We examine two different techniques for studying quantum field theories in which a 'variational' optimization of parameters plays a crucial role. In the context of the O(N)-symmetric $\lambda\phi\sp4$ theory we discuss variational calculations of the effective potential that go beyond the Gaussian approximation. Trial wavefunctionals are constructed by applying a unitary operator $U = e\sp{-is\pi\sb{R}\phi\sbsp{T}{2}}$ to a Gaussian state. We calculate the expectation value of the Hamiltonian using the non-Gaussian trial states generated, and thus obtain optimization equations for the variational-parameter functions of the ansatz. At the origin, $\varphi\sb{c} = 0,$ these equations can be solved explicitly and lead to a nontrivial correction to the mass renormalization, with respect to the Gaussian case. Numerical results are obtained for the (0 + 1)-dimensional case and show a worthwhile quantitative improvement over the Gaussian approximation. We also discuss the use of optimized perturbation theory (OPT) as applied to the third-order quantum chromodynamics (QCD) corrections to $R\sb{e\sp+e\sp-}.$ The OPT method, based on the principle of minimal sensitivity, finds an effective coupling constant that remains finite down to zero energy. This allows us to apply the Poggio-Quinn-Weinberg smearing method down to energies below 1 GeV, where we find good agreement between theory and experiment. The couplant freezes to a zero-energy value of $\alpha\sb{s}/\pi = 0.26,$ which is in remarkable concordance with values obtained phenomenologically.

A high pressure, variable temperature NMR probe for low signal to noise relaxation time and self-diffusion coefficient measurements was constructed and tested. The probe has a high pressure limit of 10,000 psia and a current temperature range of 10 to 250 C. Since the magnetic field gradient coils are inside the pressure vessel, the diffusion measurements may be performed with either pulsed or constant gradients. Spin-lattice relaxation times of octane, decane, dodecane, and hexadecane were measured at temperatures between 10 and 85 C and pressures between atmospheric and 6000 psia. These data are the first for these fluids at elevated pressures and represent a significant expansion of the data base. The relaxation rate at constant temperature is proportional to the ratio of the viscosity divided by the temperature, thus being in qualitative agreement with the Bloembergen, Pound, and Purcell (1948) theory. The corresponding states treatment of spin relaxation has been extended to fluids at arbitrary temperature and pressure. Using decane as a reference fluid, the calculated relaxation times of octane, dodecane, and, hexadecane were in good agreement with the experimental values. The low signal to noise capability of the probe was tested by measuring T$\sb1$ of $\sp{13}$CO$\sb2$ at 504 psia and 25 C. Agreement with the literature value (Smith, 1986) was excellent. The gradient coils were calibrated using benzene. Measurements of benzene at various temperatures, and water at 25 C, gave reliable diffusion coefficients when either the pulsed gradient or the constant gradient method was used.

