While the formalism of isolated horizons is known for some time, only quite recently the near horizon solution of Einstein's equations has been found in the Bondi-like coordinates by Krishnan in 2012. In this framework, the space-time is regarded as the characteristic initial value problem with the initial data given on the horizon and another null hypersurface. It is not clear, however, what ini- tial data reproduce the simplest physically relevant black hole solution, namely that of Kerr-Newman which describes stationary, axisymmetric black hole with charge. Moreover, Krishnan's construction employs the non-twisting null geodesic congruence and the tetrad which is parallelly propagated along this congruence. While the existence of such tetrad can be easily established in general, its explicit form can be very difficult to find and, in fact it has not been provided for the Kerr-Newman metric. The goal of this thesis was to fill this gap and provide a full description of the Kerr-Newman metric in the framework of isolated horizons. In the theoretical part of the thesis we review the spinor and Newman-Penrose formalism, basic geometry of isolated horizons and then present our results. Thesis is complemented by several appendices.

Notre travail de thèse aborde la question suivante : quel est le thème de l'idéographie frégéenne ? Nous y répondons en questionnant l'emploi de la terminologie modèle-théorique ordinairement employée. Notre méthode consiste en un examen détaillé des Grundgesetze, ainsi qu'en une approche comparative avec les œuvres de deux objecteurs contemporains de Frege, le Tractatus-logico philosophicus de Wittgenstein et les Fondements de la géométrie de Hilbert. Pour déterminer ce dont traite l'idéographie, il faut envisager la manière dont sont rendues signifiantes les expressions qu'elle contient. En vue de répondre à cette question, un examen du statut des notions de sens et de référence est accompli, au niveau épistémique, correspondant à la compréhension par un locuteur, ainsi qu'au niveau théorique, concernant leur place précise dans le compte-rendu des démonstrations en langage idéographique. Les notions de sens et de référence sont expliquées par des éclaircissements : leur introduction est déjà leur mise en œuvre. Nous privilégions une lecture interne de ces notions. Au centre de notre travail se trouve le défi formaliste : peut-on conjuguer l'idéal d'une corrélation bi-univoque entre signes et sens et l'exigence d'une pluralité de signes de même sens, nécessaire aux définitions ? Nous montrons que la distinction entre sens et référence conserve un rôle opératoire dans l'idéographie, qu'elle illustre la fécondité démonstrative du système, ce qui a peu été souligné jusqu'à présent dans les études frégéennes. Ainsi il est possible de défendre Frege face à ce défi en soutenant que la diversité des sens, même corrélée à la diversité des signes, ne lui est pas réductible. / Our doctoral thesis addresses the following question : what is the theme of the fregean conceptual script? We answer it in questioning the model-theoretical framework currently used. Our method consists in a close study of the fregean texts, especially the Grundgesetze, and in a comparative approach with the works of two contemporary critics of Frege, the Tractatus logico-philosophicus by Wittgenstein and the Foundations of geometry by Hilbert. To determine what the fregean conceptual script is about, we have to consider how the expressions it contains are made significant. For that purpose, a close examination of the notions of sense and reference is carried out, at the epistemic level, that corresponds to the understanding by a speaker, and at the theoretic level, that concerns the role it plays in the account of proofs in the conceptual script. Frege explains the notions of sense and reference through elucidations: their introduction is already part of their use. We favour an internal reading of these notions.Crucial in our work is what we reconstruct as a formalist challenge addressed to Frege: is it possible to combine the ideal of a one-one correlation between signs and senses with the demand of a plurality of signs with the same sense, necessary for the purpose of definitions? We show that the distinction between sense and reference retains an operative role in the conceptual script, that it highlights the fecundity of the system, which has seldom been underlined in the fregean studies. Thus we argue that Frege can face that formalist challenge, because the plurality of senses, even when it is correlated with the plurality of signs, cannot be reduced to it.

