Showing papers on "Longitudinal wave published in 2010"

Semiempirical Dissipation Source Functions for Ocean Waves. Part I: Definition, Calibration, and Validation

Abstract: New parameterizations for the spectral dissipation of wind-generated waves are proposed. The rates of dissipation have no predetermined spectral shapes and are functions of the wave spectrum and wind speed and direction, in a way consistent with observations of wave breaking and swell dissipation properties. Namely, the swell dissipation is nonlinear and proportional to the swell steepness, and dissipation due to wave breaking is nonzero only when a nondimensional spectrum exceeds the threshold at which waves are observed to start breaking. An additional source of short-wave dissipation is introduced to represent the dissipation of short waves due to longer breaking waves. A reduction of the wind-wave generation of short waves is meant to account for the momentum flux absorbed by longer waves. These parameterizations are combined and calibrated with the discrete interaction approximation for the nonlinear interactions. Parameters are adjusted to reproduce observed shapes of directional wave spect...

GyPSuM: A joint tomographic model of mantle density and seismic wave speeds

Abstract: [1] GyPSuM is a 3-D model of mantle shear wave (S) speeds, compressional wave (P) speeds, and density. The model is developed through simultaneous inversion of seismic body wave travel times (P and S) and geodynamic observations while using realistic mineral physics parameters linking wave speeds and density. Geodynamic observations include the global free air gravity field, divergence of the tectonic plates, dynamic topography of the free surface, and the flow-induced excess ellipticity of the core-mantle boundary. GyPSuM is built with the philosophy that heterogeneity that most closely resembles thermal variations is the simplest possible solution. Models of the density field from Earth's free oscillations have provided great insight into the density configuration of the mantle but are limited to very long wavelength solutions. Alternatively, scaling higher-resolution seismic images to obtain density anomalies generates density fields that do not satisfy geodynamic observations. The current study provides a 3-D density model for the mantle that directly satisfies geodynamic and seismic observations through a joint seismic-geodynamic inversion process. Notable density field observations include high-density piles at the base of superplume structures, supporting the general results of past normal mode studies. However, we find that these features are more localized and have lower amplitude than past studies would suggest. When we consider both fast and slow seismic anomalies in GyPSuM, we find that P and S wave speeds are strongly correlated throughout the mantle. However, we find a low correlation of fast S wave zones in the deep mantle (>1500 km depth) with the corresponding P wave anomalies, suggesting a systematic divergence from simplified thermal effects in ancient subducted slab anomalies. The cratonic lithosphere and D″ regions are shown to have strong compositional signatures. However, we argue that temperature variations are the primary cause of P wave speed, S wave speed, and density anomalies throughout most of the mantle.

Abruptly autofocusing waves.

Abstract: We introduce a new class of (2+1)D spatial and (3+1)D spatiotemporal waves that tend to autofocus in an abrupt fashion. While the maximum intensity of such a radial wave remains almost constant during propagation, it suddenly increases by orders of magnitude right before its focal point. These waves can be generated through the use of radially symmetric Airy waves or by appropriately superimposing Airy wave packets. Possible applications of such abruptly focusing beams are also discussed.

Capillary Rogue Waves

Abstract: We report the first observation of extreme wave events (rogue waves) in parametrically driven capillary waves. Rogue waves are observed above a certain threshold in forcing. Above this threshold, frequency spectra broaden and develop exponential tails. For the first time we present evidence of strong four-wave coupling in nonlinear waves (high tricoherence), which points to modulation instability as the main mechanism in rogue waves. The generation of rogue waves is identified as the onset of a distinct tail in the probability density function of the wave heights. Their probability is higher than expected from the measured wave background.

