, so too does the microbiome in the biofilm of the plastics. The timepoint of the plastic samples was more indicative of the microbiome than the type of plastic for the plastic samples. The timepoint of the compost samples was also more indicative of the microbiome than whether the compost had been near the plastic samples or not. The physico-chemical studies of the plastic samples showed that the primary method of degradation during the first four weeks is due to surface erosion by bacteria, before significant deterioration of the bulk properties happened at week eight. Since the type and quantity of bacteria have such a large impact on the rate of degradation of PHB and these are changing with time, it is important that in situ industrial composting is used in biodegradation studies. Due to innovation in biodegradable barrier layers, biodegradable plastics may soon be used for high barrier packaging applications, however, care must be taken to ensure the environmental impact of their use is considered. Research and development are still required to carry out shelf-life trials using these films, sourcing PHA from waste materials, and developing a framework to ensure bioplastics reach composting or anaerobic digestion facilities, as intended. Currently, there is a gap between consumer perception of the impacts of biodegradable plastic production and end-of-life and the reality; to bridge this gap, academia and the private and public sectors must work together to bring about the intended advantages of biodegradable plastic use. Biodegradable plastics have the potential to 1) reduce the reliance on crude oil for plastics production, 2) increase the circularity of plastic films and 3) reduce the amount of non-biodegradable plastics leaking into the environment.

Anthropogenic climate change is disrupting the Earth's physical environment, which in turn impacts ecosystems. Warming is a particularly important physical stressor, as organisms tend to be temperature sensitive due to the role of thermodynamics in controlling metabolic rates. Resilient ecosystems can withstand environmental changes and maintain function. High ecosystem function and resilience are often attributed to high ecosystem diversity. However, the mechanisms linking ecosystem function, resilience and diversity are far from well understood. In this thesis, mathematical models of varying complexity are used to isolate processes relevant to the relationship between ecosystem diversity and resilience. The mechanisms investigated include 'trait diffusion' and 'resource partitioning'. Trait diffusion alters the distribution of phenotypic traits in a population, generating diversity as well as influencing ecosystem function and resilience. Resource partitioning occurs when different species are specialised to different environmental niches, in this case, resources. This complementarity between species can lead to higher function and diversity. When trait diffusion is present, high initial diversity is found to lead to lower ecosystem function, whereas the opposite is the case with resource partitioning. With both mechanisms, emergent diversity is not clearly correlated with ecosystem function. Trait diffusion allows short-lived species to adapt to warming, whereas long-lived species rely on initial diversity. More complex models are necessary for a sufficiently realistic representation of an ecosystem to make quantitative predictions. In this thesis, a size-structured dynamic energy budget model of fishes and invertebrates has been coupled to a spatially explicit model of corals and algae, to understand how warming impacts a coral reef ecosystem. Warming directly affects fishes and invertebrates by increasing their metabolic rate, resulting in changes to demographic processes such as growth rates. Indirect effects include the loss of reef habitat quality as coral bleaching reduces the availability of refuges. Modelled changes in biomass for +3⁰C of warming are found to be controlled predominantly by the direct effects of warming, and crucially for fisheries, the biomass of predators is modelled to decrease by at least 50% with +3⁰C of warming.

Radiotherapy is well established as a cancer treatment modality and historically has been regarded as a simple treatment technique where a "block" of radiation is directed towards the solid tumour volume. However, in recent years, advances in research have revealed the highly complex nature of radiation response. Prominent amongst this research are cases of non-targeted radiation response where cells outside the irradiated volume have been shown to be effected by radiotherapy. For example bystander effects are noted as a short distance effect influencing cells located close to the irradiated region. This contrasts to radiotherapy induced immune responses that elicit metastatic regression in tumours located far away from the irradiated site. RIBEs and abscopal effects do not fit with the at present well defined paradigms of radiation response where the chance of cell death is thought to increase exclusively with the dose delivered to a cell. These non-targeted radiation effects have only entered the field of radiation response in recent decades and so while the traditional understanding of radiation response has been characterised through methods like the LQ model, there exists no established methodology for quantifying the non-targeted effects of radiation. As part of this project we aim to gain a better understanding of radiation's non-targeted effects, with the target of creating a mathematical model capable of recreating the survival trends associated with these responses. Any mathematical modelling work will focus primarily on the role of RIBEs and consideration will be given to how these effects impact both in vitro and in vivo response. A particular focus will be given to the relevance of these effects in spatially fractionated exposures, where they'd be expected to be highly significant in determining cell survival. As well as attempting to predict radiation response with a consideration for RIBEs another priority for this project is to gain a better understanding of the exact mechanisms underlying this response. The effects of RIBEs on out of field survival have been well documented, however, despite this, the mechanisms underlying these trends are yet to be elucidated, although many have been proposed. This project aims to investigate the role of the cGAS-STING pathway and dsDNA in transmission of the bystander effect.

The synthesis of bio-based products, fuels, and materials in large-scale closed-photobioreactors (PBRs) presents a sustainable option for tackling the ever-increasing mass and energy demands of the world's rapidly growing population. With the scale-up of production comes significant cost reductions and increased commercial viability. However, successful PBR scale-up must overcome key hurdles relating to the local environmental conditions, including uneven light distribution caused by cellular absorption and mutual shading, as well as nutrient and biohydrogen partial pressure gradients. Therefore, this thesis confronts these engineering challenges with advanced mathematical modelling techniques by tackling the biotechnology's multi-scale complexities with minimum simulation cost strategies. The proposed models were thoroughly validated using both literature and experimental data collected from cultivating different microbial species in PBRs of different configurations and scales. In a "journal format" style thesis, Chapters 1 to 2 covers the general introduction and comprehensive literature review whereas Chapters 3 to 5 present the published original contributions. More specifically, Chapter 3 proposes the first-ever mechanistic model to directly integrate the effect of PBR mixing-induced light/dark cycles into the biomass growth kinetics. This enables the manipulation of the PBR mixing rate to alleviate light attenuation challenges and maintain higher biomass growth rates. Chapter 4 extends the mechanistic model's capabilities to account for the effects of temperature and PBR biohydrogen partial pressure, which were previously ununified for any microbial species. To evaluate the biotechnological transfer across two types of PBR, namely the Schott bottle-based and vertical tubular-based PBR, two parameters related to the PBR's local environmental conditions were derived: the effective light coefficient and the biohydrogen enhancement coefficient for recalibration. The successful systematic upscaling approach was recommended for other similar biosystems. Building on these achievements, Chapter 5 focuses on the multi-physics coupling within a Computational Fluid Dynamics (CFD) solver to facilitate optimisation and upscaling of biohydrogen production. For this, accelerated growth kinetics and parallel computing were combined to greatly reduce the simulation cost, enabling uncertainty estimation via Monte Carlo simulation for the first time. Finally, Chapter 6 concludes the thesis and presents two future directions: the exploitation of the models developed in Chapters 3 and 5 for (i) model-based optimal control of PBR mixing, (ii) the optimisation of PBR static mixers to enhance biomass growth and biohydrogen productivity, and (iii) application to other scalable PBR configurations.

The aim of improving resource efficiency while offsetting the environmental impact of industrial processes is directly linked to the optimal management of heat and power flows. The heating requirements of industrial processes are primarily met by the process utility system, or more specifically: steam systems. In most industrial processes, steam systems are also the primary source of electricity generation. Therefore, it is often the case that several processes are linked to a common utility system that generates heat and power. Despite extensive research in this field, most sites' steam systems have developed without basic concerns being addressed, particularly in relation to design and operation. Moreover, if emissions are to be mitigated and driven to zero, fundamental changes in the design and operation of such systems are required. Future process utility systems should not only ensure efficient use of energy, but also shift to low carbon technology alternatives. To make current utility system designs more sustainable, an optimization framework is needed to provide cost-effective pathways to transition from current to future designs. The variety of technologies available, the amount of data, and their strong correlations make energy system design a complex optimization problem. Furthermore, unlike other energy systems such as district heating, central grids, and local integrated energy systems, process utility systems present additional challenges for decarbonization. First, process industries require high amounts of process heating, usually far more than power: a heat/power ratio between 3.5 to 5.6. Second, heat at different temperature levels is typically required, especially between 100 to 400 °C. These barriers, coupled with the need for flexible systems to cope with the variable demand and energy price fluctuations (due to renewable energy's unpredictable nature), make developing sustainable utility systems a challenging enterprise. To address this challenge, this thesis provides an optimization framework for the design and operation of process utility systems. It ranges from site-specific data (stream information, energy demands, energy sources and energy market prices) to the thermo-economic modelling of the energy conversion technologies (considering part-load performance), system design, operation strategy while providing an environmental and economic analysis. The framework also includes practical constraints for heat integration and steam system operation, such as steam superheating and desuperheating, selection of steam temperature, pressure distribution levels, and steam temperature constraints. Due to the increasing share of intermittent renewable energy supplies, electrical and thermal energy storage are included in the framework. A range of different energy resources is included (fossil and renewable) to allow an orderly transition from the current framework to a sustainable future. The resulting optimization problem is complex and multi-objective and utilizes new approaches to solve the resulting nonconvex mixed-integer nonlinear programming problem. A bilevel solution strategy is provided to decompose the original problem in master and slave sub problems, maintaining computational tractability. Moreover, to capture the short- and long-term dynamic nature of the integrated systems, a multi-period optimization approach is developed based on time-series aggregation of the input data. To address the issue of sustainability, the framework not only allows for cost optimization but also includes life-cycle analysis. The resulting multi-objective problem uses Pareto optimal curves to illustrate the distribution of costs and emissions for different system configurations that satisfy the site energy demand. Finally, the applicability of the methodology is demonstrated in relevant case studies from the industry. These highlight the importance of a holistic optimization approach for the accurate evaluation of the utility system design regarding economic and environmental impact. The methodological framework has the potential to provide informed decisions for the design of a wide range of energy systems that utilize energy integration.

