The work of this thesis concerns depolarization regions in the homogenization of random, particulate composites. In conventional approaches to homogenization, the depolarization dyadics which represent the component phase particles are provided by the singularity of the corresponding dyadic Green function. Thereby, the component particles are effectively treated as vanishingly small, point-like entities. However, through neglecting the spatial extent of the depolarization region, important information may be lost, particularly relating to coherent scattering losses. In this thesis, depolarization regions of nonzero volume are considered. In order to estimate the constitutive parameters of homogenized composite materials (HCMs), the strong-property-fluctuation theory (SPFT) is implemented. This is done through a standard procedure involving the calculation of successive corrections to a preliminary ansatz, in terms of statistical cumulants of the spatial distribution of the component phase particles. The influence of depolarization regions of nonzero volume on the zeroth (and first), second and third order SPFT estimates of HCM constitutive parameters is investigated. Both linear and weakly nonlinear HCMs are considered.

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Correlation and convolution are based on the idea of getting the response of one function to another. When the data is available in two dimensional transparency form it is convenient to use optical systems. Different techniques of performing the correlation and convolution operations in coherent and noncoherent light are described. Their applications in optics are mentioned. A random-dots code is presented. This was used for coding dilute and continuous-tone pictures. The coded pictures were decoded by correlating them with the code. Coherent and non­ coherent correlation methods were employed. In the coherent method a complex filter was used and the coded pictures were decoded by coherent optical filtering. The noncoherent method is based on the idea of reversing the rays involved in the coding process. The two methods are compared, the effect of the decoding on dilute and continuous-tone objects is illustrated, noise analysis is given and the decoded images resolution is considered. Theories of formation of Fourier images are discussed. A confusion is shown to exist between Fourier images derived from related objects. Coherent and noncoherent correlation experiments are reported. Their results serve to confirm the possibility of confusion. Finally a new method of noncoherent spatial filtering, using blocking filters, is presented.

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Optical methods have been used to examine the topography of the small erosion areas that are produced at the cathode and anode due to single, short duration, high current discharges. A plane parallel electrode arrangement has been used with gap separation of between one and two millimetres or less, and allowing electrical breakdown to occur under nearly uniform field conditions. The electrode erosion has been studied for discharges passed in oil dielectric, and also hydrogen, air, and argon at atmospheric pressure. High and low melting point metal electrodes have been used in the investigation. Constant current discharges have been produced by using pulse forming networks, but for slower rates of current rise in the external circuit, a single section condenser-inductance network was used. Some of the erosion areas have been suitable for examination by Fizeau reflexion interferometry, and the light profile techniques, which made possible an estimation of the volume of material lost from these areas. Observations were made using reflexion microscopy, which also served as a means for making erosion measurements. The results of the measurements of erosion loss at the anode for discharges in oil and gases, indicate that the electrode material cannot have been removed by a thermal evaporation process alone. From observations on the topography of the anode erosion areas, it would appear that the molten metal within the area is drawn into one or more peaks, and metal is lost from the area by some mechanical force action. The erosion areas at the lower melting point electrodes for discharges in oil and gas dielectric appear similar, but usually more intensive melting is produced for the discharges in oil. The molten multiple marks left on the anode and cathode, have been discussed in the light of recent research by other workers, studying the luminous areas formed at the electrodes during the discharge.