The study investigated the impact of computer simulations on the teaching and learning of photoelectric effect in Grade 12. The Grade 12 Physical Sciences curriculum has components of physics and chemistry. The photoelectric effect is a section in the physics curriculum and examination in the National Senior Certificate. In this case study, thirty learners were randomly divided into three groups in one rural school in the Frances Baard district in the Northern Cape Province. A randomised pre-test - post-test control group design was implemented. Data were collected through pre and post tests, by observation of the lessons and learner interviews. An analysis of variance performed showed that there was no significant difference on pre-test scores for the three groups. A paired -sample t-test on the post-test scores discovered that the Teacher-Centred Experimental Group (TCEG) performed better than the Learner-Centred Experimental Group (LCEG); (t statics, t (9) = -6.135, p < 0.05). In addition, the Control Group (CG) where the teacher used the traditional method of teaching performed even better than the Learner-Centred Experimental group. An analysis of covariance on the post-test scores with learners' pre-test scores as the covariate showed a significant effect on the instructional group favouring the TCEG (F (2,29) = 52.763, p < 0.05). The Hake's normalised gain, <g> was used to measure the effectiveness of the intervention. The normalised gain showed a high-g (0.794) for the TCEG, a medium-g (0.405) for the CG and a low-g (0.134) for the LCEG. The interview data also confirms that the TCEG learners benefited more than the LCEG learners. It is, therefore, suggested that the TCEG approach is a better method for the effective teaching of photoelectric effect. / Science and Technology Education / M. Sc. (MSTE)

The chemistry of actinides in solution is a very important aspect of the nuclear fuel cycle, especially as the energy needs of the world continue to increase. However, the radio-active nature of the actinides makes experimentation very difficult and dedicated expensive instruments are required. In addition, the disposal of radio-active waste materials requires a proper understanding of their chemistry at a molecular level. To tackle the problem, and to underpin the experimental studies, in this thesis we have studied the redox chemistry and disproportionation mechanism of actinyl complexes in solution using state-of-the art computational methods. Reduction potentials of actinyl complexes in solution have been estimated in solution using density functional theory (DFT) approaches. Solvation effects were included in the quantum chemistry calculations with the conductor like polarisable continuum model (CPCM) solvation method. First of all, we have validated our computational method by studying a variety of solute cavity definitions within the CPCM solvation model and assessed the performance of a range of DFT functionals to suitable to accurately describe the actinide chemistry in solution. Penta-valent uranyl(V) ions are unstable and readily disproportionate; in this study we have explored outer-sphere electron transfer and disproportionation mechanisms to determine the stability of these ions in solution. We have found that the process of outer-sphere disproportionation is unlikely to occur in non-aqueous solutions, such as DMSO, DMF, DCM, acetonitrile and pyridine, when the uranyl(V) ion is bound with a multi-dentate organic ligand. However, our computational results hypothesise that the presence of a trace of water in the experimental conditions can promote a disproportionation reaction by protonating the uranyl(V) ‘yl’ oxygen atoms and then the electron transfer process would proceed through either inner or outer sphere mechanism. In addition, the effect of alkali metal cations on the outer-sphere disproportionation mechanisms was also studied. Overall it has been shown that DFT can be used to accurately predict the redox properties of actinyl complexes in solution and thus contributing for an effective and efficient design of nuclear material separations, proper as well as safer radioactive waste disposal.

