Showing papers on "Longitudinal wave published in 1994"

Dynamic Behavior of Materials

Abstract: Dynamic Deformation and Waves. Elastic Waves. Plastic Waves. Shock Waves. Shock Waves: Equations of State. Differential Form of Conservation Equations and Numerical Solutions to More Complex Problems. Shock Wave Attenuation, Interaction, and Reflection. Shock Wave-Induced Phase Transformations and Chemical Changes. Explosive-Material Interactions. Detonation. Experimental Techniques: Diagnostic Tools. Experimental Techniques: Methods to Produce Dynamic Deformation. Plastic Deformation at High Strain Rates. Plastic Deformation in Shock Waves. Shear Bands (Thermoplastic Shear Instabilities). Dynamic Fracture. Applications. Indexes.

Propagation of Sound in Porous Media: Modeling Sound Absorbing Materials

Abstract: Preface to the second edition. 1 Plane waves in isotropic fluids and solids. 1.1 Introduction. 1.2 Notation - vector operators. 1.3 Strain in a deformable medium. 1.4 Stress in a deformable medium. 1.5 Stress-strain relations for an isotropic elastic medium. 1.6 Equations of motion. 1.7 Wave equation in a fluid. 1.8 Wave equations in an elastic solid. References. 2 Acoustic impedance at normal incidence of fluids. Substitution of a fluid layer for a porous layer. 2.1 Introduction. 2.2 Plane waves in unbounded fluids. 2.3 Main properties of impedance at normal incidence. 2.4 Reflection coefficient and absorption coefficient at normal incidence. 2.5 Fluids equivalent to porous materials: the laws of Delany and Bazley. 2.6 Examples. 2.7 The complex exponential representation. References. 3 Acoustic impedance at oblique incidence in fluids. Substitution of a fluid layer for a porous layer. 3.1 Introduction. 3.2 Inhomogeneous plane waves in isotropic fluids. 3.3 Reflection and refraction at oblique incidence. 3.4 Impedance at oblique incidence in isotropic fluids. 3.5 Reflection coefficient and absorption coefficient at oblique incidence. 3.6 Examples. 3.7 Plane waves in fluids equivalent to transversely isotropic porous media. 3.8 Impedance at oblique incidence at the surface of a fluid equivalent to an anisotropic porous material. 3.9 Example. References. 4 Sound propagation in cylindrical tubes and porous materials having cylindrical pores. 4.1 Introduction. 4.2 Viscosity effects. 4.3 Thermal effects. 4.4 Effective density and bulk modulus for cylindrical tubes having triangular, rectangular and hexagonal cross-sections. 4.5 High- and low-frequency approximation. 4.6 Evaluation of the effective density and the bulk modulus of the air in layers of porous materials with identical pores perpendicular to the surface. 4.7 The biot model for rigid framed materials. 4.8 Impedance of a layer with identical pores perpendicular to the surface. 4.9 Tortuosity and flow resistivity in a simple anisotropic material. 4.10 Impedance at normal incidence and sound propagation in oblique pores. Appendix 4.A Important expressions. Description on the microscopic scale. Effective density and bulk modulus. References. 5 Sound propagation in porous materials having a rigid frame. 5.1 Introduction. 5.2 Viscous and thermal dynamic and static permeability. 5.3 Classical tortuosity, characteristic dimensions, quasi-static tortuosity. 5.4 Models for the effective density and the bulk modulus of the saturating fluid. 5.5 Simpler models. 5.6 Prediction of the effective density and the bulk modulus of open cell foams and fibrous materials with the different models. 5.7 Fluid layer equivalent to a porous layer. 5.8 Summary of the semi-phenomenological models. 5.9 Homogenization. 5.10 Double porosity media. Appendix 5.A: Simplified calculation of the tortuosity for a porous material having pores made up of an alternating sequence of cylinders. Appendix 5.B: Calculation of the characteristic length LAMBDA'. Appendix 5.C: Calculation of the characteristic length LAMBDA for a cylinder perpendicular to the direction of propagation. References. 