Thermal conductivity measurements have been used to study the low lying energy levels of Cr ions in GaAs. Strong resonant phonon scattering was observed in semi-insulating (SI) and p-type samples, which is attributed to Cr 2+ or Cr 3+ ions, while the scattering in the n-type samples additional to that in undoped material was very small. From the computer fits of the thermal conductivity, zero-field ground state splittings have been deduced. A splitting at ~ 23 cm -1 is attributed to Cr 3+ ions, others at ~ 0.7 cm and 4.9 cm are due to Cr 2+. The phonon scattering in the n-type samples did not show any magnetic field dependence while big effects were observed in SI and p-type ones. This seems consistent with the results of the zero-field work. The effect of uniaxial stress on the phonon scattering has been measured in the temperature range ~2-15 K. Again no effects were seen in n-type material. The results for SI and p-type material are interpreted in terms of a static Jahn-Tellereffect of Cr 2+ ions. A preliminary investigation was made of the effect on the phonon scattering of sub-band-gap illumination. In an-type sample, the decay in the increase in the thermal resistivity produced by photoexcitation showed two parts. The first part with a characteristic time of ~ 1 hour is attributed to electron-capture at Cr 2+ ions. The second decay was very slow (persistent) with a characteristic time T » 10 5 s. This effect has tentatively been attributed to the occurrence of large lattice relaxation. The phonon scattering by the Cr ions is found to be consistent with the 'double acceptor' model for Cr in GaAs. Another model where er can act as a hole trap is discussed. Finally the effect of high magnetic fields on the thermal conductivity of acceptors in Ge was measured. From this and previous results, the g-values describing the ra8 ground state were found to be much lower than the predicted ones. A Thermally Detected EPR apparatus was designed and constructed in an attempt to check on the ground state structure of p-Ge and also p-Si but no results were obtained. This is believed to be due to the very large line widths resulting from strain splitting of the ra8 ground state.

In this thesis, problems of structural optimisation are approached through analytic and computational techniques. A particular focus is the effect of hierarchical design. The first chapter forms an introduction for the reader. Chapter 2 investigates the optimisation of elastic support on a buckling rod. A cost function is associated with the strength of the total elastic support provided to a beam of uniform cross-section supporting a compressive load. Through a perturbative method, it is found that for a low cost of support, a single, centrally placed support is optimal; furthermore it is found, using simulational and analytic methods, that the optimal support placement undergoes a series of bifurcations as the cost increases. The nature of these bifurcations is non-trivial and, although the analogy is not complete, there exist similarities between the solution to this problem and Landau theory of second-order phase transitions. In Chapter 3, the theme of hierarchical design is introduced. By analysing all possible failure modes, it is shown that a hierarchical design is highly efficient for withstanding external pressure loading in the limit of low applied pressures. By changing the level of hierarchy, the scaling law for volume of material required for structural stability against the applied external pressure can be changed systematically. For a given applied pressure, a particular level of hierarchy is shown to be optimal. This optimal level of hierarchy increases without bound as the pressure decreases. The Hausdorff dimension of the optimal structure and its dependence on applied pressure is found. Two example structures are presented, although the design is applicable to any convex shape. The fourth chapter of this thesis investigates the use of hierarchical geometry for a highly efficient interface between two surfaces. It is proposed that for a given strength of surface interaction, alterations to the geometry of the interface play a strong role in determining the force that is required to separate the surfaces. In particular the case of two surfaces with one being very much more rigid than the second is investigated. Increasing the hierarchical order of the design is seen to change the scaling relationship between the interface interaction strength and failure load. In Chapter 5, a hierarchical design for high mechanical efficiency under compressive loading is fabricated and mechanically tested. The particular design has previously been shown to be highly efficient under compressive loading. The scaling of material required to build a stable structure against a specific loading has previously been shown to be dependent on the level of hierarchy. A second order design is fabricated using rapid prototyping techniques. Additionally, a similar design based on hollow tubes rather than solid beams is proposed and is shown to make further savings on volume when compared to the original design. The final investigation presented in this thesis focuses on the role of imperfections in determining the buckling load of a hierarchical design. A two-dimensional design is proposed before simple, single beam, imperfections are added to the structure. The dependence of the structure on the magnitude of the imperfections is calculated analytically for the generation-1 and 2 designs. In the generation-1 structure, the magnitude of the imperfection is related to the reduction in failure load by a one-half power-law. The behaviour of a generation-2 frame with a single beam perturbed in thickness is found to be dominated by the behaviour of the generation-1 subframe. The behaviour found analytically is confirmed with finite element simulations for the generation-1 structure.

