Studies in vortex motion

This thesis covers four different problems in the understanding of vortex sheets, and these are presented in four chapters.

In Chapter 1, free streamline theory is used to determine the steady solutions of an array of identical, hollow or stagnant core vortices in an inviscid, incompressible fluid. Assuming the array is symmetric to rotation through π radians about an axis through any vortex centre, there are two solutions or no solutions depending on whether A^(1/2)/L is less than or greater than 0.38 where A is the area of the vortex and L is the separation distance. Stability analysis shows that the more deformed shape is unstable to infinitesimal symmetric disturbances which leave the centres of the vortices undisplaced.

Chapter 2 is concerned with the roll-up of vortex sheets in homogeneous fluid. The flow over conventional and ring wings is used to test the method of Fink and Soh (1974). Despite modifications which improve the accuracy of the method, unphysical results occur. A possible explanation for this is that small scales are important and an alternate method based on "Cloud-in-Cell" techniques is introduced. The results show small scale growth and amalgamation into larger structures.

The motion of a buoyant pair of line vortices of opposite circulation is considered in Chapter 3. The density difference between the fluid carried by the vortices and the fluid outside is considered small, so that the Boussinesq approximation may be used. A macroscopic model is developed which shows the formation of a detrainment filament and this is included as a modification to the model. The results agree well with the numerical solution as developed by Hill (1975b) and show that after an initial slowdown, the vortices begin to accelerate downwards.

Chapter 4 reproduces completely a paper that has already been published (Baker, Barker, Bofah and Saffman (1974)) on the effect of "vortex wandering" on the measurement of velocity profiles of the trailing vortices behind a wing.

The LIN-3 gene of the nematode C. elegans is the vulval-inducing signal

The development of the vulva of the nematode Caenorhabditis elegans is induced by a signal from the anchor cell of the somatic gonad. Activity of the gene lin-3 is required for the Vulval Precursor Cells (VPCs) to assume vulval fates. It is shown here that lin-3 encodes the vulval-inducing signal.

lin-3 was molecularly cloned by transposon-tagging and shown to encode a nematode member ofthe Epidermal Growth Factor (EGF) family. Genetic epistasis experiments indicate that lin-3 acts upstream of let-23, which encodes a homologue of the EGF-Receptor.

lin-3 transgenes that contain multiple copies of wild-type lin-3 genomic DNA clones confer a dominant multivulva phenotype in which up to all six of the VPCs assume vulval fates. The properties of these trans genes suggest that lin-3 can act in the anchor cell to induce vulval fates. Ablation of the gonadal precursors, which prevents the development of the AC, strongly reduces the ability of lin-3 transgenes to stimulate vulval development. A lin-3 recorder transgene that retains the ability to stimulate vulval development is expressed specifically in the anchor cell at the time of vulval induction.

Expression of an obligate secreted form of the EGF domain of Lin-S from a heterologous promoter is sufficient to induce vulval fates in the absence of the normal source of the inductive signal. This result suggests that Lin-S may act as a secreted factor, and that Lin-S may be the sole vulval-inducing signal made by the anchor cell.

lin-3 transgenes can cause adjacent VPCs to assume the 1° vulval fate and thus can override the action of the lateral signal mediated by lin-12 that normally prevents adjacent 1° fates. This indicates that the production of Lin-3 by the anchor cell must be limited to allow the VPCs to assume the proper pattern of fates of so 3° 3° 2° 1° 2° 3°.

Nonlinear optics and wavelength translation via cavity-optomechanics

The field of cavity-optomechanics explores the interaction of light with sound in an ever increasing array of devices. This interaction allows the mechanical system to be both sensed and controlled by the optical system, opening up a wide variety of experiments including the cooling of the mechanical resonator to its quantum mechanical ground state and the squeezing of the optical field upon interaction with the mechanical resonator, to name two.

