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Doctor of Philosophy(PhD) / Polymer manufacturing is a major worldwide industry, attracting the attention of numerous industrial units and research institutes. Increasing demands on polymer quality, process safety and cost reduction are the main reasons for growing interest in the design and control of emulsion polymerisation. Emulsion polymerisation process implemented with free radical polymerisation has significant advantages over other processes, such as the production of polymer of higher molecular weights at high conversion rates, easier temperature control due to the low viscosity of the reaction media, high degree of selectivity and more friendly to environment due to the use of an aqueous medium. It allows for the production of particles with specially-tailored properties, including size, composition, morphology, and molecular weights. Introducing two or more different monomers to the polymerisation process (named multi-polymerisation) can lead to the synthesis of an almost unlimited number of new polymers types. Emulsion polymers are products by process, meaning that the manner in which the polymerisation is carried out is perhaps more important than the raw materials in determining the form of the final product. This highlights the significance of the systematic approach in online process control which requires thorough understanding of the process phenomena as a prerequisite for development of a mathematical description of the process as the model. It is thus evident and based on research observations that process control for emulsion terpolymerisation is a particularly difficult task because of the lack of validated models and the lack of online measurements of most of polymer properties of interest. Therefore, a well validated model is crucial for optimising and controlling the emulsion terpolymerisation operations allowing for design of the polymer product properties. In this study, a framework for process design and control of emulsion terpolymerisation reactors was developed. This framework consisted of three consecutive stages, dynamic modelling of the process, optimising the process for finding the optimal operating strategies and final online controlling the obtained optimal trajectories through multivariable constrained model predictive control. Within this framework, a comprehensive dynamic model was developed. Then a test case of emulsion terpolymerisation of styrene, methyl methacrylate and methyl acrylate was investigated on state of the art facilities for predicting, optimising and control end-use product properties including global and individual conversions, terpolymer composition, the average particle diameter and concentration, glass transition temperature, molecular weight distribution, the number- and weight-average molecular weights and particle size distribution. The resulting model was then exploited to understand emulsion terpolymerisation behavior and to undertake model-based optimization to readily develop optimal feeding recipes. The model equations include diffusion-controlled kinetics at high monomer conversions, where transition from a ‘zero-one’ to a ‘pseudo-bulk’ regime occurs. Transport equations are used to describe the system transients for batch and semi-batch processes. The particle evolution is described by population balance equations which comprise of a set of integro-partial differential and nonlinear algebraic equations. Backward finite difference approximation method is used to discretise the population equation and convert them from partial differential equations to ordinary differential equations. The model equations were solved using the advanced simulation environment of the gPROMS package. The dynamic model was then used to determine optimal control policies for emulsion terpolymerisation in a semi-batch reactor using the multiobjective dynamic optimisation method. The approach used allows the implementation of constrained optimisation procedures for systems described by complex mathematical models describing the operation of emulsion terpolymerisation reactors. The control vector parameterisation approach was adopted in this work. Styrene monomer feed rate, MMA monomer feed rate, MA monomer feed rate, surfactant feed rate, initiator feed rate and the temperature of reactor were used as the manipulating variables to produce terpolymers of desired composition, molecular weight distribution (MWD) and particle size distribution (PSD). The particle size polydispersity index (PSPI), molecular weight polydispersity index (MWPI) and the overall terpolymer composition ratios were incorporated as the objective functions to optimise the PSD, MWD and terpolymer composition, respectively. The optimised operational policies were successively validated with experiments via one stirred tank polymerisation reactor. Due to the lack of online measurements of key process product attributes for emulsion terpolymerisation, an inferential calorimetric soft sensor was developed based on temperature measurements. The calorimetric soft sensor obtains online measurements of reactor temperature, jacket inlet and outlet temperatures helped estimate the rate of polymerisation. The model includes the mass and energy balance equations over the reactor and its peripherals. Energy balance equations include the heat of reaction, internal and external heat transfer effects, as well as external heat losses. An online multivariable constrained model predictive control was formulated and implemented for online control of the emulsion terpolymerisation