Basics of Biomedical Ultrasound for Engineers

Abstract: Preface. Acknowledgments. Introduction. Prelude and Basic Definitions. The Advantages of Using Ultrasound in Medicine. A General Statement on Safety. Some Common Applications of Ultrasound. What Is It that We Need to Know? References. 1 Waves A General Description. 1.1 General Definitions of Waves A QualitativeDescription. 1.2 General Properties of Waves A QualitativeDescription. 1.3 Mechanical One-Dimensional Waves. 1.4 The Wave Function. 1.5 The Wave Equation. 1.6 Harmonic Waves. 1.7 Group Waves. 1.8 Wave Velocity. 1.9 Standing Waves (a Mathematical Description). 1.10 Spherical Waves. 1.11 Cylindrical Waves. 1.12 The Wave Equation in a Nonhomogeneous Medium. References. 2 Waves In A One-Dimensional Medium. 2.1 The Propagation Speed of Transverse Waves in a String. 2.2 Vibration Frequencies for a Bounded String. 2.3 Wave Reflection (Echo) in a One-Dimensional Medium. 2.4 Special Cases. 2.5 Wave Energy in Strings. 2.6 Propagation of Longitudinal Waves in an Isotropic Rod orString. 2.7 A Clinical Application of Longitudinal Waves in aString. References. 3 Ultraspmoc Waves in Fluids. 3.1 Waves in Fluids. 3.2 Compressibility. 3.3. Longitudinal Waves in Fluids. 3.4 The Wave Energy. 3.5 Intensity. 3.6 Radiation Pressure. 3.7 A Perfect Reflector. References. 4 Propogation of Acoustic Waves in Solid Materials. 4.1 Introduction to the Mechanics of Solids. 4.2 The Elastic Strain. 4.3 Stress. 4.4 Hooke s Law and Elastic Coefficients. 4.5 The Wave Equation for an Elastic Solid Material. 4.6 Propagation of a Harmonic Planar Wave in a SolidMaterial. References. 5 Attenuation and Dispersion. 5.1 The Attenuation Phenomenon. 5.2 Explaining Attenuation with a Simple Model. 5.3 Attenuation Dependency on Frequency. 5.4 The Complex Wave Number. 5.5 Speed of Sound Dispersion. 5.6 The Nonlinear Parameter B/A. References. 6 Reflection and Transmission. 6.1 The Acoustic Impedance. 6.2 Snell s Law. 6.3 Reflection and Transmission from Boundaries Separating TwoFluids (or Solids with No Shear Waves). 6.4 Reflection from a Free Surface in Solids (ModeConversion). 6.5 Reflection and Transmission from a Liquid SolidBoundary. References. 7 ACOUSTIC LENSES AND MIRRORS. 7.1 Optics. 7.2 Optics and Acoustics. 7.3 An Ellipsoidal Lens. 7.4 Spherical Lenses. 7.5 Zone Lenses. 7.6 Acoustic Mirrors (Focusing Reflectors). References. 8 Transducers and Acoustic Fields. 8.1 Piezoelectric Transducers. 8.2 The Acoustic Field. 8.3 The Field of a Point Source. 8.4 The Field of a Disc Source. 8.5 The Field of Various Transducers. 8.6 Phased-Array Transducers. 8.7 Annular Phased Arrays. References. 9 Ultrasonic Imaging Using the Pulse-Echo Technique. 9.1 Basic Definitions in Imaging. 9.2 The A-Line . 9.3 Scatter Model for Soft Tissues. 9.4 Time Gain Compensation. 9.5 Basic Pulse-Echo Imaging (B-Scan). 9.6 Advanced Methods for Pulse-Echo Imaging. References. 10 Special Imaging Techniques. 10.1 Acoustic Impedance Imaging Impediography. 10.2 Elastography. 10.3 Tissue Speckle Tracking. 10.4 Through-Transmission Imaging. 10.5 Vibro-acoustic Imaging. 10.6 Time Reversal. 10.7 Ultrasonic Computed Tomography. 10.8 Contrast Materials. 10.9 Coded Excitations. References. 11 Doppler Imaging Techniques. 11.1 The Doppler Effect. 11.2 Velocity Estimation. 11.3 Frequency Shift Estimation. 11.4 Duplex Imaging (Combined B-Scan and Color FlowMapping). References. 12 Safety and Therapuetic Applications. 12.1 Effects Induced by Ultrasound and Safety. 12.2 Ultrasonic Physiotherapy. 12.3 Lithotripsy. 12.4 Hyperthermia HIFU and Ablation. 12.5 Drug Delivery. 12.6 Gene Therapy. 12.7 Cosmetic Applications. References. Appenidx A: Typical Acoustic Properties of Tissues. Appendix B: Exemplary Problems. Appendix C: Answers to Exemplary Problems. Index.

