On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.

Antioxidant activity of selected phenols and herbs used in diets for medical conditions.

The antioxidant capacity of some herbs used in dietology practice was determined by the DPPH free radical method, which was calibrated with ascorbic acid. Partially hydrophilic phenolic compounds are the most active compounds in plants, and therefore water was used as the extraction agent. Besides antioxidant capacity, the content of total phenolic compounds was also measured and a strong correlation between these two variables was found. The extracts of lemon balm (Melissa officinalis L.), peppermint (Mentha x piperita L.), oregano (Origanum vulgare L.), Greek oregano (Origanum heracleoticum L.), sage (Salvia officinalis L.) and winter savory (Satureja montana L.) showed very significant activity. It was comparable with the activity of green tea in the case of oregano and peppermint. Lower activity was observed in the case of rosemary (Rosmarinus officinalis L.), marjoram (Majorana hortensis), hyssop (Hyssopus officinalis L.), sweet basil (Ocimum basilicum), and lovage (Levisticum officinale Koch.). The inhibitory activity of the herb extracts was monitored also during the autooxidation of lard. Very high antioxidant capacity was observed mainly in sage samples, but also in marjoram and Greek oregano. The extracts of peppermint, oregano, rosemary, winter savory, lemon balm and hyssop showed middle activity comparable to that of alpha-tocopherol. The antioxidant capacity of sweet basil and lovage was insignificant.

A new frequency-uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L2(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star-combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second-kind integral operator for which convergence of the Galerkin method in L2(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star-combined operator implies frequency-explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high-frequency case. The proof of coercivity of the star-combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains.

O pão e a festa: patrimônio imaterial e turismo em Juiz de Fora

Esta pesquisa tem por objetivo analisar os pedidos de registro do Pão Alemão e da Deutsches Fest como bens culturais de natureza imaterial de Juiz de Fora, sendo elementos representantes da cultura e da tradição dos imigrantes alemães que fazem parte da história da cidade. A Festa Alemã ou Deutsches Fest é, atualmente, um dos maiores eventos do calendário cultural e turístico de Juiz de Fora, cidade localizada na Zona da Mata do Estado de Minas Gerais. Realizada no bairro Borboleta, antiga Colônia Alemã, a festa foi criada em 1969, por descendentes dos alemães que imigraram para o município, em meados do século XIX. O Pão Alemão, encontrado nas festas e casas do bairro, além de ser o principal elo de preservação da memória construída por esses descendentes alemães, tornou-se importante elemento simbólico, enquanto modo de preparo da legítima culinária alemã. Pão e Festa fazem parte de uma tradição constituída, ao longo de anos, para afirmar a identidade do grupo, proporcionando-lhe ampliar sua participação nos âmbitos políticos e econômicos locais.

Síntese, caracterização e estudo da regeneração do silicoaluminofosfato-11 (SAPO-11)

heterogeneous catalyst such as a silicoaluminophosphate, molecular sieve with AEL (Aluminophosphate eleven) structure such as SAPO-11, was synthesized through the hydrothermal method starting from silica, pseudoboehmite, orthophosphoric acid (85%) and water, in the presence of a di-isopropylamine organic template. For the preparation of SAPO-11 in a dry basis it was used as reactants: DIPA; H3PO4; SiO4; Pseudoboehmite and distilled water. The crystallization process occurred when the reactive hydrogel was charged into a vessel and autoclaved at 200ºC for a period of 72 hours under autogeneous pressure. The obtained material was washed, dried and calcined to remove the molecular sieves of DIPA. The samples were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), infrared spectroscopy (FT-IR), nitrogen adsorption (BET) and thermal analysis (TG/DTG). The acidic properties were determined using adsorption of nbutylamine followed by programmed thermodessorption. This method revealed that SAPO-11 shows an acidity that ranges from weak to moderate. However, a small quantity of strong acid sites could be detected there. The deactivation of the catalysts was conducted by artificial coking followed by the cracking of the n-hexane in a fixed bed with a continuous flow micro-reactor coupled on line to a gas chromatograph. The main products obtained were: ethane, propane, isobutene, n-butane, n-pentane and isopentane. The Vyazovkin (model-free) kinetics method was used to determine the regeneration and removal of the coke

