Mean-speed measurements in two-dimensional, incompressible, fully-developed turbulent channel flow

Mean velocity profiles were measured in the 5” x 60” wind channel of the turbulence laboratory at the GALCIT, by the use of a hot-wire anemometer. The repeatability of results was established, and the accuracy of the instrumentation estimated. Scatter of experimental results is a little, if any, beyond this limit, although some effects might be expected to arise from variations in atmospheric humidity, no account of this factor having been taken in the present work. Also, slight unsteadiness in flow conditions will be responsible for some scatter.

Irregularities of a hot-wire in close proximity to a solid boundary at low speeds were observed, as have already been found by others.

That Kármán’s logarithmic law holds reasonably well over the main part of a fully developed turbulent flow was checked, the equation u/u_t = 6.0 + 6.25 log₁₀ y^ut/v being obtained, and, as has been previously the case, the experimental points do not quite form one straight line in the region where viscosity effects are small. The values of the constants for this law for the best over-all agreement were determined and compared with those obtained by others.

The range of Reynolds numbers used (based on half-width of channel) was from 20,000 to 60,000.

Distribuição de tensões em próteses parciais fixas posteriores livres de metal com retentores intracoronários: análise em elementos finitos

Para reabilitar a ausência de um elemento dentário posterior, as próteses parciais fixas (PPF) com retentores intracoronários são uma alternativa aos implantes osseointegrados. O objetivo deste estudo foi avaliar a distribuição de tensões nessas próteses com três combinações de materiais: cerâmica de zircônia parcialmente estabilizada por ítria (ZPEI) revestida por cerâmica de fluorapatita (α), cerâmica de dissilicato de lítio (β) ou compósito fibrorreforçado (γ). Na composição α, foram analisadas a presença ou ausência da cerâmica de revestimento na parede cervical das caixas proximais e três variações na área total da seção transversal dos conectores (4 mm de largura x 3,2, 4,2 ou 5,2 mm de altura). Em 8 modelos bidimensionais de elementos finitos, uma carga vertical de 500 N foi aplicada na fossa central do pôntico e as tensões principais máximas (tração) e mínimas (compressão) foram apontadas em MPa. Inicialmente foram avaliados os 6 modelos com PPF de ZPEI e suas variações. Os maiores valores das tensões de tração foram encontrados no terço cervical dos conectores. Quando presente nestas regiões, a cerâmica de revestimento recebeu tensões acima do limite de sua resistência à flexão. Na comparação entre os modelos sem cerâmica de revestimento na parede cervical das caixas proximais, mesmo aquele com conectores de 3,2 x 4 mm, cuja infraestrutura apresentava 2,5 x 3 mm, poderia ser recomendado para uso clínico. Altos valores de tensões de compressão foram registrados entre o terço oclusal e médio dos conectores, correspondente à união entre as cerâmicas, o que poderia ocasionar, devido à flexão, falhas adesivas. Posteriormente, o modelo de ZPEI com a cerâmica de fluorapatita ausente da parede cervical das caixas proximais e área total dos conectores de 4,2 x 4 mm foi comparado aos dois outros materiais com conectores de mesma área. Na PPF de dissilicato de lítio, os valores representaram uma provável violação do limite de sua resistência à flexão. A PPF de compósito fibrorreforçado apresentou tensões bem abaixo do limite de resistência à flexão de sua infraestrutura, mas, como no modelo de ZPEI, tensões compressivas se concentraram com alto valor entre o terço oclusal e médio dos conectores, local de união entre a resina composta e a infraestrutura de fibras. Os resultados mostraram que a cerâmica de dissilicato de lítio e a presença da cerâmica de fluorapatita na parede cervical das caixas proximais deveriam ser contraindicadas para a condição proposta. Parece viável uma área de conectores na infraestrutura de ZPEI com no mínimo 2,5 x 3 mm. A PPF de compósito fibrorreforçado apresenta resistência estrutural para a situação estudada, mas, como também aquelas compostas de ZPEI, aparenta ter como pontos fracos a adesão entre a infraestrutura e o material de cobertura e a própria resistência deste último.

