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We investigated the thermal stability and performance of AlGaN/AlN/GaN Hall-effect sensors under industry-relevant atmospheric conditions. The thermal stability and performance of Hall sensors are evaluated by monitoring Hall sensitivity, two-dimensional electron gas density, and Ohmic contact resistance during aging at 200 °C for up to 2800 h under atmospheric conditions. This was accomplished by characterizing AlGaN/AlN/GaN micro-Hall sensors, with and without contacts, and before and after being placed under different thermal aging times. Observed electrical performance was correlated with the micro-structural evolution of AlGaN/AlN/GaN Hall sensor heterostructures. Results indicate that the AlGaN/AlN/GaN Hall sensor provides stable performance for as long as 2800 h aging at 200 °C without any significant degradation of (i) Hall sensitivity, (ii) two-dimensional electron gas, and (iii) Ohmic contacts. However, there was a small change in sheet density and mobility, which is due to a decrease in polarization, resulting from local inhomogeneous strain relief at the barrier layer. During the early stage of thermal aging, a decrease in contact resistance was also observed and attributed to (i) out-diffusion of "Ga" at the vicinity of the contact interface, and (ii) a reduction in oxygen concentration and formation of Al–Ti intermediate alloy at the GaN/Ti interface, resulting in a reduced barrier and enhanced electron transport at the contacts. However, despite these small changes, results indicate that the AlGaN/AlN/GaN Hall sensor provides stable performance for as long as 2800 h thermal aging at 200 °C. [ABSTRACT FROM AUTHOR]

Carbon fibers passing current are subject to resistive heating. When failure occurs, this is related to their local temperature. The failure temperature and its location are estimated. The temperature variation is calculated using analytical models for electrical and thermal conductivities based on the temperature dependent electron–phonon relaxation time. In the absence of radiative heat loss, an analytic expression of temperature along the fiber is given from which a maximum possible emission current is derived and is governed by a single introduced parameter ω o. A method of treating the radiative heat loss is developed and is governed by a second parameter γ , which allows a rapid numerical means to calculate the correction to the analytic form. Heat variation along a thick carbon fiber is contrasted to that along a multi-walled carbon nanotube (MWNT): it is shown that the relative magnitude of ω o compared to γ determines that the analytical formula is a good approximation for MWNTs but requires numerical correction for fibers. Furthermore, it is shown that the analytical form of ω o specified a maximum current beyond which the carbon emitter fails due to thermal runaway. The theoretical models are used to interpret observed behavior of field emission from carbon fibers and the resulting damage they endure when the extracted field-emission current is high. Results from implementing the developed temperature variation model into the MICHELLE beam optics simulation code are presented, with an example application predicting the conditions for stable equilibrium operation as well as for the onset of fiber failure. [ABSTRACT FROM AUTHOR]

A methodology for implementing the recently developed reformulated general thermal-field equation describing simultaneous thermal and field emission contributions to electron emission is developed, with modifications directed to enhancing speed and accuracy of computation as demanded by emitter characterization and electron beam simulations. An accurate factor to correct both thermal-field (T F) and high field (Fowler-Nordheim or FN) predictions based on a rapid Lorentzian fit model is given. The analytic protrusion model is constructed from modifications to a point dipole model that allow surface elements and field enhancement factors to be rapidly evaluated. The model is applied to an analytical model of a protrusion on a bump in a diode configuration to characterize how current-voltage I (V) relations are affected by T F emission conditions. In addition, it is also shown (i) how aggressively Schottky's conjecture is undermined as the protrusion dimensions become larger; (ii) how the total current in the T F regime can be substantially larger than predicted by canonical [FN and Richardson-Laue-Dushman (RLD)] formulations; (iii) how an optimal protrusion size may exist; and (iv) how the inference of field enhancement, notional emission area, and work function are poorly predicted using conventional methods relying on the canonical FN and RLD equations even outside the thermal-field regime, even though data can be linear on FN and RLD plots. [ABSTRACT FROM AUTHOR]

