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.

Filtros acústicos em cristais fonônicos

In this work, we have studied the acoustic phonon wave propagation within the periodic and quasiperiodic superlattices of Fibonacci type. These structures are formed by phononic crystals, whose periodicity allows the raise of regions known as stop bands, which prevent the phonon propagation throughout the structure for specific frequency values. This phenomenon allows the construction of acoustic filters with great technological potential. Our theoretical model were based on the method of the transfer matrix, thery acoustics phonons which describes the propagation of the transverse and longitudinal modes within a unit cell, linking them with the precedent cell in the multilayer structure. The transfer matrix is built taking into account the elastic and electromagnetic boundary conditions in the superllatice interfaces, and it is related to the coupled differential equation solutions (elastic and electromagnetic) that describe each model under consideration. We investigated the piezoelectric properties of GaN and AlN the nitride semiconductors, whose properties are important to applications in the semiconductor device industry. The calculations that characterize the piezoelectric system, depend strongly on the cubic (zinc-bend) and hexagonal (wurtzite) crystal symmetries, that are described the elastic and piezoelectric tensors. The investigation of the liquid Hg (mercury), Ga (gallium) and Ar (argon) systems in static conditions also using the classical theory of elasticity. Together with the Euler s equation of fluid mechanics they one solved to the solid/liquid and the liquid/liquid interfaces to obtain and discuss several interesting physical results. In particular, the acoustical filters obtained from these structures are again presented and their features discussed

The use of pulsed electric acoustic technique for measuring the polarization reversal in ferroelectric ceramic samples

The pulsed electric acoustic technique, PEA, has been usually applied to probe space charge profiles in polymers. Preliminary PEA results using a ferroelectric ceramic are presented. If the reverse applied electric field i of the order of the coercive field the switching polarization process occurs in a period larger than hundreds of seconds. Such a slow process allows one to use the PEA setup to follow the polarization switching dynamics and determine the electric field profile. The PEA signal obtained in the lead zirconate-titanate doped with niobium ceramic, PZTN, indicates that the polarization distribution and field are not uniform during the switching period. We were also able to observe that the acoustic wave velocity and attenuation depends on the stage of the polarization switching, which agrees with results obtained using the ultrasonic method.

Interaction between wave and coastal structure: Validation of two lagrangian numerical models with experimental results marine 2011

Numerical modeling of the interaction among waves and coastal structures is a challenge due to the many nonlinear phenomena involved, such as, wave propagation, wave transformation with water depth, interaction among incident and reflected waves, run-up / run-down and wave overtopping. Numerical models based on Lagrangian formulation, like SPH (Smoothed Particle Hydrodynamics), allow simulating complex free surface flows. The validation of these numerical models is essential, but comparing numerical results with experimental data is not an easy task. In the present paper, two SPH numerical models, SPHysics LNEC and SPH UNESP, are validated comparing the numerical results of waves interacting with a vertical breakwater, with data obtained in physical model tests made in one of the LNEC's flume. To achieve this validation, the experimental set-up is determined to be compatible with the Characteristics of the numerical models. Therefore, the flume dimensions are exactly the same for numerical and physical model and incident wave characteristics are identical, which allows determining the accuracy of the numerical models, particularly regarding two complex phenomena: wave-breaking and impact loads on the breakwater. It is shown that partial renormalization, i.e. renormalization applied only for particles near the structure, seems to be a promising compromise and an original method that allows simultaneously propagating waves, without diffusion, and modeling accurately the pressure field near the structure.

