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Technical requirements for elastic (metal) cylindrical shells include the knowledge of their natural frequency spectrum. These shells may be empty and fluid-immersed, or fluid-filled in an ambient medium of air, or doubly fluid-loaded inside and out. They may support circumferential waves, or axially propagating waves both in the shell material, and in the fluid loading. Previous results by Bao et al. (J. Acoust. Soc. Am. 105 (1999) 2704) were obtained for the circumferential-wave dispersion curves on doubly loaded aluminum shells; the present study extends this to fluid-filled shells in air. For practical applications, steel shells are most important and we have here obtained corresponding results for these. To find the natural frequencies of cylindrical shells, one may invoke the principle of phase matching where resonating standing waves are formed around the circumference, or in the axial direction if the cylindrical shell is terminated at both ends. In this way, we obtain (circumferential and axial wave) eigenfrequency spectra for water filled aluminum and steel shells, and also for brass shells (axial-wave resonances only).

Exact calculations of the scattering of radar pulses from a perfectly conducting wire, employing the Einarsson expression for the wire scattering amplitude, have indicated (Y. Guo, Ph.D. thesis, Catholic University, Washington, DC) the appearance of multiple return pulses, related to back-and-forth reflections of traveling waves along the wire. These reflections give rise to resonances in the scattering amplitude. We here show, using a method devised by Werby for an analogous acoustic scattering problem, that the set of resonances can be mathematically related to the appearance of pulsed multiple returns, hereby providing an alternate, simplified approach to the study of traveling wave pulses and their generating of return pulses in radar scattering from wires.

In earlier studies of acoustic scattering resonances and of the dispersive phase velocities of surface waves that generate them [see, e.g., Talmant et al., J. Acoust. Soc. Am. 86, 278–289 (1989) for spherical aluminum shells] we have demonstrated the effectiveness and accuracy of obtaining phase velocity dispersion curves from the known acoustic resonance frequencies. This possibility is offered through the condition of phase matching after each complete circumnavigation of these waves [Überall et al., J. Acoust. Soc. Am. 61, 711–715 (1977)], which leads to a very close agreement of resonance results with those calculated from three-dimensional elasticity theory whenever the latter are available. The present investigation is based on the mentioned resonance frequency/elasticity theory connection, and we obtain comparative circumferential-wave dispersion-curve results for water-loaded, evacuated spherical metal shells of aluminum, stainless steel, and tungsten carbide. In particular, the characteristic upturn of the dispersion curves of low-order shell-borne circumferential waves (A or A0 waves) which takes place on spherical shells when the frequency tends towards very low values, is demonstrated here for all cases of the metals under consideration. ©2002 Acoustical Society of America.

Water-filled elastic shells present more complicated backscattered echoes when compared to evacuated shells and are less well understood. The objective here is to determine and explain features peculiar to such objects and to use these features to aid in object characterization. Towards that end, an acoustic background suitable for such targets in conjunction with "residual" partial wave analysis obtained from subtracting the background from the elastic response is used. This analysis is aided by the determination and comparison of plate modes and resonance locations of evacuated unloaded, evacuated loaded, and loaded water-filled shells. Analysis of water-filled shells suggests that there exist isolated narrow, uniformly spaced eigenmodes in addition to the elastic modes. The broader elastic modes appear split in comparison to their unloaded counterparts. Otherwise, the elastic modes are not greatly affected by the included eigenmodes. The isolated (included) eigenmodes are extremely well modeled by a water inclusion in an infinite elastic matrix composed of the elastic shell material. The splitting of elastic modes proves to be due to interference of the included eigenmodes and the elastic body resonances. This leads to what appear to be separate branches of dispersion curves related to the elastic modes. Because of the numerous and usually evenly spaced included eigenmodes, dispersion curves are dominated by the abundance of these modes. A clear picture of the physical processes emerges from this analysis that explains all features of this event. Simple sets of rules that lead to tractable calculations are introduced that facilitate analysis of this interesting physical process.