6 Biot theory of sound propagation in porous materials having an elastic frame. 6.1 Introduction. 6.2 Stress and strain in porous materials. 6.3 Inertial forces in the biot theory. 6.4 Wave equations. 6.5 The two compressional waves and the shear wave. 6.6 Prediction of surface impedance at normal incidence for a layer of porous material backed by an impervious rigid wall. Appendix 6.A: Other representations of the Biot theory. References. 7 Point source above rigid framed porous layers. 7.1 Introduction. 7.2 Sommerfeld representation of the monopole field over a plane reflecting surface. 7.3 The complex sin theta plane. 7.4 The method of steepest descent (passage path method). 7.5 Poles of the reflection coefficient. 7.6 The pole subtraction method. 7.7 Pole localization. 7.8 The modified version of the Chien and Soroka model. Appendix 7.A Evaluation of N. Appendix 7.B Evaluation of p r by the pole subtraction method. Appendix 7.C From the pole subtraction to the passage path: Locally reacting surface. References. 8 Porous frame excitation by point sources in air and by stress circular and line sources - modes of air saturated porous frames. 8.1 Introduction. 8.2 Prediction of the frame displacement. 8.3 Semi-infinite layer - Rayleigh wave. 8.4 Layer of finite thickness - modified Rayleigh wave. 8.5 Layer of finite thickness - modes and resonances. Appendix 8.A Coefficients r ij and M i,j. Appendix 8.B Double Fourier transform and Hankel transform. Appendix 8.B Appendix .C Rayleigh pole contribution. References. 9 Porous materials with perforated facings. 9.1 Introduction. 9.2 Inertial effect and flow resistance. 9.3 Impedance at normal incidence of a layered porous material covered by a perforated facing - Helmoltz resonator. 9.4 Impedance at oblique incidence of a layered porous material covered by a facing having cirular perforations. References. 10 Transversally isotropic poroelastic media. 10.1 Introduction. 10.2 Frame in vacuum. 10.3 Transversally isotropic poroelastic layer. 10.4 Waves with a given slowness component in the symmetry plane. 10.5 Sound source in air above a layer of finite thickness. 10.6 Mechanical excitation at the surface of the porous layer. 10.7 Symmetry axis different from the normal to the surface. 10.8 Rayleigh poles and Rayleigh waves. 10.9 Transfer matrix representation of transversally isotropic poroelastic media. Appendix 10.A: Coefficients T i in Equation (10.46). Appendix 10.B: Coefficients A i in Equation (10.97). References. 11 Modelling multilayered systems with porous materials using the transfer matrix method. 11.1 Introduction. 11.2 Transfer matrix method. 11.3 Matrix representation of classical media. 11.4 Coupling transfer matrices. 11.5 Assembling the global transfer matrix. 11.6 Calculation of the acoustic indicators. 11.7 Applications. Appendix 11.A The elements T ij of the Transfer Matrix T ]. References. 12 Extensions to the transfer matrix method. 12.1 Introduction. 12.2 Finite size correction for the transmission problem. 12.3 Finite size correction for the absorption problem. 12.4 Point load excitation. 12.5 Point source excitation. 12.6 Other applications. Appendix 12.A: An algorithm to evaluate the geometrical radiation impedance. References. 13 Finite element modelling of poroelastic materials. 13.1 Introduction. 13.2 Displacement based formulations. 13.3 The mixed displacement-pressure formulation. 13.4 Coupling conditions. 13.5 Other formulations in terms of mixed variables. 13.6 Numerical implementation. 13.7 Dissipated power within a porous medium. 13.8 Radiation conditions. 13.9 Examples. References. Index.