In this work we explore two very different systems with different types of optomechanical coupling. The first system consists of two microdisk optical resonators stacked on top of each other and separated by a very small slot. The interaction of the disks causes their optical resonance frequencies to be extremely sensitive to the gap between the disks. By careful control of the gap between the disks, the optomechanical coupling can be made to be quadratic to first order which is uncommon in optomechanical systems. With this quadratic coupling the light field is now sensitive to the energy of the mechanical resonator and can directly control the potential energy trapping the mechanical motion. This ability to directly control the spring constant without modifying the energy of the mechanical system, unlike in linear optomechanical coupling, is explored.

Next, the bulk of this thesis deals with a high mechanical frequency optomechanical crystal which is used to coherently convert photons between different frequencies. This is accomplished via the engineered linear optomechanical coupling in these devices. Both classical and quantum systems utilize the interaction of light and matter across a wide range of energies. These systems are often not naturally compatible with one another and require a means of converting photons of dissimilar wavelengths to combine and exploit their different strengths. Here we theoretically propose and experimentally demonstrate coherent wavelength conversion of optical photons using photon-phonon translation in a cavity-optomechanical system. For an engineered silicon optomechanical crystal nanocavity supporting a 4 GHz localized phonon mode, optical signals in a 1.5 MHz bandwidth are coherently converted over a 11.2 THz frequency span between one cavity mode at wavelength 1460 nm and a second cavity mode at 1545 nm with a 93% internal (2% external) peak efficiency. The thermal and quantum limiting noise involved in the conversion process is also analyzed and, in terms of an equivalent photon number signal level, are found to correspond to an internal noise level of only 6 and 4 times 10x^-3 quanta, respectively.

We begin by developing the requisite theoretical background to describe the system. A significant amount of time is then spent describing the fabrication of these silicon nanobeams, with an emphasis on understanding the specifics and motivation. The experimental demonstration of wavelength conversion is then described and analyzed. It is determined that the method of getting photons into the cavity and collected from the cavity is a fundamental limiting factor in the overall efficiency. Finally, a new coupling scheme is designed, fabricated, and tested that provides a means of coupling greater than 90% of photons into and out of the cavity, addressing one of the largest obstacles with the initial wavelength conversion experiment.

Experimental study of the upper hybrid echo in plasmas

The two-pulse stimulated radiation of dense (10^9/cm^3 < ne ≤ 10^(11) /cm^3) nonuniform neon and argon afterglow plasma columns longitudinally immersed in a magnetic field is studied. The magnetic field is very homogeneous over the plasma volume (∆B/B~.01%). If the S-band microwave pulses' center frequency is such that they resonantly excite a narrow band of plasma upper hybrid oscillations close to the maximum upper hybrid frequency of the column, strong two pulse echoes are observed. This new echo process is called the upper hybrid echo. The echo spectrum, echo power and echo width were studied as a function of the pulse peak power P, pulse separation τ, relative density (ω_(po)/ω)^2, and relative cyclotron frequency (ω_c/ω). The complex but systematic variations of the echo properties as a function of the above-mentioned parameters arc found to be in qualitative agreement with those predicted by a theory of Gould and Blum based upon a simple nonuniform unidimensional cold plasma slab model. The possible effects of electron neutral and electron ion collisions not retained in the theoretical model are discussed.

The existence of a new type of cyclotron echo, different from that of Hill and Kaplan and not predicted by the Blum and Gould model is documented. It is believed to be also of a collective effect nature and can probably be described in terms of a theory retaining some hot plasma effects.

Mechanics of landslides

The purpose of this investigation was to determine whether landslides could be predicted for hill slopes of known inclinations from data secured by laboratory tests performed on samples of the ground under consideration. Specifically, the investigation was to show whether a correlation existed between experimentally determined values for friction and cohesion of ground and calculated values based upon the configuration of earth masses that had slid. The ability to determine the stability of slopes from experimental data is of obvious significance.

Geology of the Pacoima Area, Los Angeles County, California

The Pacoima area is located on an isolated hill in the northeast section of the San Fernando, the northeast portion of the Pacoima Quadrangle, Los Angeles County, California. Within it are exposed more than 2300 feet of Tertiary rocks, which comprise three units of Middle Miocene (?) age, and approximately 950 feet of Jurassic (?) granite basement. The formations are characterized by their mode of occurrence, marine and terrestial origin, diverse lithology, and structural features.