Cells in living organisms are constantly subjected to mechanical perturbations. It is vital that cells are able to adapt and respond to mechanical stimuli in order to maintain tissue homeostasis, and to facilitate developmental processes such as gastrulation. Cells may experience tensile (stretching), compressive (squashing) and shearing forces (a combination of tensile and compressive forces). It is known that stretch- ing single cells or epithelial tissue explants via applying an external force changes cell division. The mitotic spindle, which controls the direction of cell division, aligns with the direction of applied mechanical force in stretched epithelial tissues and the proliferation rate of cells increases. Much of the knowledge about changes in cell division is obtained from stretch experiments where force is applied instantly, in a manner that is biologically analogous to wounding experiments. However, little is known about how the rate of stretch affects the regulation of cell division. In particular, it is interesting to know how cell division behaviour may change in an environment where a tensile force is experienced over a long period of time, such as has been observed during early development. Mathematical models are able to provide insights into the mechanical description of tissues, in particular the possible mechanical stress (force per unit area) and the mechanical strain (deformation) the cells are experiencing. The vertex model is a popular model used for modelling epithelial tissue. In this work the vertex model is presented in a novel incidence matrix formulation that explicitly states mathematically the topology of the cells, something which is normally lacking in the classical implementation of the vertex model. This model shows how applied mechanical force at the periphery of an epithelial monolayer diffuses inwards in a manner that can be described with the use of a 'Cell Laplacian', a discrete operator which is analogous to the classic Laplacian. Using experimental datasets of living tissue explants, the vertex model is used here to provide a description of the mechanical environment within a living tissue layer. The mechanical stresses of individual cells can be estimated from cell geometries obtained from confocal images. A description of the shear strain and shear stress of a cell, a feature that has not been presented for the vertex model previously, is presented here to complement descriptions of the isotropic stress. Xenopus laevis tissue explants from embryos are stretched to the same degree at different rates; a fast-instant stretch and a slow-incremental stretch. Notably, the slow-stretch experiment does not result in an increase in proliferation, however the divisions that occur still align with the direction of stretch. Measured descriptions of cell geometric properties show that the cells in fast-stretched tissue experience a greater increase in apical area which is resolved over time, whereas the apical area of cells in slow-stretched tissue is more consistent. Despite this, the changes in cell strain appear to be similar between the two stretch protocols. Estimates of mechanical stress provided by the vertex model suggest how stretching the tissue changes the mechanical environment. There is an induction of a distinctive structure of isotropic stress arising from the application of force that persists over time. There is also an increase in the level of shear stress within the tissue, which reduces after the stretch, in the apical cells of both slow- and fast-stretched tissue. Complementary mathematical simulations of monolayers under the influence of the different stretch protocols suggest that the total monolayer mechanical energy and the shear stress within the fast-stretched tissue increase to a greater degree than that of the slow-stretched tissue. The work presented in this project highlights the benefits of interdisciplinary research and forms the foundations of possible future applications of the vertex model that take advantage of the novel, topologically explicit, framework presented here.

Bacteria are constantly sensing their environment, and must respond as it changes. Some of their most common systems for sensing and responding to change are alternative sigma factors. These are a type of transcription factor, and unique in that they integrate into the RNA polymerase molecule itself, often with dramatic effect on the bacterium's transcriptional program. They exist in great diversity, both within and across bacterial species. Recent advances in single-cell experimental techniques have enabled studies of alternative sigma factor responses in individual cells, revealing a range of possible behaviours. These are often heterogeneous across isogenic populations, suggesting that sigma factor systems are highly noisy. In this thesis, we use stochastic modelling techniques to study what responses alterna- tive sigma factors can generate, and how these are generated. First, we present the Catalyst.jl tool for modelling chemical reaction networks. It is a useful systems biology tool that we will use to implement models of one general, and two specific (σV and σB , both in Bacillus subtilis), sigma factor circuits. Our σV model demonstrates how this circuit's bistability properties can generate the heterogeneous activation dynamics observed experimentally. It makes additional predictions (including a memory of previous environmental conditions) that are then validated experimentally. Next, our σB model shows how this circuit's properties enable it to generate two distinct responses, single pulse and stochastic pulsing dynamics, both previously observed in experiments. We show that, by tuning system parameters, the network can be biased towards either response behaviour, and that it can generate previously unobserved ones. Finally, we note that both the σV and the σB circuit generate their response through a mixed positive/negative feedback loop (a common alternative sigma factor circuit motif). We use this fact to build a general sigma factor model. In it, we predict a range of behaviours that these circuits should be capable of producing, including both previously observed and novel ones. We also predict how the circuit can be modulated to generate each behaviour. Our work provides detailed insight into two alternative sigma factor systems. In addition, it explains a general response mechanism these systems use, and how it can be tuned. This will be useful for synthetic biology applications, where alternative sigma factors can be used as controllers of synthetic circuits. It also reveals how bacteria can use alternative sigma factors to enable a range of strategies to respond to environmental change.

Plant diseases pose a significant threat to food security, and fungal plant pathogens can be particularly damaging due to enormous evolutionary potential. Two major control strategies for fungal pathogens include chemical control with fungicides and use of disease-resistant cultivars. Both strategies are threatened by pathogen evolution leading to fungicide resistance and loss of cultivar efficacy ('cultivar breakdown'). Both fungicide resistance and cultivar breakdown can be characterised as qualitative or quantitative, depending on the genetic basis for resistance/breakdown. Mathematical models have an important role in understanding fungicide resistance and cultivar breakdown, and modelling studies offer numerous advantageous over experimental studies. We present a model of qualitative fungicide resistance and one of quantitative fungicide resistance and cultivar breakdown. The model of qualitative resistance extends a model from the literature, while the quantitative resistance model is entirely novel. Both models are parameterised to address Septoria, the most prevalent disease of wheat. Although qualitative resistance has been widely studied, many single-site fungicides (i.e. those challenged by qualitative resistance) face widespread resistance, meaning that quantitative resistance is increasingly important. However, the mechanisms underlying quantitative resistance/breakdown are more complex and suitable data for model fitting is harder to source. We present the first model of quantitative resistance to be fitted to field data for both fungicide resistance and cultivar breakdown. Fungicide mixtures can help delay resistance. Although many studies focus on mixtures of fungicides to which resistance is qualitative, the optimal strategy is not characterised if the initial resistance frequencies (RFs) to two fungicides in a mixture differ. Past work showed that equal selection for single resistant strains in the first year was the optimal strategy when initial RFs were equal but did not consider when the initial RFs differ. We show that this strategy is often sub-optimal if the initial RFs differ and present an alternative strategy based on equalising RFs in the breakdown year. We test the robustness of this strategy to changes in parameters controlling fungicide efficacy and pathogen epidemiology, including between-season pathogen sexual reproduction. Previous modelling studies of Septoria neglected pathogen sexual reproduction, for simplicity, despite evidence that sexual reproduction is an important part of Septoria's life cycle. We use the quantitative resistance model to determine how the number of fungicide applications per year affects resistance development, disease severity and yield. We consider how the optimal strategy varies depending on the time-frame of interest, before exploring how cultivar and fungicide control can be optimally combined to control the pathogen whilst minimising degradation of host and fungicide. We explore the effect of fungicide dose and compare the recommendations from the quantitative resistance model to those from the qualitative resistance model. Most fungicide resistance studies consider strategies which are fixed in time - i.e. rely on the same tactic used every year until failure. We present a flexible approach to optimise time-variable strategies, based on dynamic programming. This allows us to address an otherwise computationally infeasible problem to find the optimal strategy when time-variable strategies are permitted. We compare the improvement offered by the optimal time-variable strategy to the optimal fixed-time strategy.

Mathematical modelling and machine learning algorithms have been successfully applied to the healthcare domain and epidemiological chronic disease including diabetes mellitus, which is classified as an epidemic due to its high rates of prevalence around the world. Machine learning and statistical techniques are useful for the processes of description, prediction, and evaluation of various diseases, including diabetes. These techniques can be efficient tool in modelling diabetes and the most related risk factors. Although, Machine learning methods have been utilised in different aspects of diabetes research, but most of them were based on diagnosing or detecting the disease, and little research attention has explored the adoption of machine learning methods to study the trends in the prevalence of diabetes and forecast its future in specific populations. Thus, this thesis attempts to apply various machine learning and combination methods for studying diabetes and make future predictions. This thesis has investigated the application of machine learning and statistical techniques for developing prediction models for diabetes and the relevant risk factors (smoking, obesity, and physical inactivity) in the Kingdom of Saudi Arabia that can be used to support health policy planning and diabetes controlling. Regression, classification, and time series modelling approaches were used for diabetes modelling. Several models were developed namely, Multiple Linear Regression, Adaptive Neuro-Fuzzy Interference System ANFIS, Artificial Neural Network ANN, Support Vector Regression, Bayesian Linear Regression, Support Vector Machine, K-Nearest Neighbour KNN, Linear Discriminant, Neural Network Pattern Recognition, and Neural Network Time Series NARX-NN models. These models integrate historical data on diabetes, smoking, obesity, and inactivity prevalence to achieve its aim for examining the trends in prevalence of diabetes mellitus in the Kingdom of Saudi Arabia, to predict the future level of the disease. A combination of regression models is performed to improve the prediction accuracy using combination methods (Average, Weighted Average, Majority Voting, Weighted Majority, Minimum, and Maximum, and a new combination method consensus model). Several statistical evaluation metrics were applied to evaluate the performance of regression and time series models: mean squared error, root mean squared error, mean absolute percentage error, and the coefficient of determination R-squared. Classification models' accuracy performance was evaluated. Results from the regression and combined models were validated by comparison with some observed data from existing studies by the World Health Organization, International Diabetes Federation, and Family Health Survey from the Saudi General Authority for Statistics, revealing that improved accuracy was achieved with ANFIS model and the combined weighted average model in comparison to previous studies. The experimental results demonstrate the effectiveness of regression and combined models compared to classification and time series models. The ANFIS and WAVR models were found to be suitable for diabetes prediction due to their flexibility and high accuracy.

Moisture migration in manufactured foods can significantly affect their quality, nutrition, sensory attributes and shelf life. It can occur between foods and the surrounding atmosphere or between different compartments of manufactured foods when they have different water activities. Currently, most of the published research focuses on room temperature conditions. In this research, the temperature dependence of important material mass transport properties is studied considering sub-zero temperatures as well. To achieve this, experimental data at different temperatures were obtained and analysed using mathematical models. The effect of temperature on moisture migration in multicomponent food systems can subsequently be assessed using a one-dimensional model which was developed for this research. This model can consider food systems comprising one or more dry materials in contact with a wet material wrapped in a moisture impermeable packaging and was validated against previously published experimental data. Using this model, moisture migration in the wafer of a manufactured ice cream cone as a function of storage temperature and time was assessed. It was observed that while the wafer is anticipated to lose its crispness during the time kept in factory cold store, the average moisture content would still remain below the threshold for a wafer to be considered "soggy".

Modelling biological evolution is a growing area of research with different approaches used with ever-growing applications, proved to be beneficial in various real-world applications such as engineering, economics, biology, machine learning, optimal control. However, many aspects of modelling evolution remain understudied, especially concerning the situation where the life history trait/behaviour is described by a set of functions whose shape is unknown and/or the underlying system is highly complex, for example, infinite-dimensional. This thesis is comprised of two main parts, each of which investigates a different mathematical approach to reveal behaviours and life-history traits that emerged as a result of long-term evolution. Here, we attempt to formalise Darwin's fundamental ideas of survival of the fittest to develop a new framework to obtain evolutionarily optimal life-history traits/behavioural patterns based on the reconstruction of evolutionary fitness using underlying equations for population dynamics, applicable to Hilbert spaces with infinitely high dimensional spaces for life-history traits. This inspired the novel method, based on the principles of evolution, of stochastic global optimisation in high or even infinite-dimensional Hilbert spaces, named Survival of the Fittest Algorithm (SoFA). We test the novel algorithm on a phenomenon of particular interest, the mass synchronised diel vertical migration (DVM) of zooplankton, whose fitness is highly dependent on the trajectories of these movements. Using this ecologically relevant case study, we demonstrate that for maximising fitness in high-dimensional spaces, our proposed novel evolutionary algorithm, SoFA, provides better performances compared to other stochastic global optimisation algorithms. We then apply current game-theoretical approaches to evolutionary optimisation to various complex models. Among many insightful results are the following. Considering an SI model with the infected subpopulation described by a von Förster-type model, in which the infection load plays the role of age. We demonstrate that in this infinite-dimensional system, for simple trade-off functions between virulence, disease transmission and parasite growth rates, multiple evolutionary attractors are possible. A result not observed in the case of unstructured models, indicating the benefits of additional complexity within modelling pathogens. Furthermore, theoretically exploring the co-evolution of life-history traits in a generic host-parasite-hyperparasite system, we find that in the presence of hyperparasites, the evolutionarily optimal pathogen virulence generally shifts towards more virulent strains. However, the use of hyperparasites in biocontrol is still justifiable since overall host mortality decreases. An intriguing possible outcome of the evolution of the hyperparasite can be its evolutionary suicide. The presented results help warrant biocontrol agents and programs in pathogen management and provide a better understanding of pathogenic infections.

