Surface meshing algorithms require certain relationships among the number of intervals on the curves that bound the surface. Assigning the number of intervals to all of the curves in the model such that all relationships are satisfied is called interval assignment. Volume meshing algorithms also require certain relationships among the numbers of intervals on each of the curves on the volume. These relationships are not always captured by surface meshing requirements. This thesis presents a news technique for automatically identifying volume constraints. In this technique, volume constraints are grouped with surface constraints and are solved simultaneously. A sweepable volume has source, target and linking surfaces. The technique described in this thesis uses graph algorithms to identify independent, parallel sets of linking surfaces, and determine if they correspond to through-holes or blind-holes. For blind-holes, the algorithm generates constraints that prevent the hole from being too deep in interval parameter space and, thus, penetrating opposite target surfaces. For each linking set, the adjoining source and target surfaces are partially ordered by the structure of the linking set. A small set of representative paths for each linking set is found, and the representative paths for all linking sets are gathered and distilled by Gaussian elimination into a small set of constraints.

Doctor of Philosophy / Department of Mathematics / Louis Crane / We exhibit a static, cylindrically symmetric, exact solution to the Euler-Heisenberg field equations (EHFE) and prove that its effective geometry contains (optical) black holes. It is conjectured that there are also soliton solutions to the EHFE which contain black hole geometries.

We firstly numerically recalculate the Ricci tensor of non-stationary axisymmetric space-times (originally calculated by Chandrasekhar) and we find some discrepancies both in the linear and non-linear terms. However, these discrepancies do not affect the results concerning linear perturbations of a Schwarzschild black hole. Secondly, we use these Ricci tensors to derive the Zerilli and Regge-Wheeler equations and use the Newman-Penrose formalism to derive the Bardeen-Press equation. We show the relation between these equations because they describe the same linear perturbations of a Schwarzschild black hole. Thirdly, we illustrate heuristically (when the angular momentum (l) is 2) the relation between the linearized solution of the Einstein vacuum equations obtained from the Bondi-Sachs metric and the Zerilli equation, because they describe the same linear perturbations of a Schwarzschild black hole. Lastly, by means of a coordinate transformation, we extend Chandrasekhar's results on linear perturbations of a Schwarzschild black hole to the Bondi-Sachs framework. / Mathematical Sciences / M. Sc. (Applied Mathematics)

Angular distributions of jet pairs (dijets) produced in proton-proton collisions at a centre-of- mass energy √s = 7 TeV have been studied with the ATLAS detector at the Large Hadron Collider using the full 2011 data set with an integrated luminosity of 4.8 fb−1, and reaching dijet masses up to 4.5 TeV. All angular distributions are consistent with QCD predictions. Analysis of the dijet angular distribution, using a novel technique simultaneously employing the dijet mass, is employed. This analysis is sensitive to both resonant new physics and phenomena with a slow-onset in mass. Using this technique, new exclusion limits have been set at 95% credibility level for several hypotheses of physics beyond the standard model including: quantum gravity scales, with 6 extra dimensions, below 4.11 TeV, quark contact interactions below a compositeness scale of 7.6 TeV, and excited quarks with a mass below 2.75 TeV. In a large and complex scientific experiment, such as ATLAS, the collection, management and usability of coherent data and metadata is a challenging operation. The availability of these data to physicists within the experiment is essential to all analysis efforts. A new web-based interface called “RunBrowser”, which makes ATLAS and LHC operations data available to the ATLAS Collaboration, is introduced.