A methodology of modeling nonplanar surfaces, in which the microscale features of the emission sites can be orders of magnitude smaller than the mesoscale features defining the active emission area, has been developed and applied to both ordered arrays of identical emitters and random variations characteristic of a roughened surface. The methodology combines a general thermal-field-photoemission model for electron emission, a point charge model for the evaluation of field enhancement factors and surface geometry, and a Ballistic-Impulse model to account for the trajectories of electrons close to the cathode surface. How microscale and mesoscale features can both undermine the estimation of thermal-field emission parameters, such as characteristic field enhancement and total current predictions, as well as give rise to changes in the distribution of transverse velocity components used to estimate beam quality features such as emittance that are important to photocathodes, is quantified. The methodology is designed to enable both the proper characterization of emitters based on experimental current-voltage data and the development of a unit cell model of emission regions that will ease the emission model demands in beam optics codes. [ABSTRACT FROM AUTHOR]

Quantum tunneling by field emission from nanoscale features or sharp field emission structures for which the anode-cathode gap is nanometers in scale (“nano diodes”) experience strong deviations from the planar image charge lowered tunneling barrier used in the Murphy and Good formulation of the Fowler-Nordheim equation. These deviations alter the prediction of total current from a curved surface. Modifications to the emission barrier are modeled using a hyperbolic (prolate spheroidal) geometry to determine the trajectories along which the Gamow factor in a WKB-like treatment is undertaken; a quadratic equivalent potential is determined, and a method of shape factors is used to evaluate the corrected total current from a protrusion or wedge geometry. [ABSTRACT FROM AUTHOR]

Although Fowler and Nordheim developed the basics of field emission nearly one century ago with their introduction of the Fowler-Nordheim equation (FNE), the topic continues to attract research interest particularly with the development of new materials that have been proposed as field emitters. The first order analysis of experiments typically relies upon the FNE for at minimum a basic understand of the physical emission process and its parameters of emission. The three key parameters in the FNE are the work function, emission area, and field enhancement factor, all of which can be difficult to determine under experimental conditions. This paper focuses in particular, on the field enhancement factor β. It is generally understood that β provides an indication of the surface roughness or sharpness of a field emitter cathode. However, in this paper, we experimentally and computationally demonstrate that cathodes with highly similar surface morphologies can manifest quite different field enhancements solely through having different emission regions. This fact can cause one to re-interpret results in which a single sharp emitter is proposed to dominate the emission from a field emitting cathode. [ABSTRACT FROM AUTHOR]

Models of space-charge affected thermal-field emission from protrusions, able to incorporate the effects of both surface roughness and elongated field emitter structures in beam optics codes, are desirable but difficult. The models proposed here treat the meso-scale diode region separate from the micro-scale regions characteristic of the emission sites. The consequences of discrete emission events are given for both one-dimensional (sheets of charge) and three dimensional (rings of charge) models: in the former, results converge to steady state conditions found by theory (e.g., Rokhlenko et al. [J. Appl. Phys. 107, 014904 (2010)]) but show oscillatory structure as they do. Surface roughness or geometric features are handled using a ring of charge model, from which the image charges are found and used to modify the apex field and emitted current. The roughness model is shown to have additional constraints related to the discrete nature of electron charge. The ability of a unit cell model to treat field emitter structures and incorporate surface roughness effects inside a beam optics code is assessed. [ABSTRACT FROM AUTHOR]

The influence of a polymer capping layer on the deformation of purified single-wall carbon nanotube (SWCNT) networks is analyzed through the wrinkling of compressed SWCNT-polymer bilayers on polydimethylsiloxane. The films exhibit both wrinkling and folding under compression and we extract the elastoplastic response using conventional two-plate buckling schemes. The formation of a diffuse interpenetrating nanotube-polymer interface has a dramatic effect on the nanotube layer modulus for both metallic and semiconducting species. In contrast to the usual percolation exhibited by the pure SWCNT films, the capped films show a crossover from "composite" behavior (the modulus of the SWCNT film is enhanced by the polymer) to "plasticized" behavior (the modulus of the SWCNT film is reduced by the polymer) as the SWCNT film thickness increases. For almost all thicknesses, however, the polymer enhances the yield strain of the nanotube network. Conductivity measurements on identical films suggest that the polymer has a modest effect on charge transport, which we interpret as a strain-induced polymer penetration of interfacial nanotube contacts. We use scaling, Flory-Huggins theory, and independently determined nanotubenanotube and nanotube-polymer Hamaker constants to model the response. [ABSTRACT FROM AUTHOR]