Bovine Tuberculosis (bTB) is a chronic, zoonotic disease caused by Mycobacterium bovis. It is endemic in Northern Ireland (NI), affecting the cattle population which contributes approximately £1 bn per annum to the local economy. The most recent incidence level (rate of occurrence) for bTB in NI is 7.85% during 2019 despite the test-and-slaughter control programme that follows EU guidelines. Mathematical methods such as epidemic modelling and social network analysishave been successively applied to bTB-affected locations such as Great Britain, New Zealand, and the USA. However, these methodshave not previously applied to bTB in NI; therefore, applying these methods in this research provides new insight and knowledge for NI. This research contains the first use of social network analysis of cattle movements in NI. Networks between herds using cattle movements for each month in 2010-2015 were analysed. Influential herds were identified and markets were highlighted as being extremely important to herd connectivity. The cattle movement network is shown to be Scale-Free with a high level of interconnection between herds. Targeted restrictions are more effective than random restrictions when more than 25% of herds are targeted, although the network remains highly connected. The first epidemic metapopulation model of bTB for NI was also created in this research, which builds upon a simple within-herd model using cattle movements (stratified by geographical area) and wildlife interactions. Using geographically stratified movements, wildlife interactions, and considering NI as a metapopulation increases the amount of knowledge generated on bTB in NI. Additionally, this model is able to further push epidemic modelling in general, as it is novel in explicitly modelling the movements, wildlife, and metapopulation aspects at the same time.

Current environmental rhetoric has highlighted the importance of seeking livestock production systems that reconcile competing objectives, especially environmental impacts. Profit margins in cattle systems are small and feeding the animals accounts for most of the costs. Hence, diet optimisation is an important aspect of beef systems. A promising sustainability strategy in Brazil is the integration of beef cattle with biofuel production, reducing environmental impact footprint, restoring pasture, and using agro-industrial by-products of ethanol in animal diet. These strategies can help reduce land-use change, minimising biodiversity loss and greenhouse gas emissions (GHGs). This is an important challenge in Brazil and helps in achieving its commitments presented at COP21 to reduce GHGs by 37% (vs 2005 baseline). Minimising environmental impact (EI) in these systems is a complex problem that can be solved through optimisation models, e.g., linear programming, nonlinear programming, heuristics. However, reducing EI may incur trade-offs in operational profit. Such models can also be used for sensitivity analysis, i.e. to assess the impact on the solution from changes in variables and input parameters, e.g., by-products costs, beef demand. This PhD thesis aims to fill gaps in cattle diet optimisation. Chapter 1 introduces and contextualises the scope of this thesis. Chapter 2 addresses the nonlinear animal growth problem, showing that the (usually avoided) nonlinearity can be efficiently solved using modern techniques. Chapter 3 presents a methodology to obtain the competitive cost of agro-industrial by-products to be included in animal diet considering market competition with other feedstuff. Chapter 4 builds on state-of-the-art research to minimise environmental impacts through diet optimisation. The novelties of this model are (i) working with maximum profit diet formulation rather than least-cost diet, and (ii) adding predicted enteric fermentation and manure emissions to be considered in the formulation along with the feedstuff life cycle assessment (LCA). Finally, Chapter 5 concludes the work by commenting on the issues addressed and the remaining challenges on the topic.

Chemical production scheduling is responsible for providing the allocation, sequencing and timings of operations into units to produce several valuable products. As a result, optimal scheduling is crucial for the vitality and prosperity of the chemical industry as it directly affects its productivity and its operational costs. Although many mathematical models have been developed in the past three decades, most models either lead to large model sizes and intractable computational time or generate suboptimal solutions in some cases. Additionally, mathematical models for scheduling of multipurpose batch plants do not allow related production and consumption tasks in different units to start or/and end at the same time points, which is different from the models for scheduling of semicontinuous/continuous and multistage multiproduct batch plants. Therefore, there is no generic and efficient framework for chemical production scheduling problems. In this Thesis, a generic and efficient modelling framework is proposed using the unitspecific event-based time representation. The main features of this framework include (a) defining all timing variables based on units instead of tasks, (b) allowing related nonrecycling production and consumption tasks to take place at the same event-point where a new definition for recycling tasks is presented, (c) sequencing different units processing related production and consumption tasks only if there is an indirect material transfer (i.e. there are not enough materials in the storage for consuming tasks), (d) aligning different units processing related tasks only if there is a direct material transfer (i.e. there is not enough storage for producing materials), (e) allowing processing units to hold materials for multiple event points. It is demonstrated that the proposed framework outperforms existing approaches in both solution quality and computational expenses. For large-scale problems, which require significantly high computational time, an enhanced rollinghorizon decomposition approach is developed in which a grouping strategy using the mixed-integer programming is proposed to divide the entire problem into subproblems. It is shown that the enhanced decomposition approach can generate optimal or nearoptimal solutions in significantly less computational time. Finally, a hybrid solution approach through a combination of gene expression programming with the mathematical programming approach is explored to solve large-scale energy-efficient flexible job-shop scheduling problems. The results demonstrate that the hybrid approach can significantly improve the solution quality.

The innate immune system plays a vital role in the control of infection, but many aspects of its behaviour are not fully understood. In this dissertation, I use mathematical modelling approaches to elucidate two linked processes which are key to the innate immune response to Salmonella infection. First, I consider the inflammasome, a large protein complex which forms in cells following infection. The inflammasome is responsible for coordinating cell death and the release of cytokines, which promote further activation of the immune system. Despite its importance, there are many conflicting accounts of this process in the existing literature, and there is no accepted single conceptual model of inflammasome formation. In the first chapters of this dissertation, I present a suite of deterministic ordinary differential equation models and discrete stochastic models which highlight different elements of the inflammasome formation process. By comparing the results from these models with an existing dataset describing the innate immune response to infection in macrophages, I construct a cohesive conceptual model of inflammasome formation. In particular, I propose a novel `branching' mechanism of protein recruitment to the inflammasome complex. I also show that variation in inflammasome formation times can arise from differences in the initial abundance of NLR oligomers present in the cell prior to inflammasome formation. The remainder of this dissertation focuses on the formation of clusters of infected cells (or `lesions') in tissues following Salmonella infection. Inflammasome formation on the cellular level is a crucial part of this larger-scale process; however, the precise downstream effects of inflammasome-coordinated signalling and cell death in this context remain unclear. In the later chapters of this thesis, I outline a spatial partial differential equation model of lesion formation in liver tissue following Salmonella infection, with a particular focus on motility of infected cells and multiple forms of cell death. Through use of Turing instability analysis and simulated solutions of the lesion model, I show that the spatial structure of lesions can arise simply through the interactions of infected and uninfected phagocytes, bacteria and a chemokine. I also demonstrate the importance of decreased motility of infected cells, and a balance of different forms of cell death with influx of uninfected immune cells, for the successful control of infection.

To avoid driving climate change on a dangerous path, a substantial reduction in greenhouse gases emissions is required. Hence, a high penetration of renewable energy technologies is essential, but most renewables are either affordable or dispatchable but not both. Energy storage systems integrated into concentrating solar power (CSP) plants can enhance dispatchability and solar-to-electricity efficiency. Besides, the combination of dispatchable CSP plants with lower cost photovoltaic (PV) plants exploits synergies between the reliability of CSP with energy storage and cost of PV. However, this integration leads to complex interactions between the different technologies and requires sophisticated design guidelines to achieve low costs and high dispatchability simultaneously. In this thesis, a two-stage multi-objective optimisation framework for the design and operation of hybrid CSP-PV plants with energy storage is developed. The two-stage optimisation simultaneously optimises the design and operation of a hybrid solar power plant with respect to competing technical and financial performances. The multi-objective operational optimisation stage finds the best operational strategy of a hybrid power plant with energy storage systems. The model, written in Python, uses a typical meteorological year to optimise one-year hourly operation. The results demonstrate that the integration of an energy storage system in a concentrating solar power plant provides dispatchability and, when hybridised with photovoltaic, enhances its competitiveness with current electricity prices. The low mismatch between supply and demand, even when a fixed commitment is required throughout the year, together with high overall efficiency, indicates that the integration of energy storage in hybrid solar power plants is an opportunity to increase the penetration of solar energy in the power sector. The design of reliable and cost-competitive hybrid solar power plants requires the careful balancing of trade-offs between financial and technical performance. Hence, the design optimisation stage optimises the capacities of the main components of the hybrid power plant and handles financial and technical objectives. Different configurations are analysed as case studies throughout the thesis to analyse the impacts, interactions, and synergies of technology integration. Three locations are investigated, which present different solar resource profiles: Seville (Spain), Tonopah (USA), and the Atacama Desert (Chile). The optimisation results are used to develop some guidelines for the optimal design of dispatchable hybrid solar power plants with energy storage based on the given solar resource and required dispatchability. These guidelines provide an initial design for affordable and dispatchable hybrid solar power plants and can enable their widespread deployment. The model developed can be applied to other locations under different input parameters and demand profiles. Besides, the flexibility of the model allows it to be extended in order to evaluate different energy conversion and storage technologies to design hybrid power plants with energy storage under different configurations and requirements. Thus, the optimisation framework can provide valuable information for the integration of different technologies to support the affordable and sustainable transition to a clean energy system.

