Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions. They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems. The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems. The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals. This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods.

A frequency-independent boundary element method for scattering by two-dimensional screens and apertures

We propose and analyse a hybrid numerical–asymptotic hp boundary element method (BEM) for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high-frequency asymptotics of the solution. We provide a rigorous frequency-explicit error analysis which proves that the method converges exponentially as the number of degrees of freedom N increases, and that to achieve any desired accuracy it is sufficient to increase N in proportion to the square of the logarithm of the frequency as the frequency increases (standard BEMs require N to increase at least linearly with frequency to retain accuracy). Our numerical results suggest that fixed accuracy can in fact be achieved at arbitrarily high frequencies with a frequency-independent computational cost, when the oscillatory integrals required for implementation are computed using Filon quadrature. We also show how our method can be applied to the complementary ‘breakwater’ problem of propagation through an aperture in an infinite sound-hard screen.

Solid-liquid transition in Nb powder determined by third harmonic susceptibility

Measurements of the third harmonic of the AC-susceptibility were employed to determine the boundaries of the linear regime of the magnetic response of Nb powder. Non-linear contributions to the magnetic response reveal the occurrence of a structured phase, disappearing as the vortex lattice melts to the liquid state. A systematic study of the third harmonic was conducted to determine how its onset temperature depends on experimental parameters, such as the frequency and amplitude of the excitation field. The melting line (ML) has been extracted from the onset temperature measured at low-frequencies and low-excitation fields in the presence of DC magnetic fields. The study indicates that the ML can be described by a 3D vortex-glass model, except at lower fields, where the system experiences a depinning crossover, and the best description of the experimental data is provided by a 3D Bose-glass model. (c) 2008 Elsevier B. V. All rights reserved.

Low-frequency absorption cross section of the electromagnetic waves for extreme Reissner-Nordstrom black holes in higher dimensions

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

A multi-cell variable frequency interleaved ZCS boost rectifier digitally controlled by FPGA

This paper presents a multi-cell single-phase high power factor boost rectifier in interleave connection, operating in critical conduction mode, employing a soft-switching technique, and controlled by Field Programmable Gate Array (FPGA). The soft-switching technique is based on zero-current-switching (ZCS) cells, providing ZC (zero-current) turn-on and ZCZV (zero-current-zero-voltage) turn-off for the active switches, and ZV (zero-vohage) turn-on and ZC (zero-current) turn-off for the boost diodes. The disadvantages related to reverse recovery effects of boost diodes operated in continuous conduction mode (additional losses, and electromagnetic interference (EMI) problems) are minimized, due to the operation in critical conduction mode. In addition, due to the interleaving technique, the rectifier's features include the reduction in the input current ripple, the reduction in the output voltage ripple, the use of low stress devices, low volume for the EMI input filter, high input power factor (PF), and low total harmonic distortion (THD) in the input current, in compliance with the IEC61000-3-2 standards. The digital controller has been developed using a hardware description language (VHDL) and implemented using a XC2S200E-SpartanII-E/Xilinx FPGA device, performing a true critical conduction operation mode for all interleaved cells, and a closed-loop to provide the output voltage regulation, like as a preregulator rectifier. Experimental results are presented for a implemented prototype with two and with four interleaved cells, 400V nominal output voltage and 220V(rms) nominal input voltage, in order to verify the feasibility and performance of the proposed digital control through the use of a FPGA device.

Violet-blue emissions due to frequency up-conversion in Nd3+-doped fluoroindate glasses

We report the observation of intense frequency up-conversion in Nd3+-doped fluoroindate glasses pumped by the second harmonic of a cw mode-locked Nd: YAG laser. Mechanisms for generating the observed emissions are discussed.

A virtual experiment for the detection of specific features in the frequency response of a coupled nonlinear and linear oscillator

This paper presents an investigation into some practical issues that may be present in a real experiment, when trying to validate the theoretical frequency response curve of a two degree-of-freedom nonlinear system consisting of coupled linear and nonlinear oscillators. Some specific features, such as detached resonance curves, have been theoretically predicted in multi degree-of-freedom nonlinear oscillators, when subject to harmonic excitation, and the system parameters have been shown to be fundamental in achieving such features. When based on a simplified model, approximate analytical expression for the frequency response curves may be derived, which may be validated by the numerical solutions. In a real experiment, however, the practical achievability of such features was previously shown to be greatly affected by small disturbances induced by gravity and inertia, which led to some solutions becoming unstable which had been predicted to be stable. In this work a practical system configuration is proposed where such effects are reduced so that the previous limitations are overcome. A virtual experiment is carried out where a detailed multi-body model of the oscillator is assembled and the effects on the system response are investigated.

