Knot/Knotting Practice in Craft and Space

Knot/knotting Practice in Craft and Space is a three part research-creation project that used a study of knotting techniques to locate craft in an expanded field of spatial practice. The first part consisted of practical, studio based exercises in which I worked with various natural and synthetic fibres to learn common knotting techniques. The second part was an art historical study that combined craft and architecture history with critical theory related to the social production of space. The third part was an exhibition of drawing and knotted objects titled Opening Closures. This document unifies the lines inquiry that define my project. The first chapter presents the art historical justification for knotting to be understood as a spatial practice. Nineteenth-century German architect and theorist Gottfried Semper’s idea that architectural form is derived from four basic material practices allies craft and architecture in my project and is the point of departure from which I make my argument. In the second chapter, to consider the methodological concerns of research-creation as a form of knowledge production and dissemination, I adopt the format of an instruction manual to conduct an analysis of knot types and to provide instructions for the production of several common knots. In the third chapter, I address the formal and conceptual underpinnings of each artwork presented in my exhibition. I conclude with a proposal for an expanded field of spatial practice by adapting art critic and theorist Rosalind Krauss’s well-known framework for assessing sculpture in 1960s.

Using phase-space localized basis functions to obtain vibrational energies of molecules

For decades scientists have attempted to use ideas of classical mechanics to choose basis functions for calculating spectra. The hope is that a classically-motivated basis set will be small because it covers only the dynamically important part of phase space. One popular idea is to use phase space localized (PSL) basis functions. This thesis improves on previous efforts to use PSL functions and examines the usefulness of these improvements. Because the overlap matrix, in the matrix eigenvalue problem obtained by using PSL functions with the variational method, is not an identity, it is costly to use iterative methods to solve the matrix eigenvalue problem. We show that it is possible to circumvent the orthogonality (overlap) problem and use iterative eigensolvers. We also present an altered method of calculating the matrix elements that improves the performance of the PSL basis functions, and also a new method which more efficiently chooses which PSL functions to include. These improvements are applied to a variety of single well molecules. We conclude that for single minimum molecules, the PSL functions are inferior to other basis functions. However, the ideas developed here can be applied to other types of basis functions, and PSL functions may be useful for multi-well systems.

Axis Mapping: The Estimation of Surface Orientations and its Applications in Vehicle Localization and Structural Geology

The map representation of an environment should be selected based on its intended application. For example, a geometrically accurate map describing the Euclidean space of an environment is not necessarily the best choice if only a small subset its features are required. One possible subset is the orientations of the flat surfaces in the environment, represented by a special parameterization of normal vectors called axes. Devoid of positional information, the entries of an axis map form a non-injective relationship with the flat surfaces in the environment, which results in physically distinct flat surfaces being represented by a single axis. This drastically reduces the complexity of the map, but retains important information about the environment that can be used in meaningful applications in both two and three dimensions. This thesis presents axis mapping, which is an algorithm that accurately and automatically estimates an axis map of an environment based on sensor measurements collected by a mobile platform. Furthermore, two major applications of axis maps are developed and implemented. First, the LiDAR compass is a heading estimation algorithm that compares measurements of axes with an axis map of the environment. Pairing the LiDAR compass with simple translation measurements forms the basis for an accurate two-dimensional localization algorithm. It is shown that this algorithm eliminates the growth of heading error in both indoor and outdoor environments, resulting in accurate localization over long distances. Second, in the context of geotechnical engineering, a three-dimensional axis map is called a stereonet, which is used as a tool to examine the strength and stability of a rock face. Axis mapping provides a novel approach to create accurate stereonets safely, rapidly, and inexpensively compared to established methods. The non-injective property of axis maps is leveraged to probabilistically describe the relationships between non-sequential measurements of the rock face. The automatic estimation of stereonets was tested in three separate outdoor environments. It is shown that axis mapping can accurately estimate stereonets while improving safety, requiring significantly less time and effort, and lowering costs compared to traditional and current state-of-the-art approaches.