Defect detection using ultrasonic arrays: The multi-mode total focusing method

Abstract: Ultrasonic arrays allow a given scatterer to be illuminated from a wide range of angles and hence are capable of extracting significant information about the scatterer. In this paper a general imaging methodology, termed multi-mode total focusing method, is proposed in which any combination of modes and reflections can be used to produce an image of the test structure. Like the total focusing method, this approach is implemented by post-processing the full matrix of array data to achieve a synthetic focus at every pixel in the image. A hybrid model is used to predict the array data and demonstrate the performance of the multi-mode imaging concept. This hybrid model combines far field scattering coefficient matrices with a ray-based wave propagation model. This allows the inclusion of longitudinal waves, shear waves and wave mode conversions. It is shown that, with prior knowledge of likely scatterer location and orientation, the mode combination and array location can be optimised to maximise the performance of array inspections. A practically relevant weld inspection application is then described and its optimisation is discussed.

Selective spatial damping of propagating kink waves due to resonant absorption

Abstract: Context. There is observational evidence of propagating kink waves driven by photospheric motions. These disturbances, interpreted as kink magnetohydrodynamic (MHD) waves are attenuated as they propagate upwards in the solar corona. Aims. We show that resonant absorption provides a simple explanation to the spatial damping of these waves. Methods. Kink MHD waves are studied using a cylindrical model of solar magnetic flux tubes, which includes a non-uniform layer at the tube boundary. Assuming that the frequency is real and the longitudinal wavenumber complex, the damping length and damping per wavelength produced by resonant absorption are analytically calculated in the thin tube (TT) approximation, valid for coronal waves. This assumption is relaxed in the case of chromospheric tube waves and filament thread waves. Results. The damping length of propagating kink waves due to resonant absorption is a monotonically decreasing function of frequency. For kink waves with low frequencies, the damping length is exactly inversely proportional to frequency, and we denote this as the TGV relation. When moving to high frequencies, the TGV relation continues to be an exceptionally good approximation of the actual dependency of the damping length on frequency. This dependency means that resonant absorption is selective as it favours lowfrequency waves and can efficiently remove high-frequency waves from a broad band spectrum of kink waves. The efficiency of the damping due to resonant absorption depends on the properties of the equilibrium model, in particular on the width of the non-uniform layer and the steepness of the variation in the local Alfven speed. Conclusions. Resonant absorption is an effective mechanism for the spatial damping of propagating kink waves. It is selective because the damping length is inversely proportional to frequency so that the damping becomes more severe with increasing frequency. This means that radial inhomogeneity can cause solar waveguides to be a natural low-pass filter for broadband disturbances. Kink wave trains travelling along, e.g., coronal loops, will therefore have a greater proportion of the high-frequency components dissipated lower down in the atmosphere. This could have important consequences for the spatial distribution of wave heating in the solar atmosphere.

Direct-simulation-based study of turbulent flow over various waving boundaries

Abstract: We use direct numerical simulation of stress-driven turbulent Couette flows over waving surfaces to study turbulence in the vicinity of water waves. Mechanistic study is performed through systematic investigation of different wavy surface conditions including plane progressive Airy and Stokes waves with and without wind-induced surface drift, as well as stationary wavy walls and vertically waving walls for comparison. Two different wave steepness values ak = 0.1 and 0.25 are considered, where a is the wave amplitude and k is the wavenumber. For effects of wave age, defined as the ratio between the wave phase speed c and the turbulence friction velocity u*, we consider three values, namely c/u* = 2, 14 and 25, corresponding to slow, intermediate and fast waves, respectively. Detailed analysis of turbulence structure and statistics shows their dependence on the above-mentioned parameters. Our result agrees with previous measurement and simulation results and reveals many new features unreported in the literature. Over progressive waves, although no apparent flow separation is found in mean flow, considerable intermittent separations in instantaneous flow are detected in slow waves with large steepness. The near-surface coherent vortical structures are examined. We propose two conceptual vortex structure models: quasi-streamwise and reversed horseshoe vortices for slow waves and bent quasi-streamwise vortices for intermediate and fast waves. Detailed examination of Reynolds stress with quadrant analysis, turbulent kinetic energy (TKE) and TKE budget with a focus on production shows large variation with wave phase; analysis shows that the variation is highly dependent on wave age and wave nonlinearity. Comparison between Airy waves and Stokes waves indicates that although the nonlinearity of surface water waves is a high-order effect compared with the wave age and wave steepness, it still makes an appreciable difference to the turbulence structure. The effect of wave nonlinearity on surface pressure distribution causes substantial difference in the wave growth rate. Wind-induced surface drift can cause a phase shift in the downstream direction and a reduction in turbulence intensity; this effect is appreciable for slow waves but negligible for intermediate and fast waves. In addition to providing detailed information on the turbulence field in the vicinity of wave surfaces, the results obtained in this study suggest the importance of including wave dynamics in the study of wind–wave interaction.