Cancer is a complex disease causing millions of deaths worldwide every year. To date, despite the increasing knowledge in cancer biology, risk factors and important discoveries in cancer treatments, numerous cancers cannot be treated due to a lack of effective therapies. Drug development is a long and complex process including a succession of pre-clinical and clinical phases evaluating drug efficacy and safety. In oncology clinical trials, overall survival (OS) remains the gold standard to assess treatment efficacy. However, OS necessitates the enrolment of a large number of patients in trials and a long follow-up period in order to establish drug-related clinical benefit with a significant statistical power. Therefore, regulatory agencies allow the use of surrogate endpoints for OS that offer an opportunity to assess drug-related patient benefit at an earlier stage, support go-no go decisions to the next phase and help to accelerate a new drug approval. The majority of surrogates for OS are categorical endpoints based on tumour size (TS) imaging that allow a qualitative evaluation of drug efficacy. Lately, the use of TS measurements as a longitudinal variable has been suggested to allow a quantitative evaluation of drug efficacy using modelling approaches. However, TS measurements have been observed to be subject to inter-operator variability, which could lead to misinterpretation of clinical outputs. Therefore, the first objective of this thesis was to quantify TS measurement variability in a non-small cell lung cancer Phase III clinical trial and to assess to what extent it could influence the evaluation of drug efficacy using tumour growth inhibition models. This work revealed high TS measurement variability that did not seem to affect the evaluation of drug effect at a population level using modelling approaches. In order to determine clinical response-to-treatment, it is necessary to define TS burden at baseline for each patient based on existing individual lesion measurements. Guidelines, such as the Response Evaluation Criteria in Solid Tumours (RECIST) criteria, provide a recommendation for the number of lesions to be followed. However, there is limited knowledge about the impact of target lesion selection on drug effect evaluation using tumour growth inhibition (TGI) models in malignant pleural mesothelioma patients. Therefore, the second objective of this thesis was to understand to what extent the number of lesions to be selected to follow tumour size burden over the treatment time course could influence the modelling outcomes in patients with malignant pleural mesothelioma. In this analysis, reducing the number of target lesion did not seem to compromise the determination of drug effect using TGI models. Being able to characterise drug efficacy at an early stage during oncology clinical trials is of primary necessity for patients and drug developers. Therefore, with a better understanding of the TS variable, the thesis was refocused on exploring the use of TS metrics as a surrogate for overall survival, to inform drug-related clinical benefit at an earlier stage after treatment initiation in malignant pleural mesothelioma patients. In this work, two TS-related surrogates for overall survival were identified. Chemotherapy treatments are known to have high interindividual variability in pharmacokinetics and haematological toxicity. However, therapeutic drug monitoring is rarely used in clinical practice. Thus, identifying a routinely measured biomarker that could be used to perform dose optimisation in oncology clinical practice would be of great interest. Therefore, the last objective of this thesis was to develop a modelling framework to adapt docetaxel dose at patient level using a dose-limiting toxicity biomarker, neutrophil counts, that is routinely collected in clinical practice. This analysis highlighted a neutrophil metric could be used to individualise dosing of chemotherapy with dose-limiting neutropenia. Assuming that the confidence we have in TS data will continue to increase with improvement in imaging machines and measuring methods, the use of TS represents an important means to gather information on drug efficacy of cancer drugs at an early stage after treatment initiation. In a clinical setting, neutrophil counts, a chemotherapy dose-limiting toxicity biomarker that is routinely collected, constitutes a real opportunity to control and optimise chemotherapy exposure in order to minimise haematological toxicities without affecting drug efficacy.

The aim of this work is to present and analyse various dynamical models of the human population, including external migration flows, as well as models that consider the interplay of demography and economy. In chapter 1, we present theoretical, methodological, and computational advances in the study of population growth, as well as combined economic and demographic dynamics. In chapter 2, we introduce a two-component PPM model with external migration. Using this model, we have analysed both temporary and long-term population dynamics, using data from Destatis for specific calculations, and introduced a significant concept of the threshold degree of migrant flow growth. In chapter 3, we introduce a continuous analogy of the model from previous chapter - McKendrickvon Foerster model, which is a system of first order PDE's with non-lassical boundary conditions, and reduce its solution to Volterra integral equation of the second type. In chapter 4, we introduce a spatial-temporal economic-demographic model, which is a system of partial differential equations of the diffusion-reaction type. Using computer calculations, we investigated the underlying dynamical system, i.e. the corresponding nonspatial model. We have found unexpected regimes that show that in the long run, with a large initial wealth, the population may become extinct, despite experiencing growth in the short term. In chapter 5, we analysed the spatial-temporal model. More precisely, with the help of computer simulations we have considered different scenarios: the demographic invasion, needle-like perturbations, inhomogeneous perturbation of steady states. Interesting effects have been found such as a violation of the stability of the equilibrium in the needle perturbation of the initial state and the occurrence of chaos in the case of a space-inhomogeneous perturbation of the saddle point. In chapter 6, we have shown that Turing instability takes place in the economic-demographic model.

The uninterrupted spread of malaria, besides its seasonal uncertainty, is due to the lack of suitable planning and intervention mechanisms and tools. Several studies have been carried out to understand the factors that affect the development and transmission of malaria, but these efforts have been largely limited to piecemeal specific methods, hence they do not offer comprehensive solutions to predict disease outbreaks. This thesis introduces a 'holistic' approach to understand the relationship between climate parameters and the occurrence of malaria using both mathematical and computational methods. In this respect, we develop new climate-based models using mathematical, agent-based and data-driven modelling techniques. A malaria model is developed using mathematical modelling to investigate the impact of temperature-dependent delays. Although this method is widely applicable, but it is limited to the study of homogeneous populations. An agent-based technique is employed to address this limitation, where the spatial and temporal variability of agents involved in the transmission of malaria are taken into account. Moreover, whilst the mathematical and agent-based approaches allow for temperature and precipitation in the modelling process, they do not capture other dynamics that might potentially affect malaria. Hence, to accommodate the climatic predictors of malaria, an intelligent predictive model is developed using machine-learning algorithms, which supports predictions of endemics in certain geographical areas by monitoring the risk factors, e.g., temperature and humidity. The thesis not only synthesises mathematical and computational methods to better understand the disease dynamics and its transmission, but also provides healthcare providers and policy makers with better planning and intervention tools.

Through a combination of epidemiological and proteomic methods, the aim of this thesis was to advance understanding of antibody-driven immune responses that partially protect against infection and reduce fecundity in human schistosome infections. The relative contribution of exposure to infection and IgE antibody responses against schistosomes were explored using a mathematical modelling approach. Age intensity and serology profiles of sub-cohorts were reproduced to good approximation by incorporating explicitly defined exposure and immunity functions, fitted to field data, into an age- and sex-structured S. mansoni transmission model. However, the inferior model fit for males from one tribal group highlights the need to capture heterogeneity in antibody responses that occur with varying cumulative exposure of different demographic groups. The progressive development of protective immunity against S. mansoni infection is associated with cross-reactivity between members of the Tegument Allergen-Like (TAL) protein family. This relationship was explored further and evidence for involvement of an additional TAL family member in the development of IgE-mediated anti-infection immunity found. Evidence supporting similar cross-reactive relationships between S. haematobium TAL proteins is provided. In addition to anti-infection immunity, S. haematobium is thought subject to an anti-fecundity immune response. It is proposed that IgG1 antibodies raised to proteins within whole worm extract are responsible. A proteomic approach used to identify targets of the IgG1 returned 191 proteins, several of which are closely associated with the parasite-host interface. Three were successfully expressed and analysis identified possible associations between target specific IgG1 and reduced worm fecundity, although this was strongly confounded by host age and village of residence, a proxy for the force of transmission. These findings all demonstrate associations between the development of protective antibody responses and variations in exposure behaviour, host age or the force of transmission; the combined contribution of which will determine the level of exposure to immunostimulatory antigens and ultimately development of immunity.

Cardiovascular disease (CVD) was the second-largest cause of death in the United Kingdom in 2014 [1], accounting for 32% of all deaths in 2009 [2]. CVD encompasses many diseases, one of which is coronary artery disease (CAD), otherwise known as atherosclerosis. Atherosclerosis is the build-up of fatty material, called plaque, inside the wall of the artery. Over time, this plaque will grow too large or break o , causing a blockage resulting in a heart attack. Currently, mortality from CAD has decreased by 72% between 1979 and 2013 [3]. However, predictions show that if the increasing trend of Body Mass Index (BMI) continues, then mortality from CAD could start increasing again [4]. There are several di erent methods currently available to the National Health Service (NHS) to diagnose CAD. However, there are long waiting lists and expensive costs associated with current diagnosis methods. Our aim is to look at a non-invasive approach of diagnosing CAD. We have limited our investigation to simple model problems. Therefore, further work would be required to consider more complex cases which align with the real-world application. In this thesis, we consider both 1-dimensional (1D) and 2-dimensional (2D) problems modelled by an acoustic wave equation with a forcing function which attempts to emulate a localised disturbance caused by CAD.We use an explicit nite di erence method (FDM) to approximate the solution in our partial di erential equation (PDE) and discard the disturbance location used. Having added noise to these approximations in an attempt to mimic noise from real readings, we record these approximations at speci c locations on the surface of our domains to imitate data collected from actual sensors. Using this data in the Kalman lter (KF), where guesses for the disturbance location are made, we can estimate the approximation of u throughout our domain. Using data generated by the KF, we compute likelihood estimates for each guess made and obtain the most probable disturbance location used to generate our sensor readings.

DNA methylation is a key epigenetic process which has been intimately associated with gene regulation. In recent years growing evidence has associated DNA methylation status with a variety of diseases including cancer, Alzheimer's disease and cardiovascular disease. Moreover, changes to DNA methylation have also recently been implicated in the ageing process. The factors which underpin DNA methylation are complex, and remain to be fully elucidated. Over the years mathematical modelling has helped to shed light on the dynamics of this important molecular system. Although the existing models have contributed significantly to our overall understanding of DNA methylation, they fall short of fully capturing the dynamics of this process. In this work DNA methylation models are developed and improved and their suitability is demonstrated through mathematical analysis and computational simulation. In particular, a linear and nonlinear deterministic model are developed which capture more fully the dynamics of the key intracellular events which characterise DNA methylation. Furthermore, uncertainty is introduced into the model to describe the presence of intrinsic and extrinsic cell noise. This way a stochastic model is constructed and presented which accounts for the stochastic nature in cell dynamics. One of the key predictions of the model is that DNA methylation dynamics do not alter when the quantity of DNA methylation enzymes change. In addition, the nonlinear model predicts DNA methylation promoter bistability, which is commonly observed experimentally. Moreover, a new way of modelling DNA methylation uncertainty is introduced.

Cardiac computational modelling has offered an alternative method to experimental cardiology for heart function studies. Although different electrophysiological models in several species have been developed, no such models exist for the fish heart. Fish are vertebrate ectothermic animals, and their body temperature is affected by temperature changes in their aquatic environment. Given the prominence of global warming effects, temperature changes and the rise of water temperature influence different organs in the fish body, including the heart. A better understanding of the process of thermal acclimation of the fish heart at single cell and tissue levels where cardiac ion channels and pumps remodel after prolonged exposure to a different temperature, is of scientific interest. Also, a 3D model based on an accurate anatomy model is a valuable tool for the study of ventricular electrical activities. Furthermore, investigating the effects of heart diseases on cardiac mechanical dynamics and the contracting dynamics of the human ventricular cells is also valuable to study. Thus, the objective of this thesis consists of three parts: In part I, a novel biophysically computer model for the teleost fish ventricular myocyte has been developed at the physiological body temperature of 4°C. First, novel formulations of the major ionic currents including I_Na, I_CaL, I_Kr and I_K1, were developed at 4°C and then incorporated into the basal model developed by Luo and Rudy for the guinea-pig ventricle myocytes. The developed model was then used to assess the effects of changing temperatures on ventricle electrical dynamics. The developed models matched experimental findings quantitatively. In Part II, a novel 3D biophysically and anatomically accurate model for the teleost ventricle was developed. First, a 3D geometry of the heart was reconstructed and segmented into the heart's major chambers using a micro-CT scan with sustaining iodine technique. Then, the 3D geometry of the ventricle was incorporated into a 3D computational model to investigate the electrical excitation propagation in the teleost heart. In Part III, a multi-scale electromechanical model of human ventricle cells was modified to assess the impacts of hypertension (HP) on the contractile function of the human left ventricle myocytes. A single cell electromechanical model was modified by integrating experimental data from rat ventricular cells under Sham (control) and HP conditions. Simulations showed that HP prolonged APD₉₀ and increased [Ca²⁺]ᵢ with no marked change in the sarcomere length or the contractile force at cellular level, but in 2D tissue simulations, there was an increase in the tissue's vulnerability for initiation and maintenance of re-entrant excitation waves indicating a pro-arrhythmic effect of hypertension.

