The interaction between water waves and a floating or fixed body is bi-directional: wave forces act on and cause motion in the body, and the body alters the wave field. The impact of the body on its wave field is important to understand because: 1) it may have positive or negative consequences on the natural or built environment; 2) multiple bodies in proximity interact via the waves that are scattered and radiated by them; and 3) in ocean wave energy conversion, by conservation of energy, as a device absorbs energy, so too must the energy be removed from the wave field. Herein, the cylindrical solutions to the linear wave boundary-value problem are used to analyze the floating body wave field. These solutions describe small-amplitude, harmonic, potential-flow waves in the form of a Fourier summation of incoming and outgoing, partial, cylindrical, wave components. For a given geometry and mode of motion, the scattered or radiated waves are characterized by a particular set of complex cylindrical coefficients. A novel method is developed for finding the cylindrical coefficients of a scattered or radiated wave field by making measurements, either computationally or experimentally, over a circular-cylindrical surface that circumscribes the body and taking a Fourier transform as a function of spatial direction. To isolate evanescent modes, measurements are made on the free-surface and as a function of depth. The technique is demonstrated computationally with the boundary-element method software, WAMIT. The resulting analytical wave fields are compared with those computed directly by WAMIT and the match is found to be within 0.1%. A similar measurement and comparisons are made with experimental results. Because of the difficulty in making depth-dependent measurements, only free-surface measurements were made with a circular wave gauge array, where the gauges were positioned far from the body in order to neglect evanescent modes. The experimental results are also very good. However, both high-order harmonics and wave reflections led to difficulties. To compute efficiently the wave interactions between multiple bodies, a well-known multiple-scattering theory is employed, in which waves that are scattered and radiated by one body are considered incident to another body, which in turn radiates and scatters waves, sending energy back to the first. Wave fields are given by their cylindrical representations and unknown scattered wave amplitudes are formulated into a linear system to solve the problem. Critical to the approach is the characterization of, for each unique geometry, the cylindrical forces, the radiated wave coefficients, and the scattered waves in the form of the diffraction transfer matrix. The method developed herein for determining cylindrical coefficients is extended to new methods for finding the quantities necessary to solve the interaction problem. The approach is demonstrated computationally with WAMIT for a simple cylinder and a more complex wave energy converter (WEC). Multiple-scattering computations are verified against direct computations from WAMIT and are performed for spectral seas and a very large array of 101 WECs. The multiple-scattering computation is 1,000- 10,000 times faster than a direct computation because each body is represented by 10s of wave coefficients, rather than 100s to 1,000s of panels. A new expression for wave energy absorption using cylindrical coefficients is derived, leading to a formulation of wave energy absorption efficiency, which is extended to a nondimensional parameter that relates to efficiency, capture width and gain. Cylindrical wave energy absorption analysis allows classical results of heaving and surging point absorbers to be easily reproduced and enables interesting computations of a WEC in three-dimensions. A Bristol Cylinder type WEC is examined and it is found that its performance can be improved by flaring its ends to reduce "end effects". Finally, a computation of 100% wave absorption is demonstrated using a generalized incident wave. Cylindrical representations of linear water waves are shown to be effective for the computations of wave-body wave fields, multi-body interactions, and wave power absorption, and novel methods are presented for determining cylindrical quantities. One of the approach's greatest attributes is that once the cylindrical coefficients are found, complex representations of waves in three dimensions are stored in vectors and matrices and are manipulated with linear algebra. Further research in cylindrical water waves will likely yield useful applications such as: efficient computations of bodies interacting with short-crested seas, and continued progress in the understanding of wave energy absorption efficiency.

D.Phil. / Spin-density-wave (SDW) effects were studied in diluted Cr-Si and Cr-Ga alloy single cristals. Ga and Si impurities in Cr are respectively from groups 3 and 4 non-magnetic non-transitional elements from the periodic table. Both influence the magnetic behaviour of Cr in a special way. The alloying of Cr with Si and Ga impurities influences the magnetic phase transition temparatures, namely the Néel temparature (Tn) and the transition temparature (T1c) for the incommensurate to commensurate (C) SDW transition, in a very complex way. The magnetic phase diagrams of both Cr-Si and Cr-Ga show a triple phase where the paramegnetic (P), CSDW and ISDW phases co-exist.