Class two p groups as fixed point free automorphism groups

Suppose that AG is a solvable group with normal subgroup G where (|A|, |G|) = 1. Assume that A is a class two odd p group all of whose irreducible representations are isomorphic to subgroups of extra special p groups. If p^c ≠ r^d + 1 for any c = 1, 2 and any prime r where r^2d+1 divides |G| and if C_G(A) = 1 then the Fitting length of G is bounded by the power of p dividing |A|.

The theorem is proved by applying a fixed point theorem to a reduction of the Fitting series of G. The fixed point theorem is proved by reducing a minimal counter example. IF R is an extra spec r subgroup of G fixed by A₁, a subgroup of A, where A₁ centralizes D(R), then all irreducible characters of A₁R which are nontrivial on Z(R) are computed. All nonlinear characters of a class two p group are computed.

Imaging the earth with ambient noise and earthquakes

In this thesis, I develop the velocity and structure models for the Los Angeles Basin and Southern Peru. The ultimate goal is to better understand the geological processes involved in the basin and subduction zone dynamics. The results are obtained from seismic interferometry using ambient noise and receiver functions using earthquake- generated waves. Some unusual signals specific to the local structures are also studied. The main findings are summarized as follows:

(1) Los Angeles Basin

The shear wave velocities range from 0.5 to 3.0 km/s in the sediments, with lateral gradients at the Newport-Inglewood, Compton-Los Alamitos, and Whittier Faults. The basin is a maximum of 8 km deep along the profile, and the Moho rises to a depth of 17 km under the basin. The basin has a stretch factor of 2.6 in the center decreasing to 1.3 at the edges, and is in approximate isostatic equilibrium. This "high-density" (~1 km spacing) "short-duration" (~1.5 month) experiment may serve as a prototype experiment that will allow basins to be covered by this type of low-cost survey.

(2) Peruvian subduction zone

Two prominent mid-crust structures are revealed in the 70 km thick crust under the Central Andes: a low-velocity zone interpreted as partially molten rocks beneath the Western Cordillera – Altiplano Plateau, and the underthrusting Brazilian Shield beneath the Eastern Cordillera. The low-velocity zone is oblique to the present trench, and possibly indicates the location of the volcanic arcs formed during the steepening of the Oligocene flat slab beneath the Altiplano Plateau.

The Nazca slab changes from normal dipping (~25 degrees) subduction in the southeast to flat subduction in the northwest of the study area. In the flat subduction regime, the slab subducts to ~100 km depth and then remains flat for ~300 km distance before it resumes a normal dipping geometry. The flat part closely follows the topography of the continental Moho above, indicating a strong suction force between the slab and the overriding plate. A high-velocity mantle wedge exists above the western half of the flat slab, which indicates the lack of melting and thus explains the cessation of the volcanism above. The velocity turns to normal values before the slab steepens again, indicating possible resumption of dehydration and ecologitization.

(3) Some unusual signals

Strong higher-mode Rayleigh waves due to the basin structure are observed in the periods less than 5 s. The particle motions provide a good test for distinguishing between the fundamental and higher mode. The precursor and coda waves relative to the interstation Rayleigh waves are observed, and modeled with a strong scatterer located in the active volcanic area in Southern Peru. In contrast with the usual receiver function analysis, multiples are extensively involved in this thesis. In the LA Basin, a good image is only from PpPs multiples, while in Peru, PpPp multiples contribute significantly to the final results.

Normal structures and automorphism groups of t-designs

Combinatorial configurations known as t-designs are studied. These are pairs ˂B, ∏˃, where each element of B is a k-subset of ∏, and each t-design occurs in exactly λ elements of B, for some fixed integers k and λ. A theory of internal structure of t-designs is developed, and it is shown that any t-design can be decomposed in a natural fashion into a sequence of “simple” subdesigns. The theory is quite similar to the analysis of a group with respect to its normal subgroups, quotient groups, and homomorphisms. The analogous concepts of normal subdesigns, quotient designs, and design homomorphisms are all defined and used.

This structure theory is then applied to the class of t-designs whose automorphism groups are transitive on sets of t points. It is shown that if G is a permutation group transitive on sets of t letters and ф is any set of letters, then images of ф under G form a t-design whose parameters may be calculated from the group G. Such groups are discussed, especially for the case t = 2, and the normal structure of such designs is considered. Theorem 2.2.12 gives necessary and sufficient conditions for a t-design to be simple, purely in terms of the automorphism group of the design. Some constructions are given.

