Measurement of the Polarization of the Cosmic Microwave Background with the BICEP2 and Keck Array Telescopes

Precision polarimetry of the cosmic microwave background (CMB) has become a mainstay of observational cosmology. The ΛCDM model predicts a polarization of the CMB at the level of a few μK, with a characteristic E-mode pattern. On small angular scales, a B-mode pattern arises from the gravitational lensing of E-mode power by the large scale structure of the universe. Inflationary gravitational waves (IGW) may be a source of B-mode power on large angular scales, and their relative contribution to primordial fluctuations is parameterized by a tensor-to-scalar ratio r. BICEP2 and Keck Array are a pair of CMB polarimeters at the South Pole designed and built for optimal sensitivity to the primordial B-mode peak around multipole l ~ 100. The BICEP2/Keck Array program intends to achieve a sensitivity to r ≥ 0.02. Auxiliary science goals include the study of gravitational lensing of E-mode into B-mode signal at medium angular scales and a high precision survey of Galactic polarization. These goals require low noise and tight control of systematics. We describe the design and calibration of the instrument. We also describe the analysis of the first three years of science data. BICEP2 observes a significant B-mode signal at 150 GHz in excess of the level predicted by the lensed-ΛCDM model, and Keck Array confirms the excess signal at > 5σ. We combine the maps from the two experiments to produce 150 GHz Q and U maps which have a depth of 57 nK deg (3.4 μK arcmin) over an effective area of 400 deg² for an equivalent survey weight of 248000 μK². We also show preliminary Keck Array 95 GHz maps. A joint analysis with the Planck collaboration reveals that much of BICEP2/Keck Array's observed 150 GHz signal at low l is more likely a Galactic dust foreground than a measurement of r. Marginalizing over dust and r, lensing B-modes are detected at 7.0σ significance.

Estudo da influência do teor de segmentos hidrofílicos na síntese de poliuretanos dispersos em água

Considerações ambientais têm aumentado a pesquisa e o desenvolvimento de sistemas poliméricos aquosos para diversos tipos de aplicações, principalmente como revestimentos. Nesta dissertação, foram sintetizadas formulações não-poluentes à base de poliuretanos dispersos em água (PUDs), com 40% de teor de sólidos, na ausência de solventes orgânicos. Os monômeros empregados foram copolímeros em bloco à base de poli(glicol etilênico) e poli(glicol propilênico) (EG-b-PG), com teor de 25% de segmento hidrofílico EG, poli (glicol propilênico) (PPG), ácido dimetilolpropiônico (DMPA), diisocianato de isoforona (IPDI) e hidrazina (HYD), como extensor de cadeia. Foram variadas as razões entre o número de equivalente-grama de grupamentos isocianato e hidroxila (NCO/OH) e a proporção em equivalente-grama de PPG e dos copolímeros em bloco (EG-b-PG). Foi observado que a incorporação de altas quantidades de copolímero dificultou a síntese dos poliuretanos dispersos em água, levando à formação de géis. O tamanho médio de partícula e a viscosidade das dispersões foram determinados. Os filmes vazados a partir dessas dispersões foram avaliados quanto à capacidade de absorção de água, resistência mecânica, termogravimetria (TG), e caracterizados por espectroscopia na região do infravermelho (FTIR). As dispersões poliuretânicas produzidas se mostraram satisfatórias quando aplicadas como revestimento para madeira, metais e vidro

Eigenvalue problems associated with Korn's inequalities in the theory of elasticity

Interest in the possible applications of a priori inequalities in linear elasticity theory motivated the present investigation. Korn's inequality under various side conditions is considered, with emphasis on the Korn's constant. In the "second case" of Korn's inequality, a variational approach leads to an eigenvalue problem; it is shown that, for simply-connected two-dimensional regions, the problem of determining the spectrum of this eigenvalue problem is equivalent to finding the values of Poisson's ratio for which the displacement boundary-value problem of linear homogeneous isotropic elastostatics has a non-unique solution.

Previous work on the uniqueness and non-uniqueness issue for the latter problem is examined and the results applied to the spectrum of the Korn eigenvalue problem. In this way, further information on the Korn constant for general regions is obtained.

A generalization of the "main case" of Korn's inequality is introduced and the associated eigenvalue problem is a gain related to the displacement boundary-value problem of linear elastostatics in two dimensions.

Ratio of natural isotopes of nitrogen. I. Primary results: soils of Dombes [Translation from: Revue d'Ecologie et de Biologie du Sol 14, 279-287, 1977]

Utilization of the heavy isotope of nitrogen as a tracer has found numerous applications in soil biology. It allows better definition of different stages of the nitrogen cycle, in particular the immobilization-mineralization cycle. In this work, the authors report the results of calculations of natural isotope ratios of nitrogen in samples of water, soil and vegetation prevailing in Dombes and discuss the possibilities of errors and coefficients of fractionation.

