Circular source and detector trajectories in cone-beam computed tomography (CT) are known to collect insufficient data for accurate object reconstruction. One model predicts that the lacking information corresponds to a shift-variant cone of missing spatial frequency components in the local Fourier domain. These predictions were experimentally verified by imaging small, localized objects and observing their Fourier transforms. Measurements indicated that the internal angle of the ‘missing cone’ varies as the angle of locally intersecting x rays with respect to the horizontal plane, as expected. Object recovery was also found to depend greatly on the distribution of the object’s frequency spectrum relative to the missing cone, as predicted. Findings agreed with more anatomically relevant phantoms, which showed preferential intensity discrepancies at gradients oriented within or near the missing cone. Methods for artefact correction are in general limited to approximation unless a priori information is incorporated.

Columnar jointing is a fracture pattern, best known from locations such as the Giant's Causeway, or Fingal's Cave, in which cracks self-organize into a nearly hexagonal arrangement, leaving behind an ordered colonnade. In this thesis observations of columnar jointing are reported from both a controlled laboratory setting, and in cooled lava flows. Experiments were performed in slurries of corn starch and water, which form columnar joints when dried. This drying process is examined in detail, and it is shown how desiccation leads to the propagation of a sharp shrinkage front. In general, but with some significant exceptions, the size of columnar joints is inversely dependent on the speed of this shrinkage front during their formation. The exceptions, which include sudden jumps in column scale, show that hysteresis is also important in choosing the column scale. Novel observations of the 3D structure of joints in starch show that columnar joints do not settle down to a perfect hexagonal pattern, but rather mature into a continuously evolving dynamic pattern. This pattern is scale invariant, and the same statistical distribution of column shapes applies equally to joints in both starch and lava. Field work was performed to study columnar jointing in the basalts of the Columbia River Basalt Group and the island of Staffa, and the more heterogeneous lava flows of Southwestern British Columbia. The widths of columns and the heights of striae (chisel-like markings that record details of cooling) were examined in detail, and these length scales are shown to be inversely proportional to each other. An additional length scale, that of wavy columns, is also first reported here. Based on these measurements, empirical advective-diffusive models are developed to describe the transport of water in a drying starch-cake, and the transport of heat in a cooling lava flow. These models have only a single scaling parameter, the Péclet number, which relates the fracture front velocity times the column size to the (thermal or hydraulic) diffusivity. In both cases, the formation of columnar joints occurs at a Péclet number of about 0.2. This model explains the hundred-fold differences in scale between columnar joints in starches and lavas, and can be used as a tool for the interpretation of joint patterns in the field.

Circular source and detector trajectories in cone-beam computed tomography (CT) are known to collect insufficient data for accurate object reconstruction. One model predicts that the lacking information corresponds to a shift-variant cone of missing spatial frequency components in the local Fourier domain. These predictions were experimentally verified by imaging small, localized objects and observing their Fourier transforms. Measurements indicated that the internal angle of the ‘missing cone’ varies as the angle of locally intersecting x rays with respect to the horizontal plane, as expected. Object recovery was also found to depend greatly on the distribution of the object’s frequency spectrum relative to the missing cone, as predicted. Findings agreed with more anatomically relevant phantoms, which showed preferential intensity discrepancies at gradients oriented within or near the missing cone. Methods for artefact correction are in general limited to approximation unless a priori information is incorporated.

When the tensor product of two irreducible representations contains multiple copies of some of its irreducible constituents, there is a problem of choosing specific copies: resolving the multiplicity. This is typically accomplished by some ad hoc method chosen primarily for convenience in labelling and calculations. This thesis addresses the possibility of making choices according to other criteria. One possible criterion is to choose copies for which the Clebsch-Gordan coefficients have a simple form. A method fulfilling this is introduced for the tensor product of three irreps of $su(2)$. This method is then extended to the tensor product of two irreps of $su(3)$. In both cases the method is shown to construct a full nested sequence of basis independent highest weight subspaces. Another possible criterion is to make choices which are intrinsic, independent of all choices of bases. This is investigated in the final part of the thesis with a basis independent method that applies to the tensor product of finite dimensional irreps of any semisimple Lie algebra over $\mathbb{C}$.

