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A prediction method for sound attenuation in acoustically lined circular ducts of uniform cross section containing radially sheared fluid flow is developed. The flow is regarded as consisting of a core of uniform flow surrounded by a thin layer near the duct wall in which the flow is sheared. The method is based on the solutions (acoustic modes) of an eigenfunction derived from the governing wave equation and the boundary conditions. Sound attenuation is computed by assuming equal distribution of the acoustic energy among the propagating acoustic modes at the reference plane. Amplitudes of modes reflected from the duct termination are considered negligible. To test the method, predictions are compared with measured data from circular section flow duct absorber test facilities and from liner tests in the intake duct of the RB 211 turbofan engine. The agreement between the measured and the predicted attenuation spectra is very good when sound propagation is upstream. In the downstream propagation case, equal modal energies lead to slight over prediction of sound attenuation at higher frequencies. An empirical solution to this problem is found by restricting the computation to the modes of the first four circumferential orders. A numerical technique is developed which uses only a fraction of the modal solutions to compute attenuations without loss of accuracy, thus considerably saving computing time and costs. A detailed study is carried out to highlight the effects on modal and total attenuations of changes in the values of the principal parameters and a number of design guidelines are deduced. Procedures for the prediction of sound attenuation in engine ducts are discussed and an approach to design the most effective liners is suggested. A comprehensive set of computer programs is developed to assist the Noise Engineer in the predictions and design optimisations of acoustic liners in project engines.

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On short timescales, the brain represents, transmits, and processes information through the electrical activity of its neurons. On long timescales, the brain stores information in the strength of the synaptic connections between its neurons. This thesis examines the surprising implications of two separate, well documented microscopic processes — the stochastic gating of ion channels and the plasticity of dendritic spines — for neural information processing and storage. Electrical activity in neurons is mediated by many small membrane proteins called ion channels. Although single ion channels are known to open and close stochastically, the macroscopic behaviour of populations of ion channels are often approximated as deterministic. This is based on the assumption that the intrinsic noise introduced by stochastic ion channel gating is so weak as to be negligible. In this study we take advantage of newly developed efficient computer simulation methods to examine cases where this assumption breaks down. We find that ion channel noise can mediate spontaneous action potential firing in small nerve fibres, and explore its possible implications for neuropathic pain disorders of peripheral nerves. We then characterise the magnitude of ion channel noise for single neurons in the central nervous system, and demonstrate through simulation that channel noise is sufficient to corrupt synaptic integration, spike timing and spike reliability in dendritic neurons. The second topic concerns neural information storage. Learning and memory in the brain has long been believed to be mediated by changes in the strengths of synaptic connections between neurons — a phenomenon termed synaptic plasticity. Most excitatory synapses in the brain are hosted on small membrane structures called dendritic spines, and plasticity of these synapses is dependent on calcium concentration changes within the dendritic spine. In the last decade, it has become clear that spines are highly dynamic structures that appear and disappear, and can shrink and enlarge on rapid timescales. It is also clear that this spine structural plasticity is intimately linked to synaptic plasticity. Small spines host weak synapses, and large spines host strong synapses. Because spine size is one factor which determines synaptic calcium concentration, it is likely that spine structural plasticity influences the rules of synaptic plasticity. We theoretically study the consequences of this observation, and find that different spine-size to synaptic-strength relationships can lead to qualitative differences in long-term synaptic strength dynamics and information storage. This novel theory unifies much existing disparate data, including the unimodal distribution of synaptic strength, the saturation of synaptic plasticity, and the stability of strong synapses.

Many evolutionary game theory papers have obtained their results when the bounded rationality which creates change vanishes. In our first chapter we consider whether such results are actually a good reflection of a population whose bounded rationality is small yet persistent. Our model consists of a two type population with three stable equilibria. Firstly we find that results from the standard vanishing noise approach can be very different from those obtained when noise is small but constant. Secondly when the results differ the small and persistent noise approach selects an equilibrium with a co-existence of conventions. Our second chapter generalises the model of our first chapter to a population of many player types and several stable equilibria. Firstly we produce the characteristics of the long run equilibria under vanishing noise analysis. Secondly we find that the introduction of a small neutral group into a divided society can produce a welfare improving switch in the long run equilibrium towards social co-ordination. Our third chapter combines the model of the second chapter with the message of the first. We show numerically that the long run location of a heterogenous population with extremely low levels of bounded rationality can be completely different to the equilibria selected through vanishing noise analysis. We also show that such an event is not a rare occurrence and find that over a third of populations are misrepresented by stochastic stability. Our final chapter conducts a review of the literature on social threshold models. We give a thorough description of each paper and discuss the main assumptions that drive the key results.

The objective of this study was to determine how a new experimental methodology for measuring Total-Harmonic-Distortion (THD) of operational amplifiers functioned when compared with two standard methodologies, and whether the new methodology offers any improvement in noise floor and dynamic range along with distortion canceling of the sine-wave source used in the testing. The new methodology (THD) is being tested against two standard methodologies: Spectral Analysis using a tuned receiver type Spectrum Analyzer with Notch Filter pre-processing, and a digitized Fast Fourier Transform (FFT) using Notch Filter pre-processing. The THD results appear to agree across all methodologies, and across all items of the sample within all methodologies, to within a percent or less. The distortion and noise canceling feature of the new methodology appeared to function as expected and in accordance with theory. The sample tested in the study consisted of thirty-five NE5534 operational amplifiers produced by Texas Instruments, Inc. and purchased from a local store. The NE5534 is a low-noise, low-distortion, operational amplifier that is widely used in industry and is representative of today's best audio amplifiers.

This thesis presents a preliminary investigation into the determination of enginerring important surface texture (of around a few microns) using ultrasonic pulse-echo signals. Current texture measurements and parameterisation techniques are reviewed, identifying their deficiencies, the requirements of a texture measurement device and the potential benefits of an ultrasonic technique. Plane compressional wave, high resolution, commercial NDT probes are considered, with the received signal being modelled as a first type Fredholm equation. The characteristics of these probes are considered in detail and realistic numerical simulations are presented, showing the variation in sound field and receiver voltage with the geometry and electrical condition of the test configuration. Inversion of the signal model is considered as a direct and useful route to characterising the surface. Techniques for this inversion are reviewed indicating their salient features and showing their inter-relationships. Several linear inversion techniques are considered in detail, using numerical simulations. These demonstrate their characteristics and the predictability of their performance. A simple 'interpolation' technique is shown to yield excellent results when applied under appropriate conditions. The Maximum Entropy algorithm is shown to yield significant improvements over linear techniques, in terms of reduced noise and filter artefacts and also possibly in improved resolution. Various characteristics of the algorithm performance are considered. Finally, preliminary results using real pulse echo signals are considered, with Maximum Entropy again yielding considerably superior results. While the achievable resolution is still somewhat below that desired, these results clearly demonstrate that the use of ultrasonics for surface texture evaluation is highly feasible and that the continued investigation of these, and other, ultrasonic techniques is fully justified.