Equivalent differential equations for nonlinear dynamical systems

A technique for obtaining approximate periodic solutions to nonlinear ordinary differential equations is investigated. The approach is based on defining an equivalent differential equation whose exact periodic solution is known. Emphasis is placed on the mathematical justification of the approach. The relationship between the differential equation error and the solution error is investigated, and, under certain conditions, bounds are obtained on the latter. The technique employed is to consider the equation governing the exact solution error as a two point boundary value problem. Among other things, the analysis indicates that if an exact periodic solution to the original system exists, it is always possible to bound the error by selecting an appropriate equivalent system.

Three equivalence criteria for minimizing the differential equation error are compared, namely, minimum mean square error, minimum mean absolute value error, and minimum maximum absolute value error. The problem is analyzed by way of example, and it is concluded that, on the average, the minimum mean square error is the most appropriate criterion to use.

A comparison is made between the use of linear and cubic auxiliary systems for obtaining approximate solutions. In the examples considered, the cubic system provides noticeable improvement over the linear system in describing periodic response.

A comparison of the present approach to some of the more classical techniques is included. It is shown that certain of the standard approaches where a solution form is assumed can yield erroneous qualitative results.

Effect of microcosmic optical parameters of dopants on the signal-to-noise ratio in doubly doped LiNbO3 crystals

We propose a united theory that describes the two-center recording system by taking scattering noise into account. The temporal evolution of the signal-to-noise ratio in doubly doped photorefractive crystals is described based on jointly solving material equations and coupled-wave equations with the fourth-order Runge-Kutta method. Roles of microcosmic optical parameters of dopants on the signal-to-noise ratio are discussed in detail. The theoretical results can confirm and predict experimental results. (c) 2005 Elsevier GmbH. All rights reserved.

Nature of the radical intermediates in a substituted cyclopropylcarbiny-allylcarbinyl system

We have sought to determine the nature of the free-radical precursors to ring-opened hydrocarbon 5 and ring-closed hydrocarbon 6. Reasonable alternative formulations involve the postulation of hydrogen abstraction (a) by a pair of rapidly equilibrating classical radicals (the ring-opened allylcarbinyl-type radical 3 and the ring-closed cyclopropylcarbinyl-type 4), or (b) by a nonclassical radical such as homoallylic radical 7.

[Figure not reproduced.]

Entry to the radical system is gained via degassed thermal decomposition of peresters having the ring-opened and the ring-closed structures. The ratio of 6:5 is essentially independent of the hydrogen donor concentration for decomposition of the former at 125° in the presence of triethyltin hydrdride. A deuterium labeling study showed that the α and β methylene groups in 3 (or the equivalent) are rapidly interchanged under these conditions.

Existence of two (or more) product-forming intermediates is indicated (a) by dependence of the ratio 6:5 on the tin hydride concentration for decomposition of the ring-closed perester at 10 and 35°, and (b) by formation of cage products having largely or wholly the structure (ring-opened or ring-closed) of the starting perester.

Relative rates of hydrogen abstraction by 3 could be inferred by comparison of ratios of rate constants for hydrogen abstraction and ortho-ring cyclization:

[Figure not reproduced.]

At 100° values of k_a/k_r are 0.14 for hydrogen abstraction from 1,4-cyclohexadiene and 7 for abstraction from triethyltin hydride. The ratio 6:5 at the same temperature is ~0.0035 for hydrogen abstraction from 1,4-cyclohexadiene, ~0.078 for abstraction from the tin hydride, and ≥ 5 for abstraction from cyclohexadienyl radicals. These data indicate that abstraction of hydrogen from triethyltin hydride is more rapid than from 1,4-cyclohexadiene by a factor of ~1000 for 4, but only ~50 for 3.

Measurements of product ratios at several temperatures allowed the construction of an approximate energy-level scheme. A major inference is that isomerization of 3 to 4 is exothermic by 8 ± 3 kcal/mole, in good agreement with expectations based on bond dissociation energies. Absolute rate-constant estimates are also given.

The results are nicely compatible with a classical-radical mechanism, but attempted interpretation in terms of a nonclassical radical precursor of product ratios formed even from equilibrated radical intermediates leads, it is argued, to serious difficulties.

The roles played by hydrogen abstraction from 1,4,-cyclohexadiene and from the derived cyclohexadienyl radicals were probed by fitting observed ratios of 6:5 and 5:10 in the sense of least-squares to expressions derived for a complex mechanistic scheme. Some 30 to 40 measurements on each product ratio, obtained under a variety of experimental conditions, could be fit with an average deviation of ~6%. Significant systematic deviations were found, but these could largely be redressed by assuming (a) that the rate constant for reaction of 4 with cyclohexadienyl radical is inversely proportional to the viscosity of the medium (i.e., is diffusion-controlled), and (b) that k_a/k_r for hydrogen abstraction from 1,4-cyclohexadiene depends slightly on the composition of the medium. An average deviation of 4.4% was thereby attained.

