Browsing by Author "Ellis, GFR"

Now showing 1 - 15 of 15
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    Approaches to ensembles of universes
    (2003) Kirchner, Ulrich; Ellis, GFR
    This thesis consists of three parts - each of them focusing on different aspects relating to ensembles of universes and causally disconnected regions. In the first part I investigate possible measures over the space of FLRW models. In the second part I examine the behaviour of such transition regions for spherically symmetric space-times. In the last part of this thesis I discuss philosophical, physical, and probabilistic issues related to the concept of a multiverse - an ensemble of universes. The difference between ensembles of really existing universes and ensembles of possible universes is emphasized.
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    A comparative quality of life survey in Elsies River and Basuto QwaQwa
    (1985) Erlank, D; Ellis, GFR
    This thesis is concerned with developing a method for determining the Quality of Life of a group or community in quantitative terms. The method devised is aimed at providing decision-makers with a useful tool when allocating public funds. The method involves setting critical values for indicators and then applying a mathematical formula, in order to standardise information gathered from several different sources. A value for the indicator of a particular group or community is thus calculated. This procedure made it possible to compare data from these different sources. Arising out of this the values for individual indicators were aggregated to produce indices evaluating the Quality of Life, which are in a form that may be readily used by decision-makers. Surveys were run in Elsies River, a coloured suburb of Cape Town, and in Basuto QwaQwa, a homeland in the Orange Free State, using two questionnaires. The results were computed and the method developed here used to compare and aggregate the data. Other sources of data included opinions from experts and objective data concerning the two survey areas which were also standardised and aggregated. The results show that the method is pragmatic and could be useful to decision-makers. The standardisation provided the means for arriving at the indices which show how different aspects of the Quality of Life may be assessed. The results, however, are not absolute and could change through a process of negotiation: in fact this is an essential qualification.
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    Cosmological perturbation theory and the variational principle in gravitation
    (2000) Laatz, C D; Ellis, GFR; Dunsby, P K S
    In this thesis firstly the theory of relativistic cosmological perturbations is studies, in the process being reviewed over the period 1960-1993. Secondly the variational principle, apropos of gravitation, is formulated and discussed. These two fields are then synthesised via a variational formulation of general relativity and cosmological perturbation theory. In the process new light is shed on Covariant Perturbation Theory via the development of generalised alternative variables, culminating in a unique variational formulation.
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    Dynamical studies in relativistic cosmology
    (2000) Mustapha, Nazeem; Ellis, GFR
    We conduct three investigations in Relativistic Cosmology that is the Einstein Field Equations applied to the largest scales with source field typically taken to be a perfect fluid and fundamental observers comoving with the preferred fluid four-velocity. We show using a tetrad analysis of the evolution equations for the dynamical variables and all the constraints these satisfy in classical General Relativity, that there are no new consistent perfect fluid cosmologies with the kinematic variables and the electric and/or magnetic parts of the Weyl curvature all rotationally symmetric about a common axis in an open neighbourhood Ա of an event. The consistent solutions of this kind are either locally rotationally symmetric, or most generally are subcases of the Szekeres model-an inhomogeneous dust model with no Killing symmetries. This result and its obvious future generalisations provides an input into the equivalence problem in cosmology necessary for a mathematically consistent understanding of probability and a measure set for universes required in quantum cosmology, for instance. We investigate such generalisations and find that similar results hold under some further assumptions dependent on the level of generalisation. In particular, we examine situations where either the electric part or the magnetic part of the free gravitational field are not rotationally symmetric, and also make a brief comment on the most general case where only the shear is rotationally symmetric. We use a tetrad analysis to show that the well-known result that holds for relativistic shear-free dust cosmologies in Einstein's classical theory either the expansion vanishes or the flow is irrotational - has an analogue in the Kaluza-Klein universe model, which has its roots presumably in string theory (or M-theory), recently proposed by Randall and Sundrum. The Big Bang singularity of General Relativity can not be avoided in these so-called brane universes in the situation where we neglect non-local tidal effects on the dynamics by allowing the vorticity to spin up as the singularity is approached in shear-free cases. Moreover, we show that in the general case of a shearing perfect fluid, the singularity at the start of the universe is approached even more strongly than in classical General Relativity in the case of no tidal interaction. Finally, we reconsider the issue of proving large scale spatial homogeneity of the universe in classical General Relativity, given isotropic observations about us and the possibility of source evolution both in numbers and luminosities. We use a spherically symmetric dust universe model (compatible with observations) for our investigation and we solve the field equations on the null cone analytically for the first time. Two theorems make precise the freedom available in constructing cosmological models that will fit the observations. They make quite clear that homogeneity cannot be proven without either a fully determinate theory of source evolution, or availability of distance measures that are independent of source evolution. We contrast this goal with the standard approach that assumes spatial homogeneity a priori, and determines source evolution functions on the basis of this assumption.