Components of the acoustic swallowing signal: Preliminary study

Purpose: To analyze the components of the acoustic signal of swallowing using a specific software. Methods: Fourteen healthy subjects ranging in age from 20 to 50 years (mean age 31±10 years), were evaluated. Data collection consisted on the simultaneous capture of the swallowing audio with a microphone and of the swallowing videofluoroscopic image. The bursts of the swallowing acoustic signal were identified and their duration and the interval between them were later analyzed using a specific software, which allowed the simultaneous analyses between the acoustic wave and the videofluoroscopic image. Results: Three burst components were identified in most of the swallows evaluated. The first burst presented mean time of 87.3 milliseconds (ms) for water and 78.2 for the substance. The second burst presented mean time of 112.9 ms for water and 85.5 for the pasty substance. The mean interval between first and second burst was 82.1 ms for water and 95.3 ms for the pasty consistency, and between second and third burst was 339.8 ms for water and 322.0 ms for the pasty consistency. Conclusion: The software allowed the visualization of three bursts during the swallowing of healthy individuals, and showed that the swallowing signal in normal subjects is highly variable.

Modelagem sísmica via métodos das diferenças finitas: caso da bacia do Amazonas

Este trabalho tem por objetivo apresentar os resultados da modelagem sísmica em meios com fortes descontinuidades de propriedades físicas, com ênfase na existência de difrações e múltiplas reflexões, tendo a Bacia do Amazonas como referência à modelagem. As condições de estabilidade e de fronteiras utilizadas no cálculo do campo de ondas sísmicas foram analisadas numericamente pelo método das diferenças finitas, visando melhor compreensão e controle da interpretação de dados sísmicos. A geologia da Bacia do Amazonas é constituída por rochas sedimentares depositadas desde o Ordoviciano até o Recente que atingem espessuras da ordem de 5 km. Os corpos de diabásio, presentes entre os sedimentos paleozóicos, estão dispostos na forma de soleiras, alcançam espessuras de centenas de metros e perfazem um volume total de aproximadamente 90000 Km³. A ocorrência de tais estruturas é responsável pela existência de reflexões múltiplas durante a propagação da onda sísmica o que impossibilita melhor interpretação dos horizontes refletores que se encontram abaixo destas soleiras. Para representar situações geológicas desse tipo foram usados um modelo (sintético) acústico de velocidades e um código computacional elaborado via método das diferenças finitas com aproximação de quarta ordem no espaço e no tempo da equação da onda. A aplicação dos métodos de diferenças finitas para o estudo de propagação de ondas sísmicas melhorou a compreensão sobre a propagação em meios onde existem heterogeneidades significativas, tendo como resultado boa resolução na interpretação dos eventos de reflexão sísmica em áreas de interesse. Como resultado dos experimentos numéricos realizados em meio de geologia complexa, foi observada a influência significativa das reflexões múltiplas devido à camada de alta velocidade, isto provocou maior perda de energia e dificultou a interpretação dos alvos. Por esta razão recomenda-se a integração de dados de superfície com os de poço, com o objetivo de obter melhor imagem dos alvos abaixo das soleiras de diabásio.

Migração por equação de onda em meios anisotrópicos com correção de amplitude

Este trabalho discute dois aspectos da migração em profundidade através da continuação para baixo dos campos de onda: o tratamento de modos evanescentes e a correção da amplitude dos eventos migrados. Estes dois aspectos são discutidos em meios isotrópicos e para uma classe de meios anisotrópicos. Migrações por diferenças finitas (FD) e por diferenças finitas e Fourier (FFD) podem ser instáveis em meios com forte variação lateral de velocidade. Estes métodos utilizam aproximações de Padé reais para representar o operador que descreve a propagação de ondas descendentes. Estas abordagens não são capazes de tratar corretamente os modos evanescentes, o que pode levar à instabilidades numéricas em meios com forte variação lateral de velocidade. Uma solução possível para esse problema é utilizar aproximação de Padé complexa, que consegue melhor representar os modos evanescentes associados às reflexões pós-críticas, e neste trabalho esta aproximação é utilizada para obter algoritmos FD e híbrido FD/FFD estáveis para migração em meios transversalmente isotrópicos com eixo de simetria vertical (VTI), mesmo na presença de forte variação nas propriedades elásticas do meio. A estabilidade dos algoritmos propostos para meios VTI foi validada através da resposta ao impulso do operador de migração e pela sua aplicação na migração de dados sintéticos, em meios fortemente heterogêneos. Métodos de migração por equação de onda em meios heterogêneos não tratam corretamente a amplitude dos eventos durante a propagação. As equações de onda unidirecionais tradicionais descrevem corretamente apenas a parte cinemática da propagação do campo de onda. Assim, para uma descrição correta das amplitudes deve-se usar as equações de onda unidirecionais de amplitude verdadeira. Em meios verticalmente heterogêneos, as equações de onda unidirecionais de amplitude verdadeira podem ser resolvidas analiticamente. Em meios lateralmente heterogêneos, essas equações não possuem uma solução analítica. Mesmo soluções numéricas tendem a ser instáveis. Para melhorar a compensação de amplitude na migração, em meios com variação lateral de velocidade, é proposto uma aproximação estável para solução da equação de onda unidirecional de amplitude verdadeira. Esta nova aproximação é implementada nas migrações split-step e diferenças finitas e Fourier (FFD). O algoritmo split-step com correção de amplitude foi estendido para meios VTI. A migração pré e pós-empilhamento de dados sintéticos, em meios isotrópicos e anisotrópicos, confirmam o melhor tratamento das amplitudes e estabilidade dos algoritmos propostos.

