Noisy random Boolean formulae:a statistical physics perspective

Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding macroscopic phase transitions. The framework is employed for deriving results on error-rates at various function-depths and function sensitivity, and their dependence on the gate-type and noise model used. These are difficult to obtain via the traditional methods used in this field.

On the robustness of random Boolean formulae

Random Boolean formulae, generated by a growth process of noisy logical gates are analyzed using the generating functional methodology of statistical physics. We study the type of functions generated for different input distributions, their robustness for a given level of gate error and its dependence on the formulae depth and complexity and the gates used. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding typical-case phase transitions. Results for error-rates, function-depth and sensitivity of the generated functions are obtained for various gate-type and noise models. © 2010 IOP Publishing Ltd.

Resistance heating of steel conductors of circular cross-section

The object of this thesis is to develop a method for calculating the losses developed in steel conductors of circular cross-section and at temperatures below 100oC, by the direct passage of a sinusoidally alternating current. Three cases are considered. 1. Isolated solid or tubular conductor. 2. Concentric arrangement of tube and solid return conductor. 3. Concentric arrangement of two tubes. These cases find applications in process temperature maintenance of pipelines, resistance heating of bars and design of bus-bars. The problems associated with the non-linearity of steel are examined. Resistance heating of bars and methods of surface heating of pipelines are briefly described. Magnetic-linear solutions based on Maxwell's equations are critically examined and conditions under which various formulae apply investigated. The conditions under which a tube is electrically equivalent to a solid conductor and to a semi-infinite plate are derived. Existing solutions for the calculation of losses in isolated steel conductors of circular cross-section are reviewed, evaluated and compared. Two methods of solution are developed for the three cases considered. The first is based on the magnetic-linear solutions and offers an alternative to the available methods which are not universal. The second solution extends the existing B/H step-function approximation method to small diameter conductors and to tubes in isolation or in a concentric arrangement. A comprehensive experimental investigation is presented for cases 1 and 2 above which confirms the validity of the proposed methods of solution. These are further supported by experimental results reported in the literature. Good agreement is obtained between measured and calculated loss values for surface field strengths beyond the linear part of the d.c. magnetisation characteristic. It is also shown that there is a difference in the electrical behaviour of a small diameter conductor or thin tube under resistance or induction heating conditions.

Theoretical evaluation of the cataract extraction-refraction-implantation techniques for intraocular lens power calculation

PURPOSE: To evaluate theoretically three previously published formulae that use intra-operative aphakic refractive error to calculate intraocular lens (IOL) power, not necessitating pre-operative biometry. The formulae are as follows: IOL power (D) = Aphakic refraction x 2.01 [Ianchulev et al., J. Cataract Refract. Surg.31 (2005) 1530]; IOL power (D) = Aphakic refraction x 1.75 [Mackool et al., J. Cataract Refract. Surg.32 (2006) 435]; IOL power (D) = 0.07x(2) + 1.27x + 1.22, where x = aphakic refraction [Leccisotti, Graefes Arch. Clin. Exp. Ophthalmol.246 (2008) 729]. METHODS: Gaussian first order calculations were used to determine the relationship between intra-operative aphakic refractive error and the IOL power required for emmetropia in a series of schematic eyes incorporating varying corneal powers, pre-operative crystalline lens powers, axial lengths and post-operative IOL positions. The three previously published formulae, based on empirical data, were then compared in terms of IOL power errors that arose in the same schematic eye variants. RESULTS: An inverse relationship exists between theoretical ratio and axial length. Corneal power and initial lens power have little effect on calculated ratios, whilst final IOL position has a significant impact. None of the three empirically derived formulae are universally accurate but each is able to predict IOL power precisely in certain theoretical scenarios. The formulae derived by Ianchulev et al. and Leccisotti are most accurate for posterior IOL positions, whereas the Mackool et al. formula is most reliable when the IOL is located more anteriorly. CONCLUSION: Final IOL position was found to be the chief determinant of IOL power errors. Although the A-constants of IOLs are known and may be accurate, a variety of factors can still influence the final IOL position and lead to undesirable refractive errors. Optimum results using these novel formulae would be achieved in myopic eyes.

Predicting prescribed magnification

Aim: To determine the best method of estimating the optimum magnification needed by visually impaired patients. Methods: The magnification of low vision aids prescribed to 187 presbyopic visually impaired patients for reading newspapers or books was compared with logMAR distance and near acuity (at 25 cm) and magnification predicted by +4 D step near additions. Results: Distance letter (r = 0.58) and near word visual acuity (r = 0.67) were strongly correlated to the prescribed magnification as were predictive formulae based on these measures. Prediction using the effect of proximal magnification resulted in a similar correlation (r = 0.67) and prediction was poorer in those who did not benefit from proximal magnification. The difference between prescribed and predicted magnification was found to be unrelated to the condition causing visual impairment (F = 2.57, p = 0.08), the central visual field status (F = 0.57, p = 0.57) and patient psychology (F = 0.44, p = 0.51), but was higher in those prescribed stand magnifiers than high near additions (F = 5.99, p < 0.01). Conclusions: The magnification necessary to perform normal visual tasks can be predicted in the majority of cases using visual acuity measures, although measuring the effect of proximal magnification demonstrates the effect of stronger glasses and identifies those in whom prescribed magnification is more difficult to predict.