Surface plasmons (SP) are guided electromagnetic wave propagating along the surface of metal. The properties of SP are affected by the material attached to the metallic surface so they can be used as a very sensitive sensor capable of detecting the deposition of subnanometric layers of dielectric. SP has been widely investigated for biosensor applications and the theory is well established. Although SP sensors have been well studied, integrating the SP to a microscope is a relatively young field. Since the SPs are surface waves; microscopy techniques to optimise the SP microscope performance will require totally different techniques to non-surface wave microscopy. This thesis develops a theoretical framework to understand different types of SP microscope setups through the rigorous diffraction theory. The framework analyses the diffraction process through rigorous wave coupled analysis (RCWA) and a software package processes the diffracted orders to recover the microscope response for a range of different systems. In this thesis I will investigate the non-interferometric SP microscope, interferometric SP microscope and confocal SP microscope. I will show that the non-interferometric system exhibits a trade-off between lateral resolution and sensitivity, where an image obtained with a good contrast will have low lateral resolution. In order to get around the trade-off, the interferometric system can be employed; however, the main challenge for the interferometric setup is its optical alignment. I will show that a confocal SP microscope, which has been developed as a part of this thesis, can simplify the complexity of the interferometric system and give similar measurement performance. For the interferometric and confocal systems, the SP measurements are normally carried out through the interference signal, which is interference between a reference beam and the SP. I will suggest a method to extract SP propagation parameters from the interference signal by employing a spatial light modulator and also show that the SP propagation parameters do not only give us some insight to the SP effect for the interferometric system, but also gives us a new imaging mode to improve the resolution.

In this thesis, we present a theoretical study of the effects that a current-carrying Two-Dimensional Electron Gas (2DEG) produce on a neighbouring magnetically trapped Bose-Einstein Condensate of alkali atoms (BEC). We suggest that technology used for magnetic micro-controlling of cold gases could be improved by replacing or combining the metallic wires used in such structures with 2DEG-based conductors or quantum electronic devices. All calculations presented in this thesis consider parameters attainable with present technology, suggesting that experimental realization of the scenarios proposed here is already feasible. In Chapter one we present the general context in which this thesis is developed. It includes a definition of the Bose-Einstein condensate state, a description of the principles of magnetic trapping and a brief review of the developments in the area of micromanipulation of atomic BECs. Chapter two is devoted to describe the characteristics of the heterojunction considered in the thesis, and a simple model used to evaluate the electron flow in the 2DEG it contains. Chapter three shows in detail the properties of magnetic trapping configurations considered afterwards. We study two simple applications that can be developed by bringing a BEC near to a current carrying 2DEG. Firstly, in Chapter four, we demonstrate the feasibility of creating magnetic trapping potentials using a current-carrying 2DEG and an external magnetic field. We identify the advantages of such a 2DEG-based trap over traditional metal-based traps and the conditions needed for operability. Recently developed techniques of magnetic field microscopy with BECs motivate our second considered application, namely, using a Bose-Einstein Condensate to probe the electron transport in 2DEGs and structural characteristics of the heterojunction. In Chapter five, we demonstrate how the quantization of conductance occurring in Quantum Point Contacts (QPC) fabricated from the heterojunction in the 2DEG, can be detected through a localized depletion of the BEC caused by a small inhomogeneity of the magnetic field that originates from a current through the QPC. In addition, we show that the electron density fluctuations in the 2DEG can be measured by detecting the corresponding inhomogeneous magnetic field produced when current flows, via modulation of the BEC’s density. We establish the conditions under which a sensitive response of the BEC to the magnetic field is possible. We also derive a general relation between the modulation of the magnetic field affecting the BEC and the distribution of ionized donors in the heterojunction. Creating semiconductor-cold-atom hybrid systems, where electrons in the semiconductor and atoms in the BEC are coupled to each other, requires a full understanding of the properties of both systems. Since typical micro-traps have an elongated geometry, in Chapter six we present a study of phase correlations of BECs in such geometries. To do this, we use a recently proposed effective one-dimensional equation that takes into account the 3D character of the BEC. Finally, in Chapter seven, we conclude and identify directions for future work emerging from this thesis.