Modelagem sísmica por diferenças finitas em meios bidimensionais com difratores

Este trabalho tem por objetivo a modelagem sísmica em meios com fortes descontinuidades de propriedades físicas, com ênfase na existência de difrações. Como parte deste estudo foi feita a análise numérica visando as condições de estabilidade e de fronteiras utilizadas no cálculo do campo de ondas sísmicas. Para a validação do programa de diferenças finitas foi feita a comparação cinemática com a Teoria do Raio para um modelo simples. O motivo deste estudo é ter uma melhor compreensão e controle sobre os problemas de modelagem, visando contribuir para a solução de problemas na interpretação de dados sísmicos. Segundo vários autores na literatura geológica, Derby (1877), Evans (1906), Paiva (1929) e Moura (1938). A Bacia do Amazonas é constituída por rochas sedimentares depositadas desde o Ordoviciano até o recente, atingindo espessuras da ordem de 5 km. Os corpos de diabásio, presentes entre os sedimentos paleozóicos, estão dispostos na forma de soleiras, alcançando espessuras de centenas de metros, perfazendo um volume total de 90.000 quilômetros cúbicos. A ocorrência de tais estruturas é responsável pela existência de reflexões múltiplas durante a propagação da onda sísmica, impossibilitando uma melhor interpretação dos horizontes refletores que se encontram abaixo das soleiras. Para representar situações geológicas desse tipo foi usado um modelo acústico de velocidades. Para o cálculo dos sismogramas foi utilizado um programa de diferenças finitas com aproximação de quarta ordem da equação da onda acústica no espaço e no tempo. As aplicações dos métodos de diferenças finitas para o estudo de propagação de ondas sísmicas têm melhorado a compreensão sobre a propagação em meios onde existem heterogeneidades significativas, tendo como resultado boa resolução na interpretação dos eventos de reflexão sísmica em áreas de interesse. Como resultado dos experimentos numéricos realizados em meio de geologia complexa, foi observado a influência significativa das múltiplas devido a camada de alta velocidade, o que faz com que haja maior perda de energia dificultando a interpretação dos alvos. Por esta razão recomendo a integração de dados de superfície com os dados de poço, com o objetivo de se obter uma melhor imagem dos alvos abaixo das soleiras de diabásio.

Ultrasonic non-destructive testing of plate-like structures using piezoelectric array transducers

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

From acoustic waves to microwaves

We present here some results of our research related to the optoelectronics and photonics and show all the experimental setups used. Starting with a discussion on the importance of the waves, we demonstrate our achievements based on employment of acoustic, optical, and microwaves and their technological use. The results concern the acousto-optic and electro-optic effects. The generalized analysis of the electro-optic effect reveals a new high induced birefringence in lithium niobate. A patented optical fiber microphone is presented, and its applications to the measurements of acoustic wave velocity in gases and in the laser ultrasound non-destructive evaluation system are discussed. Finally, the generation of microwaves by an optical method with substantial cost reduction is presented.