The basement complex is composed of intrusive granite, small masses of granodiorite and a granodiorite gneiss with the development of schistosity in sections. During the long period of erosion of the metamorphics, the granitic rocks were exposed and may have provided clastic constituents for the overlying formations.

As a result of rapid sedimentation in a transitional environment, the Middle Miocene Twin Peaks formation was laid down unconformably on the granite. This formation is essentially a large thinning bed of gray to buff pebble and cobble conglomerate grading to coarse yellow sandstone. The contact of conglomerate and granite is characterized by its faulted and depositional nature.

Beds of extrusive andesite, basalt porphyry, compact vesicular amygdaloidal basalts, andesite breccia, interbedded feldspathic sands and clays of terrestial origin, and mudflow breccia comprise the Pacoima formation which overlies the Twin Peaks formation unconformably. A transgressing shallow sea accompanied settling of the region and initiated deposition of fine clastic sediments.

The marine Topanga (?) formation is composed of brown to gray coarse sandstone grading into interbedded buff sandstones and gray shales. Intrusions of rhyolitedacite and ash beds mark continued but sporatic volcanism during this period.

The area mapped represents an arch in the Tertiary sediments. Forces that produced the uplift of the granite structural high created stresses that were relieved by jointing and faulting. Vertical and horizontal movement along these faults has displaced beds, offset contacts and complicated their structure. Uplift and erosion have exposed the present sequence of beds which dip gently to the northeast. The isolated hill is believed to be in an early stage of maturity.

Behavior of spherical particles at low Reynolds numbers in a fluctuating translational flow

The behavior of spheres in non-steady translational flow has been studied experimentally for values of Reynolds number from 0.2 to 3000. The aim of the work was to improve our qualitative understanding of particle transport in turbulent gaseous media, a process of extreme importance in power plants and energy transfer mechanisms.

Particles, subjected to sinusoidal oscillations parallel to the direction of steady translation, were found to have changes in average drag coefficient depending upon their translational Reynolds number, the density ratio, and the dimensionless frequency and amplitude of the oscillations. When the Reynolds number based on sphere diameter was less than 200, the oscillation had negligible effect on the average particle drag.

For Reynolds numbers exceeding 300, the coefficient of the mean drag was increased significantly in a particular frequency range. For example, at a Reynolds number of 3000, a 25 per cent increase in drag coefficient can be produced with an amplitude of oscillation of only 2 per cent of the sphere diameter, providing the frequency is near the frequency at which vortices would be shed in a steady flow at the mean speed. Flow visualization shows that over a wide range of frequencies, the vortex shedding frequency locks in to the oscillation frequency. Maximum effect at the natural frequency and lock-in show that a non-linear interaction between wake vortex shedding and the oscillation is responsible for the increase in drag.

Junto dum seco, fero e estéril monte: uma Canção de Camões

Tendo como incipt Junto dum seco, fero e estéril monte, a Canção V de Luís de Camões, presente no corpus mínimo proposto pelo Professor Leodegário de Azevedo Filho é tema deste estudo que se propõe a fazer uma análise literária à luz do Maneirismo, onde se buscam observar as principais características temáticas presentes na mesma. Dessa forma, temas como o desconcerto do mundo, a fugacidade do tempo e da vida e, consequentemente, o pessimismo e a ausência da amada serão relacionados à poesia. Há a preocupação de se atentar para a influência tardo-gótica no Maneirismo e como isso se dá nessa canção, o que faz com que se perceba não haver traços clássicos ou renascentistas na mesma. Faz-se necessário ainda que se analisem as referências geográficas, as construções e os recursos estilísticos utilizados pelo poeta, uma vez que estes são significativos para uma boa compreensão da canção, bem como para um possível questionamento acerca da obra de Camões ser considerada por alguns autores clássica