Frequency upconversion involving triads and quartets of ions in a Pr3+/Nd3+ codoped fluoroindate glass

Frequency upconversion (UC) processes involving energy transfer (ET) among Nd 3+ and Pr 3+ ions in a fluoroindate glass are reported. In a first experiment, the excitation of Pr 3+ [transition 3H 4→ 1D 2] and of Nd 3+ [transition 4I 9/2→( 2G 7/2+ 4G 5/2)] was achieved with a dye laser operating in the 575-590 nm range. In a second experiment, the Nd 3+ ions were excited with the second harmonic of a Nd: YAG laser at 532 nm. The ET processes leading to UC in both experiments were studied by monitoring the blue fluorescence decay at 480 nm due to the transition 3P 0→ 3H 4 in Pr 3+. In the more relevant UC process, quartets of ions (Nd-Nd-Pr-Pr) are excited due to absorption of three laser photons by two Nd 3+ ions which transfer their energy to two Pr 3+ ions. Each Pr 3+ ion promoted to the 3P 0 level decays to the ground state emitting one photon in the blue region. This conclusion was achieved investigating the dependence of the UC fluorescence intensity as a function of laser intensity, samples concentrations, and temporal behavior of the UC signal. Other UC processes involving nonisoionic groups of three ions are also reported. © 2002 American Institute of Physics.

Tunable second harmonic generation by phase-modulated ultrashort laser pulses

We report on the generation of tunable light around 400 nm by frequency-doubling ultrashort laser pulses whose spectral phase is modulated by a sum of sinusoidal functions. The linewidth of the ultraviolet band produced is narrower than 1 nm, in contrast to the 12 nm linewidth of the non-modulated incident spectrum. The influence of pixellation of the liquid crystal spatial light modulator on the efficiency of the phase-modulated second harmonic generation is discussed.

Dynamic identification of structures: experimental assessment of modal parameteres through methods in frequency domain, in time-frequency domain and model updating

Among the experimental methods commonly used to define the behaviour of a full scale system, dynamic tests are the most complete and efficient procedures. A dynamic test is an experimental process, which would define a set of characteristic parameters of the dynamic behaviour of the system, such as natural frequencies of the structure, mode shapes and the corresponding modal damping values associated. An assessment of these modal characteristics can be used both to verify the theoretical assumptions of the project, to monitor the performance of the structural system during its operational use. The thesis is structured in the following chapters: The first introductive chapter recalls some basic notions of dynamics of structure, focusing the discussion on the problem of systems with multiply degrees of freedom (MDOF), which can represent a generic real system under study, when it is excited with harmonic force or in free vibration. The second chapter is entirely centred on to the problem of dynamic identification process of a structure, if it is subjected to an experimental test in forced vibrations. It first describes the construction of FRF through classical FFT of the recorded signal. A different method, also in the frequency domain, is subsequently introduced; it allows accurately to compute the FRF using the geometric characteristics of the ellipse that represents the direct input-output comparison. The two methods are compared and then the attention is focused on some advantages of the proposed methodology. The third chapter focuses on the study of real structures when they are subjected to experimental test, where the force is not known, like in an ambient or impact test. In this analysis we decided to use the CWT, which allows a simultaneous investigation in the time and frequency domain of a generic signal x(t). The CWT is first introduced to process free oscillations, with excellent results both in terms of frequencies, dampings and vibration modes. The application in the case of ambient vibrations defines accurate modal parameters of the system, although on the damping some important observations should be made. The fourth chapter is still on the problem of post processing data acquired after a vibration test, but this time through the application of discrete wavelet transform (DWT). In the first part the results obtained by the DWT are compared with those obtained by the application of CWT. Particular attention is given to the use of DWT as a tool for filtering the recorded signal, in fact in case of ambient vibrations the signals are often affected by the presence of a significant level of noise. The fifth chapter focuses on another important aspect of the identification process: the model updating. In this chapter, starting from the modal parameters obtained from some environmental vibration tests, performed by the University of Porto in 2008 and the University of Sheffild on the Humber Bridge in England, a FE model of the bridge is defined, in order to define what type of model is able to capture more accurately the real dynamic behaviour of the bridge. The sixth chapter outlines the necessary conclusions of the presented research. They concern the application of a method in the frequency domain in order to evaluate the modal parameters of a structure and its advantages, the advantages in applying a procedure based on the use of wavelet transforms in the process of identification in tests with unknown input and finally the problem of 3D modeling of systems with many degrees of freedom and with different types of uncertainty.