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    The influence of structure formation on the evolution of the universe
    (2013) Umeh, Obinna; Clarkson, Chris; Ellis, GFR
    The next generation of telescopes will usher in a new era of precision cosmology capable of determining key parameters of a cosmological model to percent level and beyond. For this to be effective, the theoretical model must be understood to at least the same level of precision. A range of subtle physical spacetime effcts remain to be explored theoretically, for example, the effect of backreaction on cosmological observables. A good understanding of this effect is paramount given that it is a consequence of any space-time theory of gravity. We provide a comprehensive study of this effect from the perspective of geometric averaging on a hyper-surface and averaging on the celestial sphere. We concentrate on Friedmann-Lemaitre-Robertson-Walker spacetime with small perturbation up to non-linear order . This enables us to quantify by how much this effect could change the standard model interpretation of the universe. We study in great detail key parameters of the standard model, Hubble rate, deceleration parameter and area distance.
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    Legitimacy and decision making in developmental local government : participative MCDA in Stellenbosch
    (2003) Scott, Leanne; Parnell, Sue; Ellis, GFR
    This thesis is concerned with the problem of how to effectively address the complex issue of poverty in the context of limited resources. Poverty is a multi-dimensional problem that affects different communities in different ways. In order to use the available resources in such a way as to most effectively tackle poverty, a means of measuring and benchmarking outcomes as well as evaluating choices of intervention is required. However, smart methods of allocating scarce resources are not in themselves sufficient, if they are not regarded as legitimate by the participants of the process. The imperative of legitimacy demands that we both address the issue of quantitative rigour in resource allocation methods and that we look beyond and explore too the mechanics of effective participatory methods. The approach of developmental local government adopted by the new South African government post apartheid, places this complex problem in the sphere of local government. The primary tool available to local administrators for addressing poverty, amongst other issues, is that of integrated development planning. This process draws together the stakeholders who fall broadly into three groups of participants, namely the communities that live in the municipality, the municipal officials and the elected politicians, and allocates them the task of identifying and prioritising community and municipal issues, and developing appropriate plans to address them. This package of plans or projects is compiled into a municipal budget that targets priority issues for the area, in an integrated and coherent manner. This thesis proposes a new method for tackling this specific group decision making problem, namely Participative Multi-Criteria Decision Analysis. This method was developed in an action research setting in the municipality of Stellenbosch, South Africa, and applied to their 2001/2002 integrated development planning process. The method is grounded in the principles of participative action research in which the participation of all interested and affected patties is valued, and in which there is a commitment to work for change to the fundamental fabric of knowledge and power, leading to a greater empowerment of ordinary people. This participative framework strengthens the legitimacy of the approach by promoting a stronger sense of ownership of process and products by all participants. Within this participative framework, tools of multi-criteria decision analysis are used to support the decision making process by quantifying difficult decisions that need to be addressed. It is the synthesis of these two approaches (action research and multi-criteria decision analysis) that provides both legitimacy and rigour for this method within a highly contested and complex public decision making arena. In the spirit of action research, the method is developed by drawing on theory about developmental local government and poverty, as well as multi-criteria decision analysis. In the process of the research, over forty community workshops were held throughout the Stellenbosch municipal area. Community representatives identified and prioritised the issues of their areas; and in conjunction with municipal officials, developed and evaluated projects in response to these issues. These evaluations assisted the local council to compile the final budget for 2001/2002 in Stellenbosch. In this process, the communities (divided into nine development areas) also developed community development measurement scales which formed the basis for the project evaluations and an ongoing basis for monitoring progress in these communities. It unfolded during the course of this research that a fundamental component of this proposed participative public decision making approach is the role of a central co-ordinating person, not connected to or answerable to any of the constituent groups, who can manage the process of participation, promote an awareness of effective and informative data; ensure the appropriate use of quantification tools and maintain a focus on sustainable poverty alleviation. The method developed in this thesis was successfully applied to the process of identifying, prioritising and making choices about community issues in Stellenbosch, under conditions of significant polarisation of the constituent decision making groups, conclude that this method can be used to implement key aspects of integrated development planning as it addresses the issues of legitimacy and rigour in participative public decision making.