Facilitated by the development of various direct-write techniques and functional polymeric materials including polymer based conductors and semiconductors, printed electronics are flourishing both commercially and as a research topic. This is not only because of their simpler manufacturing routes and lower cost, but also as a result of lower processing temperatures and better compatibility with flexible substrates, compared with conventional electronics. The development of conventional electronics has been guided by Moore s Law, the driver for which lies in the demand for electronic devices with better performance and portability at lower prices. Therefore, one can expect a similar trend for printed electronics to guide its development. Multi-layered printing can be adopted in printed electronics to achieve higher density integration, so that this development trend can be maintained. In such circumstances, creation of electrical connections between multiple layers emerges as an important issue for printed electronics. Inkjet-etched via holes are one potential solution to providing such electrical interconnections, and which can provide good integration with other inkjet-printed features simply by switching nozzles. This thesis aims to elicit a better understanding of the physics involved in inkjet etching and investigate the capability of the inkjet etching technique. In the thesis, the factors that can affect the size of via holes produced by inkjet etching are evaluated, which is significant for evaluating the capability of this technique to deliver industrially relevant features. Identified factors include droplet ejection frequency, droplet diameter, solvent properties and substrate temperature. Droplet ejection frequency, i.e. the reciprocal of the time interval between drops, determines the extent of evaporation of the solvent between two consecutive drop impacts. Droplet diameter determines the radius of the wetted area after the droplet I impacts on the surface and spreads into a sessile drop. Solvents with different evaporation properties result in different size evolution with the number of drops dispensed, as does droplet ejection frequency. Higher substrate temperatures can reduce the drop diameter during flight and decrease the evaporation time on polymer surfaces, which can shrink the size of via holes. Another important issue is achieving complete polymer penetration as residual polymer creates an electrical conduction barrier after such holes are subsequently filled with conductive materials or act as a barrier to filling by electroplating. Experiments have been carried out to test the effect of outer diameter and polymer thickness on polymer penetration. Electroplating is utilised to test the completeness of via hole penetration. A mechanism using the Marangoni effect to explain the protrusion drying pattern other than a hole in the polymer layer is proposed.

Thesis (MSc)--University of Stellenbosch, 2006. / ENGLISH ABSTRACT: Entropy bounds arise from Black hole thermodynamics and are a significant departure from the conventional understanding of the information in a given region. This shift in paradigm is a consequence of the the fact that there is an unexpected relationship between the area and the entropy of a given region of spacetime. Entropy bounds are simplified formulations which are ultimately attempting to be developed into the complete and broad conjecture of the Holographic Principle. This hasn’t been achieved successfully as yet. In this thesis the aim is to introduce how the notion of an entropy bound was first suggested and it’s subsequent development into more robust formulations. The shortcomings of these conjectures are highlighted along with their strengths. A foundational introduction of the mathematical requirements for General Relativity is addressed along with an overview of Einstein’s theory of gravity. This is illustrated by showing the curvature of relative geodesics as being a consequence of gravity. This is contrasted with Newtonian theory where gravity is also shown to manifests as the curvature of relative geodesics. The working background is concluded with a discussion of Einstein’s field equations along with simple and common solutions often used and required. / AFRIKAANSE OPSOMMING: Swartgat Termodinamika impliseer grense op die entropie, en dus inligting, in ’n gegewe ruimtetyd volume, wat ’n drastiese afwyking van die tradisionele denkwyse oor inligting impliseer. Hierdie paradigma skuif het sy oorsprong in ’n onverwagte verband tussen die oppervlakte van, en entropie bevat, in ’n gegewe ruimte tyd volume. Entropie grense is eenvoudige formulerings van hierdie verwantskap wat uiteindelik beslag moet kry in die vollediger en wyer holografiese beginsel. Hierdie doelwit is nog nie bereik nie. Die doel van hierdie tesis is om die oorsprong en verdere formalisering van entropie grense te verduidelik. Beide die sterk en swak punte van die formulerings word bespreek. Algemene relatiwiteits teorie as ’n teorie van gravitasie, sowel as die wiskundige onderbou daarvan, word oorsigtelik bespreek. Die geometries onderbou van gravitasie word geillustreer aan die hand van die buiging van relatiewe geodete. Dit word met Newton se gravitasie teorie vergelyk wat ook in die buiging van relatiewe geodete gemanifesteer word. Hierdie oorsigtelike agtergrond word afgesluit met ’n oorsig van Einstein se vergelykings, asook eenvoudige en algemene oplossings wat dikwels nodig is en gebruik word.