Estudos comparativos do ciclo de regeneração de diferentes tipos de silicoaluminofosfatos

Different types of heterogeneous catalysts of the silicoaluminophosphate type, (SAPO-5, SAPO-11, SAPO-31, SAPO-34 and SAPO-41), molecular sieves with a: AFI, AEL, ATO, CHA and AFO structure, respectively, were synthesized through the hydrothermal method. Using sources such as hydrated alumina (pseudobohemita), phosphoric acid, silica gel, water, as well as, different types of organic structural templates, such as: cetyltrimethylammonium bromide (CTMABr), di-isopropylamine (DIPA), di-n- propylamine (DNPA) and tetraethylammonium hydroxide (TEOS), for the respective samples. During the preparation of the silicoaluminophosphates, the crystallization process of the samples occurred at a temperature of approximately 200 ° C, ranging through periods of 18-72 h, when it was possible to obtain pure phases for the SAPOs. The materials were furthermore washed with deionized water, dried and calcined to remove the molecules of the templates. Subsequently the samples were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), absorption spectroscopy in the infrared region (FT-IR), specific surface area and thermal analysis via TG/DTG. The acidic properties were determined using adsorption of n-butylamine followed by programmed termodessorption. These methods revealed that the SAPO samples showed a typically weak to moderate acidity. However, a small amount of strong acid sites was also detected. The deactivation of the catalysts was conducted by artificially coking the samples, followed by n-hexane cracking reactions in a fixed bed with a continuous flow micro-reactor coupled on line to a gas chromatograph. The main products obtained were: ethane, propane, isobutene, n-butane, n-pentane and isopentane. The Vyazovkin (model-free) kinetics method was used to determine the catalysts regeneration and removal of the coke

The effects of inter-crop cultivation Between rows of citrus crop on spreading of Guignardia citricarpa Ascospores and in the citrus black spot occurrence

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Análise de onda completa de superfície seletiva em freqüência do tipo anteparo duplo

This work presents a theoretical analysis and numerical and experimental results of the scattering characteristics of frequency selective surfaces, using elements of type patch perfectly conductor. The structures are composed of two frequency selective surfaces on isotropic dielectric substrates cascaded, separated by a layer of air. The analysis is performed using the method of equivalent transmission line in combination with the Galerkin method, to determine the transmission and reflection characteristics of the structures analyzed. Specifically, the analysis uses the impedance method, which models the structure by an equivalent circuit, and applies the theory of transmission lines to determine the dyadic Green's function for the cascade structure. This function relates the incident field and surface current densities. These fields are determined algebraically by means of potential incidents and the imposition of the continuity of the fields in the dielectric interfaces. The Galerkin method is applied to the numerical determination of the unknown weight coefficients and hence the unknown densities of surface currents, which are expanded in terms of known basis functions multiplied by these weight coefficients. From the determination of these functions, it becomes possible to obtain numerical scattered fields at the top and bottom of the structures and characteristics of transmission and reflection of these structures. At work, we present numerical and experimental results for the characteristics of transmission and reflection. Comparisons were made with other results presented in literature, and it was observed a good agreement in the cases presented suggestions continuity of the work are presented

Análise espectral de reflectarrays com substratos de duas camadas dielétricas anisotrópicas uniaxiais