THIS THESIS IS IN THE EXAMINATION PROCESS Christian Frederik Louis Leipoldt was born in on 28 December 1880 in the Rhenish House in Worcester, Cape Province, the fourth child of the Reverend Christian Friedrich Leipoldt and Anna Meta Christina Leipoldt (born Esselen). His father left the mission field to take up the position of the dominee in the Dutch Reformed Church in Clanwilliam where the Leipoldt family went to live, from 1884. Leipoldt received his education from his father at home, on a broad range of subjects, including several languages and also in the natural sciences. He became interested in writing from a very young age and sent pieces of his writing for publication when still a boy. When he was fifteen he began sending dried plant specimens to Professor McOwan in Cape Town, from Clanwilliam. It was through his interest in botany that Leipoldt met Dr Harry Bolus, a life-long friend. Leipoldt wrote the Civil Service examinations in 1897 after which he went to Cape Town to work as a journalist. Living in Cape Town he served on the staff of the pro-Boer newspaper, The South African News from 1898 until it was closed down by the British authorities in 1902, when he travelled to Britain to look for work as a journalist in London. Soon after arriving there he took up the offer from Bolus who would lend him money to study medicine at Guy’s Hospital. It was more or less at this time that some of his early literature on the South African War was written, for instance, his well-known poem, Oom Gert Vertel (published in 1911). After successfully obtaining his MRCS medical qualification in 1907, winning gold medals for medicine and surgery in the process, he briefly served as Acting House Surgeon at Guy’s until 1908 when he travelled to Europe to work in a number of hospitals to receive further training. Later the same year he took up a post as medical adviser to J D Pulitzer, the American newspaper owner. Thereafter he worked as a doctor in London except for the time he proceeded on a four month visit to the East in 1912, the experience of which he penned in a manuscript entitled ‘Visit to the East Indies.’In 1914 he returned to South Africa to take up a post as Medical Inspector of Schools with the Transvaal Education Department. During the First World War in South Africa, he was drafted into the army as the personal medical doctor to the Prime Minister at the time, Genl Louis Botha. He resigned from his post as Medical Inspector in 1923 to take up an offer from Dr F V Engelenburg to serve on the editorial staff of the pro-Smuts newspaper De Volkstem,. He worked there until 1925 when he and the newly appointed editor Gustav Preller did not see eye to eye and it was then that he decided to return to Cape Town. His second Cape Town period (1925 – 1947) was characterized by the most prolific writing, during which he published a great many works across a broad range of topics. Furthermore, though he never married, he adopted Jeffrey Leipoldt, and took in a number of boys as boarders in his home ‘Arbury’ in Kenilworth, Cape Town. At the same time as he wrote most prolifically for a wide range of publications including many novels, he taught pediatrics at the University of Cape Town Medical School and practised as a pediatrician in the city. C Louis Leipoldt was a versatile person who published across a wide range of fields, to include literature, medical studies, letters to friends and associates, the history of wine and cookery, and what few seem to be aware of, his three English historical novels that make up The Valley, written in English between 1928 and 1932. Whilst Leipoldt’s early work such as Oom Gert Vertel gave voice to the suffering of the Afrikaner people, in The Valley, his voice is one of protest against the isolationist policies of the National Party of the 1920s.</p/> Whilst Leipoldt will be known for his work as the inaugural medical inspector of schools of the Transvaal Education Department, the inaugural lecturer in pediatrics at the University of Cape Town and Cape Town’s first practising pediatrician, he will also be known for his wide oeuvre as a writer. For example, he served as the Medical Association of South Africa’s first editor of its South African Medical Journal, a post he held for 18 years. Leipoldt never married and died on 13 April 1947 in Cape Town. His ashes were scattered in the Pakhuis Pass near Clanwilliam, where there is a memorial to his life. / Thesis (DPhil)--University of Pretoria, 2012. / Historical and Heritage Studies / unrestricted

Whether on paper, on site or mediating between both, means for reading and writing geometry have been central to architecture: the use of compasses and rulers, strings, pins, stakes or plumb-lines enabled the analysis and reproduction of congruent figures on different surfaces since antiquity, and from the renaissance onwards, the consistent planar representation of three-dimensional shapes by means of projective geometry. Tacitly through practice, or explicitly encoded in classical geometry, the operational syntaxes of drawing instruments, real or imaginary, have determined the geometric literacies regulating the production and instruction of architecture. But making marks on the surfaces of paper, stone or the ground has recently given way to the fundamentally different sequential operations of computers as the material basis of architectural inscription. Practices which have dominated architecture since antiquity make little sense in its current reading and writing systems.  This thesis examines technologies of digital inscription in a search for literacies equivalent to those of drawn geometry. It particularly looks at programming as a form of notation in close correspondence with its material basis as a technology, and its effects on architecture. It includes prototypes and experiments, graphics, algorithms and software, together with their descriptions and theoretical analyses. While the artefacts and texts respond to the different forms, styles, interests and objectives specific to the fields and contexts in which they have originated, their fundamental purpose is always to critique and propose ways of writing and reading architecture through programming, the rationale of the research and practice they stem from. / <p>QC 20171129</p>