Pharmaceutical compounding and dispensing

This is a detailed and practical guide to the theory and practice of extemporaneous compounding and dispensing, and a source of reference to extemporaneous formulae. Pharmacists have been responsible for compounding medicines for centuries and there is currently a dearth of current information on the topic, yet it is still taught in schools of pharmacy and required in community and hospital departments and by "specials" manufacturers and in development of new products in industry. This is a modern, detailed and practical guide to the theory and practice of extemporaneous compounding and dispensing, which will equip readers with the knowledge required for producing extemporaneous formulations safely and effectively.

Diversity and the perceived barriers to participation in volunteer activity by older people

The first chapter introduces the subject from a psychological and sociological perspective emphasising the basic human activity of helping those in need. Governmental prominence for policies that assist this activity is briefly discussed with special mention of the programmes that encourage volunteering. Programmes particularly directed at older people, such as the Age Concern ‘Debate of the Age’ are considered briefly. An extensive review of the extant literature is the subject of the second chapter. The pervious research is explored to discover the formulae used to define a volunteer. A definition relative to this research is created. Volunteering issues aggravated by the demographic situation of older people are explored. Empirical volunteer survey research by mutual organisations is explored to ascertain the extent and nature of the already recorded volunteer population. The penultimate section of this chapter investigates the nature of old age and the strategies that older people adopt to enjoy the benefits and contain the problems. The issue of diversity arises from consideration of the literature suggesting that, although it is an essential voluntary sector strength, it is also a further barrier to recruitment. A model diversity is proposed. Chapter three reviews the theoretical processes, procedures and technologies used to collect and analyse the data required to discover the answer to the research problem. Analysis of the questionnaire survey data received is the subject of chapter four. The discovery of the agency uniqueness of volunteer profiles is the principle finding of this part of the research. The fifth chapter is the qualitative analysis of the oral and written statements received. A content analysis of the scripts and texts provided rich data covering motivational factors. Motivational factors were the same for volunteers in the same organisation, but differed between organisations. Finally, the analysed data is collated and discussed progressively toward a theory of diversity. The individuality of each branch of each agency is progressively described culminating in the creation of a model that infers that diversity is a barrier that aggravates all other barriers. The personal realisations of the researcher are described.

The fatigue properties of pressure diecast zinc-aluminium based alloys

The fatigue behaviour of the cold chamber pressure-die-cast alloys: Mazak3, ZA8, ZA27, M3K, ZA8K, ZA27K, K1, K2 and K3 was investigated at temperature of 20°C. The alloys M3K, ZA8K and ZA27K were also examined at temperatures of 50 and 100°C. The ratio between fatigue strength and tensile strength was established at 20°C at 107 cycles. The fatigue life prediction of the alloys M3K, ZA8K and ZA27K was formulated at 20, 50 and 100°C. The prediction formulae were found to be reasonably accurate. All of the experimental alloys were heterogeneous and contained large but varying amounts of pores. These pores were a major contribution and dominated the alloys fatigue failure. Their effect, however, on tensile failure was negligible. The ZA27K possessed the highest tensile strength but the lowest fatigue strength. The relationship between the fracture topography and the microstructure was also determined by the use of a mixed signal of a secondary electron and a back-scattered electron on the SEM. The tensile strength of the experimental alloys was directly proportional to the aluminium content within the alloys. The effect of copper content was also investigated within the alloys K1, K2, ZA8K and K3 which contained 0%, 0.5%, 1.0% and 2.0% respectively. It was determined that the fatigue and tensile strengths improved with higher copper contents. Upon ageing the alloys Mazak3, ZA8 and ZA27 at an ambient temperature for 5 years, copper was also found to influence and maintain the metastable Zn-Al (αm) phase. The copper free Mazak3 upon ageing lost this metastable phase. The 1.0% copper ZA8 alloy had lost almost 50% of its metastable phase. Finally the 2.0% copper ZA27 had merely lost 10% of its metastable phase. The cph zinc contained a limited number of slip systems, therefore twinning deformation was unavoidable in both fatigue and tensile testing.