The goal of systems biology is to provide a predictive and quantitative understanding of complex biological systems and their experimental data using mathematical and computational models. Mathematical modelling and computational simulation has been a crucial tool for basic research in cardiac electrophysiology for decades, and has provided remarkable insights into many physiological mechanisms. More recently these quantitative cardiac models have begun to transition into safety-critical clinical and pharmaceutical development applications. Using cardiac mathematical models in such applications requires high levels of credibility as well as an accurate quantification of the uncertainty in the model predictions. In this thesis, we develop a suite of Bayesian inference and uncertainty quantification techniques and software tools to study cardiac cellular electrophysiology. We then design and perform high-throughput experiments to construct and validate cell-specific mathematical models for human Ether-à-go-go-Related Gene (hERG) channel dynamics, and to study its temperature dependence, which is important for cardiac safety pharmacology and cardiac action potential models. Using the Bayesian statistical framework together with the high-throughput measurements allows us to quantify the uncertainty and variability of the model parameters. We also model and analyse how experimental artefacts contribute to the observed variability of these recordings, allowing us to separate the effects of these artefacts from physiological behaviour. A similar approach for uncertainty characterisation and experimental design will have to be adapted for other ion currents to create better predictive models, as accurate ion channel models are essential for constructing trustworthy cardiac action potential models.

Good understanding of individual animal movement is needed in the context of epidemiology in order to predict the rate of spread of infectious diseases. It is also required for problems arising in nature conservation such as biological invasions or pest monitoring. A question that often appears in the centre of the movement studies is which movement pattern is 'faster' or more efficient. For instance, it is widely believed that the pattern quantified by a power law distribution of movement steps is faster than Brownian motion. Another common query is do animals actually move using power law distributions. Would other distributions be a better fit for the movement? In pest monitoring a key area is the efficiency of the traps used to calculate the population density of insects. Different shaped traps are rarely compared equally, often the traps will vary in size or surface area. This thesis has three distinct parts and aims to provide insight into three different overlapping areas. The first part looks at different ways to compare probability distributions, and describes a way of comparing distributions without a mean or variance. The second part looks at the movement pattern of Tenebrionid beetles and has a detailed analysis of how these beetles move in a laboratory setting, with an emphasis on checking if any of the beetles tested moved with super-diffusive or ballistic motion. The third part is a comparison of the capture rate of different shaped traps using simulations of particles moving like Tenebrionid beetles.

There are many challenges in modelling granular media, in particular due to hard particle interactions such as collisions. Modelling and simulating at a microscopic level produces very accurate results, but simulations are generally restricted to relatively small systems of particles. It is also difficult to construct a simple continuum model which accurately describes all the properties of granular media. In this thesis, we consider a number of the problems associated with modelling granular media. We first look at the microscopic dynamics of individual particles and how to derive physically appropriate interactions between them, and discuss Event-Driven Particle Dynamics (EDPD) as an accurate and efficient way to model a system of hard, spherical particles. We then present a novel derivation of the weak form of the Liouville equation which can model systems where particles interact instantaneously (e.g. via inelastic collisions). From here we construct the BBGKY hierarchy and use moment closure methods to construct a new, accurate continuum model for granular media, based on Dynamical Density Functional Theory (DDFT). We then use EDPD to construct approximations for the radial correlation function which accounts for friction, packing fraction and inelasticity. This is then included in the DDFT in simulated examples.

Maximising the durability of crop disease resistance genes in the face of pathogen evolution is a major challenge in modern agricultural epidemiology. Spatial diversification in the deployment of resistance genes, where susceptible and resistant fields are more closely intermixed, is predicted to drive lower epidemic intensities over evolutionary timescales. This is due to an increase in the strength of dilution effects, caused by pathogen inoculum challenging host tissue to which it is not well-specialised. The factors that interact with and determine the magnitude of this spatial effect are not currently well understood however, leading to uncertainty over the pathosystems where such a strategy is most likely to be cost-effective. We initially use a spatially explicit model, incorporating seasonality and localised reservoirs of inoculum, to explore disease dynamics within landscapes containing a mixture of fields planted with either susceptible or resistant cultivars. When the spatial diversification of these fields is maximised, with lower aggregation of similar fields, the overall intensity of the landscape scale epidemic is reduced. The strength of this spatial effect however depends strongly on the pathogen dispersal characteristics, any fitness cost(s) of the resistance breaking trait, the efficacy of host resistance, and the length of the timeframe of interest. The conclusions drawn from this initial work, about how multi-strain disease dynamics respond to the scale of spatial diversification in a multi-host landscape, allow us to construct a general spatially implicit model that captures these fundamental dynamics. This new model features a novel method for incorporating spatial structure using an intuitive spatial aggregation metric that can be easily estimated from spatially explicit landscape data. The model is simple enough to be amenable to mathematical invasion analysis, while being flexible enough that questions of resistance durability can be thoroughly explored. In particular, results demonstrating interaction between spatial heterogeneity and cultivar cropping ratio are presented, an investigation that was not easily possible in our earlier more complex model. These results indicate that optimal spatial deployment strategies depend on a variety of factors, and may not necessarily be constant over time. Overall, these models allow us to make general predictions of the types of system for which spatial diversification is most likely to be cost-effective, paving the way for potential economic modelling and pathosystem specific evaluation. In addition, this approach for capturing detailed spatial structure and multi-species interactions within simple mathematical models could be applied to a wide variety of ecological and evolutionary systems. This study highlights the importance of studying the effect of genetics on landscape scale spatial dynamics within host-pathogen disease systems, as well as providing new mathematical tools to do so.

Plants can adjust the biochemical processes in their existing organs and tailor them to their surrounding environment. This biochemical adjustment to a change in environmental condition is known as dynamic acclimation. The way in which plants dynamically acclimate their rates of photosynthesis and the downstream carbon metabolism to changes in temperature is poorly understood. With the aim of understanding, holistically, the coordinated changes in carbon uptake and utilization that encapsulate dynamic acclimation, I use both experimental and computational methods to assess the biochemical responses of mature Arabidopsis leaves to different temperature treatments. Arabidopsis leaves accumulate starch, malate and fumarate during the day and consume these carbon stores at night when the plant cannot photosynthesize. My measurements of photosynthetic parameters and diurnal metabolite concentrations show that the amount and the form of carbon stored in Arabidopsis leaves changes non-linearly with temperature. Fumarate, for example, has previously been shown to accumulate to a greater extent in the cold and was speculated to be a cold-sensor for photosynthetic acclimation. However, working across the full physiological temperature range of Arabidopsis, I observe an increased fumarate accumulation at both high and low temperatures. I use both kinetic and constraint-based metabolic modelling techniques to unveil how these changes in carbon metabolism in response to temperature support a photosynthetic acclimation response. I demonstrate how unbiased constraint-based methods, which do not require an objective function and thus minimize the observer bias imposed on the model, are particularly suited to studying dynamic acclimation of plants. Combining my own experimental data with existing omics data sets as model constraints, I propose the ratio of triose phosphate to 3-phosphoglycerate export from the chloroplast as a new metabolic signal for cold acclimation. Furthermore, I adapt a reliability engineering approach called Failure Mode and Effect Analysis to build a framework for studying the reliability of metabolism. Using this approach, I conclude that cytosolic fumarase, the enzyme responsible for fumarate accumulation in Arabidopsis leaves, acts as a fail-safe to carbon metabolism. Increased fumarate accumulation in response to extreme temperatures maintains system stability and is required for photosynthetic acclimation.

This thesis investigates the wetting behaviour of liquids on solid surfaces both in and out of equilibrium using two different general approaches from statistical mechanics. These are based on generalised lattice-gas models. Properties such as wettability and the contact angle are determined by the attraction strength parameters between the particles and with the solid surface. The wetting behaviour of liquids is characterised by the binding or interface potential, which we calculate. The two approaches used are kinetic Monte Carlo (KMC) and density functional theory (DFT). The time evolution in our KMC model involves two processes: (1) single-particle moves, which incorporates into the model particle diffusion over the surface and within the droplets, evaporation and condensation, i.e., the exchange of particles between droplets and the surrounding vapour; (2) larger-scale collective moves, which model advective hydrodynamic fluid motion, which are determined by considering the dynamics predicted by a thin-film equation. We calculate the thermodynamic quantities such as the contact angle using various methods and make a comparison between results from the different approaches. We present results for droplets joining, spreading, sliding under gravity, dewetting, the effects of evaporation, the interplay of diffusive and advective dynamics, and how all this behaviour depends on the temperature and other parameters. In addition, we consider the interfacial phase behaviour of binary liquid mixtures. We develop a DFT based method for calculating the binding potential as a function of the local adsorption of each species at the interface. This function characterises the interfacial phase behaviour of the mixture. Moreover, we show that in certain cases it can be multivalued.

With the aim of defining a Quantum Systems Engineering paradigm, we show that the systems engineering of quantum technologies is materially different from systems engineering in general. The thesis is based upon a two pronged mixed-methods research approach considering: (a) a comprehensive theoretical analysis of the difficulties in deriving systems engineering modelling tools; (b) identifying systems engineering challenges in practical quantum technology development through direct observation and case-study methods. We show a modified systems approach should benefit early stage quantum technologies design and development, a stage characterised by a low Technology Readiness Level (TRL), with the aim of accelerating capitalisation. The research showed that systems engineering applied to quantum technologies will require processes that are both more complex, and different from, those used for conventional systems technology development. This is fundamentally caused by the quantum properties of the system. Furthermore, the research evidenced that applying systems methods, tools, and approaches to low Technology Readiness Level development, both quantum and classical, is very likely to accelerate development, increase the quality of deliverables, and improve the alignment of early research to end-user needs and natural technology pull. Based on these results we have developed a series of recommendations, and a selection of systems tools, which together constitute a light-weight systems approach for low Technology Readiness Level development (some of which also apply to non-quantum domains). These are contained within the concluding chapter of the report. Findings are presented both as a verbal narrative and with full mathematical derivations.

