In this thesis we model spherically symmetric radiating stars dissipating energy in the form of a radial heat flux. We assume that the spacetime for the interior matter distribution is shear-free. The junction conditions necessary for the matching of the exterior Vaidya solution to an interior radiating line element are obtained. In particular we show that the pressure at the boundary of the star is nonvanishing when the star is radiating (Santos 1985). The junction conditions, with a nonvanishing cosmological constant, were obtained. This generalises the results of Santos (1985) and we believe that this is an original result. The Kramer (1992) model is reviewed in detail and extended. The evolution of this model depends on a function of time which has to satisfy a nonlinear second order differential equation. We solve this differential equation in general and thereby completely describe the temporal behaviour of the Kramer model. Graphical representations of the thermodynamical and gravitational variables are generated with the aid of the software package MATHEMATICA Version 2.0 (Wolfram 1991). We also analyse two other techniques to generate exact solutions to the Einstein field equations for modelling radiating stars. In the first case the particle trajectories are assumed to be geodesics. We indicate how the model of Kolassis et al (1988) may be extended by providing an ansatz to solve a second order differential equation. In the second case we review the models of de Oliveira et al (1985, 1986, 1988) where the gravitational potentials are separable functions of the spatial and temporal coordinates. / Thesis (M.Sc.)-University of Natal, 1994.

Note: Pages have been removed from this digital copy due to copyright restrictions. A print copy is available in the McGill Library. / This dissertation presents the history of space in the musical thought of the 2Othcentury (from Kurth to Clifton, from Varèse to Xenakis) and outlines the development of spatialization in the theory and practice of contenlporary music (after 1950). The text emphasizes perceptual and temporal aspects of musical spatiality, thus reflecting the close connection of space and time in human experience. A new definition of spatialization draws from Ingarden’s notion of the musical work; a new typology of spatial designs embraces music for different acoustic environments, movements of performers and audiences, various positions of musicians in space, etc. The study of spatialization includes a survey of the writings of many composers (e.g. Ives, Boulez, Stockhausen, Cage) and an examination of their compositions. The final part of the dissertation presents three approaches to spatialization: Brant’ s simultaneity of sound layers, Xenakis’s movement of sound, and Schafer’s music of ritual and soundscape. / Cette thèse présente l’histoire de l’espace dans la pensée musicale du vingtième siècle (de Kurth à Clifton, de Varèse à Xenakis) et retrace le développement de la spatialisation dans la théorie et la pratique de la musique contemporaine (après 1950). Le texte souligne les aspects perceptuels et temporels de la spatialisation musicale, reflétant ainsi le lien étroit entre temps et espace t!ans l’expérience humaine. Une nouvelle définition de la spatialisation tire son origine de la notion de l’oeuvre musicale d’Ingarden; une nouvelle typologie des plans spatiaux prend en considération des musiques pour différents environnements acoustiques, diverses positions des musiciens dans l’espace de même que le mouvement de ceux-ci et des auditeurs, etc. L’étude de la spatialisation inclut un survol des écrits de plusieurs compositeurs (Ives, Stockhausen, Boulez et Cage, par exemple) de même qu’un examen de leurs oeuvres. La dernière partie de la thèse présente trois approches compositionnelles de la spatialisation: la simultanéité de strates sonores ,:hez Brant, le mouvement du son chez Xenakis et la musique du rituel et l’écologie sonore chez Schafer.