Après la découverte de la magnéto-résistance géante (GMR) par Albert Fert et Peter Grünberg, l'électronique a connu une véritable avancée avec la naissance d'une nouvelle branche appelée spintronique. Cette discipline, encore jeune, consiste à exploiter le spin des électrons dans le but notamment de stocker de l'information numérique. La plupart des dispositifs exploitant cette propriété quantique des électrons consistent en une alternance de fines couches magnétiques et non magnétiques sur un substrat semi-conducteur. L'un des outils de choix pour la caractérisation de ces structures, inventé en 1988 par Kaiser et Bell, est le microscope à émission d'électrons balistiques (BEEM). A l'origine, ce microscope, dérivé du microscope à effet tunnel (STM), était dédié à l'imagerie d'objets (nanométriques) enterrés ainsi qu'à l'étude de la barrière de potentiel (barrière Schottky) qui se forme à l'interface d'un métal et d'un semi-conducteur lors de leur mise en contact. Avec l'essor de la spintronique, le BEEM est devenu une technique de spectroscopie essentielle mais encore fondamentalement incomprise. C'est en 1996 que le premier modèle réaliste, basé sur le formalisme hors équilibre de Keldysh, a été proposé pour décrire le transport des électrons dans cette microscopie. Il permettait notamment d'expliquer certains résultats expérimentaux jusqu'alors incompris. Cependant, malgré son succès, son usage a été limité à l'étude de structures semi-infinies via un méthode de calcul appelée décimation de fonctions de Green. Dans ce contexte, nous avons étendu ce modèle au cas des films minces et des hétéro-structures du type vanne de spin : partant du même postulat que les électrons suivent la structure de bandes du matériaux dans lesquels ils se propagent, nous avons établi une formule itérative permettant le calcul des fonctions de Green du système fini par la méthode des liaisons fortes. Ce calcul des fonctions de Green a été encodé dans un programme Fortran 90, BEEM v3, afin de calculer le courant BEEM ainsi que la densité d'états de surface. En parallèle, nous avons développé une autre méthode, plus simple, qui permet de s'affranchir du formalisme hors équilibre de Keldysh. En dépit de sa naïveté, nous avons montré que cette approche permettait l'interprétation et la prédiction de certains résultats expérimentaux de manière intuitive. Cependant, pour une étude plus fine, le recours à l'approche “hors équilibre” reste inévitable, notamment pour la mise en évidence d'effets d'épaisseur, lés aux interfaces inter-plans. Nous espérons que ces deux outils puissent se révéler utiles aux expérimentateurs, et notamment pour l'équipe Surfaces et Interfaces de notre département. / After the discovery of Giant Magneto-Resistance (GMR) by Albert Fert and Peter Grünberg, electronics had a breakthrough with the birth of a new branch called spintronics. This discipline, while still young, exploit the spin of electrons, for instance to store digital information. Most quantum devices exploiting this property of electrons consist of alternating magnetic and nonmagnetic thin layers on a semiconductor substrate. One of the best tools used for characterizing these structures, invented in 1988 by Kaiser and Bell, is the so-called Ballistic Electron Emission Microscope (BEEM). Originally, this microscope, derived from the scanning tunneling microscope (STM), was dedicated to the imaging of buried (nanometer-scale) objects and to the study of the potential barrier (Schottky barrier) formed at the interface of a metal and a semiconductor when placed in contact. With the development of spintronics, the BEEM became an essential spectroscopy technique but still fundamentally misunderstood. It was in 1996 that the first realistic model, based on the non-equilibrium Keldysh formalism, was proposed to describe the transport of electrons during BEEM experiments. In particular, this model allowed to explain some experimental results previously misunderstood. However, despite its success, its use was limited to the study of semi-infinite structures through a calculation method called decimation of Green functions. In this context, we have extended this model to the case of thin films and hetero-structures like spin valves: starting from the same postulate that electrons follow the band structure of materials in which they propagate, we have established an iterative formula allowing calculation of the Green functions of the finite system by tight-binding method. This calculation of Green’s functions has been encoded in a FORTRAN 90 program, BEEM v3, in order to calculate the BEEM current and the surface density of states. In parallel, we have developed a simpler method which allows to avoid passing through the non-equilibrium Keldysh formalism. Despite its simplicity, we have shown that this intuitive approach gives some physical interpretation qualitatively similar to the non-equilibrium approach. However, for a more detailed study, the use of “non-equilibrium approach” is inevitable, especially for the detection of thickness effects linked to layer interfaces. We hope these both tools should be useful to experimentalists, especially for the Surfaces and Interfaces team of our department.