The present study extends our previous work that concerned the effective permittivities and absorptivities of particulate composites consisting of graphite-type microsphere inclusions in a dielectric matrix, and their suitability as radar-absorbing materials. Whereas in that work spheres of one size (radius a=50 μm) had been considered only, we here study the dependence of the results on the sphere radius of up to one or several millimeters, and find sizable effects on permittivities for a⩾1 mm, and below that for the absorptivities, indicating the increasing importance of multiple scattering effects. While the multiple-scattering formulas utilized here are based on a low-frequency approximation, we devise a modification of these formulas in order to extend their validity to higher frequencies (or larger particle sizes).

The existence of a unique axisymmetric non-radiating surface wave near a cylindrical elastic shell submerged in a fluid and described by Kennard's model is proved.

We present a numerical study of the frequency dependent, complex effective permittivity e for a composite material which consists of lossy graphite-type microsphere inclusions randomly imbedded in a dielectric matrix, with a view towards assessing the suitability of such a composite for its use as a radar absorbing material (RAM). This suitability is determined by the material possessing a large effective absorptivity while at the same time not giving rise to an overly large reflectivity. In this vein we here evaluate, as a function of frequency up to 20 GHz, the effective magnitudes of Re e and Im e for particulate composites and their dependence on the volume fraction φ of the particles, while independently varying conductivities. Our calculations are carried out using both the effective-medium theory (mixture theory, valid for small φ), and the multiple-scattering theory of Tsang and Kong valid for general φ but for small particle sizes. Multiple-scattering effects lead to increased effective absorptiv...

The complex eigenfrequencies of a fluid-immersed evacuated infinite cylindrical shell, when plotted in the complex frequency plane, can be grouped into families corresponding to different types of circumferential waves. The dispersion curves versus frequency of the phase velocities of these circumferential waves are analogous to those of the Lamb waves on a plate A0, A1,… and S0, S1,…, but contain an additional branch reminiscent of the fluid-borne Scholte–Stoneley wave. This branch together with the A0-analog forms an interacting pair of dispersion curves A0+ (upper branch) and A0− (lower branch) which exhibit a repulsion phenomenon near the ambient fluid sound speed. Results of a recent numerical study of this phenomenon are here explained by perturbation theory, showing that during repulsion the wave character gets exchanged so that at frequencies above repulsion A0+ is a flexural and A0− a fluid-borne wave, and vice versa below repulsion.

International audience; The scattering of acoustic waves by an elastic sphere embedded in an elastic isotropic medium is investigated. Expressions for the scattered waves are given in terms of monostatic and bistatic scattering cross sections. The resonances of the solid sphere were determined numerically in the individual normal mode amplitudes; dispersion curves for the phase velocities of the circumferential waves were also obtained. Computations and experimental results for an aluminum sphere embedded in Plexiglas were in good agreement.

Experimental results are presented for sound scattering from elastic prolate and oblate spheroidal scattering objects. The backscattered waveform, the target strength versus incident angle, and the frequency response of the echoes are obtained directly from experimental data or via numerical processing of these data. Analytical models and computer codes are developed for estimating the arrival times of the elastic echoes and the resonance modes.

The predictions of resonance frequencies for elongated elastic cylinders and spheroids, based on various methods of approach, were discussed in a number of papers in recent years. In the present study, the regions of applicability of the phase matching method for surface waves and of the longitudinal bar wave approximation are examined by comparing the predicted results with the results of T-matrix calculations or with the results of scattering experiments.