Nonlinear Water Waves

Abstract: Basic Equations of Motion of Inviscid and Viscous Fluids. The Theory of Surface Waves on Water. Transient Wave Motions in an Inviscid Fluid. Nonlinear Shallow Water Waves and Solitons. Ship Waves and Wave Resistance. NonlinearDiffraction of Water Waves. The Theory of Nonlinear Dispersive Waves. Nonlinear Instability of Dispersive Waves with Applications to Water Waves. Bibliography. Index.

Introduction to elastic wave propagation

Abstract: Earthquakes are detected and studied by measuring the waves they create. Waves are transmitted through the Earth to detect oil and gas deposits and to study the Earth's geological structure. Properties of materials are determined by measuring the behaviour of waves transmitted through them. In recent years, elastic waves transmitted through the human body have been used for medical diagnosis and therapy. Many students and professionals in various branches of engineering encounter problems requiring an understanding of elastic waves. In this book, they will find the basic concepts and methods of the theory of wave propagation in elastic materials. One-dimensional waves, transient waves and harmonic waves including reflections of plane waves at interfaces. Rayleigh waves, waves in elastic layers and in layered materials are discussed. Analytical methods in nonlinear wave propagation are presented. This book includes exercises with solutions and many explanatory figures.

Simulation of the frictional stick-slip instability

Abstract: A lattice solid model capable of simulating rock friction, fracture and the associated seismic wave radiation is developed in order to study the origin of the stick-slip instability that is responsible for earthquakes. The model consists of a lattice of interacting particles. In order to study the effect of surface roughness on the frictional behavior of elastic blocks being rubbed past one another, the simplest possible particle interactions were specified corresponding to radially dependent elastic-brittle bonds. The model material can therefore be considered as round elastic grains with negligible friction between their surfaces. Although breaking of the bonds can occur, fracturing energy is not considered. Stick-slip behavior is observed in a numerical experiment involving 2D blocks with rough surfaces being rubbed past one another at a constant rate. Slip is initiated when two interlocking asperities push past one another exciting a slip pulse. The pulse fronts propagate with speeds ranging from the Rayleigh wave speed up to a value between the shear and compressional wave speeds in agreement with field observations and theoretical analyses of mode-II rupture. Slip rates are comparable to seismic rates in the initial part of one slip pulse whose front propagates at the Rayleigh wave speed. However, the slip rate is an order of magnitude higher in the main part of pulses, possibly because of the simplified model description that neglected intrinsic friction and the high rates at which the blocks were driven, or alternatively, uncertainty in slip rates obtained through the inversion of seismograms. Particle trajectories during slip have motions normal to the fault, indicating that the fault surfaces jump apart during the passage of the slip pulse. Normal motion is expected as the asperities on the two surfaces ride over one another. The form of the particle trajectories is similar to those observed in stick-slip experiments involving foam rubber blocks (Bruneet al., 1993). Additional work is required to determine whether the slip pulses relate to the interface waves proposed by Brune and co-workers to explain the heat-flow paradox and whether they are capable of inducing a significant local reduction in the normal stress. It is hoped that the progressive development of the lattice solid model will lead to realistic simulations of earthquake dynamics and ultimately, provide clues as to whether or not earthquakes are predictable.

Surface Waves in Functionally Gradient Piezoelectric Plates

Abstract: The hybrid numerical method, which has been proposed by the present authors for wave propagation analysis in anisotropic laminated plates, is extended for functionally gradient piezoelectric material (FGPM) plates. The properties of the plate changes continuously in the thickness direction. Characteristics of waves in the plates, and responses of the plates in the time and frequency domain are considered. A technique for calculating responses in the frequency domain is presented. Energy velocities, mode shapes of the waves in an FGPM plate, and the responses of the plate excited by mechanical loads and electrodes are computed. It is found that waves of lower modes in the FGPM plates for large wave numbers appear as surface waves and that a strong surface wave is excited on the softer surface of the FGPM plate. These surface waves can be expected to be used in surface acoustic wave devices.