Doctor of Philosophy / Physics / Christopher M. Sorensen / We demonstrated that gram quantities of pristine graphene nanosheets (GNs) can be produced via detonation of a hydrocarbon. This one-step and catalyst-free method is eco-friendly and economical for the production of GNs. The hydrocarbons detonated were C₂H₂, C₂H₄, C₃H₈ and CH₄ in the presence of O₂. The carbon products obtained from the detonation were analyzed by XRD, TEM, XPS and Raman spectroscopy. Depending upon the ratio of O₂ to C₂H₂, the GNs of size up to ~ 250 nm, SSA up to ~ 200 m²/g and yield up to 70% with 2-3 layers' stack have been obtained so far. N₂O was determined as a good alternative to O₂ as an oxidizer to produce GNs by detonating C₂H₂ with it. A two-color pyrometer was designed and calibrated to measure the temperature of the detonation of hydrocarbons. The measured detonation temperatures were in between 2700 K and 4300 K. Along with the high detonation temperature, the composition of precursor hydrocarbon was observed to be crucial as well to determine its suitability to detonate with oxidizer to produce GNs. The hydrocarbons C₂H₂ and C₂H₄ were determined as the suitable precursors to produce GNs whereas detonation of C₃H₈ yields mere amorphous carbon soot and CH₄ gives no solid carbon while detonated with O₂. It has been proposed that the hydrocarbons with C/H≥0.5 are suitable for GNs production by detonation method. Highly oxidized graphene nanosheets (OGNs) were produced by solution-based oxidation of GNs prepared via a controlled detonation of acetylene at O₂/C₂H₂=0.8. The produced OGNs were about 250 nm in size and hydrophilic in nature. The C/O ratio was dramatically reduced from 49:1 in the pristine GNs to about 1:1 in OGNs, as determined by X-ray photoelectron spectroscopy. This C/O in OGNs is the least ever found in all oxidized graphitic materials that have been reported. Thus, the OGNs produced from the detonated GNs with such high degree of oxidation herein yields a novel and promising material for future applications.

Doctor of Philosophy / Department of Physics / Nobel S. Rebello / Research that investigates the dynamics of knowledge construction by students as they model phenomena at the microscopic level has not been extensively conducted in physics and science education in general. This research wherein I investigated the dynamics of knowledge construction of students in the context of microscopic friction is an attempt to do so. The study commenced with an investigation of the variations in the existing models of students about microscopic friction (phase I of the study). Clinical interviews were conducted with introductory physics students in order to elicit their models. A phenomenographic approach of data analysis was employed to establish the variations in students’ models. Results show that students’ mental models of friction at the atomic level are dominated by their macroscopic experiences. Friction at the atomic level according to most students is due to mechanical interactions (interlocking or rubbing of atoms). Can we build on these macroscopic ideas of students in order to help them construct more scientific explanations of friction at the atomic level? The second phase of the research was an investigation of the dynamics of knowledge construction of students as they constructed models of friction at the atomic level while building on their prior ideas. Individual as well as group teaching interviews were conducted with introductory physics students in order to investigate students learning trajectories and the processes they undergo as they created new models of friction at the atomic level. Results show that the span, zone of proximal development and the epistemological orientations of the students greatly influenced the extent to which they utilize scaffolding afforded to them during the model-building process. Moreover, results show that students undergo the process of incorporation and displacement during their model construction and reconstruction. In the third phase, an instructional material geared towards helping students develop more scientific explanations of microscopic friction was developed and pilot-tested. Overall, the results of the study have significant implications for further research, in improving instruction, and curriculum material development.

Doctor of Philosophy / Department of Physics / Dean A. Zollman / A series of teaching activities using physical models was developed to present some portions of physics of Positron Emission Tomography (PET) and investigate students’ understanding and transfer of learning in physics to a medical technology. A teaching interview protocol consistent with a qualitative research methodology was developed and administered to the students enrolled in an algebra-based introductory level physics course. 16 students participated in individual interviews and another 21 students participated in the group sessions. The major objectives of the teaching interviews were to investigate students’ transfer of physics learning from their prior experiences to the provided physical models, from one model to the other and from the models to the PET problems. The study adapted phenomenological research methodology in analyzing students’ use of cognitive resources and cognitive strategies during knowledge construction and reconstruction. A resource based transfer model framed under the cognitive theory of learning and consistent with contemporary views of transfer was used to describe the transfer of physics learning. Results of the study indicated both appropriate and inappropriate use of the students’ prior conceptual resources in novel contexts. Scaffolding and questioning were found to be effective in activating appropriate and suppressing the inappropriate resources. The physical models used as analogies were found useful in transferring physics learning to understand image construction in PET. Positive transfer was possible when the models were introduced in an appropriate sequence. The results of the study indicate the occurrence of three types of non-scaffolded transfer – spontaneous, semi spontaneous and non-spontaneous. The research found connections between sequencing of hints and phrasing of information in activating students’ different conceptual resources. A qualitative investigation based on Vygotsky’s Zone of Proximal Development (ZPD) has been completed in two contexts – one involving an instructor and the other involving peers. Significant expansion of the students’ ZPD occurred through peer interaction. The results indicate that the appropriate sequencing of learning activities and group interactions can promote learning. Additional research in transfer of physics learning from macroscopic phenomena to microscopic phenomena are warranted by the conclusions of this work.

