This thesis considers the scattering of small amplitude water waves, obliquely incident on a set of floating elastic plates occupying the entire water surface. The problem is twodimensional and assumes invariance in the width of the plates. All non-linear physical effects are neglected. The plates are floating on a body of water of finite depth and each plate has uniquely defined properties. The problem is formulated by imposing boundary conditions on the eigenfunction expansion of Laplace’s equation. A set of transmission and reflection coefficients is generated, which is solved by applying the edge conditions and matching at each plate boundary. We label this solution method the Matched Eigenfunction Expansion Method (MEEM). The problem is solved for a variety of edge conditions including free, clamped, sliding, springed and hinged. To verify the MEEM results, the problem is also solved using a Green Function Method. The convergence of the two methods is compared and found to be almost identical. The MEEM is used to simulate wave–ice interaction in the Marginal Ice Zone (MIZ). The model removes the resonance effects and predicts that the transmitted energy is independent of floe length, provided the wavelength is more than three times the floe length. The model predicts an exponential decay of wave energy with distance of propagation through the MIZ, which agrees with experimental findings. The results have been summarised in a graph with the attenuation coefficient expressed as a function of period for various floe thicknesses. We also provide an estimate of the attenuation coefficient using an approximation theory. The displacements of the MEEM are compared against a series of laboratory experiments performed in a two-dimensional wave-tank and show good agreement. The attenuation model results are compared against a series of field experiments carried out in the Arctic and off the West Antarctic Peninsula. Generally, the decay rates of the model agree well with the field experiments in diffuse ice. We suggest that factors other than wave scatter are relevant in models of wave-attenuation in non-diffuse ice.

The development of a large-signal power transistor model applicable at radio frequencies is described. This model which has its basis in the classical large-signal models is valid for cut-off and active region operation but does not include saturation operation. The model is intended primarily for use in broadband linear radio frequency amplifier applications and is useful up to frequencies of the order of 1/15 f┬. The model is described by two first order nonlinear differential equations and a number of algebraic equations. Equation coefficients are determined from measurements made on the devices under study. Two methods are described for the solution of the model equations. The first and principal method is an iterative one requiring computer assistance whilst the second is analytical and depends upon piecewise linearisation of the device transfer characteristic. This analytical method whilst in some respects inadequate, e.g. distortion level predictions, is easy to implement and despite its limitations affords useful insight into output power capability and frequency limitations of specific devices. The model contains all transistor nonlinearities and parasitic elements of significance and an important feature is the inclusion of device temperature as a model variable, resulting in good accuracy over a wide range of operating conditions. A simplified input impedance representation is evolved and it is demonstrated that input impedance measurements provide a useful window on model structure and aid in the evaluation of parameter values.

The increasing use of fibre reinforced polymers in structural components often requires an accurate assessment of the strength of the component. The strength of composite materials is usually based on the strength of an individual lamina. This is then combined in a manner depending on the orientation of the plies within the laminate. The actual failure process is often ignored in this type of analysis. Composite failure is the result of damage accumulation from a number of failure modes, in particular, fibre failure, matrix failure and failure of the interface between the fibres and matrix. Measurement of the interfacial strength requires specialised testing techniques in order to obtain accurate characterization of the interfacial failure processes. This research uses a double torsion specimen reinforced with fibres in a number of configurations. The testing techniques developed allow the interaction of a matrix crack with fibres, resulting in the failure of the interface. Finite element analysis has been used to gain an insight into the deformation mechanisms. A compliance change analysis has been developed so that the load in the fibres can be calculated. Results from the finite element analysis confirm the analytical procedures and show that, for the fibre/resin combination tested, the interface has a lower fracture toughness than the matrix material. The interaction between the fibres and matrix shows that the mechanism of fibre bridging inhibits the propagation of matrix cracks. This produces an apparent increase in the toughness of the composite system. To confirm the failure processes occurring, the technique of acoustic emission has been used to monitor the development of the specimen failure. In line with other workers, it is shown that matrix failure produces low amplitude events and interfacial failure produces mid amplitude events. Fibre failure did not occur to any significant degree. This thesis shows how the contribution from the presence of an interface affects the fracture of composite materials and how, via the reinforced double torsion specimen, this contribution can be measured and interpreted.