The resonance scattering theory (RST) and the singularity expansion method (SEM) are both based on the complex-frequency poles of the scattering amplitude in the scattering of acoustic, elastic, or electromagnetic waves from elastic or impenetrable objects, or from cavities. These poles, situated off the real frequency axis at locations with negative imaginary parts, are found to yield, at the real frequencies of the experiments, prominent resonances for acoustic and elastic-wave scattering from elastic objects as discussed in our earlier review (U¨berall et al, Appl Mech Rev43(10), 1990, 235). However, as the authors demonstrated before (U¨berall et al, J Acoust Soc Am61, 1977, 711), the origin of these resonances lies in the phase matching of circumferential or surface waves generated on the target objects during the scattering; hence a study of the resonances will lead to an understanding of, and information on these surface waves. This has been the topic of a large number of studies in recent years, and the results are summarized in the present review for immersed elastic target objects of plane, spherical, and cylindrical geometry, including both elastic-type and fluid-borne surface waves. For multilayered elastic structures, we also describe possible layer-resonance identifications based on acoustic and elastic-wave scattering experiments.

The resonance scattering theory and the singularity expansion method are based on the complex‐frequency poles of the scattering amplitude; these are located off the real‐frequency axis and lead to prominent resonances. Their physical origin lies in a phase matching of surface waves generated on the scattering object; hence a study of the resonances will lead to information on these surface waves. This will be demonstrated here for immersed elastic objects of plane, spherical, and cylindrical geometry where even the physical nature (fluidborne or elastic type) of the surface waves can be identified along portions of their dispersion curves, and where for multilayered structures individual‐layer resonances can be distinguished, leading to solutions of the corresponding inverse problem.

Acoustic resonance scattering from a water‐immersed, solid tungsten carbide target in the form of a finite‐length circular cylinder terminated by two hemispherical endcaps has been studied experimentally, and analyzed theoretically. The resonance frequencies have been determined from the condition of phase matching of the generated surface waves encircling the object; for the surface waves propagating over its cylindrical portion in the axial direction, the dispersion has been properly taken into account, as well as that of surface waves on the spherical surfaces. Surface displacements corresponding to the standing waves at each resonance were determined, and were used to calculate the angular patterns of the scattered acoustic field, in excellent agreement with the observed angular distributions. The pattern of lobes is found to provide information on the mode N of the standing surface waves, although in a less straightforward fashion than this had been the case in previous studies for the simple example...

The Lamb waves propagating in an elastic plate in vacuo generate compressional (L) and shear type (T) plate vibrations that are coupled due to the boundary conditions. Without such coupling, their phase‐velocity dispersion curves would form two intersecting families, which at high frequency tend towards the elastic‐wave speeds CL and CT, respectively. It is shown that the coupling causes a repulsion of the dispersion curves, similar to that encountered in atomic physics for the energy levels of atoms combining into molecules, which prevents their intersection and at the same time exchanges the nature (L↔T) of the underlying vibrations. However, in the repulsion regions a succession of dispersion curves combines to asymptotically approach the uncoupled L or T dispersion curves, respectively. For the case of a plate bounded by fluid on one side, and vacuum on the other, the dispersion curves of the fluid‐borne (Stoneley–Scholte type) wave, which is known from the studies of Grabovska and Talmant to be prese...

The amplitude of sound scattered from submerged elastic objects is dominated by resonance phenomena corresponding to the mechanical eigenvibrations of the object. It is often difficult to predict the resonance frequencies of bounded elastic targets using exact methods. It has been shown, however, that resonances arise due to phase matching of circumferential waves traveling over the object surface. This leads to a standing-wave picture for the resonances, and a phase matching condition can be established that can lead to accurate predictions of resonances for objects of simple or complex shapes. In order to use this method, it is necessary to obtain the phase velocity of the surface waves. This is illustrated for spheroids and cylinders with hemispherical endcaps. The water loading of the object is of importance since it leads, in addition to the elastic surface waves, to the appearance of a fluid-borne "Scholte" or "Stoneley" wave which interacts with the lowest-order elastic wave, giving rise (for thin shells) to a repulsion phenomenon in the phase-velocity dispersion curves of the corresponding waves analogous to that known for energy levels in atomic or molecular systems. Of further importance is the effect of internal attachments to shell-type objects which also leads to the interaction of different wave types. For multilayered structures, it is finally shown that one may isolate and identify the resonances arising from individual layers using the method of Gérard.