La modélisation et la simulation numérique sont des outils fondamentaux pour la conception et le développement de nouveaux véhicules. Les travaux de cette thèse portent sur la modélisation et la simulation d’un véhicule innovant, étroit et inclinable, en appliquant une description systématique et générique du véhicule considéré comme un robot dont la base est mobile et les roues sont les organes terminaux. Le système d’inclinaison motorisé entraîne une cinématique complexe et comporte des chaines fermées. Le but du travail est de construire un modèle physique précis, au contraire des modèles simplifiés de type bicyclette ou quart de véhicule utilisés habituellement pour l’étude de la commande des véhicules. L’approche procède à la description de l’architecture mécanique du véhicule, le considérant comme un système multi-corps poly-articulés, s’appuyant sur le formalisme de la robotique et précisément sur la représentation géométrique de Denavit-Hartenberg modifié. Cette approche permet de calculer automatiquement les expressions symboliques des modèles géométriques, cinématiques et dynamiques des structures simples et arborescentes. Les modèles qui en résultent comportent un nombre minimum d’opérations par la mise à profit du calcul symbolique itératif et des techniques de simplification de modèles propres à la robotique. Ces techniques sont implémentées dans le logiciel de calcul symbolique SYMORO+. Le modèle dynamique est calculé d’une manière récursive à l’aide de l’algorithme de Newton-Euler. La simulation dynamique utilise un simulateur édité sous Matlab/Simulink qui intègre le modèle dynamique direct calculé automatiquement à partir du modèle inverse. Des simulations réalisées sur des modèles de complexité croissante, pour des scénarios de freinage ou d’accélération, en ligne droite ou en virage, valident la méthodologie de modélisation mécanique proposée. / Modeling and simulating are fundamental tools to develop new vehicles. The aim of this thesis is to model and simulate a urban narrow tilting car whose structure contains closed mechanical chains. Hence the goal is to build a physical model more precise and realistic than the bicycle model or quarter vehicle model used usually for some control purposes. The modeling approach is based on the modified Denavit&Hartenberg description, commonly used in robotics, by considering the vehicle as a multi-body poly-articulated system whose the terminal links are the wheels. This description allows calculating automatically the symbolic expression of the geometric, kinematic and dynamic models, by using robotics techniques and a symbolic software package named SYMORO+. The dynamic model is calculated recursively thanks to the Newton-Euler algorithm. Simulations of different dynamical model of vehicles have been performed, analyzed and compared. They validate in some sense the modeling methodology presented as an efficient way to get realistic model of non-standard vehicles.

Loop homotopy Lie algebras, which appear in closed string field theory, are a generalization of homotopy Lie algebras. For a loop homotopy Lie algebra, we transfer its structure on its homology and prove that the transferred structure is again a loop homotopy algebra. Moreover, we show that the homological perturbation lemma can be regarded as a path integral, integrating out the degrees of freedom which are not in the homology. The transferred action then can be interpreted as an effective action in the Batalin-Vilkovisky formalism. A review of necessary results from Batalin- Vilkovisky formalism and homotopy algebras is included as well. Powered by TCPDF (www.tcpdf.org)

The South African author C Louis Leipoldt is known as an Afrikaans poet and as one of the ‘Driemanskap’ with Celliers and Totius. Together with Eugene Marais, they wrote the first serious Afrikaans literary poetry in the early decades of the Twentieth Century. The ‘Driemanskap’, grouped together for its clear national(ist) thrust, is well-known as part of the Tweede Afrikaanse Taalbeweging not only for celebrating the universal effects of nature but also for extolling the virtues of forgiveness after the South African War. Apart from his extensive canon of Afrikaans literature and a sizable discourse in the culinary field, not much is known about The Valley, Leipoldt’s so-called ‘English’ novels written in the late 1920s and early 1930s in English, a language he was equally at home in. The titles of these novels making up The Valley trilogy are Gallows Gecko, Stormwrack and The Mask. Despite several efforts to have the novels published with leading publishing houses in both Britain and the United States of America, both during and after his lifetime, the three ‘English’ novels of C Louis Leipoldt remained unpublished for 69 years. It was in 2001 that for the first time they appeared unedited in a compendium volume. Prior to 2001, two of the novels were published −in 1980, the year of the centenary of Leipoldt’s birth, an abridged edition of Stormwrack appeared, edited by Stephen Gray and published by David Philip, Cape Town. It was re-published by Human&Rousseau in 2000. An abridged edition of Gallows Gecko appeared in 2001, under the title Chameleon on the Gallows which the editor Stephen Gray explains he changed for stylistic reasons. Leipoldt uses the form of historical fiction in his trilogy as a way of conveying historical meaning by relating the chronicle (1820 – 1930) of the place he calls the Valley, recognizable as Clanwilliam. Initially, the Valley is at peace and is sketched in its idyllic state. After the Jameson Raid of 1895, the prospects of the South African War become a reality for the inhabitants of the Cederberg as they are torn apart by their emotions, feelings and loyalties. The course of events drastically changes when war finally comes to the District. Discontinuity and change is a strong theme in the novels. Eventually the inhabitants ofthe Valley find that the former, respectful relations, based on tradition and tolerance, have given way to sectarian interests. This changes the social fibre of the once idyllic environment. The Valley is a lamentation of lost opportunities for a culturally unified South Africa. Its voice is one of moderateness and is inclusive for all South Africans, addressing race relations as a theme as well as decrying sectionalism. In the light of this, it is argued that Leipoldt is revealed as a political liberal and cultural pluralist. This can be heard through the voices of the characters in The Valley and seen by the way Leipoldt meant the events in his fiction to serve as an allegory for the way he saw South Africa emerging at the time. He was writing against the Nationalists, particularly against the narrative of Gustav S Preller, who spent his working life constructing a volksgeskiedenis that resulted in a significant public history that dominated Afrikaner historical thinking from circa 1905 to 1938. In this sense, it is argued, The Valley is an alternative history to the dominating Preller historiography, and because it is in the form of narrative/historical fiction, it can also be seen as an alternative form of history, to be read against certain theoretical texts, without in any way detracting from the voices of criticism against deconstructivist history. / Thesis (DPhil)--University of Pretoria, 2012. / Historical and Heritage Studies / unrestricted