Acid precipitation and its effects on aquatic systems in the English Lake District

There is no evidence of an increase in the acidity (lower pH or alkalinity) of water-bodies in the Lake District over the last 50 years. Brown trout occur in acid streams and upland tarns where pH is 4.5-5.2 throughout the year. Their occurrence in such waters in Britain and Ireland has been known for most of this century and there is no previous evidence of harmful effects on salmonid fisheries, though numbers of fish are naturally low. However, many benthic invertebrates that are common in hill-streams where pH is above 5.7 do not occur in more acid streams. This phenomenon occurs in the headwaters of several western rivers in Cumbria. It is not a recent response to "acid rain". Harmful effects of pH are undoubtedly more pronounced in waters that are poor in other dissolved ions. Low concentrations of sodium, potassium, calcium and chloride are especially important and may limit the distributions of some aquatic animals even where pH is above 5.7. The concentration of sulphate ions is usually relatively high but this is not important to the fauna; concentrations are at least two times higher in productive alkaline water-bodies than they are in unproductive acid waters.

High frequency wave propagation in the earth: theory and observation

The wave-theoretical analysis of acoustic and elastic waves refracted by a spherical boundary across which both velocity and density increase abruptly and thence either increase or decrease continuously with depth is formulated in terms of the general problem of waves generated at a steady point source and scattered by a radially heterogeneous spherical body. A displacement potential representation is used for the elastic problem that results in high frequency decoupling of P-SV motion in a spherically symmetric, radially heterogeneous medium. Through the application of an earth-flattening transformation on the radial solution and the Watson transform on the sum over eigenfunctions, the solution to the spherical problem for high frequencies is expressed as a Weyl integral for the corresponding half-space problem in which the effect of boundary curvature maps into an effective positive velocity gradient. The results of both analytical and numerical evaluation of this integral can be summarized as follows for body waves in the crust and upper mantle:

1) In the special case of a critical velocity gradient (a gradient equal and opposite to the effective curvature gradient), the critically refracted wave reduces to the classical head wave for flat, homogeneous layers.

2) For gradients more negative than critical, the amplitude of the critically refracted wave decays more rapidly with distance than the classical head wave.

3) For positive, null, and gradients less negative than critical, the amplitude of the critically refracted wave decays less rapidly with distance than the classical head wave, and at sufficiently large distances, the refracted wave can be adequately described in terms of ray-theoretical diving waves. At intermediate distances from the critical point, the spectral amplitude of the refracted wave is scalloped due to multiple diving wave interference.

These theoretical results applied to published amplitude data for P-waves refracted by the major crustal and upper mantle horizons (the Pg, P*, and Pn travel-time branches) suggest that the 'granitic' upper crust, the 'basaltic' lower crust, and the mantle lid all have negative or near-critical velocity gradients in the tectonically active western United States. On the other hand, the corresponding horizons in the stable eastern United States appear to have null or slightly positive velocity gradients. The distribution of negative and positive velocity gradients correlates closely with high heat flow in tectonic regions and normal heat flow in stable regions. The velocity gradients inferred from the amplitude data are generally consistent with those inferred from ultrasonic measurements of the effects of temperature and pressure on crustal and mantle rocks and probable geothermal gradients. A notable exception is the strong positive velocity gradient in the mantle lid beneath the eastern United States (2 x 10^-3 sec^-1), which appears to require a compositional gradient to counter the effect of even a small geothermal gradient.

New seismic-refraction data were recorded along a 800 km profile extending due south from the Canadian border across the Columbia Plateau into eastern Oregon. The source for the seismic waves was a series of 20 high-energy chemical explosions detonated by the Canadian government in Greenbush Lake, British Columbia. The first arrivals recorded along this profile are on the Pn travel-time branch. In northern Washington and central Oregon their travel time is described by T = Δ/8.0 + 7.7 sec, but in the Columbia Plateau the Pn arrivals are as much as 0.9 sec early with respect to this line. An interpretation of these Pn arrivals together with later crustal arrivals suggest that the crust under the Columbia Plateau is thinner by about 10 km and has a higher average P-wave velocity than the 35-km-thick, 62-km/sec crust under the granitic-metamorphic terrain of northern Washington. A tentative interpretation of later arrivals recorded beyond 500 km from the shots suggests that a thin 8.4-km/sec horizon may be present in the upper mantle beneath the Columbia Plateau and that this horizon may form the lid to a pronounced low-velocity zone extending to a depth of about 140 km.