Ph.D. / Spin—density—wave (SDW) effects are investigated in four dilute Cr—Ir alloy single crystals. The Ir concentrations in these crystals were chosen to cover all four magnetic phases existing on the magnetic phase diagram of the Cr—Ir system. Thermal expansion, electrical resistivity, elastic constants and ultrasonic attenuation are studied as functions of temperature and alloy concentration. The elastic constants are also studied as a function of applied hydrostatic pressure. The SDW effects in the Cr—Ir system are compared with those in other Cr alloys. The full temperature—concentration and temperature—pressure magnetic phase diagrams of the Cr—Ir system are determined. Existing theories are used to discuss the observations. The following major observations are made: Magnetoelastic interactions in Cr—Ir alloys are very large, resulting in well defined magnetic anomalies in the elastic constants and thermal expansion at all magnetic phase transition temperatures. Elastic constant measurements as a function of temperature appear to be a very sensitive tool to determine the magnetic phase transition temperatures of the Cr—Ir alloy system. Below TN of Cr—Ir alloys, where TN is the transition temperature from the incommensurate transverse spin—density-wave (TISDW) magnetic phase to the paramagnetic phase, elastic constant and thermal expansion measurements show the existence of hysteresis effects, which are probably due to a redistribution of antiferromagnetic domains. These hysteresis effects are the first evidence of such effects in Cr alloys. Spin fluctuation effects are shown to exist to temperatures well above the Neel temperatures of the Cr—Ir alloys. Analyses of the data for electrical resistivity measurements of Cr—Ir alloys show that the fraction of the electron and hole Fermi surface sheets that nests is roughly the same in the ISDW and CSDW (commensurate spin—density—wave) phases, making the resistivity anomaly near the ISDW—CSDW transition temperature very small or non—existing. Measurements of elastic constants as a function of applied pressure at different constant temperatures are shown to be a very powerful tool for an investigation of the interaction of the SDW with the acoustic phonons in dilute Cr—Ir alloys. It is found that the SDW in Cr—Ir alloys couples mainly with the longitudinal—mode acoustic phonons. Coupling to the shear—mode phonons is relatively small. Empirical correspondence is found between the temperature—concentration and temperature— pressure magnetic phase diagrams of the dilute Cr—Ir alloy system by using a linear scaling between pressure and concentration. Existing thermodynamic models fit the experimental results for the elastic constants and magnetovolume of the Cr—Ir alloys well. The main features of the temperature—concentration and temperature—pressure magnetic phase diagrams of the Cr—Ir alloy system are resonably well predicted by existing microscopic theories.

M.Sc. / Spin-density-wave (SDW) effects are investigated in a Cr + 1.9 at.% Fe alloy single crystal, where the Fe concentration lies just below the triple point found in the temperatureconcentration magnetic phase diagram of the Cr-Fe alloy system. The crystal is expected to undergo a commensurate (C) SDW to an incommensurate (I) SDW phase transition at a temperature Tc, and an ISDW-P (paramagnetic) phase transition at the Neel temperature, TN. The magnetoelastic properties and the anharmonic behaviour of this crystal were studied with the aid of velocity of sound measurements as function of temperature and pressure. Electrical transport measurements were carried out using the standard fourprobe method. In order to determine the various phases present in the crystal a preliminary neutron-diffraction study was also done. Fe belongs to the group-8 magnetic transition metals, possessing localized magnetic moments. The SDW effects in the Cr + 1.9 at.% Fe crystal are therefore compared with that of Cr-Ru and Cr-Ir alloys, as Ru and Ir also belong to the group-8 transition metals, however these impurities are nonmagnetic. The following observations were made: The longitudinal mode elastic constants and the bulk modulus show a prominent change in the slope at Tc, and a sharp, deep minimum at TN. For the c' shear propagation mode peaks were seen at Tcl as well as TN and the c4 4 propagation mode showed no anomalies at either phase transition temperatures. The longitudinal ultrasonic wave velocities for the cL propagation mode were measured as a function of temperature at different constant pressures. TN obtained from these measurements varies linearly with increasing pressure. High-pressure ultrasonic wave velocity measurements were taken at various constant temperatures in the range of 230 K to 350 K for the C L, c44 and c' propagation modes of the Cr + 1.9 at.% Fe alloy single crystal. This was used to determine the pressure derivatives of the second order adiabatic elastic constants (acu /ap). The pressure derivatives of the second order adiabatic elastic constant are shown to be a very powerful tool for investigating the interaction of the SDW with the acoustic phonons in the Cr-Fe crystal. II The long-wavelength acoustic-mode Gitmeisen parameters, calculated from (acu/ap), showed that the SDW in the Cr + 1.9 at.% Fe alloy single crystal couples mainly with the longitudinal acoustic phonons. Coupling to the shear modes is relatively small. The mean acoustic-mode GrOneisen parameter shows a small maximum between Tc, and TN. It increases on heating through TN, reaching a large maximum value above TN, and then decreases with further increase in the temperature. The electrical resistivity was measured_in the temperature region of 4 Kt() 900 K in order to obtain the nonmagnetic component of the resistivity at all temperatures. Only the Neel phase transition was observed in these measurements with no resistivity anomalies taking place at -Va. The experimental results on the resisitivity were analyzed according the model of Chui et al.. The magnetic component of the electrical resistivity was calculated from the model with and without the inclusion of the effects of resonant impurity scattering of the conduction electrons by the local impurity states lying in the SDW energy gap. The magnetic contributions were found to be appreciable above TN, even up to temperatures as high as 1.5TN. The neutron-diffraction experiments show that the Cr + 1.9 at.% Fe crystal remains in the ISDW phase at all temperatures below TN. This is an unexpected result as a CSDW-ISDW phase transition is expected at To, the temperature of the observed anomaly in elastic constant and thermal expansion measurements on the crystal

No description available.