Finally, 2-designs with k = 3 and λ = 2 are considered in detail. These designs are first considered in general, with examples illustrating some of the configurations which can arise. Then an attempt is made to classify all such designs with an automorphism group transitive on pairs of points. Many cases are eliminated of reduced to combinations of Steiner triple systems. In the remaining cases, the simple designs are determined to consist of one infinite class and one exceptional case.

A nonlinear systems model for the control mechanism of free fatty acid-glucose metabolosm in normal humans

A mathematical model is proposed in this thesis for the control mechanism of free fatty acid-glucose metabolism in healthy individuals under resting conditions. The objective is to explain in a consistent manner some clinical laboratory observations such as glucose, insulin and free fatty acid responses to intravenous injection of glucose, insulin, etc. Responses up to only about two hours from the beginning of infusion are considered. The model is an extension of the one for glucose homeostasis proposed by Charette, Kadish and Sridhar (Modeling and Control Aspects of Glucose Homeostasis. Mathematical Biosciences, 1969). It is based upon a systems approach and agrees with the current theories of glucose and free fatty acid metabolism. The description is in terms of ordinary differential equations. Validation of the model is based on clinical laboratory data available at the present time. Finally procedures are suggested for systematically identifying the parameters associated with the free fatty acid portion of the model.

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.

I. Studies on the activation of Drosophila phenol oxidase. II. Studies on serum insulin in normal subjects and diabetics

Part I

Phenol oxidase is the enzyme responsible for hardening and pigmentation of the insect cuticle. In Drosophila, phenol oxidase is a latent enzyme. Enzyme activity is produced by the interaction of a number of protein components. A minimal activation scheme consisting of six protein components, designated Pre S, S activator, S, P. P' and Ʌ₁ is described. Quantitative assays have been developed for the S activator, S, P and P' proteins and these components have been partially purified. Experiments describing the interactions of the six components have been conducted and a model for the activation of phenol oxidase in a minimal system is proposed. Possible mechanisms of the reactions between the constituents of the activating system and potential regulatory mechanisms involved in phenol oxidase production and function are discussed.

Part II

A method has been developed for the partial purification of insulin from human serum. A procedure for the determination of the electrophoretic mobility of serum insulin on polyacrylamide gels is described. An electrophoretic analysis of insulin isolated from a normal subject is reported and in addition to a major band, the existence of a number of minor bands of immunoreactive insulin is described. A comparison of the electrophoretic patterns of insulin isolated from normal and diabetic subjects was carried out and indications that differences between them may occur are reported.

Finite-Element Simulations of Earthquakes

This thesis discusses simulations of earthquake ground motions using prescribed ruptures and dynamic failure. Introducing sliding degrees of freedom led to an innovative technique for numerical modeling of earthquake sources. This technique allows efficient implementation of both prescribed ruptures and dynamic failure on an arbitrarily oriented fault surface. Off the fault surface the solution of the three-dimensional, dynamic elasticity equation uses well known finite-element techniques. We employ parallel processing to efficiently compute the ground motions in domains containing millions of degrees of freedom.

Using prescribed ruptures we study the sensitivity of long-period near-source ground motions to five earthquake source parameters for hypothetical events on a strike-slip fault (M_w 7.0 to 7.1) and a thrust fault (M_w 6.6 to 7.0). The directivity of the ruptures creates large displacement and velocity pulses in the ground motions in the forward direction. We found a good match between the severity of the shaking and the shape of the near-source factor from the 1997 Uniform Building Code for strike-slip faults and thrust faults with surface rupture. However, for blind thrust faults the peak displacement and velocities occur up-dip from the region with the peak near-source factor. We assert that a simple modification to the formulation of the near-source factor improves the match between the severity of the ground motion and the shape of the near-source factor.

For simulations with dynamic failure on a strike-slip fault or a thrust fault, we examine what constraints must be imposed on the coefficient of friction to produce realistic ruptures under the application of reasonable shear and normal stress distributions with depth. We found that variation of the coefficient of friction with the shear modulus and the depth produces realistic rupture behavior in both homogeneous and layered half-spaces. Furthermore, we observed a dependence of the rupture speed on the direction of propagation and fluctuations in the rupture speed and slip rate as the rupture encountered changes in the stress field. Including such behavior in prescribed ruptures would yield more realistic ground motions.