While it might be desirable to amend the constitution of Canada to acknowledge the distinctiveness of Indian society as an aid to construction of instruments, it is unnecessary to amend the constitution in order to add a substantive right of Indian self-government. That right is already entrenched as an existing aboriginal right within the meaning of section 35 of the <i>Constitution Act, 1982</i>. The right was constituted by prerogative legislation in the eighteenth century, and has since been reiterated in the statutes of the imperial government which also established the corresponding constitutional powers of the federal and provincial governments. As originally constituted and since perpetuated the right has meant that federal and provincial governments may not legally encroach upon the Indians' jurisdiction to govern their own civil affairs. But neither are the federal and provincial governments under any express or necessarily implied constitutional obligation financially to support Indian governments. Furthermore the Indian right is plenary, in that it applies to civil affairs generally, rather than to a delegated set of enumerated powers. Although the basis for the right was not the common law, the only basis consistent with current federal policy is as if it were common law. That policy presumes that if ever the Indian right had existed it has been superseded historically by actions of federal and provincial governments inconsistent with it. However, the thesis here suggests that since the imperial legislation which actually constituted the right and subsequently reiterated it has never been repealed, such supersession is a legal impossibility. Because it is basic to federal policy the supersession idea nevertheless dominates the current approach to law reform and the negotiation process, which proceeds upon the assumption that the municipal form of self-government on offer, with its delegated enumerated powers to carry out local works, is at least something where nothing exists at the present time. The Indian need to secure financial support renders insisting upon the application of existing law seem politically counterproductive, although it need not be so.

The main mm of this study was to investigate the prophetic calling of the Church and the role of the state in the moral renewal of the South African community. The method of research followed in this study was to study primary and secondary sources, as well as appropriate biblical teachings and theological principles relevant to this study and to systematize the information therein. The gist of the study was to outline the profile and manifestation of moral decay in South African community and, to define the role of the Church and state towards moral regeneration. What transpired was that due to the profile of moral decay within the South African context, the Church and state should play a critical and positive role towards the renewal of morality in South Africa. In conclusion, the fact that the Church and the state each have a particular role to play as driving agents for moral regeneration of South African was confirmed. It is also important to stress the fact that the State cannot be value free or neutral. The word of God speaks of human governments in two-fold way: in a normative way, and in a descriptive way; telling us what they ought to do and be and what they actually turn out to do and be. Both these elements in God's word are reflected in of the Reformed Confession. Therefore, the modern-day concept of a neutral or secular state can be questioned. / Thesis (M.A. (Ethics))--North-West University, Potchefstroom Campus, 2008.

This thesis describes theoretical investigations into the dynamics of superfluid films and the effects of disorder on the roughening transition of crystal surfaces. The dynamic theory of superfluid helium films, due to Ambegaokar et al., is refined to improve the precision of the predictions made. A detailed comparison is made between the predictions of the modified theory and the results from experiments on helium films and on superconducting systems. It is found that, despite the modifications in the theory, agreement with experiments on helium films remains only qualitative. Consideration is then given to the effects on the roughening transition of disorder arising from screw dislocations. A crystal surface which is threaded by screw dislocation pairs may be in one of three different states depending on the temperature of the system and the way in which screw pairs are distributed. At high temperatures the interface is rough: it is not pinned to the lattice. At low temperatures the state of the interface depends on how the screw dislocations are distributed: when distributed as closely spaced pairs they lead to a faceted state with a single ground state energy; when distributed randomly they lead to a state of the interface which, though pinned to the underlying crystal lattice, has a degenerate ground state. It is then shown that the dynamic sine-Gordon formulation of the roughening transition can be used, via a Hubbard-Stratonovich transformation, to model the dynamic behaviour of superfluid systems. This method provides a re-normalization group framework within which the a.c. linear response can be studied. The ways in which the approach could be extended to study the effects of disorder and atomic layering are also discussed.