A resonance effect of transient fields on thin conducting wires is observed and analyzed. The resonant response essentially depends on the matching of the spectrum of the incident pulse with the characteristic spectrum of the wire. It has been found, accordingly, that a one-cycle sine waveform with appropriate time interval can excite resonant responses in backscatter, bistatic, and specular scattering. The responding waveform can be well interpreted by the concept of a travelling wave. It gives insight into the resonance phenomenon, showing that the pulse illuminating the wire excites very strong surface waves at resonance. The resonant time interval of the sine waveform is determined by the wire length and the angle between the incident direction and the wire axis; it becomes narrower as the angle gets closer to the wire axis. >

The effects of an almost‐periodically spaced set of ribs on the scattering of sound from a submerged cylinder of finite length are investigated. The cylinder is either assumed soft (corresponding to a very thin air‐filled shell), or rigid (corresponding to a heavy thick shell) and its scattering amplitude is obtained using the geometrical theory of diffraction. The rib scattering amplitude is found from curvature‐corrected results of the theory for a flat plate carrying a rib. Numerical results were obtained for the case of soft cylinders (i.e., thin, air‐filled shells); they exhibit the onset and emergence of rib effects over the background of scattering from the body of the cylinder.

The stability of interface waves on a compliant coating, attached to a rigid substrate and exposed to a laminar or turbulent fluid flow, has been the subject of several theoretical studies, and of experimental investigations in which the onset and growth of instability waves was determined. Solutions of the characteristic equation of the problem have been obtained, which furnish dispersion curves and stability information for the interface waves, assuming a compressible fluid in order to attain the correct static limit. It is shown that the excitation of these interface waves by incident inhomogeneous acoustic signals can occur in a resonant fashion. Using this approach, an accurate experimental determination of the dispersion curves, of the onset of instability, and of the growth properties of interface waves appears to be possible.

Measured microwave attentuation values of 20–65 dB have been reported for composites and mats, containing conductive graphite fibers (‘‘fibrils’’) of 0.01 μm diameter and up to several hundredths of a millimeter length, in weight concentrations of up to 44%. The measured attenuation is interpreted here in terms of effective medium theory, according to which the composites may either behave as a ‘‘transparent’’ conductor (with essentially no conductivity) if the fibers don’t touch each other, or else as an actual, but less efficient conductor for the case where electrical contacts between the fibers have been established. Under this latter assumption, the attenuation could be well explained both in the lower frequency ranges, as well as at frequencies up to the measurement limit of 3 GHz. Quantitative fits were achieved by assuming a reduced ‘‘effective’’ conductivity of the composite due to imperfect contacts between the fibers.

In practical applications it is necessary to analyze radar scattering by a chaff cloud in a ground-based system rather than in the scattering plane-based system. By means of the Stokes-parameter method, a series of expressions of the bistatic radar scattering cross section (BRSCS) corresponding to arbitrarily polarized combinations of transmitters and receivers are derived in the ground-based system in the present study. The influence of chaff wires' orientation on the BRSCS is also studied based on the comparison between the cases of the spherically randomly oriented wires and the horizontally Gaussian-distribution-oriented wires, which may provide a valuable reference for designing various types of chaff as well as transmitter and receiver systems upon different demands.

A detailed set of measurements has been obtained using a model of a typical shallow‐water channel, which included both a sediment and a substrate, and the results have been compared with numerical prediction codes. Good agreement with the numerical calculations of the acoustic field was obtained at high frequencies if the input parameters were optimized, within realistic bounds of their measured values.