This thesis explores the seismic analysis and design of post-tensioning concrete masonry (PCM) walls. Using unbonded post-tensioning, walls are vertically prestressed by means of strands or bars which are passed through vertical ducts inside the walls. As the walls are subjected to lateral displacements (in-plane loading), gaps form at the horizontal joints, reducing the system stiffness. As long as the prestressing strands are kept within the elastic limit, or at least maintain a considerable amount of the initial prestressing force, they can provide a restoring force, which will return the walls to their original alignment upon unloading. The key feature in this behaviour is attributable to the tendons being unbonded over the entire wall height, allowing for distribution of tendon strain over the entire length of the tendon. An extensive literature review found that post-tensioning of masonry has had limited application in seismic areas and that there currently are no specific code requirements for it’s use for ductile seismic design, largely as a consequence of little knowledge about the ductility capacity and energy dissipation characteristics. It was concluded that structural testing of PCM walls and concrete masonry creep and shrinkage testing were essential to advance the understanding of this construction type. Creep and shrinkage experiments confirmed that long term prestress losses are considerable in both grouted and ungrouted concrete masonry, and must be taken into account in design. It was concluded that it is essential to use high strength steel for prestressing of PCM in order to reduce long term losses. Structural testing confirmed that fully grouted unbonded post-tensioned concrete masonry is a competent material combination for ductile structural wall systems. In particular, PCM walls strengthened in the flexural compression zones with confining plates are expected to successfully withstand severe ground shaking from an earthquake. It was suggested that partially and ungrouted PCM walls may suitably be used in strength design (non-ductile). The proposed prediction method for wall in-plane behaviour was validated by experimental results. Good correlation between predictions and results was found. Displacement spectra were developed for ductile seismic design of PCM walls. These can be used to accurately estimate the displacement demand imposed on multi-storey PCM cantilever walls.

This thesis is divided into four parts. The first part discusses the problem of using prestressed concrete for earthquake resistant structures, and examines the "equivalent viscous damping" approach to the measurement of structural damping. Part two describes the reversed cyclic testing of prestressed concrete members: end moments were applied to the members to simulate earthquake loading, and measurements were made of stiffness and damping energy. An analytical method of obtaining moment - rotation curves for prestressed members, taking account of curvature concentration at the tension cracks, is presented in part three. The last part is a study of the response of an idealized prestressed concrete structure to a recorded earthquake ground motion. The test results given in part two are used to define the properties of the idealized structure.

The investigation reported in this thesis is part of a programme of research concerning the flow behaviour of paper pulp suspensions commenced at the University of Auckland in 1969. A primary aim of the research was to supply the industry with reliable pipe friction data for the pulps manufactured in New Zealand mills. Secondly, it was hoped to increase the fundamental understanding of the mechanisms of flow of the suspensions in pipes and so devise a more satisfactory method of correlation than the one used at present. Pipe friction data were obtained for two N.Z. groundwood pulps, two N.Z. Kraft pulps and one imported Kraft pulp in 1, 2, 3 and 4 inch pipes for a wide range of consistencies and velocities. The data were of the same form as previously reported in the literature, but for a given set of conditions the friction losses were lower for the N.Z. pulps. For Kraft pulps the curves of head loss versus velocity exhibited the usual maxima and minima, but for groundwoods the decrease in head loss from the maximum to the minimum and the subsequent rise were replaced by an approximately level portion. The data in the regime before the maxima in the head loss curves for Kraft pulps were correlated to allow extrapolation to the larger pipes used in the paper mill. This regime incorporates the majority of practical flow situations for consistencies over two per cent. The limits of the regime were approximately defined by values of the dimensionless friction factor. The correlation method used was a slight modification of that employed by previous authors. The data for groundwood pulps were correlated in a similar way. The head losses predicted by the new correlations were consistently lower than those calculated from previous equations. Observation of the flow in perspex pipes confirmed the mechanisms of flow proposed by some previous authors, but disagreed with the mechanisms proposed by others. The mechanisms of flow of groundwood pulps were found to be essentially similar to those of Kraft pulps except that the groundwoods exhibited a plug cleavage phenomenon at very low velocities. The different shapes of friction curve for the two types of pulp were attributed directly to their macroscopic properties. A flow model was developed on the basis of the observed flow behaviour in pipes in which the suspensions move as a fibre/water plug surrounded by a sheared water annulus. The model assumed that the annulus formed as a result of the action of the hydrodynamic shear stress on the fibre network comprising the plug. The analysis resulted in an expression relating the average velocity and the longitudinal pressure gradient in the pipe and also incorporated the pipe radius, the viscosity of the suspending medium μ and a pseudo shear modulus for the fibre network G. The plug flow model was found to apply to the data in the regime before the maximum in the head loss curve. The relation between the pressure gradient and the pipe diameter as predicted by the model was slightly erroneous for some pulps, although it was the same as that in the standard empirical correlation used in design by the industry. This led to the conclusion that the deflection of fibre ends on the plug surface also contributed to the formation of the annulus, as proposed by previous authors. The relative importance of the two mechanisms of annulus formation was used to explain the occurrence of the maxima and minima in the head loss curves for chemical pulps. The plug flow model was found to be closely related to both the direct correlation method used in the past and to the standard pseudoplastic model for non-Newtonian pipe flow. The model was also applied to analogous flow in a rotational viscometer. The values of the pseudo shear modulus G calculated from the rotational viscometry data were the same as those calculated from pipe flow data under certain conditions. However, limitations in the equipment and the effect of gravitational settling restricted the results to a narrow range. The behaviour of the pulp suspensions in batch settling tests varied markedly from pulp to pulp. There was a high correlation between the pseudo shear modulus G obtained from pipe flow data and the final height of the suspension in a settling test. Likewise there was a relationship between the effective viscosity of the suspending medium μ (as modified by the proportion of fines in the pulp) and the initial settling rate in a batch test. This suggested that a simple and accurate method of determining pipe friction data from batch settling test data is possible. Settling tests also showed that air content and the presence of acidic and basic ions, but not the viscosity of the suspending medium, increased the strength of fibre networks. A further correlation method to incorporate all flow regimes was suggested from the results of the present investigation and from indications in the literature that fibre networks behave like Bingham plastics when they are sheared.