Nous proposons dans cette thèse de caractériser quantitativement la variabilité à différentes échelles au cours de l'embryogenèse. Pour ce faire, nous utilisons une combinaison de modèles mathématiques et de résultats expérimentaux. Dans la première partie, nous utilisons une petite cohorte d'oursins digitaux pour construire une représentation prototypique du lignage cellulaire, reliant les caractéristiques des cellules individuelles avec les dynamiques à l'échelle de l'embryon tout entier. Ce modèle probabiliste multi-niveau et empirique repose sur les symétries des embryons et sur les identités cellulaires; cela permet d'identifier un niveau de granularité générique pour observer les distributions de caractéristiques cellulaires individuelles. Le prototype est défini comme le barycentre de la cohorte dans la variété statistique correspondante. Parmi plusieurs résultats, nous montrons que la variabilité intra-individuelle est impliquée dans la reproductibilité du développement embryonnaire. Dans la seconde partie, nous considérons les mécanismes sources de variabilité au cours du développement et leurs relations à l'évolution. En nous appuyant sur des résultats expérimentaux montrant une pénétrance incomplète et une expressivité variable de phénotype dans une lignée mutante du poisson zèbre, nous proposons une clarification des différents niveaux de variabilité biologique reposant sur une analogie formelle avec le cadre mathématique de la mécanique quantique. Nous trouvons notamment une analogie formelle entre l'intrication quantique et le schéma Mendélien de transmission héréditaire. Dans la troisième partie, nous étudions l'organisation biologique et ses relations aux trajectoires développementales. En adaptant les outils de la topologie algébrique, nous caractérisons des invariants du réseaux de contacts cellulaires extrait d'images de microscopie confocale d'épithéliums de différentes espèces et de différents fonds génétiques. En particulier, nous montrons l'influence des histoires individuelles sur la distribution spatiales des cellules dans un tissu épithélial. / We propose in this thesis to characterize variability quantitatively at various scales during embryogenesis. We use a combination of mathematical models and experimental results. In the first part, we use a small cohort of digital sea urchin embryos to construct a prototypical representation of the cell lineage, which relates individual cell features with embryo-level dynamics. This multi-level data-driven probabilistic model relies on symmetries of the embryo and known cell types, which provide a generic coarse-grained level of observation for distributions of individual cell features. The prototype is defined as the centroid of the cohort in the corresponding statistical manifold. Among several results, we show that intra-individual variability is involved in the reproducibility of the developmental process. In the second part, we consider the mechanisms sources of variability during development and their relations to evolution. Building on experimental results showing variable phenotypic expression and incomplete penetrance in a zebrafish mutant line, we propose a clarification of the various levels of biological variability using a formal analogy with quantum mechanics mathematical framework. Surprisingly, we find a formal analogy between quantum entanglement and Mendel’s idealized scheme of inheritance. In the third part, we study biological organization and its relations to developmental paths. By adapting the tools of algebraic topology, we compute invariants of the network of cellular contacts extracted from confocal microscopy images of epithelia from different species and genetic backgrounds. In particular, we show the influence of individual histories on the spatial distribution of cells in epithelial tissues.

The medium is the message in the first place: the medium as presence, as the author. His contribution to the academic world is his academic Holographic Memoirs. His story, the author's memoirs, is a fictive-narrative discourse with an organic ubuntu open-endedness. The Hologram is both an autobiography, but also all the information at all places simultaneously – nonlocal in quantum physical terms - within an intense hallucinating dream: no illusion, but rather a HyperReality with all its Virtual Identities. The invention of tram hopping is the plot of the story. The plot is like an hourglass where the first part of the story is the emptying of the sand, the deconstruction of modernism, but while the top chamber runs empty and the bottom chamber fills up, so the deconstruction is simultaneously a dependent arising/(social) construction/ubuntuing to revival – the synagogal Shekinah presence of YAHWEH. The top chamber is the unreasonable Newtonian physics and the bottom chamber reasonable quantum physics. The metaphysics (before the physics) of the top chamber is poststructuralism and deconstruction, while the bottom chamber is the virtual Hebraic worldview that delutively merges ubuntu and Buddhism. The long narrow neck in the middle is the moonily narrative that lives us with psychology (Psycho-logic) lost in sociology (Social-physics). Hermeneutics is set forth in the same contrasting hourglass of the top chamber, the inherited tradition, emptying to what it should accomplish – (virtual) presence. / Philosophy and Systematic Theology / D. Th. (Systematic Theology)

