Orthogonal Functions

It was the purpose of this thesis (1) to investigate certain known orthogonal functions; (2) to exhibit elements of similarity among them; (3) to show that they arise as the solutions of differential equations in a similar way; (4) to establish that the differential equations which yield them are similar and are special cases of yet another more general differential equation; (5) to verify that the Sturm-Liouville theory can be applied to each of these differential equations; and (6) to demonstrate how each of these orthogonal functions is used to give a series representation of a given function. By direct computation it was shown that the orthogonal functions studied arose from their respective differential equations in a similar way. These differential equations were then shown to be special cases of a more general differential equation, thus showing another similarity among the orthogonal functions. The Sturm-Liouville theory was used to find certain information in order to establish the orthogonality of the functions that were a solution of the various differential equations. Finally, by direct methods each of the orthogonal functions was utilized in forming a series representation of two arbitrary functions and these series representations were put in graphic form to show yet another similarity of the orthogonal functions that were studied

Optomechanical magnetometry with a macroscopic resonator

We demonstrate a centimeter-scale optomechanical magnetometer based on a crystalline whispering gallery mode resonator. The large size of the resonator allows high magnetic field sensitivity to be achieved in the hertz to kilohertz frequency range. A peak sensitivity of 131 pT per root Hz is reported, in a magnetically unshielded non-cryogenic environment and using optical power levels beneath 100 microWatt. Femtotesla range sensitivity may be possible in future devices with further optimization of laser noise and the physical structure of the resonator, allowing applications in high-performance magnetometry

Evaluating the Potential of Using 5-Azacytidine as an Epimutagen

A number of early flowering lines were induced when 5-azacytidine was applied to germinating flax (Linum usitatissimum L.) seed. The genetics of these lines indicate that the induced changes are epigenetic and probably result from demethylation of the genomic DNA at loci that affect flowering age. Although the growth and development of three stable early flowering lines are altered and the percentage of filled seed was reduced in all three lines compared with controls, measures of seed productivity demonstrated that harvest index was unaffected in two of the lines. In the third, harvest index was lower than normal and both seed set per capsule and seed mass per 100 seed were reduced. Furthermore, six generations after induction this line began to display relatively high levels of polyembryony. The late appearance of this twinning and other aspects related to working with lines induced by 5-azacytidine and using 5-azacytidine as an epimutagen are discussed

Demonstration of Quadrature Squeezed Surface-Plasmons in a Gold Waveguide

We report on the efficient generation, propagation, and re-emission of squeezed long-range surface-plasmon polaritons (SPPs) in a gold waveguide. Squeezed light is used to excite the non-classical SPPs and the re-emitted quantum state is fully quantum characterized by complete tomographic reconstruction of the density matrix. We find that the plasmon-assisted transmission of non-classical light in metallic waveguides can be described by a Hamiltonian analogue to a beam splitter. This result is explained theoretically

Characteristics of AlGaAs/GaAs multiple quantum well infrared detectors

Researchers fabricated and characterized several AlGaAs/GaAs multiple quantum well infrared detectors to evaluate the ultimate performance of these devices for low infrared background applications. The detectors were designed to have a single bound state in the quantum well and the first excited state in the continuum above the AlGaAs conduction band edge. The difference in energy between the two levels, as determined by the quantum well width and aluminum mole fraction in the barrier, was chosen such that peak absorption would occur near 8 microns. The initial structures studied comprised 50 periods with 40 A well widths and 300 A Al(0.28)Ga(0.72)As barriers. The performance of these detectors are summarized. To better interpret these results and design optimized detectors, researchers modeled both the detector noise and tunneling currents. The noise model correctly predicts that multiple quantum well detectors will, indeed, exhibit noise lower than full shot noise. The tunneling current model predicts the dark current versus bias for any choice of design parameters in a multiple quantum well detector. This model predicts a substantially reduced dark current (x 10(exp 04)) for samples with 400 A barriers. To evaluate structures with thicker barriers, researchers fabricated and characterized detectors with 400 A and 500 A barriers; a comparison of detector dark currents is shown. These results are consistent with the predictions of the dark current model

The number of transmission channels through a single-molecule junction

We calculate transmission eigenvalue distributions for Pt-benzene-Pt and Pt-butadiene-Pt junctions using realistic state-of-the-art many-body techniques. An effective field theory of interacting $\pi$-electrons is used to include screening and van der Waals interactions with the metal electrodes. We find that the number of dominant transmission channels in a molecular junction is equal to the degeneracy of the molecular orbital closest to the metal Fermi level.Comment: 9 pages, 8 figure