Three-dimensional scattering by two-dimensional topographies

Abstract: Three-dimensional seismic responses of two-dimensional topographies are studied by means of the indirect boundary element method (IBEM). The IBEM yields, in the presented form, very accurate results and has the advantage of low computational cost. In IBEM, diffracted waves are constructed in terms of single-layer boundary souces. The appropriate Green's functions used are those of a harmonic point foce moving along the axis of the topography in a full space. Obtained reults are compared against those published by other authors. Examples of simulations are presented for different geometries, for different types of incident wave fields, and in particular, for different arrival angles to the topography to quantitatively study three-dimensional effects of the scattering. The accuracy of the results makes it possible to analyze them in both the time and drequency domaisn. Frequency-space representations allow identification of difraction and interference patterns in the seismic response of the topography. Synthetic seismograms are obtained by Fourier analysis. Using timespace domain representations, the nature of each of the scattered waves are identified in terms of, for example, creeping waves and reflected compressional waves.

Probing porous media with first and second sound. II. Acoustic properties of water‐saturated porous media

Abstract: The ultrasonic properties (reflection/transmission and bulk attenuation/speed) of porous and permeable media saturated with a Newtonian fluid, namely water, are considered. The frequency dependence of the transmission amplitudes of pulses is measured through a slab of thickness d1, repeated for another slab of thickness d2 for a given material. With these two measurements on two different thicknesses, it is possible in principle to separate bulk losses from reflection/transmission losses for compressional waves in these materials. The bulk properties are calculated from the Biot theory for which all of the input parameters have been measured separately; the attenuations are particularly sensitive to the values of Λ, determined from second‐sound attenuation measurements reported in the companion article. There is excellent quantitative agreement between the theoretical and experimental values in the cases considered; there are no adjustable parameters involved. The reflection and transmission coefficients ...

The formation of spilling breaking water waves

Abstract: Photographs from high‐speed movies of the profiles of a mechanically generated, gentle spilling breaking water wave are presented. It is found that as the wave steepens a bulge forms on the forward face of the wave near the crest and capillary waves form on the water surface ahead of the ‘toe’ of the bulge (see Fig. 1). The toe of the bulge then moves rapidly down the forward face of the wave and a train of large‐amplitude waves with short wavelength grows rapidly on the surface of the bulge. These waves quickly break down into a random pattern indicating that the flow has become turbulent.

Band structure for the propagation of elastic waves in superlattices

Abstract: A 2×2 transfer matrix approach is used to study the elastic response of multilayered systems. Superlattices with a period of n layers are considered to calculate the dispersion relations of the normal modes for both longitudinal and transverse waves, and the reflectivity of longitudinal modes for finite and semi‐infinite structures. Numerical results of the dispersion relation for a two‐ and three‐layer period superlattice are presented to show the band structure of wave propagation. For transverse waves, it is considered that the single layer may support surface modes and it is found that their interaction with those of the adjacent layers also yield a band structure. The calculated reflectivity of longitudinal elastic waves for the semi‐inifinite superlattices resembles the allowed and forbidden regions of the dispersion relations. The theoretical reflectivity curves of sound waves are compared with the experimental results for the three‐layer systems. A good agreement between theory and experiment is obtained.

The Effects of Flow Asymmetry on the Direction of Rossby Wave Breaking

Abstract: The relationship between the direction of the breaking of Rossby waves on an isolated jet and the cross-jet asymmetry of the flow is investigated. The flow structure of a circular jet is, under most circumstances, such that waves break uniquely outward, although the authors contrive a flow on which breaking is uniquely inward. The influence on the direction of the breaking of the location of critical lines in the undisturbed flow is discussed. On a straight jet with asymmetric shear, there are three wave amplitude regimes: weak waves do not break; waves of moderate amplitude break only toward the closer critical line; and waves of sufficiently large amplitude break both ways.