Degassed thermal decomposition of the ring-opened perester in the presence of the triethyltin hydride occurs primarily by attack on perester of triethyltin radicals, presumably at the –O-O- bond, even at 0.01 M tin hydride at 100 and 125°. Tin ester and tin ether are apparently formed in closely similar amounts under these conditions, but the tin ester predominates at room temperature in the companion air-induced decomposition, indicating that attack on perester to give the tin ether requires an activation energy approximately 5 kcal/mole in excess of that for the formation of tin ester.

Design of NRAs having higher aperture opening ratio and autocorrelation compression ratio by means of a global optimization method

When noises considerations are made, nonredundant arrays (NRAs) are endowed with many advantages which other arrays e.g., uniformly redundant arrays (URAs) do not possess in applications of coded aperture imaging. However, lower aperture opening ratio limits the applications of NRA in practice. In this paper, we present a computer searching method based on a global optimization algorithm named DIRECT to design NRAs. Compared with the existing NRAs e.g., Golay's NRAs, which are well known and widely used in various applications, NRAs found by our method have higher aperture opening ratio and auto correlation compression ratio. These advantages make our aperture arrays be very useful for practical applications especially for which of aperture size are limited. Here, we also present some aperture arrays we found. These aperture arrays have an interesting property that they belong to both NRA and URA. (C) 2006 Elsevier GmbH. All rights reserved.

Deep silicon grating as high-extinction-ratio polarizing beam splitter

A deep binary silicon grating as high-extinction-ratio reflective polarizing beam splitter (PBS) at the wavelength of 1550 nm is presented. The design is based on the phenomenon of total internal reflection (TIR) by using the rigorous coupled wave analysis (RCWA). The extinction ratio of the rectangular PBS grating can reach 2.5×105 with the optimum grating period of 397 nm and groove depth of 1.092 μm. The effciencies of TM-polarized wave in the 0th order and TE-polarized wave in the −1st order can both reach unity at the Littrow angle. Holographic recording technology and inductively coupled plasma (ICP) etching could be used to fabricate the silicon PBS grating.

Estudo termodinâmico da precipitação de parafinas em petróleos brasileiros

Um dos grandes desafios enfrentados pela indústria do petróleo é reduzir o impacto causado pela cristalização indesejável de hidrocarbonetos parafínicos de elevada massa molar em tubulações e equipamentos de produção. A cristalização de parafinas em petróleo é normalmente detectada através da determinação da temperatura inicial de aparecimento de cristais (TIAC), que pode ser estimada através de modelagem termodinâmica com base na composição do petróleo. Os objetivos deste trabalho são: estudar os principais modelos termodinâmicos adotados para descrever a precipitação de parafinas; verificar a validade desses modelos para os petróleos brasileiros e determinar qual modelo é o mais adequado para esses óleos. Para tanto, três formas de cálculo da razão entre as fugacidades das fases sólida e líquida e cinco modelos para calcular os coeficientes de atividade dos componentes em cada fase são aplicados aos dados de composição de vinte e três petróleos brasileiros. Os resultados mostram que o modelo ideal de múltiplas fases sólidas e o modelo de Escobar-Remolina geram valores bastante abaixo da TIAC experimental. Para os modelos de única fase sólida ideal, de Won e de Coutinho, foi possível observar que: a) a grande maioria dos erros é negativa; b) que estes se distribuem melhor em torno de zero quando se utiliza a correlação de Coutinho para o cálculo dos valores de i; c) os valores de erro médio para os modelos de Coutinho, de Won e ideal com única fase sólida se equivalem, qualquer que seja o modelo utilizado para o cálculo de i, exceto para o caso em que todos os compostos presentes na fase líquida podem precipitar; d) os valores obtidos através do modelo de Coutinho apresentam erro sistemático em relação ao modelo ideal de única fase sólida; e) as diferentes formas de se calcular a razão entre as fugacidades da fase sólida e líquida (i) influenciam fortemente a capacidade preditiva dos modelos, o que não era esperado; f) o perfil do primeiro cristal formado nos petróleos é influenciado pelas moléculas mais pesadas presentes nos resíduos, o que mostra a necessidade de se desenvolver metodologias precisas e robustas de caracterização de resíduos; g) a inclusão de uma estimativa para a composição dos resíduos efetivamente melhorou o desempenho dos modelos em petróleos médio; h) em petróleos pesados, houve um aumento do erro de previsão da TIAC devido à pouca ou nenhuma quantidade de parafinas nos resíduos desses óleos. A necessidade de uma melhor caracterização dos resíduos de petróleos é corroborada pelo fato da TIAC calculada pelos modelos ser, via de regra, mais baixa que a TIAC experimental e pela melhora no desempenho dos modelos quando se estimou a composição dos resíduos, em petróleos médios