Solid-state laser system for laser cooling of Sodium

We demonstrate a frequency-stabilized, all-solid laser source at 589 nm with up to 800 mW output power. The laser relies on sum-frequency generation from two laser sources at 1064 nm and 1319 nm through a PPKTP crystal in a doubly-resonant cavity. We obtain conversion efficiency as high as 2 W/W^2 after optimization of the cavity parameters. The output wavelength is tunable over 60 GHz, which is sufficient to lock on the Sodium D2 line. The robustness, beam quality, spectral narrowness and tunability of our source make it an alternative to dye lasers for atomic physics experiments with Sodium atoms

Quantum coherent control of highly multipartite continuous-variable entangled states by tailoring parametric interactions

The generation of continuous-variable multipartite entangled states is important for several protocols of quantum information processing and communication, such as one-way quantum computation or controlled dense coding. In this article we theoretically show that multimode optical parametric oscillators can produce a great variety of such states by an appropriate control of the parametric interaction, what we accomplish by tailoring either the spatio-temporal shape of the pump, or the geometry of the nonlinear medium. Specific examples involving currently available optical parametric oscillators are given, hence showing that our ideas are within reach of present technology.Comment: 14 pages, 5 figure

Western Bumble Bee: Declines in the Continental United States and Range-Wide Information Gaps

In recent decades, many bumble bee species have declined due to changes in habitat, climate, and pressures from pathogens, pesticides, and introduced species. The western bumble bee (Bombus occidentalis), once common throughout western North America, is a species of concern and will be considered for listing by the U.S. Fish and Wildlife Service (USFWS) under the Endangered Species Act (ESA). We attempt to improve alignment of data collection and research with USFWS needs to consider redundancy, resiliency, and representation in the upcoming species status assessment. We reviewed existing data and literature on B. occidentalis, highlighting information gaps and priority topics for research. Priorities include increased knowledge of trends, basic information on several life‐history stages, and improved understanding of the relative and interacting effects of stressors on population trends, especially the effects of pathogens, pesticides, climate change, and habitat loss. An understanding of how and where geographic range extent has changed for the two subspecies of B. occidentalis is also needed. We outline data that could be easily collected in other research projects that would increase their utility for understanding range‐wide trends of bumble bees. We modeled the overall trend in occupancy from 1998 to 2018 of Bombus occidentalis within the continental United States using existing data. The probability of local occupancy declined by 93% over 21 yr from 0.81 (95% CRI = 0.43, 0.98) in 1998 to 0.06 (95% CRI = 0.02, 0.16) in 2018. The decline in occupancy varied spatially by landcover and other environmental factors. Detection rates vary in both space and time, but peak detection across the continental United States occurs in mid‐July. We found considerable spatial gaps in recent sampling, with limited sampling in many regions, including most of Alaska, northwestern Canada, and the southwestern United States. We therefore propose a sampling design to address these gaps to best inform the ESA species status assessment through improved assessment of how the spatial distribution of stressors influences occupancy changes. Finally, we request involvement via data sharing, participation in occupancy sampling with repeated visits to distributed survey sites, and complementary research to address priorities outlined in this paper

Stress gradients structure spatial variability in coastal tidal marsh plant composition and diversity in a major Pacific coast estuary

Understanding the drivers of variability in plant diversity from local to landscape spatial scales is a challenge in ecological systems. Environmental gradients exist at several spatial scales and can be nested hierarchically, influencing patterns of plant diversity in complex ways. As plant community dynamics influence ecosystem function, understanding the drivers of plant community variability across space is paramount for predicting potential shifts in ecosystem function from global change. Determining the scales at which stress gradients influence vegetation composition is crucial to inform management and restoration of tidal marshes for specific functions. Here, we analyzed vegetation community composition in 51 tidal marshes from the San Francisco Bay Estuary, California, USA. We used model-based compositional analysis and rank abundance curves to quantify environmental (elevation/tidal frame position, distance to channel, and channel salinity) and species trait (species form, wetland indicator status, and native status) influences on plant community variability at the marsh site and estuary scales. While environmental impacts on plant diversity varied by species and their relationships to each other, overall impacts increased in strength from marsh to estuary scales. Relative species abundance was important in structuring these tidal marsh communities even with the limited species pools dominated by a few species. Rank abundance curves revealed different community structures by region with higher species evenness at plots higher in the tidal frame and adjacent to freshwater channels. By identifying interactions (species–species, species–environment, and environment–trait) at multiple scales (local, landscape), we begin to understand how variability measurements could be interpreted for conservation and land management decisions