RF-modulated electron beams, such as those produced by an RF linear accelerator, propagating through vacuum, air, and solid matter are well known to drive signals in microwave cavities and waveguides via interactions with these structures. Past experiments with a microwave waveguide in a radiation-shielded vault indicated the presence of a multipath propagation phenomenon, hypothesized to be a result of reflections of RF-modulated x rays. In this work, we study the signals induced in a microwave coaxial cable from nearby beam interactions with materials commonly found in accelerator facilities in order to better understand RF production and propagation in these environments. Our results show that (1) when an RF-modulated electron beam is incident on a block of aluminum, lead, or concrete, the frequency content of the induced microwave signals is strongly dependent on the orientation of the block and the relative position of the detector, (2) at least some of the detected signals are consistent with reflections off of the blocks, and (3) beam interactions with the blocks can induce appreciable microwave signals in detectors located tens of cm from the block. [ABSTRACT FROM AUTHOR]

An oft used approximation to predict quantum efficiency (QE) from bare metals or those with a low work function coating such as cesium is to assume that photo-excited electrons have not scattered prior to their emission. Monte Carlo simulations are used to assess that approximation, and show that, while good for bare metals, for cesiated metals a photoexcited electron may undergo several scattering events and yet be emitted. Neglecting scattered electrons therefore underestimates QE. Emitted electrons that have undergone scattering before emission elongate the response time by giving rise to a long time tail, low energy contribution to the faster non-scattered emission, for which a model is developed. The theory is applied to study variations in QE as a function of wavelength measured from cesiated metal surfaces. The extension of the findings to semiconductor photocathodes is briefly discussed. [ABSTRACT FROM AUTHOR]

Passing an electron beam through an aperture can serve to reduce the beam current or change the transverse beam profile. For a sufficiently intense beam, space charge will drive a radial expansion of the beam, which may cause the current passing through the aperture to decrease even though the current arriving at the aperture is increasing. When a gridded electron gun is used, this may be expressed by stating that the transconductance of the apertured gun is negative. Here, we explain this effect and explore some of the key factors governing when it can occur and influencing its strength. [ABSTRACT FROM AUTHOR]

A previous publication [P. D. McChesney, "Multi-plate interceptive electron beam energy diagnostic—Theoretical design," AIP Adv. (submitted)] reported a new interceptive electron beam kinetic energy measurement technique based on the beam penetration depth within a stack of conductive plates and gave results on the theoretical design of such a device. This paper expands on this and gives further results on the actual implementation of the diagnostic. The device geometry and measurement electronics system are described in detail. A prototype version of the multi-plate diagnostic was fabricated and tested using an electron linear accelerator at the Idaho Accelerator Center (IAC). A high-precision magnetic spectrometer system was designed and built for the purpose of validating the multi-plate diagnostic's energy measurement capabilities. It was found that the diagnostic provides electron beam energy estimates that are accurate to better than the 10% level. [ABSTRACT FROM AUTHOR]

Using real-time wave packet propagation we consider the scattering properties of a linear collision system consisting of a harmonic oscillator coupled by truncated Morse potentials to two particles. This system is viewed as a model for the collision of a projectile D with a three particle target ABC with interactions such that the possible final states comprise backscattering of the projectile with the target intact, the ‘‘exchange’’ reaction ABC+D→A+BCD and the ‘‘fragmentation’’ reaction ABC+D→A+BC+D. For the types of interaction considered, the exchange reaction was found to proceed primarily via inelastic resonant processes and to be the dominant event for incident energies below the oscillator energy. Fragmentation occurred via nonresonant processes and dominated at higher energy. Other features of the scattering are discussed and compared with simple quantum theory and the description of the system given by classical mechanics. [ABSTRACT FROM AUTHOR]

The dynamics of activated associative desorption is discussed with particular reference to the system H2–Cu and to the partitioning of the energy released among the various product degrees of freedom. It is argued that a simple theory based on transition-state concepts should hold for this system because the potential energy surface (PES) divides naturally into reactant and product regions, separated by a ‘‘seam’’ or ‘‘ridge’’ at which it is reasonable to assume a thermal distribution of desorbing trajectories. Using a PES constructed in accordance with available electronic structure calculations we consider the angular distributions and translational, vibrational, and rotational energy distributions of the desorbing molecules. It is shown that, whereas the rotational energy reflects the surface temperature, the vibrational energy is markedly enhanced because the energetically low-lying regions of the ridge in the PES correspond to an H–H bond distance that is distended as compared with the gas-phase equilibrium separation. The enhancement is found to be a strong function of the surface temperature. The translational energy, however, is found to be only very weakly dependent on the temperature. These results are discussed in connection with available data. [ABSTRACT FROM AUTHOR]