process. To achieve this implementation, a novel generic multilayer control architecture for real-time implementation of optimal control policies for particulate processes was developed. This strategy implements the dynamic model for the emulsion terpolymerisation as a real-time soft sensor which is incorporated within the implemented MPC. The methodology was successively validated using six case studies within the on-line control of terpolymerisation reactors. The cases were online controlled the composition of terpolymers, PSD and Mn with specific constraints for the operation conversion and particle average radius. An advanced Supervisory Control Architecture named ROBAS was used in this work. It provides a completely automated architecture allowing for the real time advanced supervisory monitoring and control of complex systems. The real time control application strategy was developed within MATLAB, Simulink, gPROMS and Excel Microsoft softwares and implemented on line through ROBAS Architecture. The manipulated variables are measured using on-line measurements connected to the DCS system through Honeywell. These measurements were sent to MATLAB and then to the dynamic model in gPROMS through an excel spread-sheet interface. Then the dynamic model used them to estimate the controlled variables of the MPC. The estimated values of the controlled variables obtained from the dynamic model, were then sent to the Simulink and fed through the DCS system to the MPC developed in MATLAB. The MPC would then calculate optimal trajectories, which are then sent as set point signals through the DCS system to the regulatory controller. The MPC formulation was found to be robust and handles disturbances to the process. The result showed that the online multivariable constrained MPC controller was able to control the desired composition and Mn as specified set points with great accuracy. The MPC algorithm succeeded under constrained conditions, in driving the PSD to the desired target. Although some offset was observed with a certain degree of model mismatch, the experimental results agreed well with predictions.

Biofilms can be simply defined as communities of microbes attached to a surface. There are various types of biofilm, which can be either beneficial or harmful to an ecosystem. Good biofilm offers valuable services to society or in the function of natural ecosystems such as those that contribute to controlled bioremediation of ground water and soils in Low Impact Development approaches called bioretention cell. This thesis researched ways to model biofilm activity at the field-scale and used experimental data (BOD5 and NO3-) to verify these models. Two mathematical models are presented in this work. The first model provides and tests the solution of substrate and biomass concentration while the second model modified the expression for the substrate flux into the biofilm. They are analyzed using a sensitivity analysis and their performance is compared using field-scale data. The solution for concentration is computed with some selected values of dimensionless biofilm thickness (0.0375 and 3.75) and dimensionless substrate concentration outside of the biofilm (0.005 to 0.5), which shows these two variables significantly affect model results. The simulations illustrate that biofilm activity mostly occurs in the summer while the substrate flux is normally stable at similar levels in the same season. / Graduate

Angiogenesis is the formation of new blood vessels from existing ones, and is a key characteristic of tumour progression. The purpose of antiangiogenic (AA) cancer therapies is to disrupt the tumour's blood supply in order to inhibit the delivery of oxygen and nutrients. However, such therapies have demonstrated limited benet to cancer patients: although they delay tumour progression for some types of cancer, they do not consistently improve survival. Several preclinical experimental studies have reported that AA therapies lead to a period of vessel normalisation, during which vessels transition from the leaky, tortuous state that is typical of tumour vasculature to a more stable state where blood perfusion is increased. It has been suggested that normalisation is the reason why some AA therapies lack effcacy. In this thesis, we develop and study mathematical models of various aspects of angiogenesis and vessel normalisation, and we use our results to suggest effective AA therapy regimens. Our first model represents the biochemical interactions and cellular dynamics involved in neovascularisation: we incorporate biological hypotheses to develop a spatially averaged ODE model of vessel formation, and we show that the model admits a number of vascular phenotypes characterised by their degrees of vessel normalisation. We showed that these phenotypes respond differently to different AA treatments. In our second model, we use preclinical tumour size data to develop and parametrise a mixed effects model of vascular tumour growth including vessel normalisation. We use our prediction about the timing of the transient normalisation window to further predict the potential benefits of combining chemotherapy and AA therapy. Lastly, we extend an existing PDE model of vascular tumour growth to incorporate AA therapy and vessel normalisation. We demonstrate that the oscillatory behaviour that arises in the spatially averaged version of the model induces spatial heterogeneity in the spatially extended version, and show that the vessel kill and normalisation parameters (among other parameters) can modulate tumour heterogeneity.