Nanoporous alumina based hypersonic phononic hybrid structures studied by brillouin spectroscopy

Phononische Kristalle sind strukturierte Materialien mit sich periodisch ändernden elastischen Moduln auf der Wellenlängenskala. Die Interaktion zwischen Schallwellen und periodischer Struktur erzeugt interessante Interferenzphänomene, und phononische Kristalle erschließen neue Funktionalitäten, die in unstrukturierter Materie unzugänglich sind. Hypersonische phononische Kristalle im Speziellen, die bei GHz Frequenzen arbeiten, haben Periodizitäten in der Größenordnung der Wellenlänge sichtbaren Lichts und zeigen daher die Wege auf, gleichzeitig Licht- und Schallausbreitung und -lokalisation zu kontrollieren, und dadurch die Realisierung neuartiger akusto-optischer Anordnungen. Bisher bekannte hypersonische phononische Kristalle basieren auf thermoplastischen Polymeren oder Epoxiden und haben nur eingeschränkte thermische und mechanische Stabilität und mechanischen Kontrast. Phononische Kristalle, die aus mit Flüssigkeit gefüllten zylindrischen Kanälen in harter Matrix bestehen, zeigen einen sehr hohen elastischen Kontrast und sind bislang noch unerforscht. In dieser Dissertation wird die experimentelle Untersuchung zweidimensionaler hypersonischer phononischer Kristalle mit hexagonaler Anordnung zylindrischer Nanoporen basierend auf der Selbstorganisation anodischen Aluminiumoxids (AAO) beschrieben. Dazu wird die Technik der hochauflösenden inelastischen Brillouin Lichtstreuung (BLS) verwendet. AAO ist ein vielsetiges Modellsystem für die Untersuchung reicher phononischer Phänomene im GHz-Bereich, die eng mit den sich in den Nanoporen befindlichen Flüssigkeiten und deren Interaktion mit der Porenwand verknüpft sind. Gerichteter Fluss elastischer Energie parallel und orthogonal zu der Kanalachse, Lokalisierung von Phononen und Beeinflussung der phononischen Bandstruktur bei gleichzeitig präziser Kontrolle des Volumenbruchs der Kanäle (Porosität) werden erörtert. Außerdem ermöglicht die thermische Stabilität von AAO ein temperaturabhängiges Schalten phononischer Eigenschaften infolge temperaturinduzierter Phasenübergänge in den Nanoporen. In monokristallinen zweidimensionalen phononischen AAO Kristallen unterscheiden sich die Dispersionsrelationen empfindlich entlang zweier hoch symmetrischer Richtungen in der Brillouinzone, abhängig davon, ob die Poren leer oder gefüllt sind. Alle experimentellen Dispersionsrelationen werden unter Zuhilfenahme theoretische Ergebnisse durch finite Elemente Analyse (FDTD) gedeutet. Die Zuordnung der Verschiebungsfelder der elastischen Wellen erklärt die Natur aller phononischen Moden.

Nanomechanical and phononic properties of structured soft materials

Significant interest in nanotechnology, is stimulated by the fact that materials exhibit qualitative changes of properties when their dimensions approach ”finite-sizes”. Quantization of electronic, optical and acoustic energies at the nanoscale provides novel functions, with interests spanning from electronics and photonics to biology. The present dissertation involves the application of Brillouin light scattering (BLS) to quantify and utilize material displacementsrnfor probing phononics and elastic properties of structured systems with dimensions comparable to the wavelength of visible light. The interplay of wave propagation with materials exhibiting spatial inhomogeneities at sub-micron length scales provides information not only about elastic properties but also about structural organization at those length scales. In addition the vector nature of q allows, for addressing the directional dependence of thermomechanical properties. To meet this goal, one-dimensional confined nanostructures and a biological system possessing high hierarchical organization were investigated. These applications extend the capabilities of BLS from a characterization tool for thin films to a method for unravelingrnintriguing phononic properties in more complex systems.

