<p>Einstein's theory of general relativity is a cornerstone in the process of gaining increased understanding about problems of gravitational nature. It can be applied to problems on the huge length scales of cosmology and as far as we know it does not break down before the Planck scale is approached. Irrespective of scale, a perturbative approach is often a very useful way to reduce the Einstein system to manageable complexity and size.</p><p>The projects included in this thesis can be divided into three subcategories. In the first category the keyword is photon-photon scattering. General relativity predicts that scattering can take place on a flat background due to the curvature of space-time caused by the photons themselves. The coupling equations and cross-section are found and a comparison with the corresponding quantum field theoretical results is done to leading order. Moreover, photon-photon scattering due to exchange of virtual electron-positron pairs is considered as an effective field theory in terms of the Heisenberg-Euler Lagrangian resulting in a possible setup for experimental detection of this phenomenon using microwave cavities. The second category of projects is related to cosmology. Here linear perturbations around a flat FRW universe with a cosmological constant are considered and the corresponding temperature variations of the cosmic microwave background radiation are found. Furthermore, cosmological models of Bianchi type V are investigated using a method based on the invariant scheme for classification of metrics by Karlhede. The final category is slowly rotating stars. Here the problem of matching a perfect fluid interior of Petrov type D to an exterior axisymmetric vacuum solution is treated perturbatively up to second order in the rotational parameter.</p>

<p>Electromagnetic transients impinging on electromagnetic power devices - such as electric machines, transformers and reactors - can stress the design severely. Thus the magnitudes of the transients are often decisive for the design of the devices. Further, the operation of a device can be transient in itself. This is the case for the explosive magnetic flux compression generator (EMG) and a ferromagnetic actuator. </p><p>Models are presented that are mainly intended for transients in the millisecond range and faster. Hence, eddy currents and the related skin and proximity effect become significant in windings, magnetic cores and in the armatures of the devices. These effects are important for, e.g., the damping of the transients. Further, the displacement current in the insulation of the winding is significant. It changes the response of the windings dramatically, as it manifests the finite velocity of propagation of the electromagnetic fields. Under such circumstances, reflections and excited resonances can make the transient voltage and current distribution highly irregular. </p><p>Induced voltages are modelled with self and mutual inductances or reluctances combined with winding templates. The displacement currents are modelled with capacitances or coefficients of potential. Cauer circuits and their dual form are used to model eddy currents in laminated cores and in conductors. The Cauer circuit enables one to consider hysteresis and the non-linear response of a magnetic core. It is also used to model the eddy currents in the moving armature of an EMG. </p><p>A set-up is presented that can be used to study the transient voltage and the current distribution along a coil. </p><p>The transient response of coaxially insulated windings is analysed and modelled in detail. A lumped circuit model is developed for a coil, Dryformer^TM - the new high-voltage transformer - and Powerformer^TM, the new high-voltage generator. An alternative model, a combined lumped circuit and FEM model, is presented for a coaxially insulated winding in two slot cores.</p>

Electromagnetic transients impinging on electromagnetic power devices - such as electric machines, transformers and reactors - can stress the design severely. Thus the magnitudes of the transients are often decisive for the design of the devices. Further, the operation of a device can be transient in itself. This is the case for the explosive magnetic flux compression generator (EMG) and a ferromagnetic actuator. Models are presented that are mainly intended for transients in the millisecond range and faster. Hence, eddy currents and the related skin and proximity effect become significant in windings, magnetic cores and in the armatures of the devices. These effects are important for, e.g., the damping of the transients. Further, the displacement current in the insulation of the winding is significant. It changes the response of the windings dramatically, as it manifests the finite velocity of propagation of the electromagnetic fields. Under such circumstances, reflections and excited resonances can make the transient voltage and current distribution highly irregular. Induced voltages are modelled with self and mutual inductances or reluctances combined with winding templates. The displacement currents are modelled with capacitances or coefficients of potential. Cauer circuits and their dual form are used to model eddy currents in laminated cores and in conductors. The Cauer circuit enables one to consider hysteresis and the non-linear response of a magnetic core. It is also used to model the eddy currents in the moving armature of an EMG. A set-up is presented that can be used to study the transient voltage and the current distribution along a coil. The transient response of coaxially insulated windings is analysed and modelled in detail. A lumped circuit model is developed for a coil, DryformerTM - the new high-voltage transformer - and PowerformerTM, the new high-voltage generator. An alternative model, a combined lumped circuit and FEM model, is presented for a coaxially insulated winding in two slot cores.