Hydrodynamic cavitation is the formation, growth and collapse of vapour/gas-filled cavities. The collapsing cavities result in intense shear and formation of hydroxyl radicals thereby leading to physicochemical transformations. These physicochemical effects can be utilised for a variety of industrially relevant applications. The promise of this technological platform arises from the absence of additives, realisation of the phenomenon by fluidic devices often without moving parts and the potential to retrofit and scale-up. In this thesis, application of hydrodynamic cavitation for effluent treatment is investigated. Despite the promise, hydrodynamic cavitation based effluent treatment is limited in industrial practice. This could be due to problems arising from the use of conventional - linear flow devices, namely venturi tubes or orifice plates that are prone to erosion and clogging. Recently a vortex-based cavitation device has been disclosed, this device employs rotational flow to harness hydrodynamic cavitation. The device does not use restrictions and shields cavities from the reactor wall – thereby lowering propensity to erosion and clogging, which are problems typically encountered in conventional hydrodynamic cavitation devices. There have been efforts to demonstrate typical applications of the vortex based hydrodynamic cavitation device, however, systematic characterisation is lacking. The lacunae for systematic characterisation were identified as, lack of i) clear guidelines to identify inception, ii) reaction engineering models to design these devices for continuous effluent treatment, and iii) understanding on the influence of scale on performance. An attempt to address the identified lacunae is made in this work as discussed here. Chapter 1 provides a background, applications, parameters influencing hydrodynamic cavitation devices and the motivation for the thesis work. Chapter 2 discusses the use of cavitation noise for identifying inception in cavitation devices. This was achieved by the use of smartphone recording of cavitation noise and post-processing of recorded data using a MATLAB code. This can be used as an unambiguous and non-invasive approach to identify cavitating conditions. Chapter 3 reviews existing reaction engineering models and proposes a model suitable for cavitation devices for effluent treatment. A per-pass modelling methodology was developed for effluent treatment, containing simulated effluent with solvents. The developed model can be used to compare cavitation devices, provides a basis for translating batch data to design continuous cavitation based wastewater treatment and provides a way towards linking sophisticated models of cavitation. Chapter 4 proposes a multi-layer model by coupling computational fluid dynamics (CFD) and cavity dynamics models to the per-pass modelling methodology, which was used to simulate the performance of vortex-based hydrodynamic cavitation devices and in general any hydrodynamic cavitation device. The multi-layer modelling approach provides a sound basis for further work on optimisation of cavitation reactors. Chapter 5 discusses the evaluation of performance of four different scales (flow capacities – 1.3, 5, 19.5 and 248 LPM at ΔP = 280 kPa) of vortex-based cavitation device using an aromatic pollutant. Correlations to explain obtained data based on per-pass degradation coefficient is proposed and discussion regarding the scale-up of vortex-based devices is made. This thesis carries out a systematic characterisation of a novel vortex-based cavitation device for effluent treatment. The important aspects of the performed work are: i) it is the first to systematically propose a per-pass model for degradation of simple pollutants such as acetone/isopropyl alcohol/ethyl acetate and complex pollutants – dichloroaniline in water and ii) to investigate the influence of scale of cavitation device (device was scaled-up 200 times). The models developed and results obtained in this work will be useful for expanding applications of hydrodynamic cavitation and vortex based devices for effluent treatment.

Changing environments are affecting individual species and the interactions between them. This includes host-parasite interactions. Although much is known about temperature effects on individual species, much progress is still to be made in understanding how complex parasite life cycles can be affected by changing temperatures. Here, several experimental approaches are presented to help study host-parasite interactions under changing temperatures. Using these experimental data on different stages of the Schistocephalus solidus under a range of temperatures are collected. Combined with (re-analysed) literature data and these newly collected data are inputted into a mathematical model that is constructed to simulate the whole life cycle. These different studies show that most parts of the parasite life cycle respond in a domeshaped fashion to changing temperatures with optimum temperature higher than current means. Overall, densities of the different life stages of S. solidus do not appear to be strongly affected by changes in mean temperature when including different, antagonistic effects on each life stage using a mathematical modelling approach.

This thesis deals with the analysis and numerical simulation of anisotropic nonlinear partial differential equations (PDEs) and dynamical systems in biology. It is divided into two parts, motivated by the simulation of fingerprint patterns and the modelling of biological transport networks. The first part of this thesis deals with a class of interacting particle models with anisotropic repulsive-attractive interaction forces and their continuum counterpart. These models are motivated by the simulation of fingerprint databases, which are required in forensic science and biometric applications. In existing interacting particle models, the forces are isotropic and the continuum limits of these particle models are given by nonlocal aggregation equations with radially symmetric potentials. The central novelty in the models we consider is an anisotropy induced by an underlying tensor field. This innovation does not only lead to the ability to describe real-world phenomena more accurately, but also renders their analysis significantly harder compared to their isotropic counterparts. We discuss the role of anisotropic interaction, study the steady states and present a stability analysis of line patterns. We also show numerical results for the simulation of fingerprints, based on discrete and continuum modelling approaches. The second part of this thesis focuses on a new dynamic modeling approach on a graph for biological transportation networks which are ubiquitous in living systems such as leaf venation in plants, blood circulatory systems, and neural networks. We study the existence of solutions to this model and propose an adaptation so that a macroscopic system can be obtained as its formal continuum limit. For the spatially two-dimensional rectangular setting we prove the rigorous continuum limit of the constrained energy functional as the number of nodes of the underlying graph tends to infinity and the edge lengths shrink to zero uniformly. We also show the global existence of weak solutions of the macroscopic gradient flow. Results of numerical simulations of the discrete gradient flow illustrate the convergence to steady states, their non-uniqueness as well as their dependence on initial data and model parameters. Based on this model we propose an adapted model in the cellular context for leaf venation, investigate the model analytically and show numerically that it can produce branching vein patterns.

Peroxisomes are oxidative subcellular organelles present in the majority of eukaryotic cells, with key functions in lipid metabolism, reactive oxygen species (ROS) homeostasis, and production of ether phospholipids (myelin lipids). Modulation of peroxisome number in the cell through coordinated proliferation and degradation is crucial for supporting these functions, with peroxisomes rapidly responding to environmental changes in order to maintain cell vitality. As a result, patients with defects in peroxisome proliferation present with a range of symptoms and severity, with vision/hearing loss, neurological defects, seizures, and organ dysfunction being common in peroxisome biogenesis disorders. To proliferate, peroxisomes follow a multi-step process of growth and division, whereby (i) the peroxisome membrane is elongated, (ii) this elongation is constricted at several points to produce a 'beads on a string' morphology, and (iii) the membrane undergoes scission at these constriction points to produce new peroxisomes. This process requires extensive remodelling of the peroxisomal membrane, through the action of dedicated division machinery. Our knowledge of the key processes underlying the regulation of this membrane remodelling and the contribution of alterations to membrane dynamics to health and disease are still not well understood. In this thesis, a literature review is presented describing knowns and unknowns in the peroxisome field, with particular focus on the role peroxisome membrane dynamics play in maintaining peroxisome function, and the role of these dynamics in human health and disease. Results chapters begin first by investigating alterations to peroxisomal membrane dynamics in response to the mitochondrial respiratory chain inhibitor rotenone, to understand the resistance of peroxisomes to mitochondria-derived ROS. Surprisingly, alterations to the peroxisome compartment are due to the microtubule-destabilising ability of rotenone, and peroxisomes are unaffected by mitochondrial ROS, despite this not being the case vice versa. The implication of these findings in understanding the peroxisome-mitochondria redox relationship are discussed, in addition to highlighting the importance of investigating peroxisome membrane dynamics in in cellulo models of disease. Second, alterations to peroxisomal membrane dynamics in response to lack of division protein MFF are investigated. It is revealed that despite completely normal biochemical parameters, there are more underlying alterations to the peroxisomes than hyper-elongation, and that MFF has a crucial role in the maturation of peroxisomes. In addition, these findings suggest that peroxisomal import complex protein PEX14 may play a role in peroxisomal membrane dynamics, by stabilising elongated peroxisomal tubules through interaction with the cytoskeleton. Third, an interdisciplinary, combined experimental-modelling approach is used to characterise alterations to peroxisomal membrane dynamics, using peroxisomes with a block in division (loss of function of MFF), and peroxisomes with altered membrane dynamics (elongation through expression of Rho GTPase MIRO1), as case studies. The key cellular processes underlying the regulation of peroxisome growth and division are highlighted, and findings from this chapter provide a proof-of-concept that this interdisciplinary approach is useful not only for characterisation and understanding mechanisms of membrane dynamics, but as a prediction tool to help suggest future therapeutics. Finally, a discussion of the key findings of this thesis and their implications is presented, highlighting the real importance of studying peroxisome membrane dynamics through interdisciplinary approaches such as the ones employed here.

In this thesis we consider the chemo-mechanical response of a multi-material lithium-ion battery anode nano-particle at equilibrium. The stresses are induced by lithium being intercalated into the nano-particle, causing the anode materials to expand. The presence of several anode materials expanding to different extents induces stress even at equilibrium. The model we primarily study is a linear elasticity model derived under the assumption that the stress-free expansion of each anode material is small. We couple the mechanical model to a diffusion-based model governing the transport of lithium in each material through stress-assisted diffusion. At equilibrium, the chemical potential of the lithium, which depends both on the lithium concentration and the hydrostatic stress, is uniform throughout the nano-particle, governing the distribution of lithium between the materials. Silicon is a promising anode material with a high capacity for lithium, but it expands to around 380% its original size when fully lithiated, leading to several issues during battery usage. We apply our equilibrium model to a nano-particle consisting of a silicon core and a surrounding graphite shell. The aim of using both materials is to mitigate the expansion of silicon without sacrificing too much capacity. We analyse the lithium concentration, displacement and stresses within each material, and use the results to optimise the volume of the silicon core based on several measures of success. Void spaces and porous silicon are introduced into the nano-particle design, using the method of multiple scales, to improve on the simple core–shell design, to moderate success. We extend the model to a geometrically nonlinear elastic model, and analyse this after finding that solutions cease to exist above a certain state of charge. Finally, we incorporate yielding and fracture of both materials into the linear model, based on perfect plasticity.

People are living longer. With this rise in life expectancy, a concomitant rise in morbidity in later life is observed; with conditions including cardiovascular disease (CVD), and cancer. However, ageing and the pathogenesis of age related disease, can be difficult to study, as the ageing process is a complex process, which affects multiple systems and mechanisms. The aim of this research was two‐fold. The first aim was to use mathematical modelling to investigate the mechanisms underpinning cholesterol metabolism, as aberrations to this system are associated with an increased risk for CVD. To better understand cholesterol from a mechanistic perspective, a curated kinetic model of whole body cholesterol metabolism, from the BioModels database, was expanded in COPASI, to produce a model with a broader range of mechanisms which underpin cholesterol metabolism. A range of time course data, and local and global parameter scans were utilised to examine the effect of cholesterol feeding, saturated fat feeding, ageing, and cholesterol ester transfer protein (CETP) genotype. These investigations revealed: the model behaved as a hypo‐responder to cholesterol feeding, the robustness of the cholesterol biosynthesis pathway, and the impact CETP can have on healthy ageing. The second aim of this work was to use electrochemical techniques to detect DNA methylation within the engrailed homeobox 1 (EN1) gene promoter, which has been implicated in cancer. Hypermethylation of this gene promoter is often observed in a diseased state. Synthetic DNA, designed to represent methylated and unmethylated variants, were adsorbed onto a gold rotating disk electrode for electrochemical analysis by 1) electrochemical impedance spectroscopy (EIS), 2) cyclic voltammetry (CV) and 3) differential pulse voltammetry (DPV). The technique was then applied to bisulphite modified and asymmetrically amplified DNA from the breast cancer cell line MCF‐7. Results indicated that electrochemical techniques could detect DNA methylation in both synthetic and cancer derived DNA, with EIS producing superiorresults. These non‐traditional techniques ofstudying age related disease were effective for the investigation of cholesterol metabolism and DNA methylation, and this work highlights how these techniques could be used to elucidate mechanisms or diagnose/monitor disease pathogenesis, to reduce morbidity in older people.

In this thesis we focus on calculating the shape of small bubbles and droplets near surfaces, in regimes where intermolecular forces are significant. In the first part of this thesis we focus on vapour nanobubbles where we use classical density functional theory (DFT) to determine the interfacial free energy (the binding potential) of simple model fluids in contact with a planar surface. This is done by calculating sequences of constrained density profiles for varying amounts of vapour adsorbed between the wall and the bulk liquid. This allows us to determine multi-scale properties of fluids at interfaces, and thereby determine the structure and the thermodynamics of vapour adsorption at solvophobic interfaces and how these depend on the microscopic properties of the fluid. We then use the binding potentials obtained as an input to the interfacial Hamiltonian (IH) model and study the properties of vapour nanobubbles at equilibrium.