Sideband-Ratio and Harmonic Response of Sub-Millimeter Wave Mixers measured with a Martin Puplett Interferometer

Heterodyne receivers at millimeter and submillimeter wavelength are widely used for radiometric spectral line observations for atmospheric remote sensing or radio astronomy. The quantitative analysis of such observations requires an accurate knowledge of the mixers's sideband ratio. In addition, its potential sensitivity to spurious harmonics needs to be well understood. In this paper, we discuss a measurement technique for these receiver characteristics, which is based on a scanning Martin Puplett Interferometer used in conjunction with a wide band digital autocorrelation spectrometer for the analysis of the intermediate frequency band. We present measurement results of different double sideband and sideband separating mixers, which were developed for the proposed 340GHz multi-beam limb sounder STEAMR.

Transient behavior of a system composed of conductive thin wire structures excited by harmonic and lightning type signals

The transient response of a system of independent electrodes buried in a semi-infinite conducting medium is studied. Using a simple and versatile numerical scheme written by the authors and based on the Electric Field Integral Equation (EFIE), the effect caused by harmonic signals ranging on frequency from Hz to hundred of MHz, and also by lightning type driving signal striking at a remote point far from the conductors, is extensively studied. The value of the scalar potential appearing on the electrodes as a function of the frequency of the applied signal is one of the variables investigated. Other features such as the input impedance at the injection point of the signal and the Ground Potential Rise (GPR) over the electrode system are also discussed

A new algorithm to accelerate harmonic analysis of time series

The Lomb periodogram has been traditionally a tool that allows us to elucidate if a frequency turns out to be important for explaining the behaviour of a given time series. Many linear and nonlinear reiterative harmonic processes that are used for studying the spectral content of a time series take into account this periodogram in order to avoid including spurious frequencies in their models due to the leakage problem of energy from one frequency to others. However, the estimation of the periodogram requires long computation time that makes the harmonic analysis slower when we deal with certain time series. Here we propose an algorithm that accelerates the extraction of the most remarkable frequencies from the periodogram, avoiding its whole estimation of the harmonic process at each iteration. This algorithm allows the user to perform a specific analysis of a given scalar time series. As a result, we obtain a functional model made of (1) a trend component, (2) a linear combination of Fourier terms, and (3) the so-called mixed secular terms by reducing the computation time of the estimation of the periodogram.

An inverse methodology for high-frequency RF coil design for MRI with de-emphasized B-1 fields

An inverse methodology for the design of biologically loaded radio-frequency (RF) coils for magnetic resonance imaging applications is described. Free space time-harmonic electromagnetic Green's functions and de-emphasized B-1 target fields are used to calculate the current density on the coil cylinder. In theory, with the B-1 field de-emphasized in the middle of the RF transverse plane, the calculated current distribution can generate an internal magnetic field that can reduce the central overemphasis effect caused by field/tissue interactions at high frequencies. The current distribution of a head coil operating at 4 T (170 MHz) is calculated using an inverse methodology with de-emphasized B-1. target fields. An in-house finite-difference time-domain routine is employed to evaluate B-1 field and signal intensity inside a homogenous cylindrical phantom and then a complete human head model. A comparison with a conventional RF birdcage coil is carried out and demonstrates that this method can help in decreasing the normal bright region caused by field/tissue interactions in head images at 170 MHz and higher field strengths.

A time-harmonic target-field method for designing unshielded RF coils in MRI

Time-harmonic methods are required in the accurate design of RF coils as operating frequency increases. This paper presents such a method to find a current density solution on the coil that will induce some desired magnetic field upon an asymmetrically located target region within. This inverse method appropriately considers the geometry of the coil via a Fourier series expansion, and incorporates some new regularization penalty functions in the solution process. A new technique is introduced by which the complex, time-dependent current density solution is approximated by a static coil winding pattern. Several winding pattern solutions are given, with more complex winding patterns corresponding to more desirable induced magnetic fields.