The vibratory response of a driven viscoelastic rod has been used in earlier investigations to measure the complex elastic modulus of the rod material. The transfer function T, i.e., the ratio of displacements (or accelerations) at the end of the rod divided by those at the driven end, is obtained as a function of frequency and rod length. In terms of these variables, it exhibits resonance peaks. In the present work, following the developments of Fiorito et al. [J. Acoust. Soc. Am. 79, 222 (1986)], the transfer function is represented as a meromorphic function of the frequency with complex poles, in order to isolate the individual resonances. Such a representation allows a clean determination of resonance frequencies and widths, and thus leads to a more sensitive measurement of the complex elastic modulus of the rod material. Comparison of exact theory and this resonance theory formulation of T is presented for various rod materials.

A definitive method for the calculation of the bistatic radar scattering cross section of a cloud of randomly oriented conducting wire dipoles has been developed by Dedrick et al. [6]. It is based on a Stokes parameter formalism, thus containing complete information regarding transmitter and receiver polarizations. Since the single-wire cross section exhibits strong resonance effects, it is of interest to investigate to what extent these resonance phenomena are affected by the orientation average in a cloud of randomly oriented wires. To study this question, we present comprehensive three-dimensional graphs of the relevant bistatic cross sections plotted versus scattering angle and frequency, as well as of the various polarization functions, using the Einarsson wire cross section. The results indicate the degree to which the resonance features persist in both cross section and polarizations after orientation averaging.

The acoustic scattering from infinite elastic cylinders or spheres is well known. It is possible to characterize these targets by their resonance spectra. The resonances are established by the generation of surface waves that propagate around the circumference of the targets. The resonances originate from the phase matching of repeatedly circumnavigating surface waves. Experimentally, it is possible to characterize a target with a complicated shape, but it is not easy to explain the spectra theoretically because the geometry is not separable and the usual analytical methods to calculate the far‐field pressure cannot be used. In this paper, resonance spectra and angular diagrams obtained from a target consisting of a finite cylinder with hemispherical endcaps are obtained experimentally. To explain the resonance spectra, an integral phase matching condition is used. Upon incidence normal to the cylinder axis, resonances due to the phase matching of surface waves traveling along a circumference or along a meridian have been observed simultaneously.

We have carried out tank experiments on the excitation of vibrational resonances of submerged elastic objects by incident short acoustic pulses. We have studied steel spheres, cylinders with hemispherical endcaps, and prolate as well as oblate spheroids. Theoretical interpretations of the resonance positions are provided by the matching of the phases of surface waves excited by the incident pulses, that encircle the object along closed paths. Some results of a French experimental study (G Maze and J Ripoche, University of Le Havre) are interpreted using the same approach.

The steady state analysis of the scattering of plane acoustic waves from submerged rigid and elastic bodies using two approaches is presented. The first approach uses a combined finite element/boundary element (FE/BE) methodology. The NASA structural analysis (NASTRAN) program is used to formulate the structural matrices based on the finite element method (FEM). The surface integral equation radiation and scattering (SIERRAS) program creates the fluid matrices based on the boundary element method (BEM) and solves the coupled fluid-structure interaction problem. A superparametric boundary element (BE) with nine nodes is employed. The combined Helmholtz integral equation formulation (CHIEF) is employed to provide a unique solution for all frequencies. In the second approach, the superposition method (SUP) is used for modeling the fluid. The SUP method is an off-boundary approach that employs a number of point sources moved inside the body to represent the fluid response at the surface. This allows the fluid...