Newton's second law, Schrödinger's equation and Maxwell's equations are all theories composed of at most second-time derivatives. Indeed, it is not often we need to take the time derivative of the acceleration. So why are we not seeing more higher-order derivative theories? Although several studies present higher derivatives' usefulness in quadratic gravity and scalar-field theories, one will eventually encounter a problem. In 1850, the physicist Mikhail Ostrogradsky presented a theorem that stated that a non-degenerate Lagrangian composed of finite higher-order time derivatives results in a Hamiltonian unbounded from below. Explicitly, it was shown that the Hamiltonian of such a system includes linearity in physical momenta, often referred to as the ''Ostrogradsky ghost''. This thesis studies how one can avoid the Ostrogradsky ghost by considering degenerate Lagrangians to put constraints on the momenta. The study begins by showing the existence of the ghost and later cover the essential Hamiltonian formalism needed to conduct Hamiltonian constraint analyses of second-order time derivative systems, both single-variable and systems coupled to a regular one. Ultimately, the degenerate second-order Lagrangians successfully eliminate the Ostrogradsky ghost by generating secondary constraints restricting the physical momenta. Moreover, an outline of a Hamiltonian analysis of a general higher-order Lagrangian is presented at the end.

In the mid-2000s, a new quantum state of topological insulators was proposed. It deeply refreshed the traditional understanding of electronic band structure, which has been the most fundamental tool to classify metals and insulators. Topological insulators with non-trivial topological charges can host robust surface states or edge states located in the bulk bandgap. To understand this new state, an understanding of the bandgap is not sufficient, and it led to the new field of topological band theory in condensed matter physics. The development of electronic band structure theory also inspired the understanding of topological band theory from the chemical point of view and results in the new topic of topological chemistry. The discovery of topological insulators motivated extensive studies of solid-state materials from topological theory, leading to many topological materials in both insulators and metals. In the last 15 years, various topological materials characterized by different topological electronic structures have been discovered. One of the most important features shared by all different topological materials is the topologically protected non-trivial surface states (TSSs). Such TSSs are essentially different from the dangling bonds because they connect to conduction bands and valence bands in insulators or bulk band crossings in metals. The extra perturbation can only change their detailed shape but not remove them. This characteristic makes TSSs attractive for practical applications in the quantum information process, data storage, and energy conversion. In particular, the robust surface state is an attractive property that benefits energy-related catalysis. The last few years have seen research in this field with a focus on developing efficient topological material catalysts for hydrogen evolution reaction (HER), oxygen evolution reaction (OER), and reduction. To date, the topological catalyst has become a new frontier in both chemistry and materials science. Within the scope of this Ph.D. thesis, several topological semimetals and their HER activity are studied with the help of density functional theory, electrochemical theory, and topological band theory, combined with experimental measurements performed within the workgroup. The spectrum of performed projects ranges from the theoretical design of the high-efficiency hydrogen evolution catalyst with the guidance of topology in close collaboration with experiments and in-depth understanding of the relationship between topological properties and catalysis.