A mathematical model of coal-fired fluidised bed boilers

A mathematical model of a large coal-fired fluidized bed boiler for power generation is synthesised. The effect of variations in the main parameters of the model on variables such as the background carbon concentrations in the bed, and the transient response of heat evolution are studied. The mechanisms of solids mixing within the bed, combustion and the flow of heat to the boiler tubes are shown to result in a characteristic dynamic response, knowledge of which is essential for the proper control and regulation of a practical system.

Mathematical modelling of patient risks in a hospital environment, using multiple regression analysis

The aim of this research work was primarily to examine the relevance of patient parameters, ward structures, procedures and practices, in respect of the potential hazards of wound cross-infection and nasal colonisation with multiple resistant strains of Staphylococcus aureus, which it is thought might provide a useful indication of a patient's general susceptibility to wound infection. Information from a large cross-sectional survey involving 12,000 patients from some 41 hospitals and 375 wards was collected over a five-year period from 1967-72, and its validity checked before any subsequent analysis was carried out. Many environmental factors and procedures which had previously been thought (but never conclusively proved) to have an influence on wound infection or nasal colonisation rates, were assessed, and subsequently dismissed as not being significant, provided that the standard of the current range of practices and procedures is maintained and not allowed to deteriorate. Retrospective analysis revealed that the probability of wound infection was influenced by the patient's age, duration of pre-operative hospitalisation, sex, type of wound, presence and type of drain, number of patients in ward, and other special risk factors, whilst nasal colonisation was found to be influenced by the patient's age, total duration of hospitalisation, sex, antibiotics, proportion of occupied beds in the ward, average distance between bed centres and special risk factors. A multi-variate regression analysis technique was used to develop statistical models, consisting of variable patient and environmental factors which were found to have a significant influence on the risks pertaining to wound infection and nasal colonisation. A relationship between wound infection and nasal colonisation was then established and this led to the development of a more advanced model for predicting wound infections, taking advantage of the additional knowledge of the patient's state of nasal colonisation prior to operation.

The mathematical modelling of the environmental performance of buildings as an aid in the design process

This thesis is a theoretical study of the accuracy and usability of models that attempt to represent the environmental control system of buildings in order to improve environmental design. These models have evolved from crude representations of a building and its environment through to an accurate representation of the dynamic characteristics of the environmental stimuli on buildings. Each generation of models has had its own particular influence on built form. This thesis analyses the theory, structure and data of such models in terms of their accuracy of simulation and therefore their validity in influencing built form. The models are also analysed in terms of their compatability with the design process and hence their ability to aid designers. The conclusions are that such models are unlikely to improve environmental performance since: a the models can only be applied to a limited number of building types, b they can only be applied to a restricted number of the characteristics of a design, c they can only be employed after many major environmental decisions have been made, d the data used in models is inadequate and unrepresentative, e models do not account for occupant interaction in environmental control. It is argued that further improvements in the accuracy of simulation of environmental control will not significantly improve environmental design. This is based on the premise that strategic environmental decisions are made at the conceptual stages of design whereas models influence the detailed stages of design. It is hypothesised that if models are to improve environmental design it must be through the analysis of building typologies which provides a method of feedback between models and the conceptual stages of design. Field studies are presented to describe a method by which typologies can be analysed and a theoretical framework is described which provides a basis for further research into the implications of the morphology of buildings on environmental design.

Immunological synapse: a mathematical model of the bond formation process:mathematical modelling of the immature synapse

The cell:cell bond between an immune cell and an antigen presenting cell is a necessary event in the activation of the adaptive immune response. At the juncture between the cells, cell surface molecules on the opposing cells form non-covalent bonds and a distinct patterning is observed that is termed the immunological synapse. An important binding molecule in the synapse is the T-cell receptor (TCR), that is responsible for antigen recognition through its binding with a major-histocompatibility complex with bound peptide (pMHC). This bond leads to intracellular signalling events that culminate in the activation of the T-cell, and ultimately leads to the expression of the immune eector function. The temporal analysis of the TCR bonds during the formation of the immunological synapse presents a problem to biologists, due to the spatio-temporal scales (nanometers and picoseconds) that compare with experimental uncertainty limits. In this study, a linear stochastic model, derived from a nonlinear model of the synapse, is used to analyse the temporal dynamics of the bond attachments for the TCR. Mathematical analysis and numerical methods are employed to analyse the qualitative dynamics of the nonequilibrium membrane dynamics, with the specic aim of calculating the average persistence time for the TCR:pMHC bond. A single-threshold method, that has been previously used to successfully calculate the TCR:pMHC contact path sizes in the synapse, is applied to produce results for the average contact times of the TCR:pMHC bonds. This method is extended through the development of a two-threshold method, that produces results suggesting the average time persistence for the TCR:pMHC bond is in the order of 2-4 seconds, values that agree with experimental evidence for TCR signalling. The study reveals two distinct scaling regimes in the time persistent survival probability density prole of these bonds, one dominated by thermal uctuations and the other associated with the TCR signalling. Analysis of the thermal fluctuation regime reveals a minimal contribution to the average time persistence calculation, that has an important biological implication when comparing the probabilistic models to experimental evidence. In cases where only a few statistics can be gathered from experimental conditions, the results are unlikely to match the probabilistic predictions. The results also identify a rescaling relationship between the thermal noise and the bond length, suggesting a recalibration of the experimental conditions, to adhere to this scaling relationship, will enable biologists to identify the start of the signalling regime for previously unobserved receptor:ligand bonds. Also, the regime associated with TCR signalling exhibits a universal decay rate for the persistence probability, that is independent of the bond length.