Cleaning is an essential domestic and industrial operation. It is particularly important in the food and pharmaceuticals sectors, where a large proportion of the total water consumption (as much as 70%) is used just for cleaning. Impinging liquid jets are frequently used for cleaning operations and currently, almost all industrial cleaning systems are based on empirical results. In an effort to develop efficient and sustainable cleaning systems, I have studied the flow field created by impinging liquid jets and their application in cleaning. On impingement of a liquid jet onto a surface, the liquid spreads radially outwards until it reaches a point where the liquid film changes its thickness abruptly. This transition from a thin film to a thick film is demarcated by a hydraulic jump. The supercritical thin film flow is also associated with higher momentum and shear stress, and is therefore, key for cleaning and heat transfer applications. For more than a century, it has been believed that these thin film hydraulic jumps are created due to gravity. However, in this dissertation it is shown both experimentally and theoretically, that these hydraulic jumps result from energy losses due to surface tension and viscous forces alone and gravity plays no significant role. The new theory allow the size of thin film region (location of the hydraulic jump) to be predicted and manipulated. The location where flow in the thin film becomes turbulent is also considered. The average-velocity and the location demarcating the laminar to turbulent transition were measured and showed good agreement with the model. The model for cleaning by normally impinging jets (by peeling mechanism) (Wilson et al., 2014) was then extended to consider cleaning by oblique impinging jets and compared with experimental data which showed a good agreement. Finally, cleaning scenarios arising in industrial systems where the liquid jets moves across a soiled surface were modelled. In these scenarios the liquid jet impinges obliquely and moves with varying velocity. A simple mathematical framework was developed for these systems on which more detailed models can build on.

This thesis is concerned with the modelling of galaxy clusters, applying these models to real and simulated data using Bayesian inference, and the development of Bayesian inference algorithms applicable to a wide range of astrophysical problems. I present a comparison of mass estimates for $54$ galaxy cluster candidates from the second Planck catalogue (PSZ2) of Sunyaev--Zel'dovich sources. I compare the mass values obtained with data taken from the Arcminute Microkelvin Imager (AMI) radio interferometer system and from the Planck satellite. The former of these uses a Bayesian analysis pipeline that parameterises a cluster in terms of its physical quantities, and models the dark matter & baryonic components of a cluster using Navarro-Frenk-White (NFW) and generalised-NFW profiles respectively. The mass estimates derived from Planck data are obtained from the results of the Bayesian detection algorithm PowellSnakes (PwS). I also analyse simulated AMI data with input values based on PwS mass estimates. I then compare three cluster models using AMI data for the 54 cluster sample. The two observational models considered only model the gas content of the cluster. To compare the physical and observational models I consider their posterior parameter estimates, including the calculation of a metric defined between two probability distributions. The models' fit to the cluster data is evaluated by looking at the Bayesian evidence values. Improvements to the physical modelling of galaxy clusters are then considered, either by relaxing some of the assumptions underlying the physical model, or by introducing a new profile for the dark matter component of clusters. The resultant models are compared with the physical model introduced previously. The final part of the cluster analysis work focuses on Bayesian analysis using a joint likelihood function of data from both AMI and the Planck satellite simultaneously. The results of this joint analysis are compared with those obtained from the individual likelihood analyses using simulated data and with real data taken from the $54$ cluster sample. Finally, a new Bayesian inference algorithm based on nested sampling is presented. The algorithm, named the "geometric nested sampler", is an adaption of the Metropolis-Hastings nested sampler and makes use of the geometrical interpretation of sets of parameters to sample from their domains efficiently. The geometric nested sampler is tested on several toy models as well as a model representing the emission of gravitational waves from binary black hole mergers. The results obtained using the geometric nested sampler are compared with those from popular nested sampling algorithms.

Initiation devices used in mining have strict requirements for safety and efficiency. However, the analysis of their operation is encumbered by their complex design which involves multiple explosive charges and inert materials. We use numerical simulations to study detonation in configurations involving complex geometry and multiple materials with the aim of revealing key features of their internal processes and improving their reliability and performance. The mathematical model is based on a two-phase reactive formulation and is extended with porosity and shock desensitization models. It is coupled with appropriate inert material models for fluids and solids to accurately capture their interaction with the detonation wave. We initially consider detonation propagation in annular charges. The model and implementation are validated against experimental data for steady state propagation. Then, the numerical solution is used to obtain a detailed description of the speed of the detonation wave along the annular arc and a new description of the transition phase is proposed. Further, a parametric study is performed in which the dependence of the transition phase and steady state on the dimensions of the annulus is analysed. The rest of the thesis examines detonation in explosive devices used in the initiation of tertiary explosives in mining. First, we consider the response of a detonator in isolation, guided by an underwater explosion test. Following validation, the strength of the blast wave is examined at several distances from the detonator. Results show that the blast wave in the near field is asymmetric and stronger along the axis of the detonator. Further, the near field blast wave varies considerably between detonators of different shell material and thickness while the pulse in the far field is similar. This indicates that the fine differences between detonators cannot be captured by tests that consider the blast wave at a single point in the far field. Lastly, we study the complete configuration used to initiate explosives in mining blastholes which involves a detonator and a booster. The reactive model is extended to account for shock desensitization. The model is validated and a series of simulations of the detonator and booster configuration, with and without desensitization, are performed. These show that the influence of desensitization is significant and can lead to the formation of dead zones in the explosive which have a critical impact on booster performance. Depending on the material of the detonator shell, the initiation of the booster can result in only a small non-reacted region or in an extensive desensitized zone which prevents the detonation of a large portion of the explosive.

Confectionery wafer baking is a complex process involving a series of physical, chemical and biochemical changes in the product, including water evaporation, formation of the porous structure, denaturation of protein, gelatinisation of starch and Maillard reactions. Mathematically it can be described as simultaneous heat and mass transfer operation involving processes such as conduction from the baking plate, natural and forced convection, evaporation of water and condensation of steam resulting in moisture diffusion A pressure profile analysis approach involving wafer baking experiments and mathematical modelling was proposed and used to study wafer structure formation. Wafers have a dense core and crispy structure obtained through baking between two hot plates (baking tongs with 90 degree or 45 degree reedings) in a gas-fired baking oven at temperatures in the region of 150°C for around 120 seconds. Previous work explains wafer baking through the investigation of the pressure profile that arises over the course of baking, with data collected from experiments and kitchen trials at Nestlé. The present study explains the pressure profile generated during the baking process in the context of structure formation of wafers. Three different pressure profile stages are identified: Stage 1, gas generation and expansion (bubble generation), during which the pressure increases; Stage 2, foam to sponge transition (structure formation), during which the pressure decreases; and Stage 3, drying through a porous structure (moisture diffusion), during which the pressure stays essentially constant. The focus of the work reported in this thesis is the study of these three stages in detail. A lab scale experimental rig was developed to study wafer baking between two hot plates in a temperature controlled environment. Varying compositions of water:flour ratio was used for this study. The results produced were meaningful but not reproducible due to the complexity of maintaining baking pressure within the system and achieving system stability. Further experiments were conducted with different product recipes using an industrial pilot plant baking system to achieve repeated results for data analysis. The results obtained indicated that with an increase in water:flour ratio the system retained pressure for a shorter duration due to increased viscosity of the wafer batter. Similarly increasing the quantity of enzymes and leaving agents does not necessarily result in increased system pressures as viscosity of the wafer batter plays a leading role in defining pressure retaining capability of the system for a set of defined process conditions. The experiments confirmed that change in recipe alone is not sufficient to obtain desired wafer structures rather a combination of controlled process variables such as batter deposit rate, baking temperature and baking plates operating mechanism have an impact on the final wafer structure. The results obtained were modelled using excel mathematical modelling tools. The model provided an accurate characterisation of the wafer baking pressure profiles and the modelling parameters obtained highlighted key features of wafer baking pressure profiles.

Antibiotic resistance is one of the major health concerns of the 21st century. Antibiotics are essential for the health and well-being of both humans and animals. However, the increase in antibiotic resistant bacteria poses a threat to the continued use of antibiotics to successfully treat bacterial infections. Current research within hospital settings has focused on the use of multi-antibiotic approaches in a variety of treatment patterns. Yet there is limited knowledge on the optimal use of single antibiotic treatments. With the spread of resistance linked to the overuse and misuse of antibiotics, optimal treatment regimens aim to maximise the success of eradicating an infection while minimising the amount of antibiotic required. This thesis therefore aimed to combine mathematical modelling with a genetic algorithm approach to identify optimal dosage regimens for the use of a single antibiotic. A mathematical model was developed to predict the dynamics of bacterial populations within an infection. A susceptible only infection was initially considered before being extended to include a resistant population. These models were incorporated into a genetic algorithm and used to search for dosage regimens which maximise bacterial eradication and minimise antibiotic use. Taking a theoretical approach, it was found that administering an antibiotic with a high initial dose followed by lowering doses is the optimal treatment regimen. A case study of a Vibrio anguillarum infection within Galleria mellonella larvae was used to parameterise the one strain bacterial model to a biologically realistic system. The results are consistent with those from the theoretical parameter sets. A tapered treatment regimen maximises the success of eradicating the bacterial infection while minimising the amount of antibiotic required. Laboratory experiments were performed which provided credibility to the results found. Finally, the assumption of fixed time intervals between doses was relaxed and the genetic algorithm used to identify both the dose and time intervals of optimal treatment regimens. Varying either the doses or the time intervals separately produced no significant difference in the success of eradicating an infection. When combined, the results showed that significantly better regimens could be identified. These regimens further increased bacterial eradication while using less antibiotic to do so. More work is required to identify a general treatment pattern when both variables are optimised due to the high variability in solutions. However, a shift away from conventional constant dose treatment regimens is required to prolong the future effectiveness of antibiotics.

The recent emergence of highly virulent strains of the pathogen causing wheat stem rust has been acknowledged as a threat to global food security. In infected wheat fields, vast amounts of pathogenic fungal spores are produced that can be carried away by wind. For targeted disease surveillance and control it is important to estimate when, where and how many fungal spores are dispersed from infected to susceptible wheat fields. In this study, high-performance computational resources are used to investigate long-distance dispersal revealing atmospheric pathways that connect entire continents. Mechanistic simulations of turbulent atmospheric spore dispersal are conducted. The analyses bring together a variety of data, including international field disease surveys and finely resolved meteorological model data. The UK Met Office's Langrangian stochastic particle dispersion model, NAME, is applied, extended and coupled to other models in a set of case studies. In the first case study, spore dispersal is analysed across Southern/East Africa, the Middle East, and Central/South Asia by simulating billions of stochastic trajectories of fungal spores over dynamically changing host and environmental landscapes. The circumstances under which virulent strains, such as Ug99, pose a risk to globally important wheat producing areas are identified. Simulation results indicate a negligible risk for dispersal from key wheat producing countries on the East African continent (Ethiopia, Kenya) directly to India and Pakistan. However, there is a considerable risk for atmospheric transport from the Arabian Peninsula to South Asia. Spore dispersal trends are quantified between all countries in the domain providing estimates which can be used to improve targeted sampling and control. In the second case study, dispersal from southern Africa to Australia is analysed. Simulation results, as well as data from phenotypic and genotypic analyses, support the hypothesis that extremely long-distance airborne dispersal across the Indian Ocean is possible, albeit rare. This indicates that the pathogen populations on the two continents are connected and underlines the importance of sharing surveillance intelligence between continents. The third case study focusses on Ethiopia, determining likely origins of strain TKTTF that recently caused severe epidemics in East Africa's largest wheat producing country. The analyses suggest inflow into Ethiopia from the Middle East via Yemen, consistent with field survey data. The risk for inflow of pathogens into Ethiopia from key neighbouring countries is ranked for different months of the wheat season. In the last results chapter a pilot study is summarized testing the feasibility of an automated short-term forecasting system for spore dispersal from the latest field disease detection sites. Whilst the functionality and practical relevance of the forecasting system is demonstrated, considerable challenges remain for testing the forecasts. The predictive simulation framework described in this thesis can be applied to any wheat producing area worldwide to assess dispersal risks. The research has broader relevance because long-distance dispersal is a key mechanism for the transmission of several crop and livestock diseases, and also plays an important role in other areas of ecology.