Physical habitat for instream biota derives from a combination of stream system structural and hydraulic phenomena. Consequently, the quantity and quality of physical habitat is dynamic both over time and in space along the river, laterally, longitudinally and vertically. Its characterization through stream assessment and classification leads to a better understanding of factors that determine and limit habitat extent and quality. This thesis investigates the effects of space and time on nearshore aquatic habitat in the gravel reach of Fraser River, British Columbia by employing a large river, stage-adaptive habitat classification system. The distribution and abundance of habitat are spatially quantified at the reach scale (32 km), and temporally quantified through a period of about 60 years at several adjacent gravel bars (7 km), and at approximately 500 m3 s-1 increments in discharge during the declining limb of the flood hydrograph at two well-developed gravel bars. Of the ten habitat types evaluated, the bar edge habitat type is most abundant by length and number of units. However, its relative importance is reduced when weighted by fish-habitat association characteristics. Preferred habitat types (channel nook, eddy pool and open nook) are frequent and available to aquatic organisms, and most common at well-developed bars and in zones of equilibrium long-term sedimentation. Preferred habitat was at a maximum 30 years ago when major new bars developed and the thalweg shifted, effectively increasing the amount of bar shoreline and nearshore habitat. This increase is due to substantial change in river planform morphology following a 30-year period of large annual floods. However, amounts of habitat did not increase exclusively during periods of higher than average flows, or decrease exclusively during periods of lower than average flows. Instead, habitat abundance response to flow may occur with a two- or three-year lag. Short term changes in stage are critical to amount of preferred habitat. Optimal discharge for maximum preferred habitat vailability is in the range of approximately 2500 m3 s-1 to 4000 m3 s-1, which approximates long term mean flow. As flow increases, the proportion of preferred habitat compared with total bar shoreline decreases. Comparison with the 2006 flow duration curve shows that 15 – 30 % of discharges are optimal for maximum fish density and biomass. These discharges occurred during April 27 to May 17 and July 14 to August 7, 2006.

Shaped pulses can be used for uniform spin-1 excitation. The effects of the pulses on spin-1 excitation is seen as distortion of two types: phase distortions and amplitude distortions. By reducing the distortions a spin-1 excitation becomes more uniform. In the case of time-symmetric shaped pulses, spin-1 excitation is free of phase distortions. The spin-1 excitation in that case can be made uniform over a larger frequency bandwidth. The number of possible shaped pulses is so large that a computer-aided search is needed to find the desirable shaped pulses. A theoretical analysis is used to find the connection between a shaped pulse and the corresponding spin-1 excitation. The theoretical analysis in density matrix formalism gives the spin-1 excitation in closed-form expressions that are too complicated. In such a case the connection between a shpaed pulse and spin-1 excitation is not straightforward. A brute-force search for a desirable shaped pulse can consume too much computer time and thus time the scope of the search. By using the formalism of quaternions in the theoretical analysis, spin-1 excitation is presented in simple closed form expressions. It is then shown tht if the choice is limited to time-symmetric shaped pulses then these closed form expressions become much simpler. It is also shown that a spin-1 excitation is free of phase distortions in that case. These simple closed form expressions can be used as the building blocks of a much more concise program code for the computer aided search. As a result a computer aided search for a desirable shaped pulse becomes much faster in speed and larger in scope. More shaped pulses for improved spin-1 can be found. / xiii, 99 leaves : ill. ; 28 cm.

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This thesis examines the role of shear in inhomogeneous spherically symmetric spacetimes in the field of general relativity. The Einstein field equations are derived for a perfect fluid source in comoving coordinates. By assuming a barotropic equation of state, two classes of nonaccelerating solutions are obtained for the Einstein field equations. The first class has equation of state p = ⅓µ and the second class, with equation of state p = µ, generalises the models of Van den Bergh and Wils (1985). For a particular choice of a metric potential a new class of solutions is found which is expressible in terms of elliptic functions of the first and third kind in general. A class of nonexpanding cosmological models is briefly studied. The method of Lie symmetries of differential equations generates a self-similar variable which reduces the field and conservation equations to a system of ordinary differential equations. The behaviour of the gravitational field in this case is governed by a Riccati equation which is solved in general. Another class of solutions is obtained by making an ad hoc choice for one of the gravitational potentials. It is demonstrated that for a stiff fluid a particular case of the generalised Emden-Fowler equation arises. / Thesis (Ph.D.)-University of Natal, Durban, 1996.

In this thesis, we seek exact solutions for the interior of a radiating relativistic star undergoing gravitational collapse. The spherically symmetric interior spacetime, when matched with the exterior radiating Vaidya spacetime, at the boundary of the star, yields the governing equation describing the gravitational behaviour of the collapsing star. The investigation of the model hinges on the solution of the governing equation at the boundary. We first examine shear-free models which are conformally flat. The boundary condition is transformed to an Abel equation and several new solutions are generated. We then study collapse with shear in geodesic motion. Two classes of solutions are generated which are regular at the stellar centre. Our treatment extends the results of Naidu et al (2006) which had the undesirable feature of a singularity at the centre of the star. In an attempt to find more general models, we transform the fundamental equation to a Riccati equation. Two general classes of solution are found and are used to study the thermal evolution in the causal theory of thermodynamics. These solutions are shown to reduce to the Friedmann dust solution in the absence of heat flow. Furthermore, we obtain new categories of solutions for the case of gravitational collapse with expansion, shear and acceleration of the stellar fluid. This is achieved by transforming the boundary condition into a Riccati equation. In special cases the Bernoulli equation is regained. The solutions are given in terms of elementary functions and they permit the investigation of the physical features of radiative stellar collapse. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2007.