Remote sensing applications to flood hydrology in Belize

The research compares the usefullness of four remote sensing information sources, these being LANDSAT photographic prints, LANDSAT computer compatible tapes, Metric Camera and SIR-A photographic prints. These sources provide evaluations of the catchment characteristics of the Belize and Sibun river basins in Central America. Map evaluations at 1:250,000 scale are compared to the results of the same scale, remotely sensed information sources. The values of catchment characteristics for both maps and LANDSAT prints are used in multiple regression analysis, providing flood flow formulae, after investigations to provide a suitable dependent variable discharge series are made for short term records. The use of all remotely sensed information sources in providing evaluations of catchment characteristics is discussed. LANDSAT prints and computer compatible tapes of a post flood scene are used to estimate flood distributions and volumes. These are compared to values obtained from unit hydrograph analysis, using the dependent discharge series and evaluate the probable losses from the Belize river to the floodplain, thereby assessing the accuracy of LANDSAT estimates. Information relating to flood behaviour is discussed in terms of basic image presentation as well as image processing. A cost analysis of the purchase and use of all materials is provided. Conclusions of the research indicate that LANDSAT print material may provide information suitable for regression analysis at levels of accuracy as great as those of topographic maps, that the differing information sources are uniquely applicable and that accurate estimates of flood volumes may be determined even by post flood imagery.

A study of the aerodynamic characteristics of captor hoods in local exhaust ventilation systems

The research objectives were:- 1.To review the literature to establish the factors which have traditionally been regarded as most crucial to the design of effectlve exhaust ventilation systems. 2. To design, construct, install and calibrate a wind tunnel. 3. To develop procedures for air velocity measurement followed by a comprehensive programme of aerodvnamic data collection and data analysis for a variety of conditions. The major research findings were:- a) The literature in the subject is inadequate. There is a particular need for a much greater understanding of the aerodynamics of the suction flow field. b) The discrepancies between the experimentally observed centre-line velocities and those predicted by conventional formulae are unacceptably large. c) There was little agreement between theoretically calculated and observed velocities in the suction zone of captor hoods. d) Improved empirical formulae for the prediction of centre-line velocity applicable to the classical geometrically shaped suction openings and the flanged condition could be (and were) derived. Further analysis of data revealed that: - i) Point velocity is directly proportional to the suction. flow rate and the ratio of the point velocity to the average face velocity is constant. ii) Both shape, and size of the suction opening are significant factors as the coordinates of their points govern the extent of the effect of the suction flow field. iii) The hypothetical ellipsoidal potential function and hyperbolic streamlines were found experimentally to be correct. iv) The effect of guide plates depends on the size, shape and the angle of fitting. The effect was to very approximately double the suction velocity but the exact effect is difficult to predict. v) The axially symmetric openings produce practically symmetric flow fields. Similarity of connection pieces between the suction opening and the main duct in each case is essential in order to induce a similar suction flow field. Additionally a pilot study was made in which an artificial extraneous air flow was created, measured and its interaction with the suction flow field measured and represented graphically.

Objective methods for anterior ocular grading

This thesis set out to develop an objective analysis programme that correlates with subjective grades but has improved sensitivity and reliability in its measures so that the possibility of early detection and reliable monitoring of changes in anterior ocular surfaces (bulbar hyperaemia, palpebral redness, palpebral roughness and corneal straining) could be increased. The sensitivity of the program was 20x greater than subjective grading by optometrists. The reliability was found to be optimal (r=1.0) with subjective grading up to 144x more variable (r=0.08). Objective measures were used to create formulae for an overall ‘objective-grade’ (per surface) equivalent to those displayed by the CCLRU or Efron scales. The correlation between the formulated objective verses subjective grades was high, with adjusted r2 up to 0.96. Determination of baseline levels of objective grade were investigated over four age groups (5-85years n= 120) so that in practice a comparison against the ‘normal limits’ could be made. Differences for bulbar hyperaemia were found between the age groups (p<0.001), and also for palpebral redness and roughness (p<0.001). The objective formulae were then applied to the investigation of diurnal variation in order to account for any change that may affect the baseline. Increases in bulbar hyperaemia and palpebral redness were found between examinations in the morning and evening. Correlation factors were recommended. The program was then applied to clinical situations in the form of a contact lens trial and an investigation into iritis and keratoconus where it successfully recognised various surface changes. This programme could become a valuable tool, greatly improving the chances of early detection of anterior ocular abnormalities, and facilitating reliable monitoring of disease progression in clinical as well as research environments.

