Method and apparatus for producing an image from a transparent object

The contrast produced from a photographic transparency is controlled by placing the transparency between a pair of partially reflecting mirrors forming walls of an optical cavity. Mirrors trap a collimated laser beam illuminating the transparency so that at least a portion of the beam energy is passed through the transparency plural times. The distance that the light beam travels between the mirrors is controlled as a function of the wavelength of the beam energy to control the phase of light interference in the beam passing through the transparency, thereby controlling the intensity of the beam derived from the mirror downstream of the transparency

A unified framework for generalized multicategories

Notions of generalized multicategory have been defined in numerous contexts throughout the literature, and include such diverse examples as symmetric multicategories, globular operads, Lawvere theories, and topological spaces. In each case, generalized multicategories are defined as the "lax algebras" or "Kleisli monoids" relative to a "monad" on a bicategory. However, the meanings of these words differ from author to author, as do the specific bicategories considered. We propose a unified framework: by working with monads on double categories and related structures (rather than bicategories), one can define generalized multicategories in a way that unifies all previous examples, while at the same time simplifying and clarifying much of the theory.Comment: 76 pages; final version, to appear in TA

Using tasks to explore teacher knowledge in situation-specific contexts

This article was published in the journal, Journal of Mathematics Teacher Education [© Springer] and the original publication is available at www.springerlink.comResearch often reports an overt discrepancy between theoretically/out-of context expressed teacher beliefs about mathematics and pedagogy and actual practice. In order to explore teacher knowledge in situation-specific contexts we have engaged mathematics teachers with classroom scenarios (Tasks) which: are hypothetical but grounded on learning and teaching issues that previous research and experience have highlighted as seminal; are likely to occur in actual practice; have purpose and utility; and, can be used both in (pre- and in-service) teacher education and research through generating access to teachers’ views and intended practices. The Tasks have the following structure: reflecting upon the learning objectives within a mathematical problem (and solving it); examining a flawed (fictional) student solution; and, describing, in writing, feedback to the student. Here we draw on the written responses to one Task (which involved reflecting on solutions of x+x−1=0 of 53 Greek in-service mathematics teachers in order to demonstrate the range of teacher knowledge (mathematical, didactical and pedagogical) that engagement with these tasks allows us to explore

Electrometry Using Coherent Exchange Oscillations in a Singlet-Triplet-Qubit

Two level systems that can be reliably controlled and measured hold promise in both metrology and as qubits for quantum information science (QIS). When prepared in a superposition of two states and allowed to evolve freely, the state of the system precesses with a frequency proportional to the splitting between the states. In QIS,this precession forms the basis for universal control of the qubit,and in metrology the frequency of the precession provides a sensitive measurement of the splitting. However, on a timescale of the coherence time, $T_2$, the qubit loses its quantum information due to interactions with its noisy environment, causing qubit oscillations to decay and setting a limit on the fidelity of quantum control and the precision of qubit-based measurements. Understanding how the qubit couples to its environment and the dynamics of the noise in the environment are therefore key to effective QIS experiments and metrology. Here we show measurements of the level splitting and dephasing due to voltage noise of a GaAs singlet-triplet qubit during exchange oscillations. Using free evolution and Hahn echo experiments we probe the low frequency and high frequency environmental fluctuations, respectively. The measured fluctuations at high frequencies are small, allowing the qubit to be used as a charge sensor with a sensitivity of $2 \times 10^{-8} e/\sqrt{\mathrm{Hz}}$, two orders of magnitude better than the quantum limit for an RF single electron transistor (RF-SET). We find that the dephasing is due to non-Markovian voltage fluctuations in both regimes and exhibits an unexpected temperature dependence. Based on these measurements we provide recommendations for improving $T_2$ in future experiments, allowing for higher fidelity operations and improved charge sensitivity

First-Principles Calculation of Born Effective Charges and Spontaneous Polarization of Ferroelectric Bismuth Titanate