Dans cette thèse, nous discutons de la dégénérescence et de la construction d’états cohérents généralisés dans les systèmes quantiques en deux dimensions d’espace. Nous développons un schéma pour obtenir des spectres non dégénérés et des combinaisons linéaires appropriées des états propres d’énergie correspondants. Lorsque la dégénérescence dans le spectre d’énergie est linéaire dans les nombres quantiques, nous définissons des opérateurs d’échelle général- isés qui conduisent à une chaîne d’états avec un ensemble naturel de coefficients. De plus, nous récupérons des relations de complétude pour les états généralisés. Lorsque le spectre d’énergie est quadratique dans les nombres quantiques, nous utilisons certains résultats de la théorie des nombres pour catégoriser la dégénérescence et, par conséquent, les combinaisons linéaires appropriées des états propres d’énergie associés. En particulier, nous étudions des oscillateurs harmoniques bidimensionnels isotropes et anisotropes ainsi que le potentiel Morse bidimensionnel et son partenaire supersymétrique non séparable. Dans tous les cas, nous construisons des états cohérents et discutons certains aspects de leur caractère non classique. On retrouve une certaine compression dans les quadratures conjuguées, une dépendance non triviale des variances des quadratures vis-à-vis des paramètres introduits lors de la définition des spectres non dégénérés, et un problème de localisation pour les fonctions d’onde. Comme application, nous étudions le problème de la quantification et de l’analyse semi-classique de l’espace des phases en deux dimensions en exploitant la complétude des familles généralisées d’états cohérents comprimés en deux dimensions. / In this thesis we discuss degeneracy and the construction of generalised coherent states in two-dimensional quantum systems. We develop a scheme for defining non-degenerate spectra and the corresponding averaged energy eigenstates. When the degeneracy in the spectrum is linear in the quantum numbers, we are able to define generalised ladder operators which lead to a chain of states with a natural set of coefficients. Additionally, we are able to recover completeness relations for the generalised states. On the other hand, when the spectrum is quadratic in the quantum numbers, we utilise some results from number theory to categorise the degeneracy and correspondingly the averaged energy eigenstates. In particular we study the two-dimensional isotropic and anisotropic oscillators as well the two-dimensional Morse potential and its non-separable supersymmetric partner. In all cases, we compute the coherent states and discuss certain aspects of their non-classicality. We find squeezing between conjugate quadratures, non-trivial dependence of the quadrature variances on the parameters introduced when defining the non-degenerate spectra, and non-localisation of wavefunctions. As an application, we study the problem of quantisation and semiclassical phase space analysis in two dimensions by exploiting the completeness of generalised families of two-dimensional squeezed coherent states.

The discovery of topological quantum states of matter has required physicists to look beyond Landau’s theory of symmetry-breaking, previously the main paradigm for<br>studying states of matter. This has led also to the development of new topological theories for describing the novel properties. In this dissertation an investigation in this<br>frontier research area is presented, which looks at the interplay between the quantum geometry of these states, defects and disorder. After a brief introduction to the topological quantum states of matter considered herein, some aspects of my work in this area are described. First, the disorder-induced band structure engineering of topological insulator surface states is considered, which is possible due to their resilience from Anderson localization, and believed to be a consequence of their topological origin.<br>Next, the idiosyncratic behavior of these same surface states is considered, as observed in experiments on thin film topological insulators, in response to competition between<br>hybridization effects and an in-plane magnetic field. Then moving in a very different direction, the uncovering of topological ‘gravitational’ response is explained: the<br>topologically-protected charge response of two dimensional gapped electronic topological states to a special kind of 0-dimensional boundary – a disclination – that encodes spatial curvature. Finally, an intriguing relation between the gravitational response of quantum Hall states, and their response to an apparently unrelated perturbation – nonuniform electric fields is reported. <br>