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    Observational space-times
    (1980) Nel, S D; Ellis, GFR
    The work presented in this thesis forms part of a programme undertaken in collaboration with G.F.R. Ellis and R. Maartens, the primary aim of which is to examine in detail how cosmological observations may be used to determine the large scale structure of space-time (see, e.g., refs. [1-5]). In order to place this work in context as part of the ongoing cosmological enterprise, it is necessary to review briefly the main objectives of cosmology, the basic assumptions underlying most modern attempts to achieve these objectives, and the observational as well as philosophical status of these assumptions.
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    On the evolution of large-scale structure in a cosmic void
    (2014) February, Sean Phillip; Clarkson, Chris; Ellis, GFR
    Future large-scale structure surveys are expected to pin-down the properties of dark energy significantly more by mapping the cosmic web to unprecedented precision. To take advantage of such state-of-the-art technologies, the evermore accurate modelling of structure formation is absolutely necessary. While relativistic linear and non-relativistic (Newtonian) non-linear effects have been well established (although improvements are still being made), a fairly unexplored area is the impact of relativistic, non-linear effects on structure formation. As an attempt in this direction, we consider linear perturbations of a Lemaître-Tolman-Bondi (LTB) spacetime. LTB models are spherically symmetric but inhomogeneous exact dust solutions to the Einstein field equations. They are known to accommodate most observations of the background universe without dark energy. In this work we present a new numerical code to solve the set of coupled partial differential equations that describe the evolution of the (polar) perturbations, test it in the case of a Hubble-scale LTB void, and demonstrate its excellent stability and convergence. We then explore the solutions for a variety of generic initial conditions. The variable that closely resembles the Newtonian potential is shown to excite propagating (tensor) as well as rotational (vector) modes at the percent-level. Comparing our results to that which ignores the full coupling, we estimate percent-level corrections to the amplitude of the galaxy correlation function when only the scalar degrees of freedom are included. In addition, we showed that the anisotropic correlation function can nevertheless be used as a test of the Copernican Principle. Note that our code has applications to other scenarios as well in which spherical symmetry is a good approximation, such as the lensing of gravitational waves by intervening halos/voids.
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    Ricci Time in Lemaître-Tolman Model and Block Universe
    (2014) Elmahalawy,Yasser Reda Ahmed Abdelhamid; Hellaby, Charles; Ellis, GFR
    It is common to think of our universe according to the "block universe" idea, which says that spacetime consists of many "stacked" 3-surfaces varied as a function of some kind of proper time Ƭ. Standard ideas do not distinguish past and future, but Ellis' "evolving block universe" tries to make a fundamental distinction. One proposal for this proper time is the proper time measured along the timelike Ricci eigenlines, starting from the big bang. The main idea of this work is to investigate the shape of the {Ƭ=constant} surfaces relative to the the null surfaces, and determine what makes these surfaces timelike or spacelike. We use the Lemaître-Tolman metric as our inhomogeneous spacetime model, and we find the necessary and sufficient conditions for these {Ƭ=constant} surfaces to be spacelike or timelike. Furthermore, we indicate whether or not timelike surfaces appear inside black holes and other strong gravity domains, by determining the location of the timelike regions relative to the apparent horizon. Based on this idea, we find that the regions where these surfaces become timelike are often close to the apparent horizons, but always outside them, and in particular timelike regions occur outside black holes. They are always spacelike near the big bang, and at late times (near the crunch or the extreme far future), they are only timelike under special circumstances.