A systematic study was made on the optical absorption spectra of permethyl oligosilanes, CH3[CH3–Si–CH3]NCH3, as a function of their backbone chain length from N=2 to 16 by using first principles [density functional with local density approximation (LDA)] electronic structure calculations. The general features of the calculated spectra agree with those of experimental measurements. Analysis of the nature of optical transition revealed the existence of two qualitative crossovers at chain lengths of N=2 and around N=10 and 12. The first one is associated with the molecular orbitals giving rise to the first ultraviolet absorption peak, while the second one is associated with the crossover from ‘‘molecular’’ to ‘‘polymeric’’ as the oligomers become larger. The broadening of the first absorption peaks is estimated by the vibration modes and electronic relaxation energies in the oligomers. Comparison with calculated results by a model Hamiltonian based on the Sandorfy C model is made and the relative merit of semiempirical and LDA calculations is discussed. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Analytic image charge approximations exist for planar and spherical metal surfaces but approximations for more complex geometries, such as the conical and wirelike structures characteristic of field emitters, are lacking. Such models are the basis for the evaluation of Schottky lowering factors in equations for current density. The development of a multidimensional image charge approximation, useful for a general thermal-field emission equation used in space charge studies, is given and based on an analytical model using a prolate spheroidal geometry. A description of how the model may be adapted to be used with a line charge model appropriate for carbon nanotube and carbon fiber field emitters is discussed. [ABSTRACT FROM AUTHOR]

This paper reports an experiment that studies the emission characteristics of small number of field emitters. The experiment consists of nine carbon fibers in a square configuration. Experimental results showthat the emission characteristics depend strongly on the separation between each emitter, providing evidence of the electric field screening effects. Our results indicate that as the separation between the emitters decreases, the emission current for a given voltage also decreases. The authors compare the experimental results to four carbon fiber emitters in a linear and square configurations as well as to two carbon fiber emitters in a paired array. Voltage-current traces show that the turn-on voltage is always larger for the nine carbon fiber emitters as compared to the two and four emitters in linear configurations, and approximately identical to the four emitters in a square configuration. The observations and analysis reported here, based on Fowler-Nordheim field emission theory, suggest the electric field screening effect depends critically on the number of emitters, the separation between them, and their overall geometric configuration. [ABSTRACT FROM AUTHOR]

In arrays of ungated field emitters, nearby emitters introduce a screening effect, reducing each emitter's field enhancement factor below its value in isolation. At the edge of the array, however, the strength of this screening effect is reduced because the number of nearby emitters is reduced, leading to a variation in the emitted current with position in the array. This may have detrimental effects on the emitted beam properties and lead to increased damage to the emitters near the edge due to increased current, heating, and ion bombardment. In this work, the authors apply line and point charge models to study the impact of screening on the performance of two-dimensional field emitter arrays, with an emphasis on quantifying the extent of the edge enhancement effect, and on assessing potential means to control it. [ABSTRACT FROM AUTHOR]

A Point Charge Model of conical field emitters, in which the emitter is defined by an equipotential surface of judiciously placed charges over a planar conductor, is used to confirm Schottky's conjecture that field enhancement factors are multiplicative for a small protrusion placed on top of a larger base structure. Importantly, it is shown that Schottky's conjecture for conical / ellipsoidal field emitters remains unexpectedly valid even when the dimensions of the protrusion begin to approach the dimensions of the base structure. The model is analytic and therefore the methodology is extensible to other configurations. [ABSTRACT FROM AUTHOR]