Pynchon's inclusion of scientific principles and mathematical concepts in his novels has been duly noted by critics as part of the encyclopedic references in his fiction. Pynchon, however, fictionally employs his scientific and mathematical acumen as part of an encompassing Metaphor of Extremes and Means that both provides a structure for his fiction and describes the great complexity human beings experience when they attempt to interpret the natural world and their unique position in it. Pynchon's metaphor has as it basis two extreme perspectives of the natural world: the mythological world view which has shaped most of human thought over the ages, and the Newtonian view which displaced the mythological in the seventeenth century and ushered in the Age of Reason. Pynchon peoples his fictional worlds with two extreme groups of characters: those who function intuitively and exhibit attributes akin to the frenzied rituals associated with the worship of Dionysus, the ancient Earth God, and those who operate on the Apollonian principles of causality and a will to power. Together, these two perspectives and these two groups of characters provide the extremes in Pynchon's Metaphor. More difficult to recognize is Pynchon's representation of the Golden Mean, identifiable by both a mediating perspective and characters open to alternative possibilities. The mediating perspective he identifies with quantum physics which contains both the mythological view point in its intuitive sense of forces operating below or behind the sensually observable world and the Newtonian perspective upon which quantum principles depend. The mediating characters in Pynchon's Metaphor are Orpheus and Eurydice figures who have connections with both Dionysians and Apollonians in the various novels and often initially exhibit Dionysian or Apollonian characteristics. Yet, they depart from such behavior to forge new paths in search of the Golden Mean. Doing so requires that they lose their Dionysian or Apollonian selves by means of a descent into a quantum-like space from which they emerge enlightened and ready to encounter an absolutely new order of existence---one in which their spiritual identity is retained and the constraints of physical existence which ends in entropy and death is transcended. Increasingly in Thomas Pynchon's novels is the idea that loss of self and interconnectedness is necessary for spiritual transformation which has ramifications far beyond the transformation of the individual. In his most recent novel, Mason & Dixon, the novel's protagonist is a dual-natured Orpheus consisting of both Mason and Dixon who are finally inseparable, joined as they are by the Line they drew. The Golden Mean is the point at which connections occur and distinctions between seemingly mutually exclusive extremes begin to blur. Each extreme is ameliorated by the Golden Mean even as it remains part of a larger pattern that can be glimpsed at and articulated through metaphor, the most human of connecting devices. In Pynchon's Metaphor the Golden Mean suggests a way back to connectedness with that which is larger than oneself and offers the possibility of spiritual redemption and continued existence after death.

<p> The Mott metal-insulator transition (MIT) in transition-metal complex oxides results from strong electron-electron interactions and is accompanied by a rich spectrum of phenomena, including magnetic, charge, and orbital ordering, superconductivity, structural distortions, polarons, and very high-density 2-dimensional interface electron liquids. Recent advances in oxide heteroepitaxy allow interface control as a promising new approach to tuning the exotic properties of materials near the quantum critical point, with potential application to technologies including phase-change electronics, high power transistors, and sensors. The dynamical conductivity of oxide heterostructures is measured using a combination of terahertz time-domain spectroscopy, Fourier transform infrared spectroscopy, and dc magnetotransport. The rare-earth nickelates <i> R</i>NiO₃ (<i>R</i> = La, Nd...) exhibit a temperature and bandwidth controlled MIT in bulk. Measurements of the Drude response in epitaxial thin films provide quantification of the strain-dependent mass enhancement in the metallic phase due to strong correlations. Reduction of LaNiO₃ film thickness leads to additional mass renormalization attributed to structural distortions at the heteroepitaxial interface, and an MIT is observed depending on the interfacing materials in coherent perovskite heterostructures. The rare-earth titanates <i>R</i>TiO₃ exhibit a bandwidth and band filling controlled Mott MIT. Furthermore, the heterointerface between Mott insulating GdTiO₃ and band insulating SrTiO₃ exhibits a 2-dimensional itinerant electron liquid, with extremely high sheet densities of 3 &times; 10¹⁴ cm^-2. The dynamical conductivity of the interface electrons is analyzed in terms of subband-dependent electron mobility and the established large polaron dynamics in bulk SrTiO₃. Additional confinement of the electron liquids is achieved by decreasing the SrTiO₃ layer thickness, with attendant increase in the dynamical mass. Taking the confinement to its extreme limit, a single (GdO)⁺ plane in Mott insulating GdTiO₃ is replaced with a (SrO)⁰ plane. This is equivalent to "delta-doping" the Mott insulator with an extremely high density sheet of holes. The transport and absorption in the resulting two-dimensional insulator are consistent with a simple model of small polaron hopping. A comparison is made to similar features in the conductivity of randomly doped Sr_1-xGd_xTiO₃ films.</p>