This thesis is a study of the large scale flows of water and heat which give rise to the geothermal fields in the Taupo Volcanic Zone (TVZ), New Zealand. To carry out this study, a super-critical equation of state module has been developed for the geothermal simulator TOUGH2, which can describe the flow of water at the conditions expected deep in the TVZ. The code is used to simulate the behaviour of a range of idealised TVZ models in 2D and 3D settings. Hydrothermal plumes which remain stable for periods comparable to the lifetime of the TVZ can occur when there is a contrast between the high permeability of the inner TVZ 'infill' region and the lower permeability exterior region. In this case, downflows of cool surface fluid in the inner TVZ 'sweep' the geothermal heat across the TVZ at depth to the permeability barrier, where the heated fluid ascends to the surface in discrete plumes. This behaviour occurs in 2D models, where separate plumes form at each side of the high permeability infill region, and also in 3D models of caldera-like structures, where perhaps four hot plumes can form around the perimeter of the caldera. This notion is then applied to the complete TVZ hydrological system, where a permeable ‘envelope’ is defined by the location of the Taupo Fault Belt and the currently known volcanic centres in the TVZ. The permeability within this envelope varies spatially according to the geothermal heat flux, and the region outside has relatively low permeability. The spatial variation of the geothermal heat flux is obtained by summing the measured heat flows from the geothermal fields for a number of areas across the TVZ. In this model, the geothermal fields form about the boundary of the envelope, as in the TVZ, and bear a striking resemblance to the actual TVZ geothermal fields. Finally, a new simulation code, NaCl-TOUGH2, is developed to provide a tool for future modelling involving the commonest chemical species in the TVZ - salt. The code incorporates the complete phase diagram for salt-water mixtures and involves liquid, vapour and solid phases over a wide range of temperatures, pressures and salt concentrations. The code is used to solve a number of simple geothermal and mathematical problems.

The forest harvesting problem, FHP, is described. A review of the existing literature is presented along with an analysis of the strengths and limitations of various attempted solutions. The diversity of model evident in recent papers is noted. The difference is explained between a strategic model that sets long-term harvesting goals in terms of total area to be cut each year, and a tactical model that produces a short-term schedule of actual blocks. Special attention is devoted to the development of FRI’s Forestry-Oriented Linear Programming Interpreter, FOLPI, which is currently used to formulate an LP model of the strategic planning problem. Reasons are presented for the desirability of an integrated model, embracing both strategic and tactical decisions, which is capable of optimisation. Accordingly the project then proceeds to a thoughtful and detailed construction of such a model. Particular care is taken to examine the status and function of FOLPI within this model. A column generation algorithm is then developed to solve the relaxed linear program formulation. Finally powerful constraint branching techniques are utilised to obtain the desired optimal solution to the integrated model. Throughout the development of the project the Whangapoua forest in Coromandel, New Zealand has been used as a case study. A concluding section presents numerical output from some of the exhaustive computational analysis associated with this application.