No description available.

M.Sc. / The aim of this study is to show that there exists a parallelism between the effect of the concentration of the itinerant electrons per atoom, and the applied hydrostatic pressure, p, on the magnetic phase diagram of a Cr + 0.2 at.% Ir alloy. This Cr-Ir alloy was chosen, because it contains all possible magnetic phases that can exist in a Cr alloy.

M.Sc. / Impurity resonance scattering effects are investigated in the Cr-Ga alloy system. This system has a triple point on its magnetic phase diagram where the paramagnetic (P), incommensurate (I) and commensurate (C) spin-density-wave (SDW) states co-exist. Alloying Cr with the nonmagnetic nontransitional element Ga affects the magnetic properties of Cr in a very unique way. In order to investigate the presence of resonant impurity scattering effects in binary Cr-Ga alloys, electrical resistivity measurements were carried out in the temperature range between 6 K and 85 K. The results of the investigation show: • A nonmonotonic increase in the residual resistivity of the Cr-Ga system with an increase in the Ga content, due to the presence of resonant impurity scattering of conduction electrons. • A low-temperature resistivity minimum observed in some of the Cr-Ga alloys, taken as further evidence for the presence of resonant impurity scattering effects on the conduction electrons. The impurity resonance scattering effects on the electrical resistivity of a Cr + 1.2 at.% Ga alloy, doped with V and Mn to tune the Fermi level through the impurity level, are also investigated. The investigation was complemented by thermal expansion and velocity of sound measurements in the temperature range 77 K to 450 K for the Cr + 1.2 at.% Ga alloy only. This specific Ga concentration was chosen to allow for studying resonant scattering effects in both the ISDW and CSDW phases of the system. This is possible because concentration of 1.2 at.% Ga is just above the triple point concentration. Doping with Mn to increase the electron concentration (eA) drives the alloy deeper into the CSDW phase region of the phase diagram, while doping with V, on the other hand, will drive the alloy towards the ISDW phase region. The results of the study are summarized as follows: • Two relatively sharp peaks, attributed to resonant impurity scattering effects, are observed in the curve of the residual resisitivity as a function of dopant concentration in the ISDW phase of the ternary (Cr0.988Ga0.012)1-xVx and (Cr0.988Ga0.012)1-yMny alloy systems. v • At 0 K the (Cr0.988Ga0.012)1-yMny alloy system transforms from the ISDW to the CSDW phase at y ≅ 0.0032, giving a CSDW phase for y > 0.0032. A peak is observed in the residual resistivity at about this Mn content. This peak can then either be ascribed to a jump occurring in the residual resistivity when the CSDW phase is entered from the ISDW phase or to resonant scattering effects. The conclusion is that the peak is rather related to the latter effect. • The resistivity as a function of temperature of the above two ternary alloy series show well-developed or weak minima at low temperatures for some of the samples. This is taken as further evidence of the influence of impurity resonant scattering effects on the resistivity of these alloys. • The resistivity and thermal expansion coefficient of the polycrystalline Cr0.988Ga0.012 alloy of the present study behaves anomalously close to the ISDW-CSDW phase transition temperature and warrant further investigation. The concentration-temperature magnetic phase diagram of the (Cr0.988Ga0.012)(Mn,V) alloy system was constructed from the magnetic transition temperatures obtained from electrical resistivity measurements. Theoretical analysis of the phase diagram was done using the two-band imperfect nesting model of Machida and Fujita. The results show: • A triple point at (0.21 at.% V, 225 K) where the ISDW, CSDW and P phases coexist on the magnetic phase diagram. • The curvature of all three theoretically calculated phase transition lines in the region of the triple point is of the same sign as that observed experimentally. • The theoretical fit is very good for the ISDW-P and ISDW-CSDW phase transition boundaries, while there is some discrepancy for the CSDW-P phase transition line. This may be attributed to the fact that the theory is one dimensional and that it does not include electron-hole pair breaking effects due to impurity scattering and also not effects of changes in the density of states due to alloying. / Dr. A.R.E Prinsloo Prof. H.L. Alberts

Using modern methods of share quotations forecasting is the main goal of this thesis. The special accent is placed on forecasting the trend by means of artificial neural network especially on the optimalization of variables in the training process. Elliot's wave theory is applied in the second part of the thesis, particularly on prediction of future share quotation progress. Buying or selling signal generated by these two methods is consequently compared with ex-post signal yielding a profit. Lastly, successfulness of using these methods for forecasting at stock market is evaluated.

This thesis is concerned with future trend prediction on capital markets on the basis of neural networks. Usage of convolutional and recurrent neural networks, Elliott wave theory and scalograms for capital market's future trend prediction is discussed. The aim of this thesis is to propose a novel approach to future trend prediction based on Elliott's wave theory. The proposed approach will be based on the principle of classification of chosen patterns from Elliott's theory by the way of convolutional neural network. To this end scalograms of the chosen Elliott patterns will be created through application of continuous wavelet transform on parts of historical time series of price for chosen stocks.