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Increasing surface runoff from the Greenland Ice Sheet due to a warming climate not only accelerates ice mass loss by altering surface mass balance, but may also lead to increased dynamic losses. This is because surface melt draining to the bed can reduce ice-bed coupling, leading to faster ice flow. Understanding the impact of surface melt on ice dynamics is important for constraining the contribution of the Greenland Ice Sheet to sea level rise. The aim of this thesis is to numerically model the influence of surface runoff on ice velocities. Three new models are presented: an updated supraglacial hydrology model incorporating moulin and crevasse drainage, along with lake drainage over the ice surface via channel incision; an ice sheet model implementing a numerically efficient formulation of ice flow; an adjoint code of the ice flow model based on automatic differentiation. Together with a subglacial hydrology model, these represent the key components of the ice sheet system. The supraglacial hydrology model is calibrated in the Paakitsoq region. Model output shows the partitioning of melt between different drainage pathways and the spatial distribution of surface drainage. Melt season intensity is found to be a relevant factor for both. A key challenge for simulations applying a coupled ice-flow/hydrology model is state and parameter initialization. This challenge is addressed by developing a new workflow for incorporating modelled subglacial water pressures into inversions of basal drag. A current subglacial hydrology model is run for a winter season, and the output is incorporated into the workflow to invert for basal drag at the start of summer in the Russell Glacier area. Comparison of the modelled subglacial system to observations suggests that model output is more in line with summer conditions than winter conditions. A multicomponent model integrating the main components of the ice sheet system is developed and applied to the Russell Glacier area. A coupled ice-flow/hydrology model is initialized using the proposed workflow, and driven using output from the supraglacial hydrology model. Three recent melt seasons are modelled. To a first order, predicted ice velocities match measured velocities at multiple GPS sites. This affirms the conceptual model that summer velocity patterns are driven by transitions between distributed and channelized subglacial hydrological systems.

An integral equation description for linear systems is developed and used as the basis for the development of various system identification, model reduction and order determination methods. The system integral equation is utilized in the problem of parameter identification in continuous linear single-input single-output, multi-input multi-output and linear in parameters nonlinear systems. The approach is developed in the time domain where the effect of non-zero initial conditions and additive disturbances occurs naturally. Parameter estimates are deduced using several weighted residual concepts which have previously been used to produce approximate solutions to differential equations.

This thesis investigates the complexing properties of synthetic macrocyclic ligands such as calix[4]arenes (L1-L6) and cryptand 222 (L7) towards lanthanide(III) cations in dipolar aprotic media (acetonitrile and N,N-dimethylformamide) at 298.15 K. Molecular modelling studies performed on calix[4]arene derivatives suggested that solvent molecules such as acetonitrile and N,N-dimethylformamide interact with the hydrophobic cavity, thus inducing conformational changes on these ligands, 'preorganising' them for complexation. 1H NMR complexation experiments established the presence of interactions between the hydrophilic cavity of calix[4]arene derivatives and the metal cations and revealed the sites of complexation of the ligands. Conductance measurements clearly demonstrated that 1:1 and 2:1 metal cation : ligand stoichiometries are found with these cations in acetonitrile. The thermodynamics of complexation of macrocyclic ligands and lanthanide(III) cations in acetonitrile and in N,N-dimethylformamide at 298.15 K was derived from titration microcalorimetry. Stability constants were also determined by the competitive potentiometric method using silver electrodes. Excellent agreement was found between the data derived from calorimetry and those derived by potentiometry. The complexation process between these cations and these ligands was enthalpically controlled for all systems studied. Enthalpy-entropy compensation effects were observed in the complexation of 5,11,17,23-tetrakis-(1,1-dimethylethyl)-25,27-bis[2-(methylthio)ethoxy]-26,28-bis[2(diethylamine)ethoxy]calix[4]arene, L1 and the different lanthanide(III) cations in acetonitrile, as well as L1, L7 and [tetrakis(N,N-diethylaminoethyl)oxyl]p-tert-butylcalix[4]arene, L2, in N,N-dimethyl formamide, as suggested by the absence of significant variations in the free energies of complexation in each case. As far as p-tert-butylcalix[4]arene tetradiisopropyl acetamide, L3, is concerned, a selective behaviour was observed for these cations in acetonitrile with the highest stabilities found for gadolinium and europium. Metal-ion complexes were isolated based on their stability and the solution thermodynamics of the free and complexed salts was investigated. Lastly, the complexation process in the two solvents was discussed, taking into account the differences in solvation of the reactants and the product in these solvents.