Relativistic quark models and the current algebra

In this thesis we are concerned with finding representations of the algebra of SU(3) vector and axial-vector charge densities at infinite momentum (the "current algebra") to describe the mesons, idealizing the real continua of multiparticle states as a series of discrete resonances of zero width. Such representations would describe the masses and quantum numbers of the mesons, the shapes of their Regge trajectories, their electromagnetic and weak form factors, and (approximately, through the PCAC hypothesis) pion emission or absorption amplitudes.

We assume that the mesons have internal degrees of freedom equivalent to being made of two quarks (one an antiquark) and look for models in which the mass is SU(3)-independent and the current is a sum of contributions from the individual quarks. Requiring that the current algebra, as well as conditions of relativistic invariance, be satisfied turns out to be very restrictive, and, in fact, no model has been found which satisfies all requirements and gives a reasonable mass spectrum. We show that using more general mass and current operators but keeping the same internal degrees of freedom will not make the problem any more solvable. In particular, in order for any two-quark solution to exist it must be possible to solve the "factorized SU(2) problem," in which the currents are isospin currents and are carried by only one of the component quarks (as in the K meson and its excited states).

In the free-quark model the currents at infinite momentum are found using a manifestly covariant formalism and are shown to satisfy the current algebra, but the mass spectrum is unrealistic. We then consider a pair of quarks bound by a potential, finding the current as a power series in 1/m where m is the quark mass. Here it is found impossible to satisfy the algebra and relativistic invariance with the type of potential tried, because the current contributions from the two quarks do not commute with each other to order 1/m³. However, it may be possible to solve the factorized SU(2) problem with this model.

The factorized problem can be solved exactly in the case where all mesons have the same mass, using a covariant formulation in terms of an internal Lorentz group. For a more realistic, nondegenerate mass there is difficulty in covariantly solving even the factorized problem; one model is described which almost works but appears to require particles of spacelike 4-momentum, which seem unphysical.

Although the search for a completely satisfactory model has been unsuccessful, the techniques used here might eventually reveal a working model. There is also a possibility of satisfying a weaker form of the current algebra with existing models.

Estudo da Comunidade de anfíbios anuros ao longo de um gradiente altitudinal na Ilha Grande, Angra dos Reis, RJ. Rio de Janeiro 2010