Einstein's theory of general relativity is a cornerstone in the process of gaining increased understanding about problems of gravitational nature. It can be applied to problems on the huge length scales of cosmology and as far as we know it does not break down before the Planck scale is approached. Irrespective of scale, a perturbative approach is often a very useful way to reduce the Einstein system to manageable complexity and size. The projects included in this thesis can be divided into three subcategories. In the first category the keyword is photon-photon scattering. General relativity predicts that scattering can take place on a flat background due to the curvature of space-time caused by the photons themselves. The coupling equations and cross-section are found and a comparison with the corresponding quantum field theoretical results is done to leading order. Moreover, photon-photon scattering due to exchange of virtual electron-positron pairs is considered as an effective field theory in terms of the Heisenberg-Euler Lagrangian resulting in a possible setup for experimental detection of this phenomenon using microwave cavities. The second category of projects is related to cosmology. Here linear perturbations around a flat FRW universe with a cosmological constant are considered and the corresponding temperature variations of the cosmic microwave background radiation are found. Furthermore, cosmological models of Bianchi type V are investigated using a method based on the invariant scheme for classification of metrics by Karlhede. The final category is slowly rotating stars. Here the problem of matching a perfect fluid interior of Petrov type D to an exterior axisymmetric vacuum solution is treated perturbatively up to second order in the rotational parameter.

Nowadays, by increasing competitions in business, decision-making in maintenance management gets higher priorities. While maintenance in many industries is known as a necessary evil, making cost-effective decisions constructed based on analytical and quantitative assessments improve maintenance position from a cost center into a profit generating one. Within the scope of rotating equipment maintenance, it is vital to consider both economic and technical variables integrated to survive in the competitive market. Taking the role of improving rotating equipment performance within a cost-effective approach into account, this project proposes a consistent model followed by substantial results. The model application can be briefed in improvement of decision-making processes from technical and economic perspectives to direct them into the company profitability aligned with the company goals. Further, it proposes technical and economic indicators and improves utilization of maintenance resources including personnel skills and experience to enhance maintenance performance and develop cost-effective scenarios. Within the model, eMDSS (software) is used as an intelligent facilitator/tool which improves accurate decision-making and identifying and prioritizing maintenance problems. To ensure from the model and its tool applicability, it is applied on a real case study and reliability of the achieved results are tested and approved in detail. In result, the project is successful in evaluating previous technical and economic decisions and selecting the most cost-effective scenario for future with a saving value exceeding 133K€ and profit of 114K€ for the case equipment.

El objetivo principal de este trabajo es desarrollar un modelo sencillo que permita la caracterización hidrodinámica de membranas selectivas integradas en sistemas bi-iónicos, mediante la determinación de coeficientes de difusión y de espesores de las capas límite alrededor de la membrana. A tal fin, se empleó una célula de difusión rotatoria (CDR), que permite el establecimiento de condiciones hidrodinámicas bien definidas para el sistema de membrana, dado que la variación de la frecuencia de giro del cilindro interior (&#969;), permite disminuir el espesor de la capa límite sobre la membrana, lo que favorece el intercambio iónico a su través. Se puede comprobar éste comportamiento, mediante consideraciones en torno al coeficiente de difusión de los cationes en el sistema de membrana y del cálculo del propio espesor de la capa límite. El mencionado coeficiente se obtendrá a partir del flujo iónico en la membrana, determinado a partir de medidas de pH, junto a medidas de conductividad, en la fase externa (receptora), a diferentes temperaturas y a distintas valores de &#969;.La medida de los flujos, una vez establecida su dependencia con &#969;, permite obtener los coeficientes de difusión catiónicos en el sistema de membrana, en función de la temperatura y de &#969;. Las medidas de la conductividad permiten testar el modelo propuesto, mediante su correlación con los valores de pH obtenidos, proporcionando información adicional acerca de los coeficientes de difusión de los cationes. / From the experimental study of the ionic transport through selective membranes in biionic systems, a simple model which allows the characterising hydrodynamic of the membrane systems through the determination of diffusion coefficients and the thickness of the limit layer has been developed. With this purpose, a rotating diffusion cell that allows the setting of hydrodynamic conditions clearly for the membrane system has been used, studying the variation of the conductivity and the pH in the external phase (receiving) at different temperatures from 20ºC to 50ºC and at different rotating velocities &#969;. The measurement of the fluxes, once set its dependence with &#969;, allows obtained the diffusion coefficients cationics in the membrane system in accordance with the temperature and &#969;. The measurements of the conductivity allow the testing of this model, through its correlation with the values of the pH measured, obtaining additional data about the diffusion coefficient of the cations in the receiving phase.