Physical properties, velocity and attenuation characteristics, and mineralogy of gabbros from ODP Hole 176-735B

Laboratory compressional wave (Vp) and shear wave (Vs) velocities were measured as a function of confining pressure for the gabbros from Hole 735B and compared to results from Leg 118. The upper 500 m of the hole has a Vp mean value of 6895 m/s measured at 200 MPa, and at 500 meters below seafloor (mbsf), Vp measurements show a mean value of 7036 m/s. Vs mean values in the same intervals are 3840 m/s and 3857 m/s, respectively. The mean Vp and Vs values obtained from log data in the upper 600 m are 6520 and 3518 m/s, respectively. These results show a general increase in velocity with depth and the velocity gradients estimate an upper mantle depth of 3.32 km. This value agrees with previous work based on dredged samples and inversion of rare element concentrations in basalts dredged from the conjugate site to the north of the Atlantis Bank. Laboratory measurements show Vp anisotropy ranging between 0.4% and 8.8%, with the majority of the samples having values less than 3.8%. Measurements of velocity anisotropy seem to be associated with zones of high crystal-plastic deformation with predominant preferred mineral orientations of plagioclase, amphiboles, and pyroxenes. These findings are consistent with results on gabbros from the Hess Deep area and suggest that plastic deformation may play an important role in the seismic properties of the lower oceanic crust. In contrast to ophiolite studies, many of the olivine gabbros show a small degree of anisotropy. Log derived Vs anisotropy shows an average of 5.8% for the upper 600 m of Hole 735B and tends to decrease with depth where the overburden pressure and the age of the crustal section suggests closure of cracks and infilling of fractures by alteration minerals. Overall the results indicate that the average shear wave splitting in Hole 735B might be influenced by preferred structural orientations and the average value of shear wave splitting may not be a maximum because structural dips are <90°. The maximum fast-wave orientation values could be influenced by structural features striking slightly oblique to this orientation or by near-field stress concentrations. However, flexural wave dispersion analyses have not been performed to confirm this hypothesis or to indicate to what extent the near-field stresses may be influencing shear wave propagation. Acoustic impedance contrasts calculated from laboratory and logging data were used to generate synthetic seismograms that aid in the interpretation of reflection profiles. Several prominent reflections produced by these calculations suggest that Fe-Ti oxides and shear zones may contribute to the reflective nature of the lower oceanic crust. Laboratory velocity attenuation (Q) measurements from below 500 m have a mean value of 35.1, which is consistent with previous vertical seismic profile (VSP) and laboratory measurements on the upper 500 m.

Amorphous piezoresistive and piezoelectric sensors for robotics applications

Ultrasonic transducers have often been used in the development of sensory systems for robotics applications. In most cases, these sensory systems are based on the determination of times of flight for signals from every transducer. In this work we have used piezoresistive and piezoelectric materials to measure the instant and position collision in metallic structures by using the difference of the times of propagation of an acoustic wave when it is produced over a ferromagnetic (iron, steel or another material) based structure. An immediate application of the proposed method is the detection and location of impacts over the metallic links of an industrial robot or the collision position in a metallic structure for an automated inspection

Characterization of Amorphous Tantalum Oxide for Insulating Acoustic Mirrors

This work describes the assessment of the acoustic properties of sputtered tantalum oxide films intended as high impedance films for the acoustic isolation of bulk acoustic wave devices operating in the GHz frequency range. The films are grown by sputtering a metallic tantalum target under different oxygen and argon gas mixtures, total pressures, pulsed DC powers and substrate bias. The structural properties of the films are assessed through infrared absorption spectroscopy and X-ray diffraction measurements. Their acoustic impedance is obtained after estimating the mass density by X-ray reflectometry measurements and the longitudinal acoustic velocity by analyzing the longitudinal λ/2 resonance induced in a tantalum oxide film inserted between an acoustic reflector and an AlN-based resonator. A second measurement of the sound velocity is achieved through picosecond acoustic spectroscopy.