Este estudo investigou a variação altitudinal da comunidade de anfíbios anuros em uma montanha de floresta Atlântica da Ilha Grande, avaliando a ocorrência, distribuição, organização e riqueza de anuros nas diferentes altitudes. Estabelecemos seis faixas de altitude para realização do estudo: 150, 300, 450, 600, 750 e 900 metros acima do nível do mar. Utilizamos duas metodologias de amostragem: o método de parcelas grandes (5 x 5 metros) e o método de transecção, entre janeiro de 2008 e março de 2009. Os dados indicaram que na região de Mata Atlântica do Pico do Papagaio ocorre uma considerável riqueza de espécies de anuros, a qual varia dependendo da faixa de altitude ao longo do gradiente altitudinal do morro. Houve em geral uma tendência a um decréscimo da riqueza com aumento da altitude, com exceção da altitude de 900 metros, onde a riqueza teve um aumento quando comparado à faixa altitudinal imediatamente abaixo. Nossos dados mostram ainda que ao longo de todo o gradiente altitudinal do morro, as maiores riquezas de anuros em geral ocorrem nas faixas de altitudes de 150 e 300 metros. Nossos dados indicaram para a região estudada uma considerável densidade de anuros, que além de variar significativamente entre as estações seca e chuvosa, foi influenciada negativamente pela altitude: na medida em que houve um aumento da altitude ocorreu uma correspondente diminuição na densidade geral de anuros da comunidade componente. A anurofauna da região do Pico do Papagaio apresentou uma queda abrupta na abundância a partir dos 450 metros de altitude, com grande dominância, em termos numéricos, de três espécies com desenvolvimento direto. Nossos dados mostraram haver uma variação sazonal na abundância e, nas densidades de anuros na região do Pico do Papagaio. Concluímos que a região de Mata Atlântica do Pico do Papagaio possui uma elevada riqueza de espécies de anuros, a qual varia ao longo do gradiente altitudinal com os maiores valores de riqueza e abundâncias encontradas entre as faixas de 150 e 300 metros, o que pode ser favorecido pela menor inclinação do terreno, pela maior ocorrência de cursos dágua e pela elevada pluviosidade que ocorre nestas faixas altitudinais na Ilha Grande. A considerável similaridade na comunidade componente de anuros entre as altitudes de 150 e 300 pode resultar da similaridade estrutural da vegetação entre estas faixas de altitudes. A região em geral teve uma alta densidade de anuros, que além de variar sazonalmente, foi negativamente influenciada pela altitude. A observada redução na abundância dos anuros a partir dos 450 metros de altitude pareceu favorecer espécies com desenvolvimento direto.

A conceptualização de bandido em expressões bandido de x: uma perspectiva cognitivista

Com vistas à conceptualização do conceito de BANDIDO em 32 expressões com a estrutura bandido de x, descrevemos, nesta dissertação, os modelos cognitivos idealizados subjacentes à construção de sentido de tais expressões, postulando-lhes um caráter de modelo cognitivo complexo, nos termos de Lakoff (1987), produtivo na língua. Constituem ainda o arcabouço teórico deste estudo a Teoria da Mesclagem Conceptual (FAUCONNIER e TURNER, 2002) e a Teoria da Metáfora Conceptual (LAKOFF e JOHNSON, 1980). A análise das construções bandido de x foi realizada a partir de 137 comentários retirados da internet e definições elaboradas por 15 alunos do ensino fundamental; 18 do ensino médio e 20 alunos do ensino superior. Os alunos que colaboraram com a pesquisa definiram 24 expressões bandido de x. A pesquisa obedeceu ao procedimento qualitativo de análise dos dados, no qual observamos as diferentes interpretações dadas para as expressões, fundamentando-as a partir dos processos cognitivos envolvidos no sentido das mesmas. Assim com base na análise dos comentários de internautas e nas definições de alunos, propomos quatro processos de conceptualização para as expressões bandido de x: (a) conceptualização com base em modelos cognitivos proposicionais, em que x é um locativo interpretado como lugar de origem ou de atuação do bandido bandido de morro, bandido de rua, bandido de cadeia ; (b) conceptualização com base em modelos esquemático-imagéticos, em que observamos a atribuição de uma espécie de escala ao sentido atribuído à construção, culminando em diferentes status para a categoria BANDIDO DE X, subjacente a expressões bandido de primeira/segunda/quinta categoria/linha; (c) conceptualização de BANDIDO DE X com base em modelos metonímicos, em que x é uma peça do vestuário/calçado/acessório, de modo a interpretar o BANDIDO como pertencendo a uma categoria que costuma utilizar determinada peça de roupa, acessório ou calçado bandido de colarinho branco, bandidos de farda, bandido de chinelo ; (d) conceptualização de BANDIDO DE X com base em modelos metafóricos, em que x é um conceito abstrato que pode ser entendido como um objeto possuído pelo bandido, de forma a caracterizá-lo pela maneira de agir ou expertise bandido de conceito, bandido de atitude, bandido de fé. Acreditamos, assim, na possibilidade de descrição de padrões que regem a conceptualização de BANDIDO DE X, cujos sentidos alcançados por meio de modificadores revelam a produtividade e complexidade do modelo cognitivo BANDIDO