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Thesis (Ph. D.) -- University of Maryland, College Park, 2006. / Includes bibliographical references (leaves 117-119). Also available online.

In his 1947 work "Theory of Braids" Emil Artin asked whether the braid group remained unchanged when one considered classes of braids under linkhomotopy, allowing each strand of a braid to pass through itself but not through other strands. We generalize Artin's question to string links over orientable surface M and show that under link-homotopy surface string links form a group PBn(M), which is isomorphic to a quotient of the surface pure braid group PBn(M). Surface braid groups and their properties are an area of active research by González-Meneses, Paris and Rolfsen, Goçalves and Guaschi, and our work explores the geometric and visual beauty of this subject. We compute a presentation of PBn(M) in terms of the generators and relations and discuss the orderability of the group in the case when the surface in question is a unit disk D.

In his 1947 work "Theory of Braids" Emil Artin asked whether the braid group remained unchanged when one considered classes of braids under linkhomotopy, allowing each strand of a braid to pass through itself but not through other strands. We generalize Artin's question to string links over orientable surface M and show that under link-homotopy surface string links form a group PBn(M), which is isomorphic to a quotient of the surface pure braid group PBn(M). Surface braid groups and their properties are an area of active research by González-Meneses, Paris and Rolfsen, Goçalves and Guaschi, and our work explores the geometric and visual beauty of this subject. We compute a presentation of PBn(M) in terms of the generators and relations and discuss the orderability of the group in the case when the surface in question is a unit disk D.

In his 1947 work "Theory of Braids" Emil Artin asked whether the braid group remained unchanged when one considered classes of braids under linkhomotopy, allowing each strand of a braid to pass through itself but not through other strands. We generalize Artin's question to string links over orientable surface M and show that under link-homotopy surface string links form a group PBn(M), which is isomorphic to a quotient of the surface pure braid group PBn(M). Surface braid groups and their properties are an area of active research by González-Meneses, Paris and Rolfsen, Goçalves and Guaschi, and our work explores the geometric and visual beauty of this subject. We compute a presentation of PBn(M) in terms of the generators and relations and discuss the orderability of the group in the case when the surface in question is a unit disk D. / Science, Faculty of / Mathematics, Department of / Graduate

The aim of investigating the 2D PbX6 inorganic organic hybrids was to study octahedral distortions, short interlayer spacing’s, and the effect of functionalized aliphatic’s terminal halogen on idealizing or destabilizing the octahedral arrangements and their effect on the band gap of the single layer 2D hybrid systems. It was found that the PbX6 metal centred distortions do display some impact on the band gap, the greater the distortion experienced in the Ieq-Pb-Ieq cis bond angles, the wider the band gap, as we suspect a decrease in I 5p antibonding character which lowers the top of the valence band. The terminal halogen interaction specifically in (BrC2)PbI4, clearly displayed some Br 4p/s character at the bottom of the conduction band, which may further explain the reduction of the band gap of this compound. This in conjunction with the shorter interlayer spacing serve to stabilize more idealized bridging angles, as seen in both the lead iodide and bromide analogues. In the short interlayer spacing compounds large idealizations of the Pb-X-Pb bridging angles are observed however display a large metal centred octahedral distortions in order accommodate the spatial occupation of the lone pair on lead. It was generally observed that the lead bromide hybrids appear to have a greater sensitivity to exciton lattice interactions, which give rise to red shifted emissions and absorptions with decreasing temperature. Structurally this behaviour is counterintuitive; because the structures increase in inorganic distortions with decreasing temperature and therefore a blue shift in the exciton absorption is expected. It should be noted that compounds displaying this phenomenon most, (C4, C6, C7)PbBr4 do display a large amount of structural disorder in their lower temperature phases. In the 1D systems investigated further structure to property correlations were made. Optically it was found that unlike the corner-shared perovskite type 1D wires of [NH2C(I)=NH2]3PbI5 and [CH3SC(=NH2)NH2]3PbI5 the first exciton absorption of the octahedral face sharing wires of (A)PbI3 appear to be largely insensitive to the inorganic structural distortions experienced as a result of the low temperature phase transitions. In one instance however a low temperature phase transition did result in a polaron emission which was directly related to a discontinuity in the inorganic wires. More generally experimental links between the STE luminescence emissions and the inter-wire spacing, organic dielectric constant, and the density of the crystal, were shown to influence the STE lattice interactions to a greater degree. This effect is increased through a decrease in crystal density and organic dielectric constant, with an associated increase in the inter-wire spacing. Therefore as the exciton lattice interactions increase, a red shift in the STE emissions is observed. In another series of systems strong 1- and interactions were present in particularly two 1D charge transfer compounds. It was noted that the inorganic wires promote interactions between the organic templates as has also been established in literature. Structurally it was also observed that the CT transitions of these compounds begin to largely coincide with the STE emission arising from the inorganic wire. Even though the CT compounds structurally have strong interactions the current experiments do not ascertain to what degree this interaction assists in electron transport. It was also established that as intermolecular interactions are absent in previously published MV and Et compounds with the dominant CT interaction was the I…N interaction which functions over a large range (4.9A). This long distance is substantiated from the strong covalent character of the I…N interaction observed in IR experiments completed on (MV)Pb2I6. It was also observed in our compounds that the position of the LUMO of the organic cation relative to the valence band of the inorganic wires appears to be largely dependent on the N…I distance and largely independent of the electron accepting templates HOMO-LUMO gap. The increased wire thickness observed in these compounds does appear to display a pronounced effect on the PL emissions as seen in three chain wide wires produced. The thicker chains begin to allow higher energy emission’s to occur i.e. the desired first exciton emission begins to become favored due to the relaxing of the wires spatial confinement on the electron-hole’s orbit. Further investigations are needed into even thicker chain wires, in order to ascertain the ideal size of the wire to obtain the desired high energy first exciton emission. To date the wire thickness that does give rise to the first exciton emission appears to still need at least six coordinated PbI6 octahedral units.

A Dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Master of Science. Johannesburg 2016. / Low dimensional carbon systems are of immense interest in condensed matter physics due to their exceptional and often startling electric and magnetic properties. In this dissertation we consider two of these materials - graphene and nanocrystalline diamond. The effect of synthesis parameters on the quality of graphene is examined and it is found that controlling the partial pressure of the synthesis gases plays a critical role in determining the quality of the sample. Superconductivity in Boron doped nanocrystalline diamond (B-NCD) is considered and weak localisation along with a Berezinsky-Kosterlitz-Thouless (BKT) transition is identified in the samples. Furthermore we explore theoretically the problem of electric transport through a double quantum dot system coupled to a nanomechanical resonator. We find resonant tunnelling when the difference between the energy levels of the dots equals an integer multiple of the resonator frequency, and that while initially increasing the electron phonon coupling (g) increases the current through the sample further increase in g inhibits electric transport through the quantum dots. / LG2017

Over the last twenty years, a main focus of low-dimensional topology has been on categorified knot invariants such as knot homologies. This dissertation studies the case of two such homologies under the iteration of branched covering maps. In the first part, we find a spectral sequence on the sutured annular Khovanov homology of periodic links of period $r=2^i$. In the second part, we study the asymptotic growth rate of Heegaard Floer homology of cyclic branched covers of a knot as the branching number increases.

In this thesis study, the surface/interface plasmon excitations in different Si nanostructures were revealed through the EELS study in TEM/STEM. In the case of the planar boundary such as the wedge-like specimen, the spatially resolved EELS results disclose the dependence of the intensity and the position of the interface plasmon peak on the sample thickness. In the case of the Si-core/ SiO2-shell nanoparticles, we found that the SP/IP peak will firstly red-shifts with the increase of the SiO2 shell thickness and eventually levels off . As the aspect ratio of the Si nanoparticles increases, (from spherical particle to nanorod and nanowire), the SP/IP will split into two branches: transverse and longitudinal modes. We also found the intensity ratio of the transverse/longitudinal mode excitations depends on the diameter of the Si core size in the nanostructures. In the one-dimensional interacting Si nanoparticle chains, the Si nanoparticles were embedded in the SiO 2 shell, the splitting of the SP excitation into transverse and longitudinal modes was also observed. As the inter-particle distance reduces to several nanometers, the coupling of the IP excitation between the adjacent particles becomes significant, and results in the local field enhancement in-between the two particles. This is directly visualized using EFTEM imaging in TEM/STEM. / Surface/interface plasmons (SP/IP) are the plasmons confined at specific boundaries, describing the surface/interface charge density oscillation. They are generated when the scattered electromagnetic wave with its scattering vector component parallel to the boundary propagates along the surface/interface. Study of surface plasmon resonance in noble metals such as gold and silver nanoparticles have started decades ago, and recent interests are focused on the plasmonic properties of individual nanoparticles, as enabled by the size/shape control in the nanostructure growth and advances made in the characterization methodologies. Besides the noble metals, semiconductor such as silicon also attracts much attention for its plasmonic behavior. The surface/interface plasmon resonance frequency of Si-based nanostructures occurs at relatively higher energies (compared to Au and Ag), making it a perfect system to be studied using electron energy loss spectroscopy (EELS) based techniques. When performed in a scanning transmission electron microscope (STEM), such a technique enjoys excellent spatial resolution, and can map the local plasmonic properties of individual nanostructures. / The plasmon excitation depends sensitively on not only the material dielectric properties but also the geometrical configurations of the material. In the present thesis work, silicon-based nanostructures with planar, spherical, and cylindrical boundaries were investigated using both experimental and theoretical approaches, with focus on the plasmon oscillation originating from the Si/SiO 2 interface. The specimens employed include silicon/silica thin films, Si-core/SiO2-shell nanoparticles with different aspect ratios and spherical-shaped nanoparticle chains, as well as Si-core/SiO2-shell nanocables. / Wang, Xiaojing = 低維硅納米結構表界面等離激元之研究 / 王笑靜. / Adviser: Li Quan. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 118-122). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Wang, Xiaojing = Di wei gui na mi jie gou biao jie mian deng li ji yuan zhi yan jiu / Wang Xiaojing.