Gravitational wave recoil in Robinson-Trautman spacetimes

We consider the gravitational recoil due to nonreflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the nonlinear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the nonaxisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Matrix Method for Acoustic Levitation Simulation

A matrix method is presented for simulating acoustic levitators. A typical acoustic levitator consists of an ultrasonic transducer and a reflector. The matrix method is used to determine the potential for acoustic radiation force that acts on a small sphere in the standing wave field produced by the levitator. The method is based on the Rayleigh integral and it takes into account the multiple reflections that occur between the transducer and the reflector. The potential for acoustic radiation force obtained by the matrix method is validated by comparing the matrix method results with those obtained by the finite element method when using an axisymmetric model of a single-axis acoustic levitator. After validation, the method is applied in the simulation of a noncontact manipulation system consisting of two 37.9-kHz Langevin-type transducers and a plane reflector. The manipulation system allows control of the horizontal position of a small levitated sphere from -6 mm to 6 mm, which is done by changing the phase difference between the two transducers. The horizontal position of the sphere predicted by the matrix method agrees with the horizontal positions measured experimentally with a charge-coupled device camera. The main advantage of the matrix method is that it allows simulation of non-symmetric acoustic levitators without requiring much computational effort.

Ultrasonic Viscosity Measurement Using the Shear-Wave Reflection Coefficient with a Novel Signal Processing Technique

Real-time viscosity measurement remains a necessity for highly automated industry. To resolve this problem, many studies have been carried out using an ultrasonic shear wave reflectance method. This method is based on the determination of the complex reflection coefficient`s magnitude and phase at the solid-liquid interface. Although magnitude is a stable quantity and its measurement is relatively simple and precise, phase measurement is a difficult task because of strong temperature dependence. A simplified method that uses only the magnitude of the reflection coefficient and that is valid under the Newtonian regimen has been proposed by some authors, but the obtained viscosity values do not match conventional viscometry measurements. In this work, a mode conversion measurement cell was used to measure glycerin viscosity as a function of temperature (15 to 25 degrees C) and corn syrup-water mixtures as a function of concentration (70 to 100 wt% of corn syrup). Tests were carried out at 1 MHz. A novel signal processing technique that calculates the reflection coefficient magnitude in a frequency band, instead of a single frequency, was studied. The effects of the bandwidth on magnitude and viscosity were analyzed and the results were compared with the values predicted by the Newtonian liquid model. The frequency band technique improved the magnitude results. The obtained viscosity values came close to those measured by the rotational viscometer with percentage errors up to 14%, whereas errors up to 96% were found for the single frequency method.

Computational Method to Determine Reflected Ultrasonic Signals From Arbitrary-Geometry Targets

A computational method based on the impulse response and on the discrete representation computational concept is proposed for the determination of the echo responses from arbitrary-geometry targets. It is supposed that each point of the transducer aperture can be considered as a source radiating hemispherical waves to the reflector. The local interaction with each of the hemispherical waves at the reflector surface can be modeled as a plane wave impinging on a planar surface, using the respective reflection coefficient. The method is valid for all field regions and can be performed for any excitation waveform radiated from an arbitrary acoustic aperture. The effects of target geometry, position, and material on both the amplitude and the shape of the echo response are studied. The model is compared with experimental results obtained using broadband transducers together with plane and cylindrical concave rectangular reflectors (aluminum, brass, and acrylic), as well as a circular cavity placed on a plane surface, in a water medium. The method can predict the measured echoes accurately. This paper shows an improved approach of the method, considering the reflection coefficient for all incident hemispherical waves arriving at each point of the target surface.

Lack of Circadian Variation of Pulse Wave Velocity Measurements in Healthy Volunteers

Arterial stiffness is an independent marker of cardiovascular events. Pulse wave velocity (PWV) is a validated method to detect arterial stiffness that can be influenced by several factors including age and blood pressure. However, it is not clear whether PWV could be influenced by circadian variations. In the present study, the authors measured blood pressure and carotid-femoral PWV measurements in 15 young healthy volunteers in 4 distinct periods: 8 am, noon, 4 pm, and 8 pm. No significant variations of systolic (P=.92), mean (P=.77), and diastolic (P=.66) blood pressure among 8 am (113 +/- 15, 84 +/- 8, 69 +/- 6 mm Hg), noon (114 +/- 13, 83 +/- 8, 68 +/- 6 mm Hg), 4 pm (114 +/- 13, 85 +/- 8, 70 +/- 7 mm Hg), and 8 pm (113 +/- 7, 83 +/- 10, 68 +/- 7 mm Hg), respectively, were observed. Similarly, carotid-femoral PWV did not change among the periods (8 am: 7.6 +/- 1.4 m/s, noon: 7.4 +/- 1.1 m/s, 4 pm: 7.6 +/- 1.0 m/s, 8 pm, 7.6 +/- 1.3 m/s; P=.85). Considering all measurements, mean blood pressure significantly correlated with PWV (r=.31; P=.016). In young healthy volunteers, there is no significant circadian variation of carotid-femoral PWV. These findings support the concept that it does not appear mandatory to perform PWV measurements at exactly the same period of the day. J Clin Hypertens (Greenwich). 2011;13:19-22. (c) 2010 Wiley Periodicals, Inc.

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.