A priori error analysis of space–time Trefftz discontinuous Galerkin methods for wave problems

We present and analyse a space–time discontinuous Galerkin method for wave propagation problems. The special feature of the scheme is that it is a Trefftz method, namely that trial and test functions are solution of the partial differential equation to be discretised in each element of the (space–time) mesh. The method considered is a modification of the discontinuous Galerkin schemes of Kretzschmar et al. (2014) and of Monk & Richter (2005). For Maxwell’s equations in one space dimension, we prove stability of the method, quasi-optimality, best approximation estimates for polynomial Trefftz spaces and (fully explicit) error bounds with high order in the meshwidth and in the polynomial degree. The analysis framework also applies to scalar wave problems and Maxwell’s equations in higher space dimensions. Some numerical experiments demonstrate the theoretical results proved and the faster convergence compared to the non-Trefftz version of the scheme.

Resonant Wave Interactions in the Presence of a Diurnally Varying Heat Source

Resonant interactions among equatorial waves in the presence of a diurnally varying heat source are studied in the context of the diabatic version of the equatorial beta-plane primitive equations for a motionless, hydrostatic, horizontally homogeneous and stably stratified background atmosphere. The heat source is assumed to be periodic in time and of small amplitude [i.e., O(epsilon)] and is prescribed to roughly represent the typical heating associated with deep convection in the tropical atmosphere. In this context, using the asymptotic method of multiple time scales, the free linear Rossby, Kelvin, mixed Rossby-gravity, and inertio-gravity waves, as well as their vertical structures, are obtained as leading-order solutions. These waves are shown to interact resonantly in a triad configuration at the O(e) approximation, and the dynamics of these interactions have been studied in the presence of the forcing. It is shown that for the planetary-scale wave resonant triads composed of two first baroclinic equatorially trapped waves and one barotropic Rossby mode, the spectrum of the thermal forcing is such that only one of the triad components is resonant with the heat source. As a result, to illustrate the role of the diurnal forcing in these interactions in a simplified fashion, two kinds of triads have been analyzed. The first one refers to triads composed of a k = 0 first baroclinic geostrophic mode, which is resonant with the stationary component of the diurnal heat source, and two dispersive modes, namely, a mixed Rossby-gravity wave and a barotropic Rossby mode. The other class corresponds to triads composed of two first baroclinic inertio-gravity waves in which the highest-frequency wave resonates with a transient harmonic of the forcing. The integration of the asymptotic reduced equations for these selected resonant triads shows that the stationary component of the diurnal heat source acts as an ""accelerator"" for the energy exchanges between the two dispersive waves through the excitation of the catalyst geostrophic mode. On the other hand, since in the second class of triads the mode that resonates with the forcing is the most energetically active member because of the energy constraints imposed by the triad dynamics, the results show that the convective forcing in this case is responsible for a longer time scale modulation in the resonant interactions, generating a period doubling in the energy exchanges. The results suggest that the diurnal variation of tropical convection might play an important role in generating low-frequency fluctuations in the atmospheric circulation through resonant nonlinear interactions.

Resonant Wave Interactions in the Equatorial Waveguide

Weakly nonlinear interactions among equatorial waves have been explored in this paper using the adiabatic version of the equatorial beta-plane primitive equations in isobaric coordinates. Assuming rigid lid vertical boundary conditions, the conditions imposed at the surface and at the top of the troposphere were expanded in a Taylor series around two isobaric surfaces in an approach similar to that used in the theory of surface-gravity waves in deep water and capillary-gravity waves. By adopting the asymptotic method of multiple time scales, the equatorial Rossby, mixed Rossby-gravity, inertio-gravity, and Kelvin waves, as well as their vertical structures, were obtained as leading-order solutions. These waves were shown to interact resonantly in a triad configuration at the O(epsilon) approximation. The resonant triads whose wave components satisfy a resonance condition for their vertical structures were found to have the most significant interactions, although this condition is not excluding, unlike the resonant conditions for the zonal wavenumbers and meridional modes. Thus, the analysis has focused on such resonant triads. In general, it was found that for these resonant triads satisfying the resonance condition in the vertical direction, the wave with the highest absolute frequency always acts as an energy source (or sink) for the remaining triad components, as usually occurs in several other physical problems in fluid dynamics. In addition, the zonally symmetric geostrophic modes act as catalyst modes for the energy exchanges between two dispersive waves in a resonant triad. The integration of the reduced asymptotic equations for a single resonant triad shows that, for the initial mode amplitudes characterizing realistic magnitudes of atmospheric flow perturbations, the modes in general exchange energy on low-frequency (intraseasonal and/or even longer) time scales, with the interaction period being dependent upon the initial mode amplitudes. Potential future applications of the present theory to the real atmosphere with the inclusion of diabatic forcing, dissipation, and a more realistic background state are also discussed.