Recently, an amazing development has been observed in telecommunication systems. Two good examples of this development are observed in mobile communication and aerospace systems. This impressive development is related to the increasing need for receiving and transmitting communication signals. Particularly, this development has required the study of new antennas and filters. This work presents a fullwave analysis of reflectarrays. The considered structures are composed by arrays of rectangular conducting patches printed on multilayer dieletric substrates, that are mounted on a ground plane. The analysis is developed in the spectral domain, using an equivalent transmission line method in combination with Galerkin method. Results for the reflection coefficient of these structures are presented and compared to those available in the literature. A good agreement was observed. Particularly, the developed analysis uses the transmission lines theory in combination with the incident potentials and the field continuity equations, at the structures interfaces, for obtaining the scattered field components expressions as function of the patch surface currents and of the incident field. Galerkin method is used to determine the unknown coefficients in the boundary value problem. Curves for the reflection coefficient of several reflectarray geometries are presented as function of frequency and of the structural parameters

Análise de antenas de microfita com patches circulares sobre substratos anisotrópicos usando o método dos potenciais de Hertz

This work consists on the theoretical and numerical analysis of some properties of circular microstrip patch antennas on isotropic and uniaxial anisotropic substrates. For this purpose, a full wave analysis is performed, using Hertz Vector Potentials method in the Hankel Transform domain. In the numerical analysis, the moment method is also used in order to determine some characteristics of the antenna, such as: resonant frequency and radiation pattern. The definition of Hertz potentials in the Hankel domain is used in association with Maxwell´s equations and the boundary conditions of the structures to obtain the Green´s functions, relating the components of the current density on the patch and the tangential electric field components. Then, the Galerkin method is used to generate a matrix equation whose nontrivial solution is the complex resonant frequency of the structure. In the analysis, a microstrip antenna with only one isotropic dielectric layer is initially considered. For this structure, the effect of using superconductor patches is also analyzed. An analysis of a circular microstrip antenna on an uniaxial anisotropic dielectric layer is performed, using the Hertz vector potentials oriented along the optical axis of the material, that is perpendicular to the microstrip ground plane. Afterwards, the circular microstrip antenna using two uniaxial anisotropic dielectric layers is investigated, considering the particular case in which the inferior layer is filled by air. In this study, numerical results for resonant frequency and radiation pattern for circular microstrip antennas on isotropic and uniaxial anisotropic substrates are presented and compared with measured and calculated results found in the literature

Análise espectral de reflectarrays com substrato de duas camadas dielétricas anisotrópicas uniaxiais

Recently, an amazing development has been observed in telecommunication systems. Two good examples of this development are observed in mobile communication and aerospace systems. This impressive development is related to the increasing need for receiving and transmitting communication signals. Particularly, this development has required the study of new antennas and filters. This work presents a fullwave analysis of reflectarrays. The considered structures are composed by arrays of rectangular conducting patches printed on multilayer dieletric substrates, that are mounted on a ground plane. The analysis is developed in the spectral domain, using an equivalent transmission line method in combination with Galerkin method. Results for the reflection coefficient of these structures are presented and compared to those available in the literature. A good agreement was observed. Particularly, the developed analysis uses the transmission lines theory in combination with the incident potentials and the field continuity equations, at the structures interfaces, for obtaining the scattered field components expressions as function of the patch surface currents and of the incident field. Galerkin method is used to determine the unknown coefficients in the boundary value problem. Curves for the reflection coefficient of several reflectarray geometries are presented as function of frequency and of the structural parameters

Estudo da regeneração de aditivos para catalisadores de craqueamento aluminofosfatos (ALPO s)e silicoaluminofosfatos (SAPO s)