A unifying fractional wave equation for compressional and shear waves.

Abstract: This study has been motivated by the observed difference in the range of the power-law attenuation exponent for compressional and shear waves. Usually compressional attenuation increases with frequency to a power between 1 and 2, while shear wave attenuation often is described with powers less than 1. Another motivation is the apparent lack of partial differential equations with desirable properties such as causality that describe such wave propagation. Starting with a constitutive equation which is a generalized Hooke's law with a loss term containing a fractional derivative, one can derive a causal fractional wave equation previously given by Caputo [Geophys J. R. Astron. Soc. 13, 529-539 (1967)] and Wismer [J. Acoust. Soc. Am. 120, 3493-3502 (2006)]. In the low omegatau (low-frequency) case, this equation has an attenuation with a power-law in the range from 1 to 2. This is consistent with, e.g., attenuation in tissue. In the often neglected high omegatau (high-frequency) case, it describes attenuation with a power-law between 0 and 1, consistent with what is observed in, e.g., dynamic elastography. Thus a unifying wave equation derived properly from constitutive equations can describe both cases.

An equivalent viscoelastic model for rock mass with parallel joints

Abstract: An equivalent viscoelastic medium model is proposed for rock mass with parallel joints. A concept of "virtual wave source (VWS)'' is proposed to take into account the wave reflections between the joints. The equivalent model can be effectively applied to analyze longitudinal wave propagation through discontinuous media with parallel joints. Parameters in the equivalent viscoelastic model are derived analytically based on longitudinal wave propagation across a single rock joint. The proposed model is then verified by applying identical incident waves to the discontinuous and equivalent viscoelastic media at one end to compare the output waves at the other end. When the wavelength of the incident wave is sufficiently long compared to the joint spacing, the effect of the VWS on wave propagation in rock mass is prominent. The results from the equivalent viscoelastic medium model are very similar to those determined from the displacement discontinuity method. Frequency dependence and joint spacing effect on the equivalent viscoelastic model and the VWS method are discussed.

Rogue waves in superfluid helium

Abstract: Rogue waves have been observed in superfluid helium. The experimental system consists of high intensity second sound (temperature-entropy) waves within a resonant cavity. Under steady state conditions, with a constant oscillatory driving force at the resonant frequency, the waves are turbulent and there are fluxes of energy towards both high and low frequencies. Rogue waves appear under the nonequilibrium conditions that prevail shortly after the drive has been switched on, prior to establishment of the steady state. The experiment is described briefly, relevant results are presented and discussed theoretically in terms of nonlinear wave interactions, and possible connections to rogue waves on the ocean are considered.

Dynamics of steep two-dimensional gravity-capillary solitary waves

Abstract: In this paper, the unsteady evolution of two-dimensional fully nonlinear free-surface gravity–capillary solitary waves is computed numerically in infinite depth. Gravity–capillary wavepacket-type solitary waves were found previously for the full Euler equations, bifurcating from the minimum of the linear dispersion relation. Small and moderate amplitude elevation solitary waves, which were known to be linearly unstable, are shown to evolve into stable depression solitary waves, together with a radiated wave field. Depression waves and certain large amplitude elevation waves were found to be robust to numerical perturbations. Two kinds of collisions are computed: head-on collisions whereby the waves are almost unchanged, and overtaking collisions which are either almost elastic if the wave amplitudes are both large or destroy the smaller wave in the case of a small amplitude wave overtaking a large one.

