This thesis describes the development of a Lattice Boltzmann (LB) model for a binary gas mixture. Specifically, channel flow driven by a density gradient with diffusion slip occurring at the wall is studied in depth. The first part of this thesis sets the foundation for the multi-component model used in the subsequent chapters. Commonly used single component LB methods use a non-physical equation of state, in which the relationship between pressure and density varies according to the scaling used. This is fundamentally unsuitable for extension to multi-component systems containing gases of differing molecular masses that are modelled with the ideal gas equation of state. Also, existing methods for implementing boundary conditions are unsuitable for extending to novel boundary conditions, such as diffusion slip. Therefore, a new single component LB derivation and a new method for implementing boundary conditions are developed, and validated against Poiseuille flow. However, including a physical equation of state reduces stability and time accuracy, leading to longer computational times, compared with 'incompressible' LB methods. The new method of analysing LB boundary conditions successfully explains observations from other commonly used schemes, such as the slip velocity associated with 'bounce-back'.The new model developed for multi-component gases avoids the pitfalls of some other LB models, a single computational grid is shared by all the species and the diffusivity is independent of the viscosity. The Navier-Stokes equation for the mixture and the Stefan-Maxwell diffusion equation are both recovered by the model. However, the species momentum equations are not recovered correctly and this can lead to instability. Diffusion slip, the non-zero velocity of a gas mixture at a wall parallel to a concentration gradient, is successfully modelled and validated against a simple one-dimensional model for channel flow. To increase the accuracy of the scheme a second order numerical implementation is needed. This can be achieved using a variable transformation method which does not result in an increase in computational time. Simulations were carried out on hydrogen and water diffusion through a narrow channel, with varying total pressure and concentration gradients. For a given value of the species mass flux ratio, the total pressure gradient was dependent on the species concentration gradients. These results may be applicable to fuel cells where the species mass flux ratio is determined by a chemical reaction and the species have opposing velocities. In this case the total pressure gradient is low and the cross-channel average mass flux of hydrogen is independent of the channel width. Finally, solutions for a binary Stefan tube problem were investigated, in which the boundary at one end of a channel is permeable to hydrogen but not water. The water has no total mass flux along the channel but circulates due to the slip velocity at the wall. The cross-channel average mass flux of the hydrogen along the channel increases with larger channel widths. A fuel cell using a mixture of gases, one being inert, will experience similar circulation phenomena and, importantly, the width of the pores will affect performance. This thesis essentially proves the viability of LB models to simulate multi-component gases with diffusion slip boundaries, and identifies the many areas in which improvements could be made.

This dissertation will attempt to answer question whether, in terms of the right to dignity in s10 and the prohibition of unfair discrimination in s9 of the South African Constitution, the State must recognise in law a third gender for transgender individuals who do not identify as either male or female. It does so, first, by asking whether the failure by the state to provide for the legal recognition of a third gender violates transgender person's right to dignity. Second, the enquiry proceeds to discuss whether s9(3) of the Constitution (which prohibits unfair discrimination on any ground, including on the listed grounds of sex, gender and sexual orientation) requires the state to recognise a third gender. After discussing the lived experiences of transgender persons in South Africa, the thesis reviews the terminology and concepts relevant to this area of study, in order to lay the foundation for the subsequent examination of relevant case law, the Constitutional Court's approach to dignity, and the analysis of the application of s(9)(3). I submit that transgender persons fall within the Constitutional Court's definition of a vulnerable group in that they have suffered past patterns of disadvantage, they constitute a minority in South Africa and are subject to stereotyping and bias. Despite the Constitutional Courts erroneous pronouncement that transsexualism falls under the umbrella of sexual orientation, it is argued, rather, that since the expression of their gender identity by gender nonconforming persons shares many of the characteristics of the specified grounds listed in s9(3), unfair discrimination can be found on a ground analogous to those grounds listed in the Constitution. The failure to allow for recognition of a third gender is thus under-inclusive. It cannot be justified under the limitations analysis. Further, if objections were to be raised by the state that recognition is not feasible or affordable and is, hence, justified, I conclude that because there are ways to accommodate individuals who do not identify as binary which are not unduly taxing on the State, this argument would fail.

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This research sought to test the notion that the non-cisgender population experiences an inordinate toll in regard to their mental well-being as a result of inaccurate or incomplete classification of their self-identified gender identity among US college students (N = 591). In accordance with the previous literature, the non-cisgender population experienced a significant increase of perceived experience of microaggressions and internalized symptoms. Contrary to expectations, there was no significance found for rates of identity distress. Previous literature did not reflect a significantly lower score of challenging the binary for Caucasians in relation to Hispanic and Asian ethnicities, as this research revealed. This research indicates that while non-cisgender persons do experience higher rates of perceived microaggressions and identity related concerns, there is a previously accounted for variance in ethnicity and cisgender identities (male and female).