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    The Sachs-Wolfe effect
    (1993) Katz, Mark; Ellis, GFR
    This thesis discusses the Sachs-Wolfe effect, which is the variation in the observed temperature of radiation emitted at the last scattering surface which occurs at the place where matter and radiation decouple at about 4000 degrees Kelvin. The work is in two parts, with the first part dealing with extensions made by George Ellis, Chongming Xu, Bill Stoeger and myself to the paper by Miroslaw Panek [13] where the gauge invariant formalism of cosmological density perturbations by James Bardeen [1] has been used to find the SW effect in the case of a perturbed Friedman-Lemaitre-Robertson-Walker (FLRW) universe with a barotropic equation of state describing the matter in the unperturbed case. In our work we extend the example given by Panek for a flat universe (K = 0) filled with dust where the density perturbations are adiabatic, to the case of non-fl.at universes (K = -1, 0 + 1) filled with a mixture of N types of matter where the density perturbations are nonadiabatic. The second part shows the agreement between the formalisms of Sachs and Wolfe's pioneering paper and the recent work of George Ellis and Marco Bruni which presents the study of cosmological perturbations in a gauge invariant and covariant way. After the overview of the work covered in this thesis, the gauge invariant formulation of Bardeen is discussed where we follow the description by Panek of a universe whose energy content is described by a mixture of N ideal fluids coupled only by gravity. From the Einstein equations we get Bardeen's evolution equation for the gauge invariant energy density perturbation which is now given for the N different matter fluids as it appears in Panek. We then checked Panek's equations where he finds an expression for the placing of the perturbed last scattering surface, after which he derives an equation for the fractional temperature variation and writes it in terms of the perturbation variables. The equation found by SW for their particular choice of K = O, pressure free dust, where the last scattering surface is placed at its unperturbed position, is verified in terms of the Bardeen formalism. Now we extend this simple case to nonadiabatic perturbations in the same scenario and find the SW effect for a mixture of two fluids: dust and radiation, with nonadiabatic perturbations in a not necessarily flat universe. We then generalise to the case of a mixture or baryons and radiation and N types of matter. This section then ends with a calculation of the difference between temperatures taken from two different directions in the sky and is written in terms of the fractional temperature perturbation defined by Panek. The second part puts forward the formulation of the gauge problem by Ellis and Bruni (EB), and then writes out their gauge invariant quantities in terms of the SW variables. Their evolution equations are verified in this form, and the shear and vorticity determined as well. Now all of the EB cosmological quantities are listed for the special gauge that SW use and then we explore the relation between the SW metric and that of Bardeen before ending off by verifying that the form for the redshift in the EB approach is in agreement with that given by Panek.
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    Salience-affected neural networks
    (2009) Remmelzwaal, Leendert Amani; Tapson, Jonathan; Ellis, GFR
    In this research, the salience of an entity refers to its state or quality of standing out, or receiving increased attention, relative to neighboring entities. By neighbouring entities we refer to both spatial (i.e. similar visual objects) and temporal (i.e. related concepts). In this research we model the effect of non-local connections using an ANN, creating a salience-affected neural network (SANN). We adapt an ANN to embody the capacity to respond to an input salience signal and to produce a reverse salience signal during testing. The input salience signal applied during training to each node has the effect of varying the node’s thresholds, depending on the activation level of the node. Each node produces a nodal reverse salience signal during testing (a measure of the threshold bias for the individual node). The reverse salience signal is defined as the summation of the nodal reverse salience signals observed at each node.
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    A space-time approach to quantum mechanics
    (1999) Kirchner, Ulrich; Ellis, GFR
    We present a systematic development and application of Geometric Algebra, an extended vector calculus. The entire algebraic structure, which is a graded Clifford algebra, is developed. To illustrate the derived results, examples are given for two and three dimensions. Here it becomes clear, how rotations and Lorentz boosts can be formulated in the Geometric Algebra. Further we realize that the Geometric Algebra contains elements, which can be used as representations of the complex unit. Having derived the necessary tools, we turn our attention to physics. We give applications to classical mechanics, quantum mechanics, ï¬ eld theory, curved manifolds, electromagnetism, and gravity as a gauge theory.
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    A study of conceptualised links in the understanding of introductory Newtonian dynamics
    (2002) Moetsana-Moeng, Irene 'Malanga; Ellis, GFR; Linder, Cedric
    Research into student understanding of university level physics has been extremely extensive over the past decade with many international studies affirming the inherent complexity and difficulty that undergraduate students typically experience in learning physics. An important and informative element of this research has focused attention on describing the variation in ways which students make sense of concepts which they experienced as being fundamentally counter-intuitive. One of the areas of most prolific research has been Newtonian dynamics. However, one important aspect from the teaching perspective which has not been examined at all is the variety of the ways in which multi-conceptual links are understood. This study has begun the examination of this aspect of Newtonian physics understanding using a group of first-year physics students enrolled at a typically good South African university. Since the study was primarily aimed at characterising the variance in understanding of conceptual links in Newtonian dynamics the fundamental theoretical framework chosen for the study was drawn from phenomenography. The data consisted of a set of concept maps created by the students involved in the study and in-depth interviews with these students about the understanding they were attempting to represent on a multi-conceptual level on these maps. Since an integral part of the study included exploring the role of counter- intuitiveness, the method involved creating ideal data-generating contexts for thematising drawn from an everyday problem with varying degrees of abstraction. In brief, these thematised scenarios incorporated the following: a familiar everyday experience with normal friction conditions; a familiar everyday experience with reduced friction conditions; and, an unfamiliar everyday experience with greatly reduced friction conditions. The set of interviews formed what is known as a 'pool of meaning' in phenomenography for its associated analytic process. The analysis had two components. The first component involved analysing the interview data across individuals to develop what is known phenomenographically as 'categories of description' to characterise the nature of the understanding in terms of conceptualisation or experience. The second component focused on learning as a function of the students' everyday and educational experiences. Here critical educational aspects emerged and their variance was identified. For example, intuition and context emerged as deeply influential factors in the ways Newtonian links are understood. Following contemporary thrusts in phenomenography this component of the analysis also looked at intra-contextual and inter-contextual shifts. The analysis produced four distinct qualitative ways of understanding or conceptualising Newtonian links and showed the critical influence of intuition and context in the development of understanding of Newtonian dynamics at the introductory level. The analysis also contributed to phenomenographic theoretical concerns about a way of experiencing or understanding a phenomenon and the evolvement of such understanding. Collectively, these results are used to suggest important pedagogical implications for informing the improvement of physics teaching at this level.