The expression for bistatic radar scattering cross section of a thin, finite-length, perfectly conducting wire given by O. Einarson (1987) appears to furnish the most accurate description of this quantity, and to be applicable to a wider range of wire lengths than other formulations. Since only randomly selected illustrative plots of the cross section appear in the literature, comprehensive three-dimensional graphs of the bistatic Einarsson cross section, plotted versus scattering angle and frequency for various angles of incidence, which exhibit both its resonances and its specular-reflection features are presented. Simplified forms of Einarsson's cross section expressions, which greatly facilitated preparation of the computer code, are also given. >

Giant nuclear dipole and higher-multipole resonances may be described by a generalized Goldhaber-Teller model I, including spin-isospin (si) and compressional (c) vibrations besides the familiar isospin (i) vibrations. Their amplitudes appear as parallel ripples in a two-dimensional surface over the (E,L) plane. Sliced at L = const this gives the usual resonance plots versus excitation energy E; sliced at E = const gives resonance plots versus L(Fig. l, case of 12C electroexcitation at i00 MeV). These resonances are manifestations of Regge poles 2 which, when traced through varying E, together with

In a previous communication,1 we presented a calculation of the total cross section for π− photoproduction in 12C leading to the ground state of 12N. This theory was based on the elementary interaction Hamiltonian of Berends., 2 with the nuclear transition density being described by a Helm model fitted to inelastic electron scattering data. The distortion of the pion wave function was obtained from an optical potential as available at that time. The results were compared with experimental data near threshold by Bernstein.,3 and at higher energies by Epaneshnikov., and were found too low compared to the former, and too high compared to the latter. Here we present improved calculations which lead to considerably better agreement with both the threshold and the high-energy data.

The ‘‘level crossing’’ phenomenon, which has been pointed out earlier [M. F. Werby et al., J. Acoust. Soc. Am. 84, 1425–1436 (1988)], is studied here for solid elastic spheroids of varying aspect ratios. Using a T‐matrix code, the frequencies (both fundamentals and overtones) of the resonances are calculated as excited by an end‐on incident plane wave. Aspect ratios of the tungsten carbide spheroids range from b/a=1 (sphere) to 4 in steps of 0.25. The resonance frequencies are presented in the form of an acoustic spectroscopic level scheme. They are expressed in units kb (b=semimajor axis) and correspond to resonating surface waves as they form standing waves around the meridional circumference. While for the resonating Rayleigh waves the resonance frequencies only rise gradually with increasing aspect ratio, those for the Whispering Gallery waves rise much more rapidly, and hence successively cross over the various overtones of the Rayleigh resonances. This phenomenon is explained on the basis of the dif...

A normal‐mode model, including absorptive effects and elastic waves in the ocean floor, is presented for a source in the water column and a receiver in the water or the elastic medium. The appropriate boundary conditions between all liquid and solid layers are taken into account, and an absorptive semi‐infinite basement is assumed, which causes the radiating wave‐number spectrum to be discrete. The adiabatic approach has been adopted for the case where the acoustic properties or the boundaries vary slowly with range. Results of these calculations display the importance of even a slight range dependence, and of bottom elasticity in shallow‐center sound propagation.

The singularity expansion method (SEM), established originally for electromagnetic-wave scattering by Carl Baum (Proc. IEEE 64, 1976, 1598), has later been applied also to acoustic scattering (H U¨berall, G C Gaunaurd, and J D Murphy, J Acoust Soc Am 72, 1982, 1014). In the present paper, we describe further applications of this method of analysis to the scattering of elastic waves from cavities or inclusions in solids. We first analyze the resonances that appear in the elastic-wave scattering amplitude, when plotted vs frequency, for evacuated or fluid-filled cylindrical and spherical cavities or for solid inclusions. These resonances are interpreted as being due to the phase matching, ie, the formation of standing waves, of surface waves that encircle the obstacle. The resonances are then traced to the existence of poles of the scattering amplitude in the fourth quadrant of the complex frequency plane, thus establishing the relation with the SEM. The usefulness of these concepts lies in their applicability for solving the inverse scattering problem, which is the central problem of NDE. Since for the case of inclusions, or of cavities with fluid fillers, the scattering of elastic waves gives rise to very prominent resonances in the scattering amplitude, it will be of advantage to analyze these with the help of the resonance scattering theory or RST (first formulated by L Flax, L R Dragonette, and H U¨berall, J Acoust Soc Am 63, 1978, 723). These resonances are caused by the proximity of the SEM poles to the real frequency axis, on which the frequencies of physical measurements are located. A brief history of the establishment of the RST is included here immediately following the Introduction.