Two-dimensional (2D) carrier systems built from semiconductor heterostructures have been at the center of a wide variety of experimental and theoretical research over the past decades. The quality improvement of GaAs/AlGaAs systems has allowed the observation of several peculiar ground states stabilized by the subtle interplay between carrier-carrier interaction, disorder and magnetic field. More recently, 2D systems in semiconductor heterostructures have also been used as a prime substrate for further confinement of the carriers to mesoscopic systems of major interest for the emerging fields of quantum computing and spintronics. This thesis addresses both magnetotransport measurements in hole open quantum dots (QDs) and thermopower studies of 2D holes in (311)A GaAs heterostructures. In the first part of this thesis, we describe the fabrication process for hole GaAs open QDs and investigate their magnetotransport properties at very low temperature T. Below 500 mK, the magnetoconductance of the open QDs exhibits clear signatures of coherent transport, namely magnetoconductance fluctuations and weak anti-localization. From these effects, we extract a T dependence for the dephasing time, together with an upper limit for the spin-orbit scattering time using the random matrix theory. Both the dephasing time and the spin-orbit scattering time are found to be much smaller than for electrons in similar systems. In the second part of this work, we report low-T thermopower measurements in the parallel magnetic field-induced metal-insulator transition (MIT) of 2D GaAs hole heterojunctions with different interface-dependent mobilities. When the magnetic field is increased, the diffusion thermopower decreases across the MIT. The reduction of the diffusion thermopower is more pronounced for the lower mobility sample where it reverses its sign. This behaviour indicates that the system does not undergo any ground state modification through the MIT but rather that the parallel magnetic field induces a dramatic change of the dominant hole scattering mechanisms. Finally, the last part of this thesis is devoted to the thermopower study of the insulating phase (IP) observed in 2D GaAs bilayer hole systems around the total Landau level filling factor n = 1. Our measurements show that the diffusion thermopower diverges with decreasing T in the IP. This divergence of the diffusion thermopower at low T indicates the opening of an energy gap in the system's ground state and suggests the formation of a pinned bilayer hole Wigner crystal around n = 1.

No description available.

Little is known about the spatial distribution and abundance of tree holes in New Zealand’s native forests, or the invertebrate communities that they support. I found that tree holes were common on five endemic tree species, belonging to the families Fagaceae and Podocarpaceae in the mixed broadleaf-podocarp rainforest of Orikaka Ecological Area, Buller District, New Zealand. However, tree holes were not uniformly distributed throughout the forest, with more holes found on the three podocarp species, Prumnopitys ferruginea, P. taxifolia and Dacrycarpus dacrydioides, than on Nothofagus fusca or N. menziesii. Nevertheless, Nothofagus fusca had the largest holes of any of the tree species sampled and larger trees generally had larger holes. Large, hole-bearing Nothofagus fusca trees support a specialist hole-dwelling vertebrate fauna in New Zealand and worldwide, tree holes provide habitat for a range of invertebrate species. Using specially-designed emergence traps, I collected invertebrates emerging from naturally-occurring dry tree holes and compared this assemblage with invertebrates inhabiting leaf litter on the forest floor and those dispersing aerially throughout the study area. At the higher taxonomic resolution (i.e., Order or Class), community composition within the tree holes was highly variable, and there was no strong distinction between invertebrates from tree holes, leaf litter or Malaise traps. Moreover, although some beetle species emerging from tree holes were found exclusively in tree holes, most of these were represented by a single individual. Consequently, only minor differences in species composition were detected between beetle assemblages from tree holes, leaf-litter and those aerially dispersing throughout the forest. In contrast, the aquatic invertebrate assemblage within water-filled tree holes was highly distinctive from that in ground-based freshwater ecosystems, with only six aquatic taxa in common between all freshwater habitats. Using experimental water-filled tree-hole microcosms, I found that species richness and community composition within these microcosms were primarily driven by resource concentration, although habitat quality (i.e., water chemistry parameters) was also an important determinant of the identity and composition of colonising species. Overall, my study has shown that tree holes are common in the study area, and are likely to be more abundant in New Zealand’s indigenous forests than previously thought. Moreover, these generally small, discrete forest ecosystems support a diverse array of terrestrial invertebrates as well as a distinctive aquatic invertebrate community that is primarily structured by organic matter resource availability. These findings not only represent an important advance in our knowledge of New Zealand’s freshwater invertebrate biodiversity, but also highlight the need for further investigation into these unique forest canopy habitats which may well be at risk from deforestation and land use change.

No description available.