Estudos de metais pesados e isótopos de Pb nos sedimentos da Baía de Sepetiba baseados em geoquímica e na distribuição pelas possíveis áreas fontes

A Baia de Sepetiba é uma laguna costeira separada do oceano por uma ilha barreira. Localiza-se a 60 km da cidade do Rio de Janeiro, em uma importante região geoeconômica do Brasil. O objetivo deste trabalho foi avaliar a distribuição espacial da contaminação dos metais Cu, Pb, V, Cr, Cd, Co, Ni e Zn nos sedimentos da Baia. O mapa das concentrações elaborado pelo método de lixiviação permitiu caracterizar anomalias ao entorno da foz do Rio Guandu, na área da Coroa Grande, do Porto de Itaguaí, da Ilha do Martins, e anomalias ao longo de faixa com direção NW-SE. Os resultados das concentrações totais indicam contaminação por Zn, Cd, próximo a Ilha da Madeira com Pb e Cr associados e Cu e Zn na Restinga de Marambaia, com Ni, Pb e Cr associados. Os resultados dos isótopos de Pb para as razões de 206Pb/207Pb entre 1,23 e 1,27 representam os resíduos industriais e ocorrem em duas áreas: na parte leste da Restinga e entre as Ilhas de Jaguanum e Itacuruçá. A leste/sudeste destas ilhas foi reportada uma razão ainda mais alta (1.30), ainda não identificável na literatura. As correntes marinhas desempenham a redistribuição dos sedimentos e metais associados na Baia, com transporte de oeste para leste da pluma sedimentar descarregada pelos rios. Os principais causadores da poluição da Baia de Sepetiba são uma pilha de rejeito de Zn abandonada, resíduos industriais e domésticos não tratados de forma eficaz, poluentes atmosféricos de siderúrgicas e veículos, e por ventura resíduos de atividades navais e militares.

Split-aperture laser pulse compressor design tolerant to alignment and line-density differences

We introduce a four-pass laser pulse compressor design based on two grating apertures with two gratings per aperture that is tolerant to some alignment errors and, importantly, to grating-to-grating period variations. Each half-beam samples each grating in a diamond-shaped compressor that is symmetric about a central bisecting plane. For any given grating, the two half-beams impinge on opposite sides of its surface normal. It is shown that the two split beams have no pointing difference from paired gratings with different periods. Furthermore, no phase shift between half-beams is incurred as long as the planes containing a grating line and the surface normal for each grating of the pair are parallel. For grating pairs satisfying this condition, gratings surfaces need not be on the same plane, as changes in the gap between the two can compensate to bring the beams back in phase. © 2008 Optical Society of America.

Efeitos da suplementação oral com L-arginina e L-glutamina sobre a próstata ventral de ratos submetidos à irradiação

O objetivo deste trabalho foi verificar o possível efeito protetor da L-glutamina e da L-arginina sobre a próstata ventral de ratos quando administradas por gavagem. Procurou-se simular as condições clinicas de pacientes submetidos à radioterapia pélvica tendo como órgão alvo outro órgão pélvico que não a próstata. Foram analisados os efeitos desta irradiação sobre a próstata considerando este órgão como normal. Foram utilizados ratos Wistar divididos em quatro grupos: Controle, animais não submetidos à irradiação (n= 10); Irradiado, submetidos à irradiação abdominal e sem suplementação adicional de aminoácido por 21 dias (n= 10); Irradiado + Lglutamina, submetidos à irradiação abdominal e com suplementação adicional de L- glutamina por 21 dias (n= 10); e Irradiado + L-arginina, submetidos à irradiação abdominal e com suplementação adicional de L- arginina por 21 dias (n= 9). Os grupos foram mantidos em condições padrão de laboratório durante todas as etapas do experimento. Os animais submetidos à irradiação abdominal receberam uma dose única de 1000 cGy no dia 8 da experimentação. A Lglutamina e a L-arginina foram dissolvidas em água destilada e administrada por gavagem através da agulha IC-810. As próstatas foram removidas e processadas para inclusão em parafina. Foram estudados os seguintes parâmetros: estrutura acinar (área dos ácinos e altura do epitélio) e colágeno analisados por métodos morfométricos e peso corporal. O ganho de peso nos grupos suplementados foi significativamente maior se comparado ao grupo irradiado. Houve redução da altura do epitélio no grupo irradiado quando comparado ao controle. A altura do epitélio no grupo suplementado com L-arginina foi significativamente maior do que nos grupos irradiado e suplementado com L-glutamina. Houve diminuição, de aproximadamente 18%, da área dos ácinos no grupo suplementado com L-glutamina. Já no grupo suplementado com Larginina o valor foi similar ao do controle. O efeito da L-glutamina sobre o parênquima prostático foi o de manter proporcionalmente o colágeno, preservando a integridade da matriz extracelular. No grupo suplementado com L-arginina, apesar da discreta redução na distribuição proporcional de colágeno este também manteve índices semelhantes ao do controle. A radiação abdominal promoveu algumas modificações estruturais na próstata ventral de ratos. Essas modificações podem ser parcialmente prevenidas pela suplementação oral com L-glutamina e de L-arginina.