Ultrasonic guided wave inspection concepts for steam generator tubing

Abstract: Some very exciting and promising results have been obtained with respect to the utilization and guided wave techniques for inspecting steam generator tubing. In addition to some theoretical considerations that were studied recently, work has been carried out in special probe design and development. This special probe is used in demonstration of law detection feasibility, and in understanding the conceptual development of a complete flaw detection system. This includes transducer, pulser-receiver system, and appropriate signal processing and pattern recognition software for reliable inspection. Ultrasonic NDE techniques have progressed quite rapidly during this decade for two principal reasons: advanced signal processing, and the use and understanding of multi-mode ultrasonic wave propagation. Both concepts are useful in the proposed work on guided wave propagation in steam generator tubing. These new directions go beyond the use of normal beam longitudinal waves and angle beam shear waves for inspection. Guided waves such as surface and Lamb waves can be used to monitor larger volumes of material with greater efficiency. The generation of these waves, however, is more complex. Theoretically one can produce a large number of modes in a structure with a simple loading arrangement. However, the generation of sufficient amounts of energy inmore » a specific mode strongly depends on several factors. They include the loading system, angle of attack, probe frequency, frequency bandwidth, and a whole host of special transducer design and instrumentation parameters.« less

Experimental measurements of seismic attenuation in microfractured sedimentary rock

Abstract: Ultrasonic compressional- and shear-wave attenuation in water-saturated Carrara Marble increase with increasing crack density and decreasing effective pressure. Between 0.4 and 1.0 MHz, empirical linear relationships between 1/Q and crack density CD were found to be:CD = 1.96 + or - 0.63 X 1/Q,for compressional waves andCD = 6.7 + or - 1.5 X 1/Q,for shear waves.

Simultaneous measurement of the acoustical properties of a thin‐layered medium: The inverse problem

Abstract: This paper presents a frequency‐domain ultrasonic technique for a simultaneous determination of the thickness (h) and wave speed (c) of the individual layers comprising a multilayered medium. The layers may be ‘‘thin’’; by thin we mean that the successive reflections of an ultrasonic pulse from the two faces of a layer are nonseparable in the time domain. Plane longitudinal waves which are normally incident upon the medium are considered. A systematic analysis of the sensitivity of the complex‐valued transfer function to the acoustical parameters of each layer has been carried out. An inverse algorithm, which utilizes either the Newton–Raphson or the Simplex method in conjunction with the incremental search method, has been developed to reconstruct simultaneously the thickness and phase velocity of each layer by minimizing the difference between the theoretical and the experimental results in the mean‐sum‐square sense; the entire complex spectrum, i.e., the amplitude as well as the phase spectrum, was used. The technique is fully automated and computer controlled and can be readily used for in situ NDE applications. Results are presented for several three‐layer specimens; aluminum/water/aluminum, aluminum/water/titanium, and titanium/water/titanium. Successful inversion was obtained for the following cases (1) simultaneous determination of h and c of any one of the three layers, given h and c of the remaining two layers; (2) simultaneous measurement of the three thicknesses, given the three wave speeds; (3) simultaneous measurement of the three wave speeds, given the three thicknesses; (4) simultaneous determination of all three thicknesses and one wave speed, given the remaining two wave speeds. The precision of our measurements was found to be excellent; typically, ±3 μm in h (for h of the order of 1 mm) and ± one part per thousand in c. The accuracy was found to be about one order of magnitude lower than the precision; typically, ±10 μm in h and ±2% in c.

Porosity, permeability, shear strength: Crosswell tomography below an iron foundry

Abstract: Crosswell tomography of a sedimentary foundation at an iron foundry was affected by very high background noise; nevertheless, high‐resolution velocity images were obtained between wells separated by long distances (120 to 250 m). A piezoelectric source in a water‐filled well used long sequences (4095 cycles) of pseudorandom binary codes at high carrier frequencies (1 to 10 kHz). A 24‐channel hydrophone array in another well received the signal. Beamforming of common‐source data selected the directions and arrival times of multiple raypaths and tube waves and further enhanced the signal‐to‐noise ratio. Inversion of first‐arrival times by damped least squares imaged the compressional wave velocities. Assuming the normal consolidation condition, the porosity and shear strength images are predicted from the compressional wave velocity image. The direct measurements of porosity and shear strength conducted on the cores and boreholes were used to verify the tomographic predictions. The slight differences in the...