<p> The use of virtual laboratories has the potential to change physics education. These low-cost, interactive computer activities interest students, allow for easy setup, and give educators a way to teach laboratory based online classes. This study investigated whether virtual laboratories could replace traditional hands-on laboratories and whether students could retain the same long-term knowledge in virtual laboratories as compared to hands-on laboratories. This study is a quantitative quasi-experiment that used a multiple posttest design to determine if students using virtual laboratories would retain the same knowledge as students who performed hands-on laboratories after 9 weeks. The study was composed of 336 students from 14 school districts. Students had their performances on the laboratories and their retention of the laboratories compared to a series of factors that might have affected their retention using a pretest and two posttests, which were compared using a <i>t</i> test. The results showed no significant difference in short-term learning between the hands-on laboratory groups and virtual laboratory groups. There was, however, a significant difference (p = .005) between the groups in long-term retention; students in the hands-on laboratory groups retained more information than those in the virtual laboratory groups. These results suggest that long-term learning is enhanced when a laboratory contains a hands-on component. Finally, the results showed that both groups of students felt their particular laboratory style was superior to the alternative method. The findings of this study can be used to improve the integration of virtual laboratories into science curriculum.</p>

<p> The physics of the atomic nucleus and supernovas are fundamental to our very being. Indeed, supernovas provide the wind that disperses the nuclei of which we are composed, and the physics of nuclei is pivotal in supernova dynamics. During supernova core collapse, the extremely high temperatures and densities and low entropy favor large, neutron-rich nuclei at high excitation energy. My collaborators and I examine two weak interactions that occur in nuclei under these conditions. First, we study the production of neutrino pairs via de-excitation of hot nuclei. In de-exciting, the nucleus can emit a virtual Z⁰ boson that decays into a neutrino-antineutrino pair. We find this to be the dominant source of neutrino pairs of all flavors during collapse. Second, we use modern shell model computation techniques to revise the Brink-Axel hypothesis method of computing electron capture rates that was pioneered by Fuller, Fowler, and Newman. Our results show that the Brink-Axel hypothesis (which posits that the bulk of nuclear transition strength is distributed among transition energies independently of initial excitation energy) fails at low and moderate excitation, but that at high initial energies, the strength is largely independent of excitation. The failure of the Brink-Axel hypothesis manifests as the redistribution of strength to low and negative transition energies, which can have the effect of increasing the overall electron capture rate in the core.</p>

<p> The Lithium Tokamak Experiment (LTX) is a spherical tokamak designed to study the lowrecycling regime through the use of lithium-coated shells conformal to the last closed flux surface (LCFS). A lowered recycling rate is expected to flatten core <i>T</i>_e profiles, raise edge <i>T</i>_e, strongly affect <i>n</i>_e profiles, and enhance confinement.</p><p> To study these unique plasmas, a Thomson scattering diagnostic uses a &le; 20 J, 30 ns FWHM pulsed ruby laser to measure <i>T</i>_e and <i>n</i>_e at 11 radial points on the horizontal midplane, spaced from the magnetic axis to the outer edge at a single temporal point for each discharge. Scattered light is imaged through a spectrometer onto an intensified CCD. The diagnostic is absolutely calibrated using a precision light source and Raman scattering. Measurements of <i>n</i>_e are compared with line integrated density measurements from a microwave interferometer. Adequate signal to noise is obtained with ne &ge; 2 &times;10¹⁸ m^&ndash;3.</p><p> Thomson profiles of plasmas following evaporation of lithium onto room-temperature plasmafacing components (PFCs) are used in conjunction with magnetic equilibria as input for TRANSP modeling runs. Neoclassical calculations are used to determine <i> T</i>_i profiles, which have levels that agree with passive charge exchange recombination spectroscopy (CHERS) measurements. TRANSP results for confinement times and stored energies agree with diamagnetic loop measurements. Results of &chi;_e result in values as low as 7 m²/s near the core, which rise to around 100 m²/s near the edge. These are the first measurements of &chi;e in LTX, or its predecessor, the Current Drive Experiment-Upgrade (CDX-U), with lithium PFCs.</p>