Engine manufacturers are constantly seeking avenues to build cleaner and more ef cient engines to meet ever increasing stringent emission legislations. This requires a closer under- standing of the in-cylinder physical and chemical processes, which can be obtained either through experiments or simulations. The advent of computational hardware, methodologies and modelling approaches in recent times make computational uid dynamics (CFD) an important and cost-effective tool for gathering required insights on the in-cylinder ow, combustion and their interactions. Traditional Reynolds-Averaged Navier-Stokes (RANS) methods and emerging Large Eddy Simulation (LES) techniques are being used as a reli- able mathematical framework tools for the prediction of turbulent ow in such conditions. Nonetheless, the combustion submodels commonly used in combustion calculations are developed using insights and results obtained for atmospheric conditions. However, The combustion characteristics and its interaction with turbulence at Internal combustion (IC) engine conditions with, high pressure and temperatures can be quite different from those in conventional conditions and are yet to be investigated in detail. The objective here is to apply FlaRe (Flamelets revised for physical consistencies) model for IC engines conditions and assess its performance. This model was developed in earlier studies for continuous combustion systems. It is well accepted that the laminar burning velocity, SL, is an essential parameter to determine the fuel burn rate and consequently the power output and ef ciency of IC engines. Also, it is involved in almost all of the sophisticated turbulent combustion models for premixed and partially premixed charges. The burning velocities of these mixtures at temperatures of 850 ≤ T ≤ 950 decrease with pressure up to about 3 MPa as it is well known, but it starts to increase beyond this pressure. This contrasting behaviour observed for the rst time is explained and it is related to the role of pressure dependent reaction for iso-octane and involving OH and the in uence of this radical on the fuel consumption rate. The results iv seem to suggest that the overall order of the combustion reaction for iso-octane and gasoline mixture with air is larger than 2 at pressures higher than 3 MPa. The FlaRe combustion is used to simulate premixed combustion inside a spark-ignition engine. The predictive capabilities of the proposed approach and sensitivity of the model to various parameters have been studied. FlaRe approach includes a parameter βc representing the effects of ame curvature on the burning rate. Since the reactant temperature and pressure inside the cylinder are continually varying with time, the mutual in uence of ame curvature and thermo-chemical activities may be stronger in IC engines and thus this parameter is less likely to be constant. The sensitivity of engine simulation results to this parameter is investigated for a range of engine speed and load conditions. The results indicate some sensitivity and so a careful calibration of this parameter is required for URANS calculation which can be avoided using dynamic evaluations for LES. The predicted pressure variations show fair agreement with those obtained using the level-set approach. DNS data of a hydrogen air turbulent premixed ame in a rectangular constant volume vessel has been analysed to see the effect of higher pressure and temperature on the curvature parameter βc. Since the reactant temperature and pressure inside the cylinder are continually varying with time, the mutual in uence of ame curvature and thermo-chemical activities are expected to be stronger in IC engines and thus the parameter βc may not be constant. To shed more light on this, two time steps from the DNS data has been analysed using dynamic βc procedure. The results show that the effect of higher pressure and temperature need to be considered and taken into account while evaluating βc. When combustion takes place inside a closed vessel as in an IC engine the compression of the un-burnt gases by the propagating ame causes the pressure to rise. In the nal part of this thesis, the FlaRe combustion model is implemented in a commercial computational uid dynamics (CFD) code, STAR-CD, in the LES framework to study swirling combustion inside a closed vessel. Different values of βc has been tested and the need for dynamic evaluation is observed.

In this thesis an analytical modelling approach is employed to predict and gain insight into the flows induced by turbulent plumes and jets above slender horizontal slots, in otherwise quiescent uniform environments. To supplement the solutions, the effect on the environment of a plume driven by an off-source supply of buoyancy was also considered. The solutions derived provide an advancement on existing idealised models for the jet and plume induced flows, and moreover, complement a number of key advances that have been made in our understanding of plume flows in recent years. The theory of functions of a complex variable, which has not previously been applied in such an application, has been utilised as a fundamental tool throughout the work. This has enabled the entrainment behaviour and geometry of the plumes to be accounted for when developing the induced flow solutions. A novel conformal mapping has been devised specifically to account for the curved perimeter of the contracting lazy plume. This modelling approach is robust in that future developments to aspects of the modelling, for instance, the formulation of a new entrainment closure, can be straightforwardly accounted for using the method. The induced flow solutions exhibit a range of flow patterns which are dependent on the source Richardson number of the plume flow. A pure plume induces a uniform horizontal flow. Forced and lazy plumes correspond to a relative deficit and excess in source buoyancy flux compared to the pure plume, respectively. Generally, forced plumes induce downwardly inclined flows, in contrast to lazy plumes, which induce upwardly inclined flows. Consistent with these solutions, the notionally lazy plume driven by a vertical uniform off-source supply of buoyancy induces an upwardly inclined flow. In addition to an improved understanding of induced flows, our solutions have provided us with insight into the plume flow. Notably, the solution corresponding to the forced plume has led us to fundamentally question existing models describing the plume and, in particular, closures that have been employed to model entrainment. We find that the existing well accepted closures exhibit some form of non-physical flow behaviour.

Language change is driven by a constellation of acquisition and usage factors operating at two ontological levels: the level of the individual and the level of the population. This thesis proposes that an improved understanding of processes of language change can be obtained through the use of mathematical models that incorporate detailed mechanisms of language acquisition and use and derive diachronic predictions as mathematical theorems of those mechanisms. Four aspects of linguistic diachrony are singled out for detailed study in the four original publications constituting the core of this journal-format dissertation: the Constant Rate Effect, stable variation in multidimensional grammatical competition, effects of social network topology and rewiring, and the relationship between processes of change and synchronic frequency and spatial distributions of linguistic traits. Through mathematical analysis and computer simulations, the dissertation suggests (i) that diachronic patterns such as the Constant Rate Effect arise through an interaction of acquisition and usage effects, the latter modelled as probabilistic post-acquisition production biases that filter the underlying grammatical state; (ii) that the fundamental result on competition between two grammatical options that outlaws diachronically stable variation does not hold of multidimensional competition; (iii) that finite-size effects such as network topology and dynamic network rewiring may give rise to orderly phenomena such as S-curves even in the absence of traditional biasing factors; and (iv) that typological distributions of linguistic features arise through a dynamic interplay of faithful transmission and mutation, subject to both local and areal effects. As a general conclusion, I propose that language change can be understood as the product of neither acquisition nor usage factors alone, but that both types of factor need to be incorporated in mechanistic models which make the interrelationships between these factors explicit. Acquisition and use constitute a diachronic feedback loop leading to nonlinear equations of linguistic change; it is in many cases a consequence of these nonlinearities that bifurcations arise which may throw change trajectories onto qualitatively unexpected courses simply as a response to minute variation in relevant control parameters. This sheds new light on explanation in diachronic linguistics: to explain a process of change is to model it with mechanisms which derive facets of that process as empirical predictions. Mathematical models are particularly well suited to this task, as they force the modeller to be explicit and exact, both qualitatively and quantitatively, about the mechanisms involved; explanations of this kind, moreover, can be either traditionally deductive-nomological, or probabilistic.

Wet age related macular degeneration (wet AMD) is a highly debilitating retinal disease, the third leading cause of blindness in the world and one the most expensive ocular conditions to care for. Wet AMD is characterised by the proliferation of neovasculature through the retinal posterior and theorised to be, at least in part, induced and driven by excess vascular endothelial growth factor (VEGF). Many current treatments for wet AMD utilise anti-VEGF macromolecules that bind to VEGF. The retina, however, remains a largely inaccessible, and delicate, anatomical region. Due to difficulties in collecting clinical and experimental data, mathematical modelling is playing an increasingly prominent role in understanding the distribution (Pharmacokinetics, PK) and drug-to-target interactions (Pharmacodynamics, PD) for treatments of wet AMD. This thesis will focus on ordinary/partial differential equation (ODE/PDE) models for the PK/PD of anti-VEGF therapeutics, administered via intravitreal (IVT) injection into the mammalian eye. We start in Chapter 2 with a 2-compartment PK/PD ODE model of drug-VEGF interactions in the eye, analysing a clinical dataset to estimate key binding parameters between VEGF and the typical anti-VEGF molecule, ranibizumab. In Chapter 3, we extend the PK ODE framework of the 2-compartment model to include a mechanistic description of the retina, to estimate retinal permeability to macromolecules used for treating wet AMD. In Chapter 4, using the retinal PK model, we reintroduce VEGF to predict concentrations of free VEGF in the retina post-IVT injection. Chapters 5 and 6 model a hypothetical class of anti-VEGF molecules designed to bind not only VEGF but also existing vitreal superstructures, analysing how dose and binding kinetics impact ocular retention. Alongside these models we present analogous PDE models, addressing whether the assumption that concentrations are homogeneous across anatomical regions, as implicit in ODE models, is appropriate for macromolecular PK/PD in the mammalian eye.

Ice shelves are important to the climate system as they control the release of fresh water from ice sheets into the ocean, with consequences for sea level rise and ocean dynamics. Channels modifying basal melt rates and structural integrity have been observed inscribed in the undersides of some ice shelves. Observations indicate that some channels run in a direction transverse to ice flow and it has been suggested that these form due to seasonal variations in ocean properties. This thesis analyses the effect of seasonal variability on ice shelves and meltwater plumes in the underlying ocean. A linear perturbation analysis on vertically integrated ice and plume models showed that seasonal forcing of subglacial discharge or ice flux can generate small ripples melted into the base of the ice shelf. These ripples did not develop into overdeepened channels, but the ripples caused by ice flux appear similar to basal terraces observed underneath some ice shelves. Code was developed to run 1-D nonlinear simulations with the vertically-integrated equations, producing similar results to the linear case. However, runs neglecting hydrostatic pressure gradients exhibited a feedback causing ice flux-generated ripples to grow into small proto-channels. A horizontally-integrated plume model was derived, incorporating the Coriolis force and transverse plume flow into a 1-D model which agreed well with a 3-D ocean simulation. Coupling this horizontally-integrated plume with a co-evolving ice shelf prevented proto-channels from forming. It appears unlikely that subglacial discharge or ice flux variations can give rise to observed transverse channels. A new approach was developed to predict the evolution of internal radar reflectors observed within ice shelves, using vertically-integrated models of ice flow. It is hoped this approach might have applications for inverse modelling and data assimilation.