When an electron beam is apertured, the transmitted beam current is the integral of the incident beam current density over the aperture area. Space charge forces generally cause an increase in incident beam current to result in an increase in incident beam spot size. Under certain circumstances, the spot size will increase faster than the current, resulting in a decrease in current extracted from the aperture. When using a gridded electron gun, this can give rise to negative transconductance. Here, this effect is explored in the case of an intense beam propagating in a uniform focusing channel. It is shown that proper placement of the aperture can decouple the current extracted from the aperture from fluctuations in the source current, thereby isolating systems downstream of the aperture from upstream current fluctuations. It is also shown that apertures can serve to alter longitudinal space charge wave propagation by changing the relative contribution of velocity and current modulation present in the beam. [ABSTRACT FROM AUTHOR]

A sawtooth waveform inspired pitch estimator (SWIPE) has been developed for speech and music. SWIPE estimates the pitch as the fundamental frequency of the sawtooth waveform whose spectrum best matches the spectrum of the input signal. The comparison of the spectra is done by computing a normalized inner product between the spectrum of the signal and a modified cosine. The size of the analysis window is chosen appropriately to make the width of the main lobes of the spectrum match the width of the positive lobes of the cosine. SWIPE′, a variation of SWIPE, utilizes only the first and prime harmonics of the signal, which significantly reduces subharmonic errors commonly found in other pitch estimation algorithms. The authors’ tests indicate that SWIPE and SWIPE′ performed better on two spoken speech and one disordered voice database and one musical instrument database consisting of single notes performed at a variety of pitches. [ABSTRACT FROM AUTHOR]

We report on a frequency doubled 980 nm vertical external cavity surface emitting laser for applications in confocal laser scanning microscopy. The beam quality, wavelength flexibility, and low noise characteristics of this compact source make this prolific imaging technique an exemplary tool. Single pass frequency doubling via KNbO3 was demonstrated, yielding 1.8 mW at 490 nm with a near diffraction limited beam quality. Detailed analysis and comparison of the laser performance with the current standard argon ion laser revealed clear advantages of the solid-state source for confocal imaging. Imaging of fluorescein and eGFP labeled biological samples using the attenuated solid-state source provided high-resolution images at lower cost and with improved reliability. [ABSTRACT FROM AUTHOR]

This article outlines the difficulties associated with measuring quantum yields for solid-state samples using a high-pressure mercury arc lamp as the irradiation source. Details are given for the conversion of an inexpensive frequency-doubled neodymium-doped yttrium aluminum garnet (Nd:YAG) diode laser pointer module into a viable irradiation source. The modified Nd:YAG laser was incorporated into a computer-controlled system, which allowed for the simultaneous irradiation and spectroscopic monitoring of the sample. The data obtained with the Nd:YAG diode laser system show far less scatter than data obtained with a high-pressure Hg arc lamp, and consequently the degradation rates obtained with the laser system could be calculated with far greater accuracy. [ABSTRACT FROM AUTHOR]

Current automatic acoustic detection and classification of microchiroptera utilize global features of individual calls (i.e., duration, bandwidth, frequency extrema), an approach that stems from expert knowledge of call sonograms. This approach parallels the acoustic phonetic paradigm of human automatic speech recognition (ASR), which relied on expert knowledge to account for variations in canonical linguistic units. ASR research eventually shifted from acoustic phonetics to machine learning, primarily because of the superior ability of machine learning to account for signal variation. To compare machine learning with conventional methods of detection and classification, nearly 3000 search-phase calls were hand labeled from recordings of five species: Pipistrellus bodenheimeri, Molossus molossus, Lasiurus borealis, L. cinereus semotus, and Tadarida brasiliensis. The hand labels were used to train two machine learning models: a Gaussian mixture model (GMM) for detection and classification and a hidden Markov model (HMM) for classification. The GMM detector produced 4% error compared to 32% error for a baseline broadband energy detector, while the GMM and HMM classifiers produced errors of 0.6±0.2% compared to 16.9±1.1% error for a baseline discriminant function analysis classifier. The experiments showed that machine learning algorithms produced errors an order of magnitude smaller than those for conventional methods. [ABSTRACT FROM AUTHOR]