Acoustoelastic effect in concrete material under uni-axial compressive loading

Abstract: This study deals with the general matter of non-destructive evaluation of pre-stressed structures in civil engineering. Usually such structures are composed of concrete and are steel reinforced. Proposed idea is the evaluation of mechanical stress state of a concrete body (instead of steel cables) via ultrasonic non-destructive evaluation (NDE), by using the link between ultrasonic velocities and mechanical stresses provided by the acoustoelasticity theory. Velocities of the ultrasonic waves (longitudinal and transversal with different polarizations) are observed during propagation through a concrete body submitted to uni-axial loading (compressive testing). Obvious variations in velocity are found depending on the mechanical stress state (e.g. Δ c =92 m/s at σ =16 MPa for longitudinal waves). Thus acoustoelastic behavior of concrete is demonstrated. Further analyses provide acoustoelastic coefficients of concrete about ten times higher than the common ones of steel. The feasibility of stress evaluation using ultrasounds in concrete structures is proved under laboratory conditions.

Seismoelectromagnetic waves radiated by a double couple source in a saturated porous medium

Abstract: SUMMARY Studied in this paper are the properties of seismoelectromagnetic waves radiated by a double couple in a saturated porous medium arising from the electrokinetic effect. First, using the Pride's equations, we derive the Green's function of the magnetic field due to a single point force as a complement of previous authors’ works, in which only the Green's functions of the solid displacement, the relative fluid–solid displacement and the electric field were expressed. Furthermore, we extend these Green's functions to cater for the moment tensor sources. Then we derive the Green's functions of the solid displacement, the electric and magnetic fields in the frequency-space domain excited by a double couple source, which is frequently used in earthquake seismology. To visualize these fields, the radiation patterns are calculated and displayed. The results illustrate that the radiation pattern of the electric far field for the longitudinal (or transverse) wave is the same in shape as that of the far field of the P (or S) wave in elastodynamics. For a transverse wave, the electric and magnetic far fields share the same radiation patterns in shape, while the electric and magnetic near fields do not. For each of the four body waves, the far, intermediate and near fields are compared at different receiver-to-source distances, respectively. The electromagnetic (EM) wave has a much longer near-field-dominating distance than the seismic waves. We calculate the waveforms in the time–space domain by numerically Fourier transforming the Green's functions into the time domain. In order to validate these Green's functions and the waveforms, we calculate the waveforms again by another method. The main idea of the method is regarding the source as a displacement–stress–EM discontinuity vector. The result shows that the waveforms from those two methods are in excellent agreement. In the waveforms, there are the electric fields accompanying both the P and S waves, as well as the magnetic field accompanying the S wave. We testify that the S wave generally has a weaker capacity than the P wave in inducing an electric field. In the waveforms, there is also an independently propagating EM wave, which has a much higher speed than the seismic waves, and reaches the observation point immediately after the source launched. By comparing the waveforms at different receiving locations, we find that waveforms differ at different observation orientations.

Scale effects on the longitudinal wave propagation in nanoplates

Abstract: In this paper, the propagation characteristics of the longitudinal wave in nanoplates with small scale effects are studied. The equation of the longitudinal wave is obtained using the nonlocal elastic theory. The phase velocity and the group velocity are derived, respectively. The dispersion relation is analyzed with different wave numbers and scale coefficients. It can be observed from the results that the dispersion properties of the longitudinal wave are induced by the small scale effects, which will disappear in local continuous models. The dispersion degree can be strengthened by increasing the scale coefficient and the wave number. Furthermore, the characteristics for the group velocity of the longitudinal wave in nanoplates can also be tuned by these factors.

Analysis of Wave Propagation Through a Filled Rock Joint

Abstract: An analytical and experimental study on a longitudinal wave (P-wave) transmission normally across a filled rock joint is presented in this paper. The dynamic property of the filling material for the artificial rock joints is derived from a series of modified split Hopkinson pressure bar (SHPB) tests. The incident and transmitted waves in granitic pressure bars are calculated by wave separations of the strain gauge readings. The incident wave is approximated by a series of half-sinusoidal waves, and an analytical model on wave propagation across a filled rock joint is then deduced. The derived wave transmission coefficients across the filled joint agree very well with those from the test results. Both the analytical and test results show that the wave transmission coefficients are influenced by the mechanical properties and the input energy of the incident waves. Analytical parametric studies with respect to pre-compaction of the filling material, the frequency and amplitude of the incident wave have also been conducted.