<p>This dissertation presents the results of an experiment that measured the learning outcomes associated with three different pedagogical approaches to introductory physics labs. These three pedagogical approaches presented students with the same apparatus and covered the same physics content, but used different lab manuals to guide students through distinct cognitive processes in conducting their laboratory investigations. We administered post-tests containing multiple-choice conceptual questions and free-response quantitative problems one week after students completed these laboratory investigations. In addition, we collected data from the laboratory practical exam taken by students at the end of the semester. Using these data sets, we compared the learning outcomes for the three curricula in three dimensions of ability: conceptual understanding, quantitative problem-solving skill, and laboratory skills. </p><p> Our three pedagogical approaches are as follows. Guided labs lead students through their investigations via a combination of Socratic-style questioning and direct instruction, while students record their data and answers to written questions in the manual during the experiment. Traditional labs provide detailed written instructions, which students follow to complete the lab objectives. Open labs provide students with a set of apparatus and a question to be answered, and leave students to devise and execute an experiment to answer the question. In general, we find that students performing Guided labs perform better on some conceptual assessment items, and that students performing Open labs perform significantly better on experimental tasks. Combining a classical test theory analysis of post-test results with in-lab classroom observations allows us to identify individual components of the laboratory manuals and investigations that are likely to have influenced the observed differences in learning outcomes associated with the different pedagogical approaches. Due to the novel nature of this research and the large number of item-level results we produced, we recommend additional research to determine the reproducibility of our results. </p><p> Analyzing the data with item response theory yields additional information about the performance of our students on both conceptual questions and quantitative problems. We find that performing lab activities on a topic does lead to better-than-expected performance on some conceptual questions regardless of pedagogical approach, but that this acquired conceptual understanding is strongly context-dependent. The results also suggest that a single &ldquo;Newtonian reasoning ability&rdquo; is inadequate to explain student response patterns to items from the Force Concept Inventory. We develop a framework for applying polytomous item response theory to the analysis of quantitative free-response problems and for analyzing how features of student solutions are influenced by problem-solving ability. Patterns in how students at different abilities approach our post-test problems are revealed, and we find hints as to how features of a free-response problem influence its item parameters. The item-response theory framework we develop provides a foundation for future development of quantitative free-response research instruments. </p><p> Chapter 1 of the dissertation presents a brief history of physics education research and motivates the present study. Chapter 2 describes our experimental methodology and discusses the treatments applied to students and the instruments used to measure their learning. Chapter 3 provides an introduction to the statistical and analytical methods used in our data analysis. Chapter 4 presents the full data set, analyzed using both classical test theory and item response theory. Chapter 5 contains a discussion of the implications of our results and a data-driven analysis of our experimental methods. Chapter 6 describes the importance of this work to the field and discusses the relevance of our research to curriculum development and to future work in physics education research. </p>

<p> It is the goal of this dissertation to demonstrate that beyond the standard model, certain theories exist which solve conflicts between observation and theory -- conflicts such as massive neutrinos, dark matter, unstable Higgs vacuum, and recent Planck observations of excess relativistic degrees of freedom in the early universe. Theories explored include a D-brane inspired construct of U(3) &times; Sp(1) &times; U(1) &times; U(1) extension of the standard model, in which we demonstrate several possible observables that may be detected at the LHC, and an ability to stabilize the Higgs mechanism. The extended model can also explain recent Planck data which, when added to HST data gives an excess of relativistic degrees of freedom of &Delta; N = 0.574 &plusmn; 0.25 above the standard result. Also explored is a possible non-thermal dark matter model for explanation of this result. Recent observations of <i> Fermi</i> bubble results indicate a signal of a 50 GeV dark matter particle annihilating into b b-bar, with a thermally averaged annihilation cross section corresponding to &lt;&sigma; v> = 8 &times; 10</p><p>(-27) cm</p><p>3/s, spurs interestin a Higgs portal model suggested by Steven Weinberg. Other implications of this model are also explored such as its ability to explain dark matter direct detection results along with LHC Higgs data, and Planck data. Particle physics is complimented by possible stochastic gravitational wave searches for which a model of second order global phase transitions is explored. These transitions generate gravitational wave spectra with amplitudes of order &Omega;(gw) h</p><p>2 = 10</p><p>(-24) - 10</p><p>(-15). Furthermore, techniques into such calculationsare investigated in hopes to improve the stability required in such lattice simulations.</p>

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