This thesis describes the behaviour of cold atoms in optical lattices. In particular, it explores how transport through the energy bands of the optical lattice can be used to study quantum chaos and Bose-Einstein condensation. Firstly, this study examines the dynamics of ultra-cold sodium atoms in a one-dimensional optical lattice and a three-dimensional harmonic trap, using both semi-classical and quantum-mechanical analyses. The atoms show mixed stable-chaotic classical dynamics, which originate from the intrinsically quantum-mechanical nature of the energy band. The quantised energy levels exhibit Gutzwiller fluctuations, and the wavefunctions are scarred by an unstable periodic orbit. Distinct types of wavefunction are identified and related directly to particular parts of the classical phase space via a Wigner function analysis. Secondly, this report studies the dynamics of a rubidium Bose-Einstein condensate in a one-dimensional optical lattice and three-dimensional harmonic trap. The condensates are set in motion by displacing the trap and initially follow simple semi-classical paths, shaped by the lowest energy band. Above a critical displacement, the condensate undergoes Bragg reflection, and performs Bloch oscillations. After multiple Bragg reflections, solitons and vortices form which damp the centre-of-mass motion. Finally, the dynamics of Bose-Einstein condensates in optical lattices are investigated for different parameter regimes, as realised in recent experiments. The results reveal how the experiments can be understood, and identify regimes in which vortices trigger explosive expansion of the condensate.

At low temperatures the predominant energy loss mechanism for a Joule-heated two dimensional electron gas (2DEG) in a metal oxide semiconductor field effect transistor (MOSFET) is by acoustic phonon emission. By very accurately measuring the temperature gradient developed along the silicon substrate the phonon emission has been investigated as a function of electron concentration, device power, magnetic field and temperature. In zero magnetic field the results show the cut-off predicted theoretically in the maximum phonon momentum that can be emitted in the plane of the 2DEG for low electron concentrations. It is also found that the momentum of the emitted phonons perpendicular to the plane of the 2DEG is restricted by the width of the 2DEG for the high resistivity (1000 [omega]cm) substrates used. For carrier concentrations greater than 4.9 x 1016 m-2 phonon emission from an upper subband is seen. Electrical measurements indicate that the high mobility (1.2 m2 V-1 S-1) of the devices used leads to changes in the screening of scattering potentials by the electrons being important. This is also seen in the phonon emission experiments. Experiments performed in quantising magnetic fields up to 7 T show that for the powers used (0.2 uW mm-2 – 500 uW mm-2) the phonons emitted arise from Lars-Landau level scattering. Oscillations in the temperature of a thermometer situated directly opposite the middle of the 2DEG are attributed to the movement of the phonon emission to the corners of the 2DEG when the Fermi level is between Landau levels (the Quantum Hall regime). Other trends are attributed to the width of the Landau level limiting the maximum phonon energy that can be emitted. Attempts to use a stress tuned phonon filter to probe the frequency dependence of the phonon emission failed due to experimental difficulties.

A novel approach to the problem of describing interacting magnetic ions has been put forward by Stevens. The work contained herein offers the first major test of the new formalism; applied specifically to binuclear systems in which magnetic Cr3+ ions occur in discrete pairs of D3h symmetry. Each interacting pair is regarded as a unit; wavefunctions suitable for describing the pair are constructed in determinantal form. The wavefunctions of D3h symmetry are used to define the unperturbed Hamiltonian. An effective Hamiltonian is then used to obtain the energy levels in a restricted energy range. (The region of the 2TI levels of the single Cr3+ ion). A set of selection rules is derived. With direct comparison with experimental results the success of theoretical predictions is estimated. Certain interval relations are obtained. There is no first order spin-orbit splitting. Through second order perturbation the maximum values of the spin-orbit coupling constant are found for three materials. The theoretical Zeeman splittings are stated.