Horizon effects with surface waves on moving water

Abstract: Surface waves on a stationary flow of water are considered, in a linear model that includes the surface tension of the fluid. The resulting gravity-capillary waves experience a rich array of horizon effects when propagating against the flow. In some cases three horizons (points where the group velocity of the wave reverses) exist for waves with a single laboratory frequency. Some of these effects are familiar in fluid mechanics under the name of wave blocking, but other aspects, in particular waves with negative co-moving frequency and the Hawking effect, were overlooked until surface waves were investigated as examples of analogue gravity [Sch\"utzhold R and Unruh W G 2002 Phys. Rev. D 66 044019]. A comprehensive presentation of the various horizon effects for gravity-capillary waves is given, with emphasis on the deep water/short wavelength case kh>>1 where many analytical results can be derived. A similarity of the state space of the waves to that of a thermodynamic system is pointed out.

Dispersion Analysis of Wave Motion in Microstructured Solids

Abstract: The Mindlin-type model is used for describing longitudinal waves in microstructured solids. This model involves explicitly the internal parameters and therefore tends to be rather complicated. An hierarchical approximation is derived, which is able to grasp the main effects of dispersion with wide variety of parameters. Attention is paid to the internal degrees of freedom of the microstructure and their influence on the dispersion effects. It is shown how the internal degrees of freedom can change the effects of dispersion.

Effect of the initial spectrum on the spatial evolution of statistics of unidirectional nonlinear random waves

Abstract: [1] Results of extensive experiments on propagation of unidirectional nonlinear random waves in a large wave tank are presented. The nonlinearity of the wavefield determined by the characteristic wave amplitude and the dominant wave length was retained constant in various series of experimental runs. In each experimental series, initial spectra of different shape and/or width were considered. Every series contained sufficient number of independent realizations to ensure reliable statistics. Evolution of various statistical parameters along the tank was investigated. It is demonstrated that the spectrum width plays an important role in the evolution of the random wavefield and strongly affects the variation of the wave spectrum as well as of parameters that characterize the deviation of the wavefield statistics from that corresponding to the Gaussian distribution. In particular, in a random wavefield that initially contains independent free harmonics within a narrow spectrum, extremely steep waves appear more often in the process of evolutions than predicted by a Rayleigh distribution, while for wider initial wave spectra the probability of those waves decreases sharply and is well below the Rayleigh values.

Solutions to the Zakharov-Kuznetsov equation with higher order nonlinearity by mapping and ansatz methods

Abstract: Solutions to the Zakharov-Kuznetsov equation with higher order nonlinearity are obtained using the mapping method. Several solutions are determined inclusing the cnoidal waves, shock waves, solitary waves, periodic singular waves and others. Finally, the ansatz method is applied to solve the equation with power law nonlinearity. It has been proved that the shock waves or topological solitons exist only for specific values of the power law parameter.

Enhanced acoustical transmission and beaming effect through a single aperture

Abstract: In this paper we explore from a fundamental theoretical point of view, transmission phenomena of acoustic waves transferred through a single subwavelength slit milled into a sound-hard plate that is textured by surface corrugations. It is shown that the enhanced acoustical transmission unambiguously is linked to the excitation of acoustic surface waves and Fabry-Perot modes within the aperture. With the former resonant condition, we give a prescription on how these surface waves are induced and connected to the formation of a collimated sound beam in the far field.

The Anelasticity of the Mantle

Abstract: The attenuation of seismic waves provides the most direct data regarding the non-elastic properties of the Earth. Recent experimental results from body waves, surface waves and free oscillations provide estimates of the anelasticity in various regions of the Earth. Results to date show that the upper mantle is more attenuating than the lower mantle, the maximum attenuation is in the vicinity of the low-velocity zone, a rapid increase in attenuation occurs in the vicinity of the C-region of the mantle and compressional waves are less attenuated than shear waves. A frequency dependence of Q has not yet been discovered. Most laboratory measurements of attenuation have been performed at ultrasonic frequencies on pure specimens of metals, glasses, plastics and ceramics. A general feature of laboratory measurements is an exponential increase of attenuation with temperature on which are superimposed peaks which can be attributed to dislocation or other defect phenomena. Measurements on natural rocks at atmospheric pressure can be attributed to the presence of cracks. The intrinsic attenuation of rocks as a function of temperature and pressure is not known. However, on other materials grain boundary phenomena dominate at high temperature. This can be attributed to increased grain boundary mobility at high temperatures. High pressure would be expected to decrease this mobility. If attenuation in the mantle is due to an activated process it is probably controlled by the diffusion rate of defects at grain boundaries. Estimates of attenuation in the lower mantle then yield an estimate of the activation volume of the defects contributing to the loss. If the lower mantle is assumed homogeneous the estimated activation volume is a small fraction of the presumed molal volume of materials making up the lower mantle. Stress induced migration of small point defects is a possible loss mechanism consistent with the observations.