The discoveries in applications of chirality in various areas of science seem to never cease to emerge. Chirality, being the property that some objects are geometrically distinguishable from their mirror image, is a tiny difference of vast importance. The fact that multiple biological structures are chiral is what permits life on Earth and its discovery had a severe impact on medical development. When the concept of quantum chirality was introduced, the connection between the chiral symmetry and the quantum states and operators that characterize quantum chirality was not particularly clear. It was shown that closed spin chains of an odd number of spins naturally had chiral states as eigenstates of a Hamiltonian describing Heisenberg and Dzyaloshinsky-Moriya (DM) interactions, and the symmetry of the system in direct relation to the chiral symmetry of the eigenstates quickly became of interest. The aim of this thesis is therefore to explore how quantum chirality is a chiral symmetry and to develop a scheme to create chiral states from systems that lack the required symmetry. The investigation showed that discretized probability current gives a good explanation to why the chiral states follow a chiral nature, but further examination is required in order to generalize a deeper connection between the probability current and the chiral states of spin chains. The results also indicated that it was possible to force open spin chains into purely chiral states, and into superpositions thereof, by time evolution. The scheme is still in its early stage and physical implementation and applications are yet to be explored. / Upptäckterna av tillämpningar av kiralitet inom ett flertal områden verkar ständigt öka i omfattning. Kiralitet är fenomenet att vissa objekt geometriskt kan särskiljas från sin spegelbild, vilket är en ringa skillnad men med väsentlig innebörd. Det faktum att flertalet biologiska strukturer är kirala är en förutsättning för liv på jorden och upptäckten av detta har haft en omfattande betydelse för medicinsk utveckling. När konceptet kvantkiralitet introducerades, var kopplingen mellan den kirala symmetrin och de kvantmekaniska tillstånden och operatorerna som utgör kvantkiralitet, inte trivial. Tidigare studier har visat att stängda spinnkedjor av ett udda antal spinn naturligt har kirala tillstånd som egentillstånd till en Hamiltonian beskrivande Heisenberg- och Dzyaloshinsky-Moriyainteraktioner. Att systemets symmetri stod i direkt relation till den kirala symmetrin av egentillstånden blev tidigt av intresse att undersöka. Syftet med denna kandidatuppsats är således att utforska en djupare förståelse till hur kvantkiralitet är en kiral symmetri samt utveckla en metod för hur kirala tillstånd kan drivas till att uppstå ur system som saknar den nödvändiga symmetrin. Resultaten visade att den diskretiserade sannolikhetsströmmen ger en god förklaring till varför de kirala tillstånden följer en kiral natur, men vidare efterforskning behövs för att kunna generalisera en djupare koppling mellan sannolikhetsströmmen och de kirala tillstånden hos spinnkedjor. Undersökningen indikerade också att det var möjligt att forcera en öppen spinnkedja till ett kiralt tillstånd, och till superpositioner därav, genom tidsutveckling. Metoden är fortfarande i sin tidiga utveckling och fysisk implementering samt tillämpningar väntar ännu på att upptäckas.

<p>In this thesis, we present novel computational methods and frameworks to address the challenges associated with the determination of free energy profiles for condensed-phase chemical reactions using combined quantum mechanical and molecular mechanical (QM/MM) approaches. We focus on overcoming issues related to force matching, molecular polarizability, and convergence of free energy profiles. First, we introduce a method called Reaction Path-Force Matching in Collective Variables (RP-FM-CV) that efficiently carries out ab initio QM/MM free energy simulations through mean force fitting. This method provides accurate and robust simulations of solution-phase chemical reactions by significantly reducing deviations on the collective variables forces, thereby bringing simulated free energy profiles closer to experimental and benchmark AI/MM results. Second, we explore the role of pairwise repulsive correcting potentials in generating converged free energy profiles for chemical reactions using QM/MM simulations. We develop a free energy correcting model that sheds light on the behavior of repulsive pairwise potentials with large force deviations in collective variables. Our findings contribute to a deeper understanding of force matching models, paving the way for more accurate predictions of free energy profiles in chemical reactions. Next, we address the underpolarization problem in semiempirical (SE) molecular orbital methods by introducing a hybrid framework called doubly polarized QM/MM (dp-QM/MM). This framework improves the response property of SE/MM methods through high-level molecular polarizability fitting using machine learning (ML)-derived corrective polarizabilities, referred to as chaperone polarizabilities. We demonstrate the effectiveness of the dp-QM/MM method in simulating the Menshutkin reaction in water, showing that ML chaperones significantly reduce the error in solute molecular polarizability, bringing simulated free energy profiles closer to experimental results. In summary, this thesis presents a series of novel methods and frameworks that improve the accuracy and reliability of free energy profile estimations in condensed-phase chemical reactions using QM/MM simulations. By addressing the challenges of force matching, molecular polarizability, and convergence, these advancements have the potential to impact various fields, including computational chemistry, materials science, and drug design.</p>

