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1-3 piezocomposites comprising of stiff piezoelectric ceramic rods embedded in a soft polymer matrix have considerable potential as the active component in ultrasonic systems for applications in such diverse fields as bio-medicine, SONAR and nondestructive testing. This is because of the ability to tailor the properties via adjustment of the ceramic pillar shape, size, type and distribution and by selection of the passive phase properties. This complex microstructure and its significant influence on resultant device performance has led to a requirement for sophisticated analytical tools to facilitate cost-effective optimisation at the design stage. This Thesis describes the use of finite element analysis to investigate the behaviour of 1-3 composites for different applications. Firstly, the influence of constituent material properties on the behaviour of thickness mode drive was studied via a combination of modal and harmonic analysis. This led to the creation of straightforward de sign rules relating to ceramic type, shape and distribution, in addition to the desired properties of the passive filler phase. The Thesis then describes the influence of mechanical loading and method of construction on composite transducer performance, over the complete range of volume fractions. Front face matching, fluid loading and mechanical damping via a backing block are considered and analysed with respect to composite transducer performance. This is extended using static analysis to include the behaviour of hydrostatic devices and the effect of adding stiffening plates. The theory is then augmented to encompass monolithic and diced imaging arrays. The influence of composite geometry, element dimensions and transducer separation is discussed with respect to sensitivity, cross-coupling and beam profile. Throughout the Thesis, the analytical work is supported by experimental evidence. This involved the manufacture of a comprehensive range of devices, followed by experimental studies on performance. Impedance analysis, transmission/reception sensitivities, surface displacement profiles and beam characteristics were all evaluated and the results compared with theoretical predictions. It is considered that the work described within the Thesis makes a valuable and original contribution to the field of 1-3 connectivity composite transducers. It should constitute a basis for ongoing theoretical work to improve further the performance of the devices.

Biological oscillators occur frequently in nature---and many systems, such as the growth of certain bacteria, are governed by the 24-hour circadian clock. Furthermore biological phase-locked oscillators, as identified by researchers, are clearly an integral part of the structure of the brain in humans, and in animals in general. Such systems are most conveniently investigated via computer models. This thesis describes the computer-modelling of phase-locked systems in which the oscillator is a cellular automaton---a device often used by scientists to model the growth or decay of populations within biological and other systems. The latter part of the thesis shows how these computer models have been implemented in a two-dimensional form using gate array technology, and results are presented to demonstrate the overall loop performance. It is not suggested that the phase-locked loops described in this thesis should be translated directly into practical commercial products---the primary objective of the research described being to originate a new type of phase-locked loop based around a novel variable frequency oscillator. However, the summary at the end of the thesis indicates how the designs might be modified so as to allow a direct silicon implementation.

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