A influência do tratamento periodontal não cirúrgico sobre o perfil lipídico e células sangüíneas de pacientes portadores de periodontite crônica generalizada

O objetivo deste estudo foi verificar se o tratamento periodontal não cirúrgico exercia alguma influência sobre o perfil lipídico, os elementos celulares das séries banca e vermelha do sangue, plaquetas e VHS de pacientes portadores de periodontite crônica generalizada. Dezoito pacientes, com média de idade de 50,6 anos ( 7,6), foram submetidos, previamente ao tratamento periodontal e 30 dias após o mesmo, à coleta de 10ml de sangue periférico, através do qual foram analisados o perfil lipídico, os elementos celulares das séries branca e vermelha, o número de plaquetas e VHS. Destes 18 pacientes, 7, com média de idade de 47,4 anos ( 5,9) também foram reavaliados 90 dias após o término do tratamento. Os parâmetros clínicos utilizados, previamente ao tratamento e nas reavaliações, foram o Índice de Placa (IP), de Silness e Löe (1964), o Índice Gengival (IG), de Löe (1967), Sangramento na Sondagem (SS), Profundidade de Bolsa à Sondagem (PBS) e Nível de Inserção (NI). Foram ainda registrados e classificados os sítios com envolvimento de furca. O tratamento periodontal consistiu de terapia básica não cirúrgica. Após 30 dias do término do tratamento periodontal todos os pacientes foram reavaliados sendo verificada melhora significativa (P<0,05) dos valores de IP, IG, SS e PBS e de NI ≥ 6mm (P=0,05). Sítios com envolvimento de furca classes II e III apresentaram também diminuição significativa (P=0,01). Os 7 pacientes submetidos às reavaliações de 30 e 90 dias pós-tratamento também mostraram melhora significativa (P<0,05) dos valores de IP, IG, SS e PBS entre estas fases. Já o NI entre 4-5mm aumentou de forma significativa (P=0,04) entre o pré-tratamento e 90 dias após o mesmo, enquanto que o NI ≥ 6mm diminui significativamente entre as reavaliações de 30 e 90 dias (P=0,01 e P=0,02, respectivamente). Quando comparados os valores de 30 com os de 90 dias resultados semelhantes aos supracitados foram observados, inclusive o aumento do NI entre 4-5mm (P=0,02). É verificado também entre estas fases um IG aumentado (P=0,07). Quanto aos valores hematológicos ocorreu uma diminuição significativa dos níveis de bastões (P=0,05) e de monócitos (P=0,03) após o tratamento periodontal (30 dias), enquanto que o colesterol total e o LDL apresentaram uma tendência ao aumento (P=0,09 para ambos). Já nos sete pacientes submetidos às duas reavaliações o colesterol total apresentou aumento significativo entre as fases pré-tratamento, 30 (P=0,04) e 90 dias (P=0,02) após terapia, assim como o LDL (P=0,04 e P=0,03, respectivamente). Quando comparados os valores plaquetários entre as fases 30 e 90 dias pós-tratamento, verifica-se uma tendência a sua diminuição (P=0,09). O Índice de Castelli II (relação colesterol/HDL) apresenta entre as fases pré e 30 dias pós-tratamento tendência a aumento (P=0,09). Através desses resultados é possível concluir que o tratamento periodontal exerceu influência sobre bastões e monócitos do sangue, caracterizada pela diminuição dessas células, e sobre o colesterol total e o LDL, representada pelo aumento de seus valores.