Doctor of Philosophy / Department of Physics / Nobel S. Rebello / Conventional wisdom has long advised that students’ learning is best supported by interaction with physical manipulative. Thus, in the physics laboratory, students typically spend their time conducting experiments with physical equipment. However, computer simulations offer a tempting alternative to traditional physical experiments. In a virtual experiment, using a computer simulation, students can gather data quickly, and measurement errors and frictional effects can be explicitly controlled. This research investigates the relative support for students’ learning offered by physical and virtual experimentation in the context of simple machines. Specifically, I have investigated students’ learning as supported by experimentation with physical and virtual manipulative from three different angles-- what do students learn, how do students learn, and what do students think about their learning. The results indicate that the virtual manipulative better supported students’ understanding of work and potential energy than the physical manipulative did. Specifically, in responding to data analysis questions, students who used the virtual manipulative before the physical manipulative were more likely to describe work as constant across different lengths of frictionless inclined planes (or pulley systems) and were more likely to adequately compare work and potential energy, whereas students who used the physical manipulative first were more likely to talk about work and potential energy separately. On the other hand, no strong support was found to indicate that the physical manipulative better supported students’ understanding of a specific concept. In addition, students’ responses to the survey questions indicate that students tend to value data from a computer simulation more than from a physical experiment. The interview analysis indicates that the virtual environment better supported the students to create new ideas than the physical environment did. These results suggest that the traditional wisdom that students learn best from physical experiments is not necessarily true. Thus, researchers should continue to investigate how to best interweave students’ experiences with physical and virtual manipulatives. In addition, it may be useful for curriculum designers and instructors to spend more of their efforts designing learning experiences that make use of virtual manipulatives.

Doctor of Philosophy / Department of Physics / N. Sanjay Rebello / Research has demonstrated that attentional cues overlaid on diagrams and animations can help students attend to the relevant areas and facilitate problem solving. In this study we investigate the influence of visual cues and outcome feedback on students’ problem solving, performance, reasoning, and visual attention as they solve conceptual physics problems containing a diagram. The participants (N=90) were enrolled in an algebra-based physics course and were individually interviewed. During each interview students solved four problem sets while their eye movements were recorded. The problem diagrams contained regions that were relevant to solving the problem correctly and separate regions related to common incorrect responses. Each problem set contained an initial problem, six isomorphic training problems, and a transfer problem. Those in the cued condition saw visual cues overlaid on the training problems. Those in the feedback conditions were told if their responses (answer and explanation) were correct or incorrect. Students’ verbal responses were used to determine their accuracy. The study produced two major findings. First, short duration visual cues coupled with correctness feedback can improve problem solving performance on a variety of insight physics problems, including transfer problems not sharing the surface features of the training problems, but instead sharing the underlying solution path. Thus, visual cues can facilitate re-representing a problem and overcoming impasse, enabling a correct solution. Importantly, these cueing effects on problem solving did not involve the solvers’ attention necessarily embodying the solution to the problem. Instead, the cueing effects were caused by solvers attending to and integrating relevant information in the problems into a solution path. Second, these short duration visual cues when administered repeatedly over multiple training problems resulted in participants becoming more efficient at extracting the relevant information on the transfer problem, showing that such cues can improve the automaticity with which solvers extract relevant information from a problem. Both of these results converge on the conclusion that lower-order visual processes driven by attentional cues can influence higher-order cognitive processes associated with problem solving.

Doctor of Philosophy / Department of Physics / Kristan L. Corwin / Optical frequency references have been widely used in applications such as navigation, remote sensing, and telecommunication industry. For stable frequency references in the near-infrared (NIR), lasers can be locked to narrow absorption features in gases such as acetylene. Currently, most Near NIR references are realized in free space setups. In this thesis, a low-loss hollow-core optical fiber with a diameter of sub millimeters is integrated into the reference setup to provide long interaction lengths between the filling gas and the laser field, also facilitate the optical interaction with low power levels. To make portable NIR reference, gas can be sealed inside the hollow-core fiber, by creating a photonic microcell. This work has demonstrated all-fiber optical frequency references in the Near IR by fabricating and integrating gas sealed photonic microcells in the reference setup. Also, a thoughtful study regarding the lineshape of the fiber-based reference has been accomplished. According the proper modeling of a shift due to lineshape, a correction was applied to our previous absolute frequency measurement of an NIR optical frequency reference. Furthermore, effects of the hollow-core fibers, including mode-dependence frequency shift related to surface modes are explored. In addition, angle splicing techniques, which will improve the performance of the fiber-based frequency reference have been created. Low transmission and return loss angle splices of photonic bandgap fiber, single mode PCF, and large core kagome to SMF-28 are developed and those fibers are demonstrated to be promising for photonic microcell based optical frequency references. Finally, a potentially portable optical metrology system is demonstrated by stabilizing a fiber-laser based frequency comb to an acetylene-filled optical fiber frequency reference. Further work is necessary to fabricate an all-fiber portable optical metrology system with high optical transmission and low molecular contamination.