The question of the possibility of intelligent machines is fundamentally intertwined with the machines’ ability to reason. Or not. The developments of the recent years point in a completely different direction : What we need is simple, generic but scalable algorithms that can keep learning on their own. This thesis is an attempt to find theoretical explanations to the findings of recent years where empirical evidence has been presented in support of phase transitions in neural networks, power law behavior of various entities, and even evidence of algorithmic universality, all of which are beautifully explained in the context of statistical physics, quantum field theory and statistical field theory but not necessarily in the context of deep learning where no complete theoretical framework is available. Inspired by these developments, and as it turns out, with the overly ambitious goal of providing a solid theoretical explanation of the empirically observed power laws in neu- ral networks, we set out to substantiate the claims that renormalization group theory may be the sought-after theory of deep learning which may explain the above, as well as what we call algorithmic universality. / La question de la possibilité de machines intelligentes est intimement liée à la capacité de ces machines à raisonner. Ou pas. Les développements des dernières années indiquent une direction complètement différente : ce dont nous avons besoin sont des algorithmes simples, génériques mais évolutifs qui peuvent continuer à apprendre de leur propre chef. Cette thèse est une tentative de trouver des explications théoriques aux constatations des dernières années où des preuves empiriques ont été présentées en faveur de transitions de phase dans les réseaux de neurones, du comportement en loi de puissance de diverses entités, et même de l'universialité algorithmique, tout cela étant parfaitement expliqué dans le contexte de la physique statistique, de la théorie quantique des champs et de la théorie statistique des champs, mais pas nécessairement dans le contexte de l'apprentissage profond où aucun cadre théorique complet n'est disponible. Inspiré par ces développements, et comme il s'avère, avec le but ambitieux de fournir une explication théorique solide des lois de puissance empiriquement observées dans les réseaux de neurones, nous avons entrepris de étayer les affirmations selon lesquelles la théorie du groupe de renormalisation pourrait être la théorie recherchée de l'apprentissage profond qui pourrait expliquer cela, ainsi que ce que nous appelons l'universialité algorithmique.

<p dir="ltr">In holographic quantum field theories, a bulk geometric semiclassical spacetime emerges from strongly coupled interacting conformal field theories in one less spatial dimension. This is the celebrated AdS/CFT correspondence. The entanglement entropy of a boundary spatial subregion can be calculated as the area of a codimension two bulk surface homologous to the boundary subregion known as the RT surface. The bulk region contained within the RT surface is known as the entanglement wedge and bulk reconstruction tells us that any operator in the entanglement wedge can be reconstructed as a non-local operator on the corresponding boundary subregion. This notion that entanglement creates geometry is dubbed "ER=EPR'' and has been the driving force behind recent progress in quantum gravity research. In this thesis, we put together two results that use Tomita-Takesaki modular theory and quantum ergodic theory to make progress on contemporary problems in quantum gravity.</p><p dir="ltr">A version of the black hole information loss paradox is the inconsistency between the decay of two-point functions of probe operators in large AdS black holes and the dual boundary CFT calculation where it is an almost periodic function of time. We show that any von Neumann algebra in a faithful normal state that is quantum strong mixing (two-point functions decay) with respect to its modular flow is a type III₁ factor and the state has a trivial centralizer. In particular, for Generalized Free Fields (GFF) in a thermofield double (KMS) state, we show that if the two-point functions are strong mixing, then the entire algebra is strong mixing and a type III₁ factor settling a recent conjecture of Liu and Leutheusser.</p><p dir="ltr">The semiclassical bulk geometry that emerges in the holographic description is a pseudo-Riemannian manifold and we expect a local approximate Poincaré algebra. Near a bifurcate Killing horizon, such a local two-dimensional Poincaré algebra is generated by the Killing flow and the outward null translations along the horizon. We show the emergence of such a Poincaré algebra in any quantum system with modular future and past subalgebras in a limit analogous to the near-horizon limit. These are known as quantum K-systems and they saturate the modular chaos bound. We also prove that the existence of (modular) future/past von Neumann subalgebras also implies a second law of (modular) thermodynamics.</p>