Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

Comparison of observed and predicted dates of eyeing, hatching and swim-up for brown trout and Atlantic salmon

Scholars recently derived simple models from published data for the prediction from water temperature of hatching times for the eggs of brown trout (Salmo trutta L.) and Atlantic salmon (Salmo salar L.). A similar model to predict eyeing time for salmon eggs was obtained and used in this study, largely by analogy, to develop equations which might be used to obtain very approximate estimates of eyeing and swim-up times for salmon and brown trout. As the models were based on data for constant temperatures and some of them also had a very inadequate data base, it was desirable that they should be tested, as far as possible, against field and hatchery observations. The present report is a brief summary based on such data as have been obtained to date. None of the data sets were ideal for the purpose and the various inadequacies are discussed later in this report.

Entrainment of fine sediments by turbulent flows

A study was made of the means by which turbulent flows entrain sediment grains from alluvial stream beds. Entrainment was considered to include both the initiation of sediment motion and the suspension of grains by the flow. Observations of grain motion induced by turbulent flows led to the formulation of an entrainment hypothesis. It was based on the concept of turbulent eddies disrupting the viscous sublayer and impinging directly onto the grain surface. It is suggested that entrainment results from the interaction between fluid elements within an eddy and the sediment grains.

A pulsating jet was used to simulate the flow conditions in a turbulent boundary layer. Evidence is presented to establish the validity of this representation. Experiments were made to determine the dependence of jet strength, defined below, upon sediment and fluid properties. For a given sediment and fluid, and fixed jet geometry there were two critical values of jet strength: one at which grains started to roll across the bed, and one at which grains were projected up from the bed. The jet strength K, is a function of the pulse frequency, ω, and the pulse amplitude, A, defined by

K = Aω^-s

Where s is the slope of a plot of log A against log ω. Pulse amplitude is equal to the volume of fluid ejected at each pulse divided by the cross sectional area of the jet tube.

Dimensional analysis was used to determine the parameters by which the data from the experiments could be correlated. Based on this, a method was devised for computing the pulse amplitude and frequency necessary either to move or project grains from the bed for any specified fluid and sediment combination.

Experiments made in a laboratory flume with a turbulent flow over a sediment bed are described. Dye injection was used to show the presence, in a turbulent boundary layer, of two important aspects of the pulsating jet model and the impinging eddy hypothesis. These were the intermittent nature of the sublayer and the presence of velocities with vertical components adjacent to the sediment bed.

A discussion of flow conditions, and the resultant grain motion, that occurred over sediment beds of different form is given. The observed effects of the sediment and fluid interaction are explained, in each case, in terms of the entrainment hypothesis.

The study does not suggest that the proposed entrainment mechanism is the only one by which grains can be entrained. However, in the writer’s opinion, the evidence presented strongly suggests that the impingement of turbulent eddies onto a sediment bed plays a dominant role in the process.

Photoproduction of charged pion pairs from hydrogen at energies up to 1500 MeV

Charged pion pair photoproduction has been investigated up to a gamma energy of 1500 MeV, using the Caltech 12-inch heavy liquid bubble chamber with a small diameter, high intensity photon beam passing through a central beam tube gaseous hydrogen target surrounded by the sensitive Freon. Scanning, analysis, and data reduction techniques have been developed to deal with the problems of two-vie stereo, hidden event origins, absence of magnetic field, and the range-energy and multiple scattering relationships that occur in the heavy materials. Roughly 5700 pictures have been scanned and analyzed, yielding 754 acceptable events. Cross section and parameter distributions are generally consistent with the results of previous experiments. A statistically insignificant “bump” was observed in the dipion mass spectrum in the region of 500 MeV, the disputed σ meson mass. This region was investigated as carefully as the limited statistics would allow; dipion angular distributions are consistent with isotropy, and there is indication that some of the events in this region might come from decay of an intermediate N*₁₁ (1425) into a proton and dipion.

Photographic materials on pp. 18, 20, 22, and 24 are essential and will not reproduce clearly on Xerox copies. Photographic copies should be ordered.

Proton-Coupled Reduction of N2 Facilitated by Molecular Fe Complexes

The activation of Fe-coordinated N₂ via the formal addition of hydrogen atom equivalents is explored in this thesis. These reactions may occur in nitrogenase enzymes during the biological conversion of N₂ to NH₃. To understand these reactions, the N₂ reactivity of a series of molecular Fe(N₂) platforms is investigated. A trigonal pyramidal, carbon-ligated Fe^I complex was prepared that displays a similar geometry to that of the resting state 'belt' Fe atoms of nitrogenase. Upon reduction, this species was shown to coordinate N₂, concomitant with significant weakening of the C-Fe interaction. This hemilability of the axial ligand may play a critical role in mediating the interconversion of Fe(N_xH_y) species during N₂ conversion to NH₃. In fact, a trigonal pyramidal borane-ligated Fe complex was shown to catalyze this transformation, generating up to 8.49 equivalents of NH₃. To shed light on the mechanistic details of this reaction, protonation of a borane-ligated Fe(N₂) complex was investigated and found to give rise to a mixture of species that contains an iron hydrazido(2-) [Fe(NNH₂)] complex. The identification of this species is suggestive of an early N-N bond cleavage event en route to NH₃ production, but the highly-reactive nature of this complex frustrated direct attempts to probe this possibility. A structurally-analogous silyl-ligated Fe(N₂) complex was found to react productively with hydrogen atom equivalents, giving rise to an isolable Fe(NNH₂) species. Spectroscopic and crystallographic studies benefited from the enhanced stability of this complex relative to the borane analogue. One-electron reduction of this species initiates a spontaneous disproportionation reaction with an iron hydrazine [Fe(NH₂NH₂)] complex as the predominant reaction product. This transformation provides support for an Fe-mediated N₂ activation mechanism that proceeds via a late N-N bond cleavage. In hopes of gaining more fundamental insight into these reactions, a series of Fe(CN) complexes were prepared and reacted with hydrogen-atom equivalents. Significant quantities of CH₄ and NH₃ are generated in these reactions as a result of complete C-N bond activation. A series of Fe(CNH_x) were found to be exceptionally stable and may be intermediates in these reactions. The stability of these compounds permitted collection of thermodynamic parameters pertinent to the unique N-H bonds. This data is comparatively discussed with the theoretically-predicted data of the N₂-derived Fe(NNH_x) species. Exceptionally-weak N-H bond enthalpies are found for many of these compounds, and sheds light on their short-lived nature and tendency to evolve H₂. As a whole, these works both establish and provide a means to understand Fe-mediated N₂ activation via the addition of hydrogen atom equivalents.