Mel frequency cepstral coefficients (MFCC) are the most widely used speech features in automatic speech recognition systems, primarily because the coefficients fit well with the assumptions used in hidden Markov models and because of the superior noise robustness of MFCC over alternative feature sets such as linear prediction-based coefficients. The authors have recently introduced human factor cepstral coefficients (HFCC), a modification of MFCC that uses the known relationship between center frequency and critical bandwidth from human psychoacoustics to decouple filter bandwidth from filter spacing. In this work, the authors introduce a variation of HFCC called HFCC-E in which filter bandwidth is linearly scaled in order to investigate the effects of wider filter bandwidth on noise robustness. Experimental results show an increase in signal-to-noise ratio of 7 dB over traditional MFCC algorithms when filter bandwidth increases in HFCC-E. An important attribute of both HFCC and HFCC-E is that the algorithms only differ from MFCC in the filter bank coefficients: increased noise robustness using wider filters is achieved with no additional computational cost. [ABSTRACT FROM AUTHOR]

Our earlier study [J. Pott and J. G. Harris, J. Acoust. Soc. Am. 76, 1829-1838 (1984)] of the reflection and refraction, at a plane fluid-solid interface, of a Gaussian beam is continued. When the angle of incidence approaches the angle at which the compressional wave is critically refracted, a lateral wave is excited both in the fluid and in the solid. In the fluid, this wave interferes with the reflected beam, making it appear shifted and distorted. A second lateral wave is excited in the fluid when the angle of incidence nears that at which the shear wave is critically refracted. However, this angle is usually quite close to the Rayleigh angle. Thus the nearly coincident excitation of a leaky Rayleigh wave (examined in our earlier paper) masks any effect the lateral wave has. But even for angles of incidence not near these three critical angles, the axis of the reflected beam is slightly rotated and displaced. The refracted beams (examined in our earlier paper) spread quite rapidly in the solid, but, by using a thin lens to focus the incident beam, this spreading can be reduced somewhat. [ABSTRACT FROM AUTHOR]

The reflection and refraction at a fluid-solid interface of an acoustic beam, whose amplitude is Gaussian in cross section and which oscillates harmonically in time, is studied. The incident and scattered beams are constructed using the complex source-point method. The incident beam is specularly reflected except at angles near one of the critical angles, of which the Rayleigh angle is the most important. Near this angle the beam excites both a leaky Rayleigh wave and a reflected beam, and the interference between these two disturbances produces the beam shifting noted by other workers. Surprisingly, a backward-traveling leaky Rayleigh wave is also excited, although its amplitude is quite small. The incident beam, near normal incidence, is refracted into a compressional beam and a shear beam, both of whose amplitudes are Gaussian in cross section. Whereas the incident beam has a circularly shaped cross section, both transmitted beams have elliptically shaped cross sections. Moreover, the transmitted beams spread rapidly so that the compressional and shear beams always overlap. This rapid spreading limits the resolution of ultrasonic probes used to find cracks or other defects in a solid. [ABSTRACT FROM AUTHOR]

At frequencies where the thickness of an elastic plate is more than a wavelength, the propagation of the two lowest Rayleigh-Lamb modes in an elastic plate can be viewed as the propagation of a Rayleigh surface wave over two weakly coupled, surface-wave waveguides. That is, a Rayleigh wave launched on one surface gradually transfers to the other and then back. It does so in a length we call the beatlength. Measurements of the beatlength for brass plates are reported as a function of frequency and thickness. This phenomenon is readily excited and persists over a wide range of thicknesses and frequencies © 1997 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

The antiplane shear, SH or scalar problem of scattering from an interface characterized by a narrow region of heterogeneity is considered. An approximate integral representation of the scattered wave fields in terms of a Green's function for a reference problem, and the stress and momentum polarizations averaged through the thickness of the interface is derived. Providing certain material contrast parameters are O(1), the error in this expression is formally O(kh)2, where k is the wave number and 2h is the thickness of the interface. To find the unknown polarizations we specialize to a model configuration that is periodic over a length scale much greater than the characteristic length scales of the heterogenities in the interface. This allows an exact formulation in terms of an infinite system of algebraic equations. Expressions modeling the reflection and transmission measured by a coaxial, confocal pair of transducers are then derived so that the effects of the transducer can be included in the modeling. These coefficients are calculated in terms of the solution of the algebraic system. Numerical results for several different model interfaces are presented. © 1996 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