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Most star formation in galaxies takes place in embedded clusters, within Giant Molecular Clouds (GMCs). Stars also generally form as part of binary star systems, with almost all massive stars having at least one close companion. Binaries shape the physical properties of older star clusters by setting their central density and ejecting low-mass stars, but also play a role during cluster formation by modifying the mechanical and radiative feedback from massive stars and shedding enriched material in the cluster’s gas reservoir. Conversely, dynamical interactions between stars in dense stellar environments are known to form, modify, and destroy binary systems. In consequence, the populations of binaries observed in the Galactic field and in old stellar clusters are understood to be shaped by a combination of the physics of star formation and subsequent dynamical interactions in embedded clusters, although the relative importance of these processes remains unknown. In this thesis, we implement a prescription for an initial population of binaries in the coupled N-body and radiation hydrodynamics star cluster formation code Torch, and investigate how this initial population is modified in the earliest stages of cluster formation, while gas and stars coexist. As an ansatz for the initial population of binaries, we use the properties of main-sequence binaries in the Galactic field. We first perform a suite of simulations initialized from a 10^4 M⦿ cloud, in which the simulations only differ by their stellar content (i.e. presence or absence of an initial population of binaries, and stochasticity of star formation). We compare the populations of binaries identified 1.2–2 Myr after the onset of star formation and find that an initial population of binaries is needed at all masses to reproduce the multiplicity fraction observed in main-sequence stars. We also show that this initial population is modified in a systematic manner before the effects of feedback from massive stars shape the gas. We further find evidence of both preferential formation and preferential destruction of binaries via dynamical interactions. The net effect of these interactions shifts the distributions of primary masses and semi-major axes to lower values, and the distributions of mass ratios and eccentricities to larger values. In a second time, we perform simulations with different virial parameters and initial turbulent velocity patterns, and find that the trends previously identified are robust to those changes in our initial conditions. We however find that both the virial parameter and the initial turbulent velocity pattern have a strong influence on the star formation rate, and therefore on the rapidity with which the distributions are modified. We conclude that dynamical interactions in embedded clusters are important for shaping the populations of binaries observed in the MilkyWay, thus opening the floor to future investigations of the impact of binaries on star cluster formation. / Thesis / Master of Science (MSc)

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<p> This investigation examines several methods designed to minimize the computational cost of retrieving records from a binary search tree.</p> <p> No knowledge of the probabilities with which these records are requested is assumed. The aim of each method is to gradually restructure an initial, arbitrary (and perhaps costly) tree into one which has minimal search cost, on the basis of experience.</p> <p> While no one such 'self-organizing' method has yet received theoretical substantiation, it is hoped that this empirial investigation may assist in this endeavour.</p> / Thesis / Master of Science (MSc)

<p> Despite numerous efforts to better understand binary star evolution, some aspects of it remain poorly constrained. In particular, the evolution of eccentric binaries has remained elusive mainly because the Roche lobe formalism derived for circular binaries does not apply, and other approximations must be used. Here, we report the results of our Smoothed Particle Hydrodynamics simulations of eccentric binaries using a novel way of modeling only the outermost layers of the stars with appropriate boundary conditions. We find that our boundary treatment conserves energy well and that it is well suited for the modeling of interacting binary stars. Using this new technique, along with properly relaxed model stars, we find clear trends in the mass transfer episodes. In particular, we show that these episodes can be described by Gaussians with a FWMH of ~ 0.12 P orb and that the peak rates occur after periastron, around an orbital phase of ~ 0.55, independent of the eccentricity and masses of the stars. The accreted material, on the other hand, is observed to form a rather sparse envelope around either or both stars. Although the fate of this envelope is not modeled in our simulations, we show that a constant fraction (~5%) of the material transferred is ejected from the systems. We discuss this result in terms of the poorly constrained non-conservative mass transfer scenario and argue that it can help calibrate it. Finally, we discuss the limitations of our technique and conditions under which it performs best. The results presented in this thesis represent an improvement upon previous hydrodynamical work and could be used in analytical and binary population synthesis studies to better constrain the evolution of eccentric binaries and the formation of exotic stellar populations. </p> / Thesis / Doctor of Philosophy (PhD)