In this study, we present the results of our first-principles calculations of the band structure, density of states and the Born effective charge tensors for the ferroelectric (ground state B1a1) and paraelectric (I4/mmm) phases of bismuth titanate. The calculations are done using the generalized gradient approximation (GGA) as well as the local density approximation (LDA) of the density functional theory. In contrast to the literature, our calculations on B1a1 structure using GGA and LDA yield smaller indirect band gaps as compared to the direct band gaps, in agreement with the experimental data. The density of states shows considerable hybridization among Ti 3d, Bi 6p and O 2p states indicating covalent nature of the bonds leading to the ferroelectric instability. The Born effective charge tensors of the constituent ions for the ground state (B1a1) and paraelectric (I4/mmm) structures were calculated using the Berry phase method. This is followed by the calculation of the spontaneous polarization for the ferroelectric B1a1 phase using the Born effective charge tensors of the individual ions. The calculated value for the spontaneous polarization of ferroelectric bismuth titanate using different Born effective charges was found to be in the range of 55+/-13 $\mu$C/cm2 in comparison to the reported experimental value of (50+/-10 $\mu$C/cm2) for single crystals. The origin of ferroelectricity is attributed to the relatively large displacements of those oxygen ions in the TiO6 octahedra that lie along the a-axis of the bismuth titanate crystal.Comment: 36 pages, 5 figure

Development of protective finishes for glass monofilaments Final report

Organic and nickel metal protective finishes to prevent degradation of stength of glass filaments in resin-glass composite

Demonstration of Entanglement of Electrostatically Coupled Singlet-Triplet Qubits

Quantum computers have the potential to solve certain interesting problems significantly faster than classical computers. To exploit the power of a quantum computation it is necessary to perform inter-qubit operations and generate entangled states. Spin qubits are a promising candidate for implementing a quantum processor due to their potential for scalability and miniaturization. However, their weak interactions with the environment, which leads to their long coherence times, makes inter-qubit operations challenging. We perform a controlled two-qubit operation between singlet-triplet qubits using a dynamically decoupled sequence that maintains the two-qubit coupling while decoupling each qubit from its fluctuating environment. Using state tomography we measure the full density matrix of the system and determine the concurrence and the fidelity of the generated state, providing proof of entanglement

Bioluminescence intensity modeling and sampling strategy optimization

Author Posting. © American Meteorological Society 2005. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Atmospheric and Oceanic Technology 22 (2005): 1267–1281, doi:10.1175/JTECH1760.1.The focus of this paper is on the development of methodology for short-term (1–3 days) oceanic bioluminescence (BL) predictions and the optimization of spatial and temporal bioluminescence sampling strategies. The approach is based on predictions of bioluminescence with an advection–diffusion–reaction (tracer) model with velocities and diffusivities from a circulation model. In previous research, it was shown that short-term changes in some of the salient features in coastal bioluminescence can be explained and predicted by using this approach. At the same time, it was demonstrated that optimization of bioluminescence sampling prior to the forecast is critical for successful short-term BL predictions with the tracer model. In the present paper, the adjoint to the tracer model is used to study the sensitivity of the modeled bioluminescence distributions to the sampling strategies for BL. The locations and times of bioluminescence sampling prior to the forecast are determined by using the adjoint-based sensitivity maps. The approach is tested with bioluminescence observations collected during August 2000 and 2003 in the Monterey Bay, California, area. During August 2000, BL surveys were collected during a strong wind relaxation event, while in August 2003, BL surveys were conducted during an extended (longer than a week) upwelling-favorable event. The numerical bioluminescence predictability experiments demonstrated a close agreement between observed and model-predicted short-term spatial and temporal changes of the coastal bioluminescence.This work has been supported by the Ocean Optics and Biology and Physical Oceanography Programs of the Office of Naval Research. Shulman’s support is through the NRL “Use of a Circulation Model to Enhance Predictability of Bioluminescence in the Coastal Ocean” project sponsored by the Office of Naval Research

Path integrals on a flux cone

This paper considers the Schroedinger propagator on a cone with the conical singularity carrying magnetic flux (``flux cone''). Starting from the operator formalism and then combining techniques of path integration in polar coordinates and in spaces with constraints, the propagator and its path integral representation are derived. "Quantum correction" in the Lagrangian appears naturally and no a priori assumption is made about connectivity of the configuration space.Comment: LaTeX file, 9 page