Shear wave splitting in refracted waves returned from the upper mantle transition zone beneath northern Australia

Abstract: The broadband recording site at Warramunga (WRA) in the Northern Territory of Australia provides good coverage of seismic wave propagation through the upper mantle for sources in the earthquake belt through Indonesia and New Guinea. $ waves recorded on the radial ($V) and tangential (SH) components are of comparable quality because the hard-rock recording site minimizes the influence of coupling to P on the radial component. Refracted $ waves from the upper- mantle transition zone show a clear advance of $H wave arrivals compared with $V. Eleven polarization analyses of waves returned from the transition zone yield an average time shift of 2.3 s with the fast direction scattered about the transverse direction. Nine polarization measurements of waves returned from the top of the lower mantle yield an average time shift of 1.7 s, again with the fast direction near the transverse. No appreciable time differences are observed between the radial and transverse polarizations for paths refracted within the lithospheric lid. Because the observations of shear wave splitting in waves passing through the low-velocity zone, 'he transition zone, and the top of the lower mantle are not coherent in their absolute polarization, the cause cannot lie in azimuthal anisotropy at shallow depths under the WRA station. The most plausible exphnation is transverse isotropy in shear within the low-velocity zone under the unusually thick mantle "lid" under Australia. A possible contribution may come from anisotroly in -olivine at the top of the upper mantle transition zone. Transverse isotropy in the 200-kin-thick layer below the lithosphere down to the transition zone with a 1% faster shear wave speeds for horizontal polarization compared with vertical polarization will explain the splitting data. For this asthenospheric region the level of anisotropy is quite reasonable and the polarization is consistent with lateral flow. The geometry of the available paths for waves propagating within the mmltle lid inot sufficient to place constraints on the anisotropic properties of this heterogeneous a,nd low-loss region.

Time signatures of impulsively generated waves in a coronal plasma

Abstract: Impulsively generated waves in solar coronal loops are numerically simulated in the frame-work of cold magnetohydrodynamics. Coronal inhomogeneities are approximated by gas density slabs embedded in a uniform magnetic field. The simulations show that an initially excited pulse results in the propagation of wave packets which correspond to both trapped and leaky waves. Whereas the leaky waves propagate outside the slab, the trapped waves occur as a result of a total reflection from the slab walls. Time signatures of these waves are made by a detection of the trapped waves at a fixed spatial location. For waves excited within the slab, time signatures exhibit periodic, quasi-periodic and decay phases. The time signatures for waves excited outside the slab, or for a multi-series of variously shaped impulses generated at different places and times, can possess extended quasi-periodic phases. The case of parallel slabs, when the presence of a second slab influences the character of wave propagation in the first slab, exhibits complex time signatures as a result of solitary waves interaction.

Elastic waves in homogeneous and layered transversely isotropic media: Plane waves and Gaussian wave packets. A general approach

Abstract: Solutions to the equation of motion are derived for transversely isotropic media such as fiber composites, ideally fiber‐textured austenitic steels, or extruded metal‐matrix composites. The approach is most general in that the orientation of the materials’ axis of rotational symmetry is arbitrary. Thus the results obtained using a coordinate‐free representation are particularly convenient in view of layered structures, where for the materials of interest the fiber axis is perpendicular to the surface normal, but variable in orientation. Plane elastic waves are characterized by the corresponding wave vectors, making especially possible a quantitative evaluation of the deviation of wave propagation direction and energy flux, which is characteristic for anisotropic materials. Reflection and refraction of plane waves at an interface between two arbitrarily oriented transversely isotropic media is examined yielding an algorithm that provides the respective reflection and transmission coefficients. The propagat...