In some of the earlier literature, it was suggested that the lowest‐order dipole mode of an elastic sphere immersed in a fluid and excited by an incident acoustic wave corresponds to a rigid‐body oscillatory motion of the sphere as a whole. The present investigation verifies and corroborates these statements in a quantitative fashion.

Acoustic resonance spectra were obtained experimentally for steel spheres and cylinders with hemispherical endcaps by acoustic backscattering (for cylinders: with both axial and oblique incidence). They were interpreted theoretically by surface wave propagation with phase matching over a closed path.

The relationship between resonances and surface waves in the scattering of an obliquely incident acoustic wave from an infinite elastic cylinder is discussed. From the three‐dimensional normal‐mode solutions for a free cylinder, the resonance frequencies of the cylinder and, correspondingly, the phase velocities of helical surface waves and their relation to the helical angles are obtained. Furthermore, as the cylinder is excited by sound waves incident through ambient water, the dispersion of phase velocity for helical surface waves as a function of the angle of incidence has also been derived. Comparing the results of the present work with the results given by Flax et al. [J. Acoust. Soc. Am. 68, 1832 (1980)], it was found that, for the case of oblique incidence, the resonance frequencies are basically in agreement with the frequencies of the minimum values of the form function, analogous to the case of perpendicular incidence.

The electromagnetic scattering amplitude for metal objects coated with a lossless dielectric exhibits a large number of resonances versus real frequency. These resonances are a function of the object shape and size, coating thickness, and coating electrical properties. Previously, it was shown that for coated spheres and nonspherical bare objects, these resonances can be understood in terms of phase matched circumnavigating surface waves and the objects' complex eigenfrequencies. The effect of dielectric loss in the coating on the complex eigenfrequencies and phase velocities of these surface waves is presented for a metal sphere coated with a uniform homogeneous dielectric coating. It is seen that the positions of the complex resonance frequencies move away from the real frequency axis under the influence of dielectric loss in the coating. The effect of this is shown to correspond to the changes in the backscatter spectrum versus real frequency as computed using a Mie series expansion. The significant difference between the lossless and lossy dielectric-coated sphere cases is seen to be due to a modification of the phase velocities of surface waves, particularly the whispering gallery types, and the increased attenuation of the surface wave modes. >

Various approaches to the solution of the inverse scattering problem are discussed here, and illustrated by selected examples. Inverse scattering, having originated with quantum mechanical scattering problems, has more recently become of interest in acoustic and electromagnetic areas, in geophysics as well as in oceanography. These topics will be described here both based on general approaches, or more specifically as based on the use of target resonances, or of surface waves on the target.

Digital subtraction angiography (DSA), also known as Dichromography, using synchrotron radiation beams has been developed at Stanford University (R. Hofstadter) and was subsequently taken over at the Brookhaven Synchrotron and later at Hamburg (HASYLAB) [see, e.g., W.R. Dix, Physik in unserer Zeit. 30 (1999) 160]. The imaging of coronary arteries is carried out with an iodine-based contrast agent which need not be injected into the heart. The radiation must be monochromatized and is applied above and below the K-edge of iodine (33.16 keV), with a subsequent digital subtraction of the two images. Monochromatization of the synchrotron radiation causes a loss of intensity of 10 -3 . We propose instead the use of coherent bremsstrahlung [see, e.g., A.W. Saenz and H. Uberall, Phys. Rev. B25 (1982) 448] which is inherently monochromatic, furnishing a flux of 10 12 photon/sec. This requires a 10-20 MeV electron linac which can be obtained by many larger hospitals, eliminating the scheduling problems present at synchrotrons. The large, broad incoherent bremsstrahlung background underlying the monochromatic spike would lead to inadmissible overexposure of the patient. This problem can be solved with the use of Kumakhovs capillary optics [see e.g., S.B.Dabagov, Physics-Uspekhi 46 (2003) 1053]: the low-energy spiked radiation can be deflected towards the patient, while the higher energy incoherent background continues forward, avoiding the patient who is placed several meters from the source. 1. INTRODUCTION Angiography (imaging of coronary arteries) using synchrotron radiation has been carried out at the Stanford and later the Brookhaven Synchrotrons and the Hamburg Synchrotron (HASYLAB). Digital subtraction angiography (DSA) with a contrast agent based on iodine is used above and below the K-edge (33.16 keV) employing a monochromatized synchrotron beam of intensity reduced by 10