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Denitrification was investigated during 1985 and 1986 in a stagnogleyic brown earth (Macmerry) and a stagnogley (Winton), both soil types widely used for cereal production in south-east Scotland. The crop was winter barley. Much of the work was devoted to the evaluation and attempted field application of the acetylene-inhibition technique. This involves blocking the terminal reduction of nitrous oxide to elemental nitrogen by acetylene concentrations in excess of 0.1% by volume; total denitrification loss is then estimated by measuring the resultant enhanced nitrous oxide flux at the soil surface. For prolonged periods during the growing season relatively high concentrations of nitrous oxide in the soil atmosphere indicated significant rates of denitrification. It proved impossible, however, to obtain an adequate distribution of acetylene throughout the profile, resulting in improbably low denitrification estimates. This finding casts doubt on any reported measurements using the acetylene- inhibition technique in wet soils with poor structure. The method was applied with more success on a freely-drained Darvel soil. An alternative technique was investigated for the gleyed soils: laboratory incubation of intact cores in an atmosphere containing acetylene. This produced increased estimates of denitrification but was found to introduce other uncertainties. It was concluded that further development was required before the technique could be used to give reliable quantitative results. Measured gaseous diffusion constants and nitrous oxide concentrations at depth were employed in the Fick?s Law calculation of nitrous oxide flux; calculated losses during 1986 ranged from 0.2-0.5 kg N /ha for direct-drilled Winton plots to 3.6-7.4 kg N /ha for normally-ploughed M acmerry soil. These were minimum values for total gaseous loss, since losses as elemental nitrogen were not recorded. A mathematical model of denitrification was developed. It depends on numerical solution of the differential equations governing the simultaneous steady-state diffusion and reduction of oxygen, nitrate, and nitrous oxide in a spherical m icro-environm ent (an aggregate where aggregates are present - an "effective aggregate" in a structureless soil). A model aggregated soil is pictured as an assembly of spherical aggregates with log-normally distributed aggregated radius and reductive potential; the radius of the effective aggregate in a structureless soil is determined by the density of air-filled pores. Intra?aggregate diffusion constants are calculated by a method which amounts to an assumption of parallel diffusion through all possible serial combinations of intra-aggregate pores. Reductive potentials for the various reactions considered in the model are assumed to be proportional to one another. The model predicts an approximately linear relationship between the denitrification rate of an assembly of soil aggregates and its anaerobic fraction calculated according to the method of Smith (1980); such a relationship has in fact been observed (Parkin and Tiedje, 1984). Model results illustrate the importance of soil structure: a model clay soil continues to denitrify at moisture potentials much lower (more negative) than a model sand. Calculated whole-soil denitrification rates range from 0 g N/ha/d to 5.2 kg N/ha/d. Reported field measurements range from 0 g N/ha/d to 4.5 kg N/ha/d.