This project explores systematic strategies for establishing a definitive mode of representation in drawing. These strategies are considered in the context of the subjectivities and contingencies of perceptual experience, the mediation of that experience and inherent limitations in representational language. The aim is to explore the possibilities of constructing two-dimensional artworks which serve to define or investigate perceptual processes, perspective devices and spatial relationships.

Problems in the demodulation of one, two, and three-dimensional signals are investigated. In one-dimensional linear systems the analytic signal and the Hilbert transform are central to the understanding of both modulation and demodulation. However, it is shown that an efficient nonlinear algorithm exists which is not explicable purely in terms of an approximation to the Hilbert transform. The algorithm is applied to the problem of finding the envelope peak of a white light interferogram. The accuracy of peak location is then shown to compare favourably with conventional, but less efficient, techniques. In two dimensions (2-D) the intensity of a wavefield yields to a phase demodulation technique equivalent to direct phase retrieval. The special symmetry of a Helmholtz wavefield allows a unique inversion of an autocorrelation. More generally, a 2-D (non-Helmholtz) fringe pattern can be demodulated by an isotropic 2-D extension of the Hilbert transform that uses a spiral phase signum function. The range of validity of the new transform is established using the asymptotic method of stationary phase. Simulations of the algorithm confirm that deviations from the ideal occur where the fringe pattern curvature is larger than the fringe frequency. A new self-calibrating algorithm for arbitrary sequences of phase-shifted interferograms is developed using the aforementioned spiral phase transform. The algorithm is shown to work even with discontinuous fringe patterns, which are known to seriously hamper other methods. Initial simulations of the algorithm indicate an accuracy of 5 milliradians is achievable. Previously undocumented connections between the demodulation techniques are uncovered and discussed.

Doctor of Philosophy (PhD) / The glass-transition traverses continuously from liquid to solid behaviour, yet the role of structure in this large and gradual dynamic transition is poorly understood. This thesis presents a theoretical study of the relationship between structure and dynamics in two-dimensional glass-forming alloys, and provides new tools and real-space insight into the relationship at a microscopic level. The work is divided into two parts. Part I is concerned with the role of structure in the appearance of spatially heterogeneous dynamics in a supercooled glass-forming liquid. The isoconfigurational ensemble method is introduced as a general tool for analysing the effect that a configuration has on the subsequent particle motion, and the dynamic propensity is presented as the aspect of structural relaxation that can be directly related to microscopic variations in the structure. As the temperature is reduced, the spatial distribution of dynamic propensity becomes increasingly heterogeneous. This provides the first direct evidence that the development of spatially heterogeneous dynamics in a fragile glass-former is related to spatial variations in the structure. The individual particle motion also changes from Gaussian to non- Gaussian as the temperature is reduced, i.e. the configuration expresses its character more and more intermittently. The ability of several common measures of structure and a measure of structural ‘looseness’ to predict the spatial distribution of dynamic propensity are then tested. While the local coordination environment, local potential energy, and local free volume show some correlation with propensity, they are unable to predict its spatial variation. Simple coarse-graining does not help either. These results cast doubt on the microscopic basis of theories of the glass transition that are based purely on concepts of free volume or local potential energy. In sharp contrast, a dynamic measure of structural ‘looseness’ - an isoconfigurational single-particle Debye-Waller (DW) factor - is able to predict the spatial distribution of propensity in the supercooled liquid. This provides the first microscopic evidence for previous correlations found between short- and long-time dynamics in supercooled liquids. The spatial distribution of the DW factor changes rapidly in the supercooled liquid and suggests a picture of structural relaxation that is inconsistent with simple defect diffusion. Overall, the work presented in Part I provides a real-space description of the transition from structure-independent to structure-dependent dynamics, that is complementary to the configuration-space description provided by the energy landscape picture of the glass transition. In Part II, an investigation is presented into the effect of varying the interparticle potential on the phase behaviour of the binary soft-disc model. This represents a different approach to studying the role of structure in glass-formation, and suggests many interesting directions for future work. The structural and dynamic properties of six different systems are characterised, and some comparisons are made between them. A wide range of alloy-like structures are formed, including substitutionally ordered crystals, amorphous solids, and multiphase materials. Approximate phase diagrams show that glass-formation generally occurs between competing higher symmetry structures. This work identifies two new glass-forming systems with effective chemical ordering and substantially different short- and medium-range structure compared to the glassformer studied in Part I. These represent ideal candidates for extending the study presented in Part I. There also appears to be a close connection between quasicrystal and glass-formation in 2D via random-tiling like structures. This may help explain the experimental observation that quasicrystals sometimes vitrify on heating. The alignment of asymmetric unit cells is found to be the rate-limiting step in the crystal nucleation and growth of a substitutionally ordered crystal, and another system shows amorphous-crystal coexistence and appears highly stable to complete phase separation. The generality of these results and their implications for theoretical descriptions of the glass transition are also discussed.

Thesis (Ph.D.)--Tufts University, 2000. / Adviser: David A. Boas. Submitted to the Dept. of Electrical Engineering and Computer Science. Includes bibliographical references (leaves 139-147). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (M.F.A.)--Rochester Institute of Technology, 2007. / Typescript. Includes bibliographical references (leaves 20-21).

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: three-dimensional analysis. Includes bibliographical references (leaves 50-51).

Diss. (sammanfattning) Linköping : Univ., 2005.

Thesis (M.D.)--Dept. of Surgery, University of Adelaide, Dept. of Surgery, 1992. / Typescript (Photocopy). Includes bibliographical references (leaves 243-284).

Thesis--Auburn University, 2005. / Abstract. Vita. Includes bibliographic references.

Thesis (M.S.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on April 14, 2008) Includes bibliographical references.