Rogue internal waves in the ocean: Long wave model

Abstract: Rogue waves can be categorized as unexpectedly large waves, which are temporally and spatially localized. They have recently received much attention in the water wave context, and also been found in nonlinear optical fibers. In this paper, we examine the issue of whether rogue internal waves can be found in the ocean. Because large-amplitude internal waves are commonly observed in the coastal ocean, and are often modeled by weakly nonlinear long wave equations of the Korteweg-de Vries type, we focus our attention on this shallow-water context. Specifically, we examine the occurrence of rogue waves in the Gardner equation, which is an extended version of the Korteweg-de Vries equation with quadratic and cubic nonlinearity, and is commonly used for the modelling of internal solitary waves in the ocean. Importantly, we choose that version of the Gardner equation for which the coefficient of the cubic nonlinear term and the coefficient of the linear dispersive term have the same sign, as this allows for modulational instability. From numerical simulations of the evolution of a modulated narrow-band initial wave field, we identify several scenarios where rogue waves occur.

Third- and fourth-order constants of incompressible soft solids and the acousto-elastic effect

Abstract: Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination of third- and fourth-order elastic constants, especially in the case of incompressible isotropic soft solids, where the expressions are particularly simple. Specifically, it is simply a matter of expanding the expression for ρv(2), where ρ is the mass density and v the wave speed, in terms of the elongation e of a block subject to a uniaxial tension. The analysis shows that in the resulting expression: ρv(2) = a+be+ce(2), say, a depends linearly on μ; b on μ and A; and c on μ, A, and D, the respective second-, third, and fourth-order constants of incompressible elasticity, for bulk shear waves and for surface waves.

Evolution of shear-induced melting in a dusty plasma.

Abstract: The spatiotemporal development of melting is studied experimentally in a 2D dusty plasma suspension. Starting with an ordered lattice, and then suddenly applying localized shear, a pair of counterpropagating flow regions develop. A transition between two melting stages is observed before a steady state is reached. Melting spreads with a front that propagates at the transverse sound speed. Unexpectedly, coherent longitudinal waves are excited in the flow region.

Anisotropic dispersion and attenuation due to wave‐induced fluid flow: Quasi‐static finite element modeling in poroelastic solids

Abstract: [1] Heterogeneous porous media such as hydrocarbon reservoir rocks are effectively described as anisotropic viscoelastic solids. They show characteristic velocity dispersion and attenuation of seismic waves within a broad frequency band, and an explanation for this observation is the mechanism of wave-induced pore fluid flow. Various theoretical models quantify dispersion and attenuation of normal incident compressional waves in finely layered porous media. Similar models of shear wave attenuation are not known, nor do general theories exist to predict wave-induced fluid flow effects in media with a more complex distribution of medium heterogeneities. By using finite element simulations of poroelastic relaxation, the total frequency-dependent complex stiffness tensor can be computed for a porous medium with arbitrary internal heterogeneity. From the stiffness tensor, velocity dispersion and frequency-dependent attenuation are derived for compressional and shear waves as a function of the angle of incidence. We apply our approach to the case of layered media and to that of an ellipsoidal poroelastic inclusion. In the case of the ellipsoidal inclusion, compressional and shear wave modes show significant attenuation, and the characteristic frequency dependence of the effect is governed by the spatiotemporal scale of the pore fluid pressure relaxation. In our anisotropic examples, the angle dependence of the attenuation is stronger than that of the velocity dispersion. It becomes clear that the spatial attenuation patterns show specific characteristics of wave-induced fluid flow, implying that anisotropic attenuation measurements may contribute to the inversion of fluid transport properties in heterogeneous porous media.