Coda wave attenuation in the Parecis Basin, Amazon Craton, Brazil: sensitivity to basement depth

Small local earthquakes from two aftershock sequences in Porto dos GaA(0)chos, Amazon craton-Brazil, were used to estimate the coda wave attenuation in the frequency band of 1 to 24 Hz. The time-domain coda-decay method of a single backscattering model is employed to estimate frequency dependence of the quality factor (Q (c)) of coda waves modeled usingwhere Q (0) is the coda quality factor at frequency of 1 Hz and eta is the frequency parameter. We also used the independent frequency model approach (Morozov, Geophys J Int, 175:239-252, 2008), based in the temporal attenuation coefficient, chi(f) instead of Q(f), given by the equation for the calculation of the geometrical attenuation (gamma) and effective attenuation Q (c) values have been computed at central frequencies (and band) of 1.5 (1-2), 3.0 (2-4), 6.0 (4-8), 9.0 (6-12), 12 (8-16), and 18 (12-24) Hz for five different datasets selected according to the geotectonic environment as well as the ability to sample shallow or deeper structures, particularly the sediments of the Parecis basin and the crystalline basement of the Amazon craton. For the Parecis basin for the surrounding shield and for the whole region of Porto dos GaA(0)chos Using the independent frequency model, we found: for the cratonic zone, gamma = 0.014 s (-aEuro parts per thousand 1), nu a parts per thousand 1.12; for the basin zone with sediments of similar to 500 m, gamma = 0.031 s (-aEuro parts per thousand 1), nu a parts per thousand 1.27; and for the Parecis basin with sediments of similar to 1,000 m, gamma = 0.047 s (-aEuro parts per thousand 1), nu a parts per thousand 1.42. Analysis of the attenuation factor (Q (c)) for different values of the geometrical spreading parameter (nu) indicated that an increase of nu generally causes an increase in Q (c), both in the basin as well as in the craton. But the differences in the attenuation between different geological environments are maintained for different models of geometrical spreading. It was shown that the energy of coda waves is attenuated more strongly in the sediments, (in the deepest part of the basin), than in the basement, (in the craton). Thus, the coda wave analysis can contribute to studies of geological structures in the upper crust, as the average coda quality factor is dependent on the thickness of sedimentary layer.

Partial spectral projected gradient method with active-set strategy for linearly constrained optimization

A method for linearly constrained optimization which modifies and generalizes recent box-constraint optimization algorithms is introduced. The new algorithm is based on a relaxed form of Spectral Projected Gradient iterations. Intercalated with these projected steps, internal iterations restricted to faces of the polytope are performed, which enhance the efficiency of the algorithm. Convergence proofs are given and numerical experiments are included and commented. Software supporting this paper is available through the Tango Project web page: http://www.ime.usp.br/similar to egbirgin/tango/.

Thermal wave scattering by two overlapping and parallel cylinders

In this paper an analytical solution of the temperature of an opaque material containing two overlapping and parallel subsurface cylinders, illuminated by a modulated light beam, is presented. The method is based on the expansion of plane and cylindrical thermal waves in series of Bessel and Hankel functions. This model is addressed to the study of heat propagation in composite materials with interconnection between inclusions, as is the case of inverse opals and fiber reinforced composites. Measurements on calibrated samples using lock-in infrared thermography confirm the validity of the model.