Numerical study of transition in the Rayleigh-B&#039 / enard problem of thermal convection between rigid plates heated from below under the influence of gravity with and without rotation is presented. The first numerical approach uses spectral element method with Fourier expansion for horizontal extent and Legendre polynomal for vertical extent for the purpose of generating a database for the subsequent analysis by using Karhunen-Lo&#039 / eve (KL) decomposition. KL decompositions is a statistical tool to decompose the dynamics underlying a database representing a physical phenomena to its basic components in the form of an orthogonal KL basis. The KL basis satisfies all the spatial constraints such as the boundary conditions and the solenoidal (divergence-free) character of the underlying flow field as much as carried by the flow database. The optimally representative character of the orthogonal basis is used to investigate the convective flow for different parameters, such as Rayleigh and Prandtl numbers. The second numerical approach uses divergence free basis functions that by construction satisfy the continuity equation and the boundary conditions in an expansion of the velocity flow field. The expansion bases for the thermal field are constructed to satisfy the boundary conditions. Both bases are based on the Legendre polynomials in the vertical direction in order to simplify the Galerkin projection procedure, while Fourier representation is used in the horizontal directions due to the horizontal extent of the computational domain taken as periodic. Dual bases are employed to reduce the governing Boussinesq equations to a dynamical system for the time dependent expansion coefficients. The dual bases are selected so that the pressure term is eliminated in the projection procedure. The resulting dynamical system is used to study the transitional regimes numerically. The main difference between the two approaches is the accuracy with which the solenoidal character of the flow is satisfied. The first approach needs a numerically or experimentally generated database for the generation of the divergence-free KL basis. The degree of the accuracy for the KL basis in satisfying the solenoidal character of the flow is limited to that of the database and in turn to the numerical technique used. This is a major challenge in most numerical simulation techniques for incompressible flow in literature. It is also dependent on the parameter values at which the underlying flow field is generated. However the second approach is parameter independent and it is based on analytically solenoidal basis that produces an almost exactly divergence-free flow field. This level of accuracy is especially important for the transition studies that explores the regions sensitive to parameter and flow perturbations.

The dynamics of rigid body motion are dependent on the inertial properties of the body - that is, the mass and moment of inertia. For complex systems, it may be necessary to derive these results empirically. Such is the case for manual wheelchairs, which can be modeled as a rigid body frame connected to four wheels. While 3D modeling software is capable of estimating inertial parameters, modeling inaccuracies and ill-defined material properties may introduce significant errors in this estimation technique and necessitate experimental measurements. To that end, this thesis discusses the design of a device called the iMachine that empirically determines the mass, location of the center of mass, and moment of inertia about the vertical (yaw) axis passing through the center of mass of the wheelchair. The iMachine is a spring-loaded rotating platform that freely oscillates about an axis passing through its center due to an initial angular velocity. The mass and location of the center of mass can be determined using a static analysis of a triangular configuration of load cells. An optical encoder records the dynamic angular displacement of the platform, and the natural frequency of free vibration is calculated using several techniques. Finally, the moment of inertia is determined from the natural frequency of the system. In this thesis, test results are presented for the calibration of the load cells and spring rate. In addition, objects with known mass properties were tested and comparisons are made between the analytical and empirical inertia results. In general, the mass measurement of the test object had greater than 99% accuracy. The average relative error for the x and y-coordinates of the center of mass was 0.891% and 1.99%, respectively. For the moment of inertia, a relationship was established between relative error and the ratio of the test object inertia to the inertia of the system. The results suggest that 95% accuracy can be achieved if the test object accounts for at least 25% of the total inertia of the system. Finally, the moment of inertia of a manual wheelchair is determined using the device (I = 1.213 kg-m²), and conclusions are made regarding the reliability and validity of results. The results of this project will feed into energy calculations for the Anatomical Model Propulsion System (AMPS), a wheelchair-propelling robot used to measure the mechanical efficiency of manual wheelchairs.

No description available.

Condition monitoring of critical machinery has many economic benefits. The primary objective is to detect faults, for example on rolling element bearings, at an early stage to take corrective action prior to the catastrophic failure of a component. In this context, it is important to be able to discriminate between stable and deteriorating fault conditions. A number of conventional vibration analysis techniques exist by which certain faults in rotating machinery may be identified. However, under circumstances involving multiple fault conditions conventional condition monitoring techniques may fail, e.g. by indicating deteriorating fault conditions for stable fault situations or vice versa. Condition monitoring of rotating machinery that may have multiple, possibly simultaneous, fault conditions is investigated in this thesis. Different combinations of interacting fault conditions are studied both through experimental methods and simulated models. Novel signal processing techniques (such as cepstral analysis and equidistant Fourier transforms) and pattern recognition techniques (based on the nearest neighbour algorithm) are applied to vibration problems of this nature. A set of signal processing and pattern recognition techniques is developed for the detection of small incipient mechanical faults in the presence of noise and dynamic load (imbalance). In the case investigated the dynamic loading consisted of varying degrees of imbalance. It is demonstrated that the proposed techniques may be applied successfully to the detection of multiple fault conditions. / Thesis (Ph.D. (Electronical Engineering))--North-West University, Potchefstroom Campus, 2004.