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    Topics in contemporary cosmology
    (2003) Solomons, Deon Mark; Ellis, GFR; Dunsby, Peter K S
    Includes bibliographical references.
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    Void boundaries in the southern sky : aspects of large scale structure in southern galaxy catalogues
    (1991) Maurellis, A; Ellis, GFR
    The evidence for structure at the largest observable scales has developed considerably in the last two and a half decades since the discovery, in 1967, of significant clustering in galaxy surveys. As will be shown by the review -material and galaxy spectrum redshift survey maps presented in chapter 1, it has become generally accepted that the universe contains a vast, lacunary structure. Naturally, a number of issues arise when the accuracy of the survey maps that display such structure is questioned. For example, visual bias on the part of the observer (chapter 1) and errors induced by the inability of a survey to pick out non-luminous or too distant matter, or errors that exist as a result of observational techniques (see chapter 2) may affect the accuracy with which redshift maps represent real structure in the universe. Attempts at mathematically modelling these effects are also reviewed in chapter 2. Redshift distributions contain more than spatial information however, and potential inaccuracies are further exacerbated by the fact that there is a wide range of galaxy properties. This fact is the source of so-called segregation effects. However it is argued that the lacunae (more commonly called voids) which are evident in redshift surveys that make use of all available redshifts, agree with features evident in controlled surveys (i.e. surveys for which galaxies are selected subject to some sort of observational criterion). In addition, voids are able to "hide" in the cosmic microwave background. Thus even though the largest structures found in redshift surveys (superclusters) tend to be as large as the extents of the surveys, it is conceivable that one way, of fitting a homogeneous and isotropic Friedmann model to the real universe is by assuming that voids are in fact the structural units of the Friedmann model. The question of examining redshift data for possible interconnections between voids has prompted the discovery of a striking two-dimensional sheet of galaxies-the main topic of this thesis. In chapter 2 the southern catalogues from which the data has been drawn are discussed. In fact the use of all available redshifts allows a detailed examination of large volumes of the 3-d distribution to be made. Computer software called COELIS has been especially developed for the purpose of providing a number of data manipulation and graphics tools for studying the 3-d distribution and, in particular, flat (i.e. 2-d) sub-sets of the real data. A description of COELIS' functions is the subject of chapter 3 (the code is included in an appendix). In chapter 4, the discovery of a remarkably planar redshift feature is presented; some 6.5 h-¹ Mpc thick and approximately 20 x 20 h-² Mpc² wide, at the interface between the southern voids of Sculptor and Eridanus-termed the Wall. The planar nature of such a feature allows for 2-d statistical methods to test for significantly under-dense regions (in effect void interconnections). There is no evidence for clustering in the Wall (which is highly diffuse) and no evidence for significant under-densities. In fact the distribution of redshifts in the Wall appears to be quite random. A preliminary examination of other void interfaces is inconclusive; it reveals a mixture of apparent interconnections and walls'. When available galaxy-property information is used to derive galaxy-property gradients perpendicular to planar features it is possible to obtain a list of likely formation histories for the feature under study, and hence obtain some idea of the formation events that gave rise to the surrounding voids. This is the subject of chapter 5. The general implications of finding non-uniform distributions of properties across diffuse redshift features are discussed in terms of the postulate of uniform thermal histories. One advantage of studying low density features (such as the Wall) is that if non-uniform property distributions exist (as indicated by segregation effects) then it may be argued that the formation of the features predates galaxy formation, that is, proto-galaxies "know" about their eventual environment. This is the case for the Wall, for which segregation effects are presented in some detail. Thereafter a comparison with generally accepted models of large-structure formation is presented. The existence of the Wall appears to be consistent with two models: cosmic strings in a HDM model, or a class of explosion scenarios with a hybrid HDM/CDM model. Thus not only do segregation effects support the existence of the Wall as a real entity in the data but the list of indicated cosmogonies, for voids in the region of the Wall, is shortened considerably.