Heterogeneous catalysts such as aluminophosphate and silicoaluminophosphate, molecular sieves with AEL of ALPO-11 and SAPO-11, were synthesized by the hydrothermal method with the following molar composition: 2.9 Al +3.2 P + 3.5 DIPA +32.5 H20 (ALPO-11); 2.9 Al +3.2 P + 0.5 Si + 3.5 DIPA +32.5 H20 (SAPO-11) starting from silica (only in the SAPO-11), pseudoboehmite, orthophosphoric acid (85%) and water, in the presence of a di-isopropylamine organic template. The crystallization process occurred when the reactive hydrogel was charged into a vessel and autoclaved at 170ºC for a period of 48 hours under autogeneous pressure. The obtained materials were washed, dried and calcined to remove the molecular sieves of DIPA. The samples were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), infrared spectroscopy (FT-IR), thermo gravimetric differential thermal analysis (TG/DTA) and nitrogen adsorption (BET). The acidic properties were determined using adsorption of n-butylamine followed by programmed thermodessorption. This method revealed that ALPO-11 has weaker acid sites due to structural defects, while SAPO-11 shows an acidity that ranges from weak to moderate. However, a small quantity of strong acid sites could be detected there. The deactivation of the catalysts was conducted by the cracking of the n-hexane in a fixed bed continuous flow microrreator coupled on line to a gas chromatograph. The main products obtained were: ethane, propane, isobutene, n-butane, n-pentane and isopentane. The Vyazovkin (model-free) kinetics method was used to determine the regeneration and removal of the organic template

Genetic parameters of racing performance traits of Quarter horses in Brazil

The data used in the present study were recorded at the Jockey Club of Sorocaba for 5094 racing performance of 1350 Quarter Horses at the Paulista Race Track of Sorocaba, state of São Paulo, Brazil, from 1991 to 1997. The considered traits were time and final rank. The model used in analysis included random animal and permanent environmental effects, and race, sex, age and origin as fixed effects. The variance and covariance components were estimated by the restricted maximum likelihood for an animal model, using the derivative-free process method and the MTDFREML software. For the time, heritability was 0.17 (0.05), while estimate of repeatability 0.55 (0.05). The lower heritability for the final rank, 0.13 (0.04), indicate that this trait is not the most appropriate one for inclusion in programs of Quarter horse selection in Sorocaba racetrack. The repeatability estimate for rank was 0.44 (0.04) and the genetic correlation between this trait and time was 0.99.

Potencial antioxidante de extratos de sementes de limão (Citrus limon)

The present study aimed at evaluating the behavior of the soybean oil with the addition of lemon seed extracts (Citrus limon), in different concentrations, through oxidative stability and also at measuring the antioxidant activity using the DPPH free radical method and total phenolic compounds. The concentration of 2,400 mg.kg(-1) for the lemon seed extract, galego variety, was the one that provided the soybean oil with the best oxidative stability. The maximum antioxidant activities and the concentration values of the natural extract sufficient to obtain 50% of maximum effect, estimated at 100% (EC(50)), determined by DPPH for the extract and gallic acid were 70.58%, 69.94 mu g.mL(-1) and 75.07%, 64.73 mu g.mL(-1), respectively. The concentration of total phenolic compounds, determined by the Folin-Ciocalteu method, was of 76 mg.g(-1). Thus, it can be said that the lemon seed extract, galego, presents natural antioxidant action demonstrating potential to be used in foods.

Low-frequency high-temperature internal friction in Ti-13Nb-13Zr alloy

Recent studies have been done to achieve biomedical alloys containing non-toxic elements and presenting low elastic moduli. It has been reported that Ti-Nb-Zr alloys rich in beta phase, especially Ti-13Nb-13Zr, have potential characteristics for substituting conventional materials such as Ti-6Al-4V, stainless steel and Co alloys. The aim of this work is to study the internal friction (IF) of Ti-13Nb-13Zr (TNZ) alloy due to the importance of the absorption impacts in orthopedic applications. The internal friction of this alloy produced by arc melting was measured using an inverted torsion pendulum with the free decay method. The measurements were performed from 77 to 700 K with heating rate of 1 K/min, in a vacuum better than 10-5 mBar. The results show a relaxation structure at high temperature strongly dependent on microstructure of the material. Qualitative discussions are presented for the experimental results, and the possibility of using the TNZ as a high damping material is briefly mentioned.