The viscous and thermal boundary layer attenuation, and the acoustic streaming that accompanies the lowest acoustic mode propagating down a long, wide circular tube are calculated asymptotically. By fully including the effects of compressibility and heat conduction, corrections are made to earlier work. The leading order acoustic wave solution is analyzed using matched asymptotic expansions. The matching gives the dispersion relation and from this a model propagation equation is proposed. These results agree with earlier ones derived quite differently. The acoustic streaming driven by the Reynolds stress in the boundary layer is analyzed next. The streaming velocities are calculated and the corrections to earlier expressions, arising from the effects of compressibility and heat conduction, are expressed in terms of the Prandtl number and the specific heat ratio. Further, a second-order time-independent temperature field caused by the passage of the wave is found. [ABSTRACT FROM AUTHOR]

A mathematical model describing how a confocal arrangement of two focused ultrasonic transducers is used to interrogate a complex interface between two materials by scanning the focal point across the interface is outlined. A complex interface is one that has roughness and partial contact at several length scales, many of which are equal to or smaller than the compressional or shear wavelength in the material. When the focused ultrasound strikes such an interface, though the focal region be small, multiple scattering takes place among the scatterers within and adjacent to the focal region, making it unclear exactly how the interface is being sampled. To clarify this issue a specific interface model, consisting of a planar array of multiple small cracks having arbitrary lengths and spacings, is used. This interface is interrogated by a focused, antiplane shear wave. While the antiplane assumption makes it scalar, the model shows that what is measured are the multiply scattered signals averaged over the aperture of the transducer, and that the dominant contribution comes from the scattered signals that phase match to the interrogating signal. Explicit expressions relating the modeled reflected and transmitted signals to the convolution of the incident wave field with the crack-opening displacements at the focal region are given. Numerical examples are worked out for similar and contrasting materials on each side of the interface. [ABSTRACT FROM AUTHOR]

The compressional and shear waves reflected from a semi-infinite crack and diffracted from its edge when it is struck by a two-dimensional compressional beam are calculated asymptotically. Both a beam whose amplitude is initially rectangular and one whose amplitude is Gaussian are studied. The crack is positioned perpendicular to the central ray of the incident beam. Further, the crack lies in the near- to farfield transition region of the incident beam. Thus the incident beam is only slightly divergent when it strikes the crack edge. For the incident rectangular beam, approximations representing the reflected and transmitted beams plus their interactions with the diffracted waves at the reflection and shadow boundaries are calculated from integral representations of the scattered waves. However, the diffracted waves outside the boundary regions are omitted. In contrast, for the incident Gaussian beam, all the waves scattered from the crack edge are calculated. However, to calculate the wave fields in the reflection and shadow boundary regions, working with the integral representations was abandoned. Instead, boundary layer equations are derived and solved. One result of these analyses, which was not anticipated, is that the reflection and shadow boundaries must be found as part of the boundary layer analyses. [ABSTRACT FROM AUTHOR]

The authors comment upon the role played by those roots of the Rayleigh equation that are referred to as extraneous, as well as upon the work of the paper given in the title. © 2002 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

The design of an acoustic lens that reduces the diffraction spreading from an ultrasonic transducer to produce a narrow focused beam is proposed. The design is based upon a description of the radiated field using the geometrical theory of diffraction. [ABSTRACT FROM AUTHOR]

The imaging of thin solid films or interfaces by a confocal arrangement of ultrasonic transducers is modeled in both a two-dimensional and a three-dimensional context. In the first model, an antiplane shear, focused beam is directed across an interface comprised of an array of cylinders, with contrasting material properties. Its periodicity is destroyed by removing cylinders arbitrarily. In the second, a thin solid film, having quite general mechanical properties, is immersed in a fluid and scanned by a three-dimensional acoustic beam. This last work is only partially completed. An approximate integral representation of wave fields scattered by these thin regions of heterogeneity in terms of a Green's function for the host media, and the stress and momentum polarizations averaged through the thickness of the film or interface is the starting point. The stress polarization measures the change in elastic properties and the momentum polarization that in inertial properties, both changes being with respect to the properties of the host media. The scattered waves are calculated by formulating and solving integral equations. Those received are estimated using a measurement model that mimics the receiving transducer. [Supported by the NSF, MSS 91-14547.] [ABSTRACT FROM AUTHOR]