The study of exact solutions to the Einstein and Einstein-Maxwell field equations, by imposing a symmetry requirement on the manifold, has been the subject of much recent research. In this thesis we consider specifically conformal symmetries in static and nonstatic spherically symmetric spacetimes. We find conformally invariant solutions, for spherically symmetric vectors, to the Einstein-Maxwell field equations for static spacetimes. These solutions generalise results found previously and have the advantage of being regular in the interior of the sphere. The general solution to the conformal Killing vector equation for static spherically symmetric spacetimes is found. This solution is subject to integrability conditions that place restrictions on the metric functions. From the general solution we regain the special cases of Killing vectors, homothetic vectors and spherically symmetric vectors with a static conformal factor. Inheriting conformal vectors in static spacetimes are also identified. We find a new class of accelerating, expanding and shearing cosmological solutions in nonstatic spherically symmetric spacetimes. These solutions satisfy an equation of state which is a generalisation of the stiff equation of state. We also show that this solution admits a conformal Killing vector which is explicitly obtained. / Thesis (Ph.D.)-University of Natal, Durban, 1993.

In this thesis we study the physical properties of the manifold in general relativity that admits a conformal motion. The results obtained are general as the metric tensor field is not specified. We obtain the Lie derivative along a conformal Killing vector of the kinematical and dynamical quantities for the general energy-momentum tensor of neutral matter. Equations obtained previously are regained as special cases from our results. We also find the Lie derivative of the energy-momentum tensor for the electromagnetic field. In particular we comprehensively study conformal symmetries in the Bianchi I spacetime. The conformal Killing vector equation is integrated to obtain the general conformal Killing vector and the conformal factor subject to integrability conditions. These conditions place restrictions on the metric functions. A particular solution is exhibited which demonstrates that these conditions have a nonempty solution set. The solution obtained is a generalisation of the results of Moodley (1991) who considered locally rotationally symmetric spacetimes. The Killing vectors are regained as special cases of the conformal solution. There do not exist any proper special conformal Killing vectors in the Bianchi I spacetime. The homothetic vector is found for a nonvanishing constant conformal factor. We establish that the vacuum Kasner solution is the only Bianchi I spacetime that admits a homothetic vector. Furthermore we isolate a class of vectors from the solution which causes the Bianchi I model to degenerate into a spacetime of higher symmetry. / Thesis (M.Sc.)-University of KwaZulu-Natal, 1992.

In this dissertation we study conformal symmetries in the Stephani universe which is a generalisation of the Robertson-Walker models. The kinematics and dynamics of the Stephani universe are discussed. The conformal Killing vector equation for the Stephani metric is integrated to obtain the general solution subject to integrability conditions that restrict the metric functions. Explicit forms are obtained for the conformal Killing vector as well as the conformal factor . There are three categories of solution. The solution may be categorized in terms of the metric functions k and R. As the case kR - kR = 0 is the most complicated, we provide all the details of the integration procedure. We write the solution in compact vector notation. As the case k = 0 is simple, we only state the solution without any details. In this case we exhibit a conformal Killing vector normal to hypersurfaces t = constant which is an analogue of a vector in the k = 0 Robertson-Walker spacetimes. The above two cases contain the conformal Killing vectors of Robertson-Walker spacetimes. For the last case in - kR = 0, k =I 0 we provide an outline of the integration process. This case gives conformal Killing vectors which do not reduce to those of RobertsonWalker spacetimes. A number of the calculations performed in finding the solution of the conformal Killing vector equation are extremely difficult to analyse by hand. We therefore utilise the symbolic manipulation capabilities of Mathematica (Ver 2.0) (Wolfram 1991) to assist with calculations. / Thesis (M.Sc.)-University of Natal, Durban, 1992.