Ab initio calculation of the BCC Fe-Al-Mo (Iron-Aluminum-Molybdenum) phase diagram: Implications for the nature of the tau(2) phase

The metastable phase diagram of the BCC-based ordering equilibria in the Fe-Al-Mo system has been calculated via a truncated cluster expansion, through the combination of Full-Potential-Linear augmented Plane Wave (FP-LAPW) electronic structure calculations and of Cluster Variation Method (CVM) thermodynamic calculations in the irregular tetrahedron approximation. Four isothermal sections at 1750 K, 2000 K, 2250 K and 2500 K are calculated and correlated with recently published experimental data on the system. The results confirm that the critical temperature for the order-disorder equilibrium between Fe(3)Al-D0(3) and FeAl-B2 is increased by Mo additions, while the critical temperature for the FeAl-B2/A2 equilibrium is kept approximately invariant with increasing Mo contents. The stabilization of the Al-rich A2 phase in equilibrium with overstoichiometric B2-(Fe,Mo)Al is also consistent with the attribution of the A2 structure to the tau(2) phase, stable at high temperatures in overstoichiometric B2-FeAl. (C) 2009 Elsevier Ltd. All rights reserved.

The electronic and optical properties of sodalite (Na(8)Al(6)Si(6)O(24)Cl(2)) from first principles

This study reports the results of ab initio electronic and optical calculations for pure socialite crystal using the linear augmented plane wave (LAPW) method within density functional theory (DFT). The calculated electronic structure revealed predominantly orbital characters of the valence band and the conduction band, and enabled us to determine the type and the value of the fundamental gap of the compound. The imaginary part of the dielectric tensor, extinction coefficient and refraction index were calculated as functions of the incident radiation wavelength. It is shown that the O 2p states and Na 3s states play the major role in optical transitions as initial and final states, respectively. The absorption spectrum is localized in the ultraviolet range between 40 and 250 nm. Furthermore, we concluded that the material does not absorb radiation in the visible range. (C) 2009 Elsevier Ltd. All rights reserved.

Er : YAB nanoparticles and vitreous thin films by the polymeric precursor method

The synthesis of Y(0.9)Er(0.1)Al(3)(BO(3))(4) crystalline powders and vitreous thin films were studied. Precursor solutions were obtained using a modified polymeric precursor method using D-sorbitol as complexant agent. The chemical reactions were described. Y(0.)9Er(0.1)Al(3)(BO(3))(4) composition presents good thermal stability with regard to crystallization. The Y(0.9)Er(0.1)Al(3)(BO(3))(4) crystallized phase can be obtained at 1,150 degrees C, in agreement with other authors. Crack- and porosity-free films were obtained with very small grain size and low RMS roughness. The films thickness revealed to be linearly dependent on precursor solution viscosity, being the value of 25 mPa s useful to prepare high-quality amorphous multi-layers (up to similar to 800 nm) at 740 degrees C during 2 h onto silica substrates by spin coating with a gyrset technology.

Continuous GRASP with a local active-set method for bound-constrained global optimization

Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic-based on the CGRASP and GENCAN methods-for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP-GENCAN on a set of benchmark multimodal test functions.

Automatic camera control in virtual environments augmented using multiple sparse videos

Automated virtual camera control has been widely used in animation and interactive virtual environments. We have developed a multiple sparse camera based free view video system prototype that allows users to control the position and orientation of a virtual camera, enabling the observation of a real scene in three dimensions (3D) from any desired viewpoint. Automatic camera control can be activated to follow selected objects by the user. Our method combines a simple geometric model of the scene composed of planes (virtual environment), augmented with visual information from the cameras and pre-computed tracking information of moving targets to generate novel perspective corrected 3D views of the virtual camera and moving objects. To achieve real-time rendering performance, view-dependent textured mapped billboards are used to render the moving objects at their correct locations and foreground masks are used to remove the moving objects from the projected video streams. The current prototype runs on a PC with a common graphics card and can generate virtual 2D views from three cameras of resolution 768 x 576 with several moving objects at about 11 fps. (C)2011 Elsevier Ltd. All rights reserved.

Square wave adsorptive cathodic stripping voltarnmetry automated by sequential injection analysis - Potentialities and limitations exemplified by the determination of methyl parathion in water samples