For in vacuo elastic plates or plates fluid-loaded on one side, it has been previously shown that dispersion curves for both plate-borne (Lamb) type and, in the latter case, also fluid-borne (Scholte–Stoneley) type fail to cross but repel each other, with the waves simultaneously exchanging their physical character. This study is extended here to the case of a plate loaded by two different fluids, where a quantitative calculation of dispersion curves for water on one side, and a lighter or a heavier fluid on the other, is carried out confirming the existence of two different Scholte–Stoneley waves.

We consider evacuated thin semi-infinite shells immersed in a fluid, which may be either of cylindrical shape with a hemispherical shell endcap, or formed two-dimensionally by semi-infinite parallel plates joined together by a semi-cylinder. The connected shell portions are joined in a manner to satisfy continuity but with a discontinuous radius of curvature. Acoustic waves are considered incident along the axis of symmetry (say the z axis) onto the curved portion of the shell, where they, at the critical angle of coincidence, generate Lamb and Stoneley-type waves in the shell. Computations were carried out using a code developed by Cao et al. [Chinese J. Acoust. 14, 317 (1995)] and was used in order to computationally visualize the waves in the fluid that have been re-radiated by the shell waves a the critical angle. The frequency range was below that of the lowest Lamb wave, and only the A0 wave (and partly the S0 wave) was observed to re-radiate into the fluid under our assumptions. The results will be compared to experimental results in which the re-radiated waves are optically visualized by the Schardin-Cranz schlieren method.

Coherent bremsstrahlung research originated with the 1955 papers by Dyson and Uberall, Ter-Mikaelian, and Ferretti. Its intermediate status thirty years later has been documented by Saenz and Uberall in the book Coherent Radiation Sources (A. W. Saenz and H. Uberall, editors), Springer, Berlin 1985. The first precision experiments were carried out by Diambrini-Palazzi et al. (1960) in Frascati shortly after the theory had been developed; see also Timm (1969). After experimentation by dozens of electron accelerator laboratories all over the world, there are presently measurements being made by Arends et al. at the University of Mainz (MAMI, 855 MeV), Klein et al. at the University of Bonn (ELSA, 3 GeV), at CERN (20-170 GeV) by Avakian of the Yerevan Physics Institute and others, and with electron energies of 6 GeV at the Jefferson Laboratory, Newport News, VA (F. J. Klein, Catholic University, spokesperson). At Jefferson Lab, linearly polarized quasi-monochromatic coherent-bremsstrahlung photons [peaked at 1.8GeV, with polarization (after collimation) of 84%] are being used for the production (off protons) of ρ and ω mesons among others. Recent theoretical research deals with coherent bremsstrahlung in quasicrystals (Fusina, Langworthy, and Saenz, 2001), and with planar and axial coherent bremsstrahlung in a diamond crystal (Chouffani, Endo, and Uberall 2001-2), both at low energies. In the latter study, in which the concept of axial coherent bremsstrahlung is now stressed (while in the related processes of planar and axial channeling radiation this distinction is well known), photon emission occurs here not necessarily in the forward direction.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.