Method for measuring liquid viscosity and ultrasonic viscometer

Abstract: An ultrasonic viscometer and method for measuring fluid viscosity are provided. Ultrasonic shear and longitudinal waves are generated and coupled to the fluid. Reflections from the generated ultrasonic shear and longitudinal waves are detected. Phase velocity of the fluid is determined responsive to the detected ultrasonic longitudinal waves reflections. Viscosity of the fluid is determined responsive to the detected ultrasonic shear waves reflections. Unique features of the ultrasonic viscometer include the use of a two-interface fluid and air transducer wedge to measure relative signal change and to enable self calibration and the use of a ratio of reflection coefficients for two different frequencies to compensate for environmental changes, such as temperature.

Compressional ULF waves in the outer magnetosphere: 2. A case study of Pc 5 type wave activity

Abstract: In previously published work (Zhu and Kivelson, 1991) the spatial distribution of compressional magnetic pulsations of period 2 - 20 min in the outer magnetosphere was described. In this companion paper, we study some specific compressional events within our data set, seeking to determine the structure of the waves and identifying the wave generation mechanism. We use both the magnetic field and three-dimensional plasma data observed by the International Sun-Earth Explorer (ISEE) 1 and/or 2 spacecraft to characterize eight compressional ultra low frequency (ULF) wave events with frequencies below 8 mHz in the outer magnetosphere. High time resolution plasma data for the event of July 24, 1978, made possible a detailed analysis of the waves. Wave properties specific to the event of July 24, 1978, can be summarized as follows: (1) Partial plasma pressures in the different energy ranges responded to the magnetic field pressure differently. In the low-energy range they oscillated in phase with the magnetic pressure, while oscillations in higher-energy ranges were out-of-phase; (2) Perpendicular wavelengths for the event were determined to be 60,000 and 30,000 km in the radial and azimuthal directions, respectively. Wave properties common to all events can be summarized as follows: (1) Compressional Pc 5 wave activity is correlated with Beta, the ratio of the plasma pressure to the magnetic pressure; the absolute magnitude of the plasma pressure plays a minor role for the wave activity; (2) The magnetic equator is a node of the compressional perturbation of the magnetic field; (3) The criterion for the mirror mode instability is often satisfied near the equator in the outer magnetosphere when the compressional waves are present. We believe these waves are generated by internal magnetohydrodynamic (MHD) instabilities.

Air-coupled piezoelectric detection of laser-generated ultrasound

Abstract: A pulsed laser has been used to generate ultrasonic transients in samples of metal and fiber-reinforced polymer composite material. These have been detected using an air-coupled piezoelectric transducer. It is demonstrated that such a transduction system can be used for longitudinal waves in bulk material, Rayleigh waves at solid surfaces and Lamb waves in thin plates. >

On the evolution of periodic plane waves in reaction-diffusion systems of l - w type

Abstract: $\lambda $–$\omega$ systems are a class of simple reaction-diffusion equations with a limit cycle in the reaction kinetics. The author considers the solution of the system given by $\lambda ( r ) = \lambda _0 - r^p $, $\omega ( r ) = \omega_0 - r^p $ on a semi-infinite spatial domain with initial data decaying exponentially across the domain. Numerical evidence is presented, showing that this initial condition induces a wave front moving across the domain, with periodic plane waves behind the front. These periodic waves can move in either direction, depending on the parameter values. The author uses intuitive criteria to derive an expression for the speed of the advancing front, and by reducing the system to ordinary differential equations for similarity solutions, the amplitude and speed of the periodic plane waves are determined. The speed of these periodic waves varies continuously with the initial data. Perturbation theory is then used to obtain an analytical approximation to the solutions. These anal...