Cryogenic Silicon Optical Reference Cavities

Thermodynamical fluctuations in temperature and position exist in every physical system, and show up as a fundamental noise limit whenever we choose to measure some quantity in a laboratory environment. Thermodynamical fluctuations in the position of the atoms in the dielectric coatings on the mirrors for optical cavities at the forefront of precision metrology (e.g., LIGO, the cavities which probe atomic transitions to define the second) are a current limiting noise source for these experiments, and anything which involves locking a laser to an optical cavity. These thermodynamic noise sources scale physical geometry of experiment, material properties (such as mechanical loss in our dielectric coatings), and temperature. The temperature scaling provides a natural motivation to move to lower temperatures, with a potential huge benefit for redesigning a room temperature experiment which is limited by thermal noise for cryogenic operation.

We design, build, and characterize a pair of linear Fabry-Perot cavities to explore limitations to ultra low noise laser stabilization experiments at cryogenic temperatures. We use silicon as the primary material for the cavity and mirrors, due to a zero crossing in its linear coefficient of thermal expansion (CTE) at 123 K, and other desirable material properties. We use silica tantala coatings, which are currently the best for making high finesse low noise cavities at room temperature. The material properties of these coating materials (which set the thermal noise levels) are relatively unknown at cryogenic temperatures, which motivates us to study them at these temperatures. We were not able to measure any thermal noise source with our experiment due to excess noise. In this work we analyze the design and performance of the cavities, and recommend a design shift from mid length cavities to short cavities in order to facilitate a direct measurement of cryogenic coating noise.

In addition, we measure the cavities (frequency dependent) photo-thermal response. This can help characterize thermooptic noise in the coatings, which is poorly understood at cryogenic temperatures. We also explore the feasibility of using the cavity to do macroscopic quantum optomechanics such as ground state cooling.

Strong visible up-conversion emission in Tb3+, Tm3+ and Tb3+-Tm3+ co-doped tellurite glasses sensitized by Yb3+

Up-conversion luminescence characteristics under 975 nm excitation have been investigated with Tb3+/Tm3+/Yb3+ triply doped tellurite glasses. Here, green (547 nm: D-5(4) --> F-7(4)) and red (660 nm: D-5(4) --> F-7(2)) up-conversion (UC) luminescence originating from Tb3+ is observed strongly, because of the quadratic dependences of emission intensities on the excitation power. Especially, the UC luminescence was intensified violently with the energy transfer from the Tm3+ ions involves in the Tb3+ excitation. To the Tb3+/Tm3+/Yb3+ triply doped glass system, a novel up-conversion mechanism is proposed as follows: the energy of (3)G(4) level (Tm3+) was transferred to D-5(4) (Tb3+) and the 477-nm UC luminescence of Tm3+ was nearly quenched. (C) 2006 Elsevier B.V. All rights reserved.

The effects of a sand layer upon swim-up success in UK salmonids

There are two main ways in which gravel composition and changes therein arising from siltation, can influence the survival of young salmonids. First, the composition of the gravel will affect its permeability and, hence, may influence the survival of eggs and alevins through its effect upon the rate of supply of oxygen and the rate of removal of metabolic products. Second, the composition of the gravel may affect the ease, or otherwise, of emergence at the time of swim-up and alevins may become trapped in the gravel and perish. This aspect is the main concern of the present report. Experiments were conducted to examine the effects upon fry emergence of a sand layer deposited on the gravel surface. The study concludes that fry of brown trout and Atlantic salmon emerged through layers of sand up to 8 cm thick but the percentage emergence, even from the controls with no sand, was relatively low (5 - 68%). There was no firm evidence that the experimental treatments influenced percentage emergence, timing of emergence or weight of fry at the time of emergence.

Why brush up your Shakespeare and your theory?: an Angela Carter companion to myths

Essa dissertação visa estudar a formação do que veio a ser conhecido como o mito Shakespeariano e sua relação com a produção literária contemporânea, exemplificada pelo romance Wise Children, da romancista inglesa Angela Carter. Tal objetivo pretende ser alcançado por meio uma revisão teórica de elementos relacionados à concepção de mito desenvolvida pelo filósofo francês Roland Barthes, tais quais a concepção tradicional de mito, o Estruturalismo, o Pós-estruturalismo, a crítica ideológica marxista e os Estudos Culturais. Um estudo dos processos históricos que deram origem ao e ajudaram a propagar o mito Shakespeariano também é levado a cabo nessa dissertação: a apropriação da figura e da obra de William Shakespeare feita pelos pré-românticos e pelos românticos em geral; a associação da figura de Shakespeare com a identidade nacional do Império Britânico; o advento da industria Shakespeariana e o papel das adaptações das peças de Shakespeare na propagação do mito Shakespeariano