Alumina performs several functions in a modern smelter - it is used to scrub the pot gases to remove fluoride, acts as a thermal insulator on top of the cell and, when added to cryolite-based electrolytes, it is the raw material used to produce aluminium. Alumina is also expected to have good flow and handling properties, and dissolve well in the bath. Unfortunately, it does not always dissolve rapidly and this leads to the formation of "sludge", which creates operating disturbances in the cell; it is difficult to remedy this problem without a basic understanding of the process of alumina dissolution. Consequently, the objective of the work presented in this thesis was to develop an apparatus and technique that would allow the dissolution behaviour of powder alumina to be measured as realistically and objectively as possible, and then determine the important factors affecting dissolution. The method developed involved the merging of three different techniques: ● electroanalytical measurement of dissolved oxide concentrations ● recording of the associated thermal phenomena ● visual observation of the interaction of alumina with the bath which were then used to investigate the effect of a range of alumina properties and smelter operating conditions on dissolution behaviour. A series of dissolution parameters was selected to evaluate the relative dissolution behaviour of the different variables. It was found that slow dissolution behaviour resulted primarily from poor feeding and/or dispersion, coupled with poor heat transfer in the first few seconds of the dissolution process. If the flow properties of the alumina were good, alumina flowed easily out of the dropper on to the surface of the bath forming relatively thin but well-distributed rafts. If not, alumina could flow out into a localized area producing very dense rafts which clumped together and eventually sank to the bottom forming sludge. properties such as loss on ignition enhanced the dispersion of the alumina through the release of volatiles, which caused the alumina to "effervesce" on the surface. Conversely, bulk density aggravated the clumping problem as the density of the formed rafts increased with increasing bulk density. Good feeder design can help to counteract deficiencies in the flow properties of an alumina, if the importance of wide coverage and the imparting of a horizontal velocity component to the alumina are kept in mind. It was also found that if the bath agitation was increased, either by increasing the amount of existing stirring or by reducing the bath volume in the feeding area for a given bath velocity, the initial heat transfer to the alumina could be dramatically improved. The presence of bath superheat was important for maintaining optimum heat transfer conditions for fast dissolutions, as alumina was found to dissolve better when a higher proportion of the heat required was supplied from the bulk of the liquid bath as opposed to localized freezing. Increasing the initial alumina concentration in the electrolyte retarded the dissolution process, with the retardation becoming increasingly more significant at higher concentration values. Similarly, reducing the cryolite ratio, which also decreased the alumina solubility, resulted in the dissolution being inhibited in the later stages, as more alumina dissolved. In situations where the mass transfer in the bath was improved, the impact of these concentration effects was minimized. The video recordings were useful for indicating potential operating difficulties with the samples, such as excessive emissions and flow problems. Six different raft formations, characterizing the degree of bath surface coverage and the raft density or cohesion, were identified from the videos and the aluminas were classified accordingly. Preliminary heat balance calculations were performed using the data obtained in this study and were used to estimate the heat of dissolution for α-Al2O3, for a variety of alumina concentrations in cryolite-based electrolytes. The results indicated heat values of 112±15 and 55±5 kJ mol-1 for alumina concentrations in the bath of 0.43 and 2.83 wt% respectively. Further work is necessary to refine these calculations, however. Reacted ore was found to dissolve more slowly than parent virgin alumina but it was difficult to ascertain which property caused the difference - whether bulk density, flowability, influence of HF, or presence of other impurities. As a result, it is recommended that a series of dissolution runs be performed on reacted samples of different compositions to establish which property associated with reacted ore causes the problem.

The onset of convection in a horizontal fluid layer, heated from below, is, examined by means of perturbation analysis. The resulting eigenvalue system of equations is solved by means of a new extension of a Fourier series technique. Two sets of coupled effects are investigated: (i) thermal buoyancy and surface-tension effects, and (ii) thermal buoyancy and solute buoyancy effects. For the first set of effects the magnetohydrodynamic problem is also studied. For the surface-tension problem, attention is focussed on the case where the lower boundary is a rigid conductor and the upper free surface is subject to a general thermal condition. It is found that for this care the surface-tension and buoyancy forces reinforce each other and are tightly coupled. Cells formed by surface tension are approximately the same size as those formed by buoyancy. The stream line patterns produced by the two agencies acting separately are again similar. When the fluid is electrically conducting and is in the presence of a vertical magnetic field, it is found that the field always has a stabilizing effect. When convection cells are formed in the presence of such a field, their horizontal dimensions are less than for cells formed in the absence of the field. The magnetic field accentuates the difference between the cells induced by surface tension and those by buoyancy, and thus reduces the coupling between the destabilizing forces. Increase of magnetic field causes the buoyancy cell pattern to become more symmetrical, but causes the streamlines in surface-tension cells to become bunched near the surface. When the magnetic field is large, the transition from one type of cell to the other type is extremely sudden, at least when the upper surface is a good thermal conductor. It has been found that, on the model considered, there can be no oscillatory for this problem. However, dimensional analysis reveals that, for a sufficiently flexible upper surface, oscillatory Instability might in fact occur. Finally the thermohaline problem, where the density varies with both temperature and the concentration of some solute, is studied. The eigenvalue equation is now found for general boundary conditions. The degree of coupling between the thermal and the solute effects again depends on the similarity between convection cells caused by the two agencies acting separately. (For one extreme case studied the coupling is zero for a certain range of parameters.) In this problem both monotonic and oscillatory instability can now occur.