This paper describes the development and evaluation of a sequential injection method to automate the determination of methyl parathion by square wave adsorptive cathodic stripping voltammetry exploiting the concept of monosegmented flow analysis to perform in-line sample conditioning and standard addition. Accumulation and stripping steps are made in the sample medium conditioned with 40 mmol L-1 Britton-Robinson buffer (pH 10) in 0.25 mol L-1 NaNO3. The homogenized mixture is injected at a flow rate of 10 mu Ls(-1) toward the flow cell, which is adapted to the capillary of a hanging drop mercury electrode. After a suitable deposition time, the flow is stopped and the potential is scanned from -0.3 to -1.0 V versus Ag/AgCl at frequency of 250 Hz and pulse height of 25 mV The linear dynamic range is observed for methyl parathion concentrations between 0.010 and 0.50 mgL(-1), with detection and quantification limits of 2 and 7 mu gL(-1), respectively. The sampling throughput is 25 h(-1) if the in line standard addition and sample conditioning protocols are followed, but this frequency can be increased up to 61 h(-1) if the sample is conditioned off-line and quantified using an external calibration curve. The method was applied for determination of methyl parathion in spiked water samples and the accuracy was evaluated either by comparison to high performance liquid chromatography with UV detection, or by the recovery percentages. Although no evidences of statistically significant differences were observed between the expected and obtained concentrations, because of the susceptibility of the method to interference by other pesticides (e.g., parathion, dichlorvos) and natural organic matter (e.g., fulvic and humic acids), isolation of the analyte may be required when more complex sample matrices are encountered. (C) 2007 Elsevier B.V. All rights reserved.

A New Indirect Electroanalytical Method to Monitor the Contamination of Natural Waters with 4-Nitrophenol Using Multiwall Carbon Nanotubes

The electrochemical detection of the hazardous pollutant 4-nitrophenol (4-NP) at low potentials, in order to avoid matrix interferences, is an important research challenge. This study describes the development, electrochemical characterization and utilization of a multiwall carbon nanotube (MWCNT) film electrode for the quantitative determination of 4-NP in natural water. Electrochemical impedence spectroscopy measurements showed that the modified surface exhibits a decrease of ca. 13 times in the charge transfer resistance when compared with a bare glassy carbon (GC) surface. Voltammetric experiments showed the possibility to oxidize a hydroxylamine layer (produced by the electrochemical reduction of 4-NP on the GC/MWNCT surface) in a potential region which is approximately 700 mV less positive than that needed to oxidize 4-NP, thus minimizing the interference of matrix components. The limit of detection for 4-NP obtained using square-wave voltammetry (0.12 mu mol L(-1)) was lower than the value advised by EPA. A natural water sample from a dam located in Sao Carlos (Brazil) was spiked with 4-NP and analyzed by the standard addition method using thee GC/MWCNT electrode, without any further purification step. the recovery procedure yielded a value of 96.5% for such sample, thus confirming the suitability of the developed method to determine 4-NP in natural water samples. The electrochemical determination was compared with that obtained by HPLC with UV-vis detection.

Electroanalytical determination of promethazine hydrochloride in pharmaceutical formulations on highly boron-doped diamond electrodes using square-wave adsorptive voltammetry

The electrochemical oxidation of promethazine hydrochloride was made on highly boron-doped diamond electrodes. Cyclic voltammetry experiments showed that the oxidation mechanisms involved the formation of an adsorbed product that is more readily oxidized, producing a new peak with lower potential values whose intensity can be increased by applying the accumulation potential for given times. The parameters were optimized and the highest current intensities were obtained by applying +0.78 V for 30 seconds. The square-wave adsorptive voltammetry results obtained in BR buffer showed two well-defined peaks, dependent on the pH and on the voltammetric parameters. The best responses were obtained at pH 4.0, frequency of 50 s(-1), step of 2 mV, and amplitude of 50 mV. Under these conditions, linear responses were obtained for concentrations from 5.96 x 10(-7) to 4.76 x 10(-6) mol L-1, and calculated detection limits of 2.66 x 10(-8) mol L-1 (8.51 mu g L-1) for peak 1 and of 4.61 x 10(-8) mol L-1 (14.77 mu g L-1) for peak 2. The precision and accuracy were evaluated by repeatability and reproducibility experiments, which yielded values of less than 5.00% for both voltammetric peaks. ne applicability of this procedure was tested on commercial formulations of promethazine hydrochloride by observing the stability, specificity, recovery and precision of the procedure in complex samples. All results obtained were compared to recommended procedure by British Pharmacopeia. The voltammetric results indicate that the proposed procedure is stable and sensitive, with good reproducibility even when the accumulation steps involve short times. It is therefore very suitable for the development of the electroanalytical procedure, providing adequate sensitivity and a reliable method.

Incommensurate spin-density-wave and metal-insulator transition in the one-dimensional periodic Anderson model

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