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We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object, so-called near-group categories. Data describing the fusion rule is reduced to an abelian group G and a nonnegative integer k. Conditions are given, in terms of G and k, for the existence or nonexistence of coherent associative structures for such fusion rules (ie, solutions to MacLane's pentagon equation). An explicit construction of matrix solutions to the pentagon equations is given for the cases where we establish existence, and classification of the distinct solutions is carried out partially. Many of these associative structures also support (braided) commutative and tortile structures and we indicate when the additional structures are possible. Small examples are presented in detail suitable for use in computational applications. / Ph. D.

Vertical drop testing of transport aircraft fuselage sections indicates that the frames play a major role in the process of absorbing the impact energy in the crushing of the substructure below the main passenger deck. Hence, static tests are performed on individual circumferential frames under a radially inward load to assess their progressive failure response and energy absorption characteristics. The test articles in the first series of tests are six-foot diameter, semicircular, I-section frames fabricated from graphite-epoxy unidirectional tape. The test articles in the second series of tests are J-section frames subtending a forty-eight degree circular arc, having an inside radius of 118 inches, a depth of 4.8 inches, and manufactured by resin transfer molding into a 2x2 2D triaxial braided composite preform made of AS4 graphite yarns. Frames of both materials exhibit fractures at the pint of load application and at selected locations around the circumference, but the delamination prevalent in the tape layup frames is not evident in the textile frames. A mathematical model developed to optimize open section curved composite frames for improved energy absorption is used to redesign the I-section frames by resizing the flanges. The test results of the redesigned frames show that the mathematical model predicted the correct sequence and locations of the failure events. However, the mathematical model does not predict the magnitude of the force and displacement at the first major failure event, which maybe due to the fact that delamination is not included in the progressive failure model Tests results from two of the J-section frames are compared with a beam finite element analysis using the computer code ABAQUS. Effective elastic moduli for the textile material are obtained from the computer code TEXCAD. The ABAQUS results correlate reasonably well with the experimental results prior to the first major failure event. / Master of Science

No description available.

This research has been undertaken to further our knowledge of decade-to-century timescale braided, gravel-bed river delta growth dynamics. The study included: a review of available literature; field studies; the development of microscale models for two study deltas; and the development of a simple numerical model incorporating movement of braided river channels across a delta topset (varying the location of sediment delivery to the delta). Results from the microscale modelling showed that successful physical modelling requires well-defined fixed boundaries and, ideally, good historical aerial photography for the estimation of the model time scale. A complex braided gravel-bed river delta system composed of two merging deltas entering a deep, low-energy receiving basins was able to be successfully modelled to provide valuable information on delta growth dynamics. However, a microscale model of a delta prograding into shallow receiving basins, with a large supply of fine sediment, was more difficult to calibrate and assess (partly due to limited field data), and was considered less reliable. The simple rule-based numerical model ‘DELGROW’, developed to simulate a braided river system entering a deep, low-energy body of water, requires a known sediment supply rate, as well as information on the braided river topography, submerged delta foreset, and lakebed bathymetry. Unlike simple 1-d width-averaged geometric models, DELGROW takes into consideration barriers (e.g. islands) as well as relatively complex converging braided river delta configurations. By changing the sediment supply, or modifying the river system, the response of the river system to various scenarios can also be assessed. Microscale models and DELGROW appear to realistically simulate decade-to-century timescale growth of braided gravel-bed river deltas entering a deep, low-energy, receiving basin. Both of these modelling methods initially use the supplied sediment to try and eliminate any riverbed irregularities (e.g. low areas), before continuing to advance and deposit sediment in a more evenly-distributed manner, whilst taking into consideration irregularities due to barriers, and asymmetric sediment sources such as merging deltas. Neither model can reliably predict locations of bank erosion, or channel avulsions that divert flow and sediment outside of the fixed model boundaries.

The recent emergence of Structure-from-Motion Photogrammetry (SfM) has created a cost-effective alternative to conventional laser scanning for the production of high-resolution topographic datasets. There has been an explosion of applications of SfM within the geomorphological community in recent years, however, the focus of these has largely been small-scale (102 - 103 m2), building on innovations in low altitude Unmanned Aircraft Systems (UAS). This thesis examines the potential to extend the scope of SfM photogrammetry in order to quantify of landscape scale processes. This is examined through repeat surveys of a ~35 km2 reach of the Dart River, New Zealand. An initial SfM survey of this reach was conducted in April 2014, following a large landslide at the Slipstream debris fan. Validation of the resulting digital elevation models using Independent Control Point's (ICPs) suggested encouraging results, however benchmarking the survey against a long-range laser scanned surface indicated the presence of significant systematic errors associated with inaccurate estimation of the SfM bundle adjustment. Using a combination of scaled laboratory field experiments, this research aimed to develop and test photogrammetric data collection and modelling strategies to enhance modelling of 3D scene structure using limited constraints. A repeat survey in 2015 provided an opportunity to evaluate a new survey strategy, incorporating a convergent camera network and a priori measurement of camera pose. This resulted in halving of mean checkpoint residuals and a reduction in systematic error. The models produced for both 2014 and 2015 were compared using a DEM differencing (DoD) methodology to assess the applicability of wide-area SfM models for the analysis of geomorphic change detection. The systematic errors within the 2014 model confound reliable change detection, although strategies to correlate the two surveys and measure the residual change show promise. The future use of SfM over broad landscape scales has significant potential, however, this will require robust data collection and modelling strategies and improved error modelling to increase user confidence.

Thesis (M. Sc.)--University of Canterbury, 2005. / Typescript (photocopy). Includes bibliographical references (leaves 160-181). Also available via the World Wide Web.