Ultrasonic transducers, operating at microwave frequencies, radiate highly directional wave fields or beams. These beams are used to probe solids for defects such as cracks. To model this process, the compressional and shear waves reflected from a semi-infinite crack and diffracted from its edge when it is struck by a two-dimensional, compressional beam are calculated asymptotically. A beam whose initial cross section is rectangular is considered. The crack is assumed to lie in the nearfield or in the nearfield-farfield transition region of the incident beam. Thus the incident beam is only slightly divergent when it strikes the crack edge, and it ensonifies only a finite region of the crack surface. But this region acts as if it were a secondary aperture. Therefore, of particular interest in the calculation are the results showing how the reflected beam diverges as it propagates away from this secondary aperture and arrives at the aperture of the incident beam. [Work supported by NSF.] [ABSTRACT FROM AUTHOR]

Analytical results are presented that describe the Rayleigh waves excited by the acoustic emission from a crack that suddenly starts to grow. At first a two-dimensional crack is considered, then the results are extended to three dimensions. The plane of crack growth is inclined to the surface. The fracture mode can be brittle or some plastic yielding at the crack edge can take place. The analysis consists of two parts. First, wavefront approximations to the acoustic emission are calculated. Second, representation integrals for the Rayleigh waves are constructed using the compressional and shear emissions in combination with an appropriate Green's tensor. The integrations are taken over the wavefronts of the emitted signals and the integrals are evaluated asymptotically. Graphs of the resultant surface motion are given. [Work supported by NSF(MEA-8104738).] [ABSTRACT FROM AUTHOR]

The steady-state response induced by an ultrasonic wave in a structure comprised of two layers, a bubbly liquid, and a viscoelastic solid with a rigid boundary, is studied in the linear approximation. This structure models a steadily cavitating liquid in contact with tissue. The upper surface of the liquid is driven harmonically and models the source. The lower surface of the solid is rigid and models bone. Though the cavitation processes are nonlinear, the propagation is approximated as linear. The model of the bubbly liquid is a simple continuum one, supplemented by allowing for a distribution of different bubble radii and for damping of the oscillations of each bubble. The model contains three functions, the probability distribution describing the distribution of bubble radii, and two functions modeling the mechanical response of, respectively, the individual bubble and the tissue. Numerical examples are worked out by adapting data taken from various published sources to deduce the parameters of these functions. These examples permit an assessment of the overall attenuation of the structure, and of the magnitude of the pressure and particle velocity in the bubbly liquid, and of the traction and the particle displacement in the tissue. [Partial support from Arjo, Inc., Morton Grove, IL.] [ABSTRACT FROM AUTHOR]

A model is proposed in this report to describe the potential growth of an existing crack in the structural component caused by collapsing bubbles during ultrasonic cleaning. A local pressure rise is generated by the collapse of a single bubble and the momentum of the collapse is described by the Kelvin impulse I(t). By assuming a uniform pressure distribution and using dynamic fracture mechanics, we obtain a simple relation that expresses the dynamic stress intensity factor K(t) as a function of the Kelvin impulse. Further simplification is achieved by assuming spherical bubble deformation in the description of the Kelvin impulse, as suggested by Blake and Gibson [Ann. Rev. Fluid Mech. 19, 99-123 (1987)], and this leads to a relation between the dynamics of a single bubble and the stress intensity factor K(t). The time history of K(t) is discussed for a completely collapsed bubble obeying the Rayleigh equation. Once the dynamical stress intensity factor exceeds the fracture toughness KIC crack will start to grow. Repeated action of collapsing bubbles eventually leads to the failure of the component. [Work supported by the Manufacturing Research Center of the University of Illinois.] [ABSTRACT FROM AUTHOR]

Ultrasound can be focused by the curved fluid-solid interface of a solid part being interrogated for cracks or by using a lens as part of an imaging system such as the acoustic microscope. In the latter case it is usually difficult to form a diffraction-limited spot when the focus lies in the solid because the focused beam field must cross a fluid-solid interface. This paper summarizes recent investigations of these two situations. A calculation of the wave fields near the caustics formed when a two-dimensional (unfocused) beam scatters from a concave fluid-solid interface is discussed. Also discussed is a calculation of the wave fields within the focal region of a three-dimensional, wide aperture source when the focused beam is directed across a plane fluid-solid interface and the focal region lies in the solid. In both cases attention is paid to the interplay between the diffraction effects of the source and of the focal region, and also to the excitation of leaky surface waves. The implications of these considerations for the quantitative interpretation of ultrasonic measurements are explored. [ABSTRACT FROM AUTHOR]