Simultaneous chemical reaction and distillation of formaldehyde

The thesis is concerned with the development and testing of a mathematical model of a distillation process in which the components react chemically. The formaldehyde-methanol-water system was selected and only the reversible reactions between formaldehyde and water giving methylene glycol and between formaldehyde and methanol producing hemiformal were assumed to occur under the distillation conditions. Accordingly the system has been treated as a five component system. The vapour-liquid equilibrium calculations were performed by solving iteratively the thermodynamic relationships expressing the phase equilibria with the stoichiometric equations expressing the chemical equilibria. Using optimisation techniques, the Wilson single parameters and Henry's constants were calculated for binary systems containing formaldehyde which was assumed to be a supercritical component whilst Wilson binary parameters were calculated for the remaining binary systems. Thus the phase equilibria for the formaldehyde system could be calculated using these parameters and good accuracy was obtained when calculated values were compared with experimental values. The distillation process was modelled using the mass and energy balance equations together with the phase equilibria calculations. The plate efficiencies were obtained from a modified A.I.Ch.E. Bubble Tray method. The resulting equations were solved by an iterative plate to plate calculation based on the Newton Raphson method. Experiments were carried out in a 76mm I.D., eight sieve plate distillation column and the results were compared with the mathematical model calculations. Overall, good agreement was obtained but some discrepancies were observed in the concentration profiles and these may have been caused by the effect of limited physical property data and a limited understanding of the reactions mechanism. The model equations were solved in the form of modular computer programs. Although they were written to describe the steady state distillation with simultaneous chemical reaction of the formaldehyde system, the approach used may be of wider application.

The development of a modified dissolution method suitable for investigating powder mixtures

A novel dissolution method was developed, suitable for powder mixtures, based on the USP basket apparatus. The baskets were modified such that the powder mixtures were retained within the baskets and not dispersed, a potential difficulty that may arise when using conventional USP basket and paddle apparatus. The advantages of this method were that the components of the mixtures were maintained in close proximity, maximizing any drug:excipient interaction and leading to more linear dissolution profiles. Two weakly acidic model drugs, ibuprofen and acetaminophen, and a selection of pharmaceutical excipients, including potential dissolution-enhancing alkalizing agents, were chosen for investigation. Dissolution profiles were obtained for simple physical mixtures. The f1 fit factor values, calculated using pure drug as the reference material, demonstrated a trend in line with expectations, with several dissolution enhancers apparent for both drugs. Also, the dissolution rates were linear over substantial parts of the profiles. For both drugs, a rank order comparison between the f1 fit factor and calculated dissolution rate, obtained from the linear section of the dissolution profile, demonstrated a correlation using a significance level of P=0.05. The method was proven to be suitable for discriminating between the effects of excipients on the dissolution of the model drugs. The method design produced dissolution profiles where the dissolution rate was linear for a substantial time, allowing determination of the dissolution rate without mathematical transformation of the data. This method may be suitable as a preliminary excipient-screening tool in the drug formulation development process.

Feasibility studies of an on-line identification technique

This thesis is concerned with the study of a non-sequential identification technique, so that it may be applied to the identification of process plant mathematical models from process measurements with the greatest degree of accuracy and reliability. In order to study the accuracy of the technique under differing conditions, simple mathematical models were set up on a parallel hybrid. computer and these models identified from input/output measurements by a small on-line digital computer. Initially, the simulated models were identified on-line. However, this method of operation was found not suitable for a thorough study of the technique due to equipment limitations. Further analysis was carried out in a large off-line computer using data generated by the small on-line computer. Hence identification was not strictly on-line. Results of the work have shovm that the identification technique may be successfully applied in practice. An optimum sampling period is suggested, together with noise level limitations for maximum accuracy. A description of a double-effect evaporator is included in this thesis. It is proposed that the next stage in the work will be the identification of a mathematical model of this evaporator using the teclmique described.