On the modulational stability of traveling and standing water waves

Abstract: Asymptotically exact evolution equations are derived for trains of small amplitude counterpropagating water waves over finite depth. Surface tension is included. The resulting equations are nonlocal and generalize the equations derived by Davey and Stewartson for unidirectional wave trains. The stability properties of stationary standing and quasiperiodic waves are determined as a function of surface tension and fluid depth for both long wavelength longitudinal and transverse perturbations.

The possible role of high-frequency waves in heating solar coronal loops

Abstract: We investigate the role of high-frequency waves in the heating of solar active region coronal loops We assume a uniform background magnetic field, and we introduce a density stratification in a direction perpendicular to this field We focus on ion compressive viscosity as the damping mechanism of the waves We incorporate viscosity self-consistently into the equations, and we derive a dispersion relation by adopting a slab model, where the density inside the slab is greater than that outside Such a configuration supports two types of modes: surface waves and trapped body waves In order to determine under what conditions these waves may contribute to the heating of active regions, we solve our dispersion relation for a range of densities, temperatures, magnetic field strengths, density ratios, wavevector magnitudes, wavevector ratios, and slab widths We find that surface waves exhibit very small damping, but body waves can potentially damp at rates needed to balance radiative losses However, the required frequencies of these body waves are very high For example, the wave frequency must be at least 50/s for a slab density of 10(exp 9,5)/cc, a slab temperature of 10(exp 6,5) K, a field strength of 100 G, and a density ratio of 5 For a slab density of 10(exp 10)/cc, this frequency increases to 88/s Although these frequencies are very high, there in no observational evidence to rule out their existence, and they may be generated both below the corona and at magnetic reconnection sites in the corona However, we do find that, for slab densities of 10(exp 10)/cc or less, the dissipation of high-frequency waves will be insufficient to balance the radiative losses if the magnetic field strength exceeds roughly 200 G Because the magnetic field is known to exceed 200 G in many active region loops, particularly low-lying loops and loops emanating from sunspots, it is unlikely that high-frequency waves can provide sufficient heating in these regions

Acoustic instability driven by cosmic-ray streaming

Abstract: We study the linear stability of compressional waves in a medium through which cosmic rays stream at the Alfven speed due to strong coupling with Alfven waves. Acoustic waves can be driven unstable by the cosmic-ray drift, provided that the streaming speed is sufficiently large compared to the thermal sound speed. Two effects can cause instability: (1) the heating of the thermal gas due to the damping of Alfven waves driven unstable by cosmic-ray streaming; and (2) phase shifts in the cosmic-ray pressure perturbation caused by the combination of cosmic-ray streaming and diffusion. The instability does not depend on the magnitude of the background cosmic-ray pressure gradient, and occurs whether or not cosmic-ray diffusion is important relative to streaming. When the cosmic-ray pressure is small compared to the gas pressure, or cosmic-ray diffusion is strong, the instability manifests itself as a weak overstability of slow magnetosonic waves. Larger cosmic-ray pressure gives rise to new hybrid modes, which can be strongly unstable in the limits of both weak and strong cosmic-ray diffusion and in the presence of thermal conduction. Parts of our analysis parallel earlier work by McKenzie & Webb (which were brought to our attention after this paper was accepted for publication), but our treatment of diffusive effects, thermal conduction, and nonlinearities represent significant extensions. Although the linear growth rate of instability is independent of the background cosmic-ray pressure gradient, the onset of nonlinear eff ects does depend on absolute value of DEL (vector differential operator) P(sub c). At the onset of nonlinearity the fractional amplitude of cosmic-ray pressure perturbations is delta P(sub C)/P(sub C) approximately (kL) (exp -1) much less than 1, where k is the wavenumber and L is the pressure scale height of the unperturbed cosmic rays. We speculate that the instability may lead to a mode of cosmic-ray transport in which plateaus of uniform cosmic-ray pressure are separated by either laminar or turbulent jumps in which the thermal gas is subject to intense heating.