Dynamic QoS management and optimisation in service-based systems

Service-based systems that are dynamically composed at run time to provide complex, adaptive functionality are currently one of the main development paradigms in software engineering. However, the Quality of Service (QoS) delivered by these systems remains an important concern, and needs to be managed in an equally adaptive and predictable way. To address this need, we introduce a novel, tool-supported framework for the development of adaptive service-based systems called QoSMOS (QoS Management and Optimisation of Service-based systems). QoSMOS can be used to develop service-based systems that achieve their QoS requirements through dynamically adapting to changes in the system state, environment and workload. QoSMOS service-based systems translate high-level QoS requirements specified by their administrators into probabilistic temporal logic formulae, which are then formally and automatically analysed to identify and enforce optimal system configurations. The QoSMOS self-adaptation mechanism can handle reliability- and performance-related QoS requirements, and can be integrated into newly developed solutions or legacy systems. The effectiveness and scalability of the approach are validated using simulations and a set of experiments based on an implementation of an adaptive service-based system for remote medical assistance.

Dynamic behaviour of rotary mechanical seals

This thesis covers both experimental and computer investigations into the dynamic behaviour of mechanical seals. The literature survey shows no investigations on the effect of vibration on mechanical seals of the type common in the various process industries. Typical seal designs are discussed. A form of Reynolds' equation has been developed that permits the calculation of stiffnesses and damping coefficients for the fluid film. The dynamics of the mechanical seal floating ring have been investigated using approximate formulae, and it has been shown that the floating ring will behave as a rigid body. Some elements, such as the radial damping due to the fluid film, are small and may be neglected. The equations of motion of the floating ring have been developed utilising the significant elements, and a solution technique described. The stiffness and damping coefficients of nitrile rubber o-rings have been obtained. These show a wide variation, with a constant stiffness up to 60 Hz. The importance of the effect of temperature on the properties is discussed. An unsuccessful test rig is described in the appendices. The dynamic behaviour of a mechanical seal has been investigated experimentally, including the effect of changes of speed, sealed pressure and seal geometry. The results, as expected, show that high vibration levels result in both high leakage and seal temperatures. Computer programs have been developed to solve Reynolds' Equation and the equations of motion. Two solution techniques for this latter program were developed, the unsuccesful technique is described in the appendices. Some stability problems were encountered, but despite these the solution shows good agreement with some of the experimental conditions. Possible reasons for the discrepancies are discussed. Various suggestions for future work in this field are given. These include the combining of the programs and more extensive experimental and computer modelling.

Damping in zinc-based alloys

The damping behaviour of the cold chamber pressure-die-casting alloy: M3, ZA8, ZA27, ZM11, Cosmal, Supercosmal and newly developed ZA27H1 and ZA27H2 was investigated at room temperature and elevated temperatures of up to 90 degrees C. The damping properties of the alloys were established at all temperatures. Formulas were established to predict damping properties of each alloy at any given temperature. The prediction formulae were found to be very accurate. All of the experimental alloys were heterogenous with varying microstructure and grain size; this was the major contribution and dominated the damping properties of the alloys. Super cosmal and ZA27 possessed the highest tensile strength but ZA27H1, ZA27H2 and ZM11 showed the highest damping properties. The relationship between microstructure and damping capacity of all alloys was also examined using back-scattered electron on the SEM. Further more detailed examinations of the microstructures of alloys ZM11, Cosmal and Supercosmal were carried out on the transmission electron microscope in order to establish the phases present in all alloys. These helped to obtain the mechanism of damping in the experimental alloys. The main damping mechanism in most of the experimental alloys was due to grain-boundary-sliding. Micro structural examinations also revealed the absence of -phase in the Cosmal and Supercosmal. This was thought to be due to a change in solid solubility of the alloys, which could have been caused by the addition of Si.

Theoretical modelling of the sulcated spring

Replacement of the traditional coil spring with one of more fibre-reinforced plastic sulcated springs is a future possibility. Spring designers of metallic coil springs have design formulae readily available, and software packages specific to coil spring design exist. However, the sulcated spring is at the prototype stage of development, so literature on these springs is very sparse. The thesis contains information on the market for sulcated springs, and their advantages and disadvantages. Literature on other types of fibre reinforced plastic springs has also been reviewed. Design software has been developed for the sulcated spring along similar lines to coil spring design software. In order to develop the software, a theoretical model had to be developed which formed the mathematical basis for the software. The theoretical model is based on a choice of four methods for calculating the flexural rigidity; beam theory, plate theory, and lamination theory assuming isotropic and orthoropic material properties. Experimental results for strain and spring stiffness have been compared with the theoretical model, and were in good agreement. Included in the design software are the results of experimental work on fatigue, and design limiting factors to prevent or warn against impractical designs. Finite element analysis has been used to verify the theoretical model developed, and to find the better approximation to the experimental results. Applications and types of assemblies for the sulcated spring were discussed. Sulcated spring designs for the automotive applications of a suspension, clutch and engine valve spring were found using the design computer software. These sulcated spring designs were within or close to the space of the existing coil spring and yield the same performance. Finally the commercial feasibility of manufacturing the sulcated spring was assessed and compared with the coil spring, to evaluate the plausibility of the sulcated spring replacing the coil spring eventually.