Showing papers on "Wave propagation published in 2004"

Ultrasonic Waves in Solid Media

Abstract: Preface 1. Introduction 2. Dispersion principles 3. Unbounded isotropic and anisotropic media 4. Reflection and refraction 5. Oblique incidence 6. Wave scattering 7. Surface and subsurface waves 8. Waves in plates 9. Interface waves 10. Layer on a half space 11. Waves in rods 12. Waves in hollow cylinders 13. Guided waves in multiple layers 14. Source influence 15. Horizontal shear 16. Waves in an anisotropic layer 17. Elastic constant determination 18. Waves in viscoelastic media 19. Stress influence 20. Boundary element methods Bibliography Appendices A. Ultrasonic nondestructive testing principles, analysis and display technology B. Basic formulas and concepts in the theory of elasticity C. Basic formulas in complex variables D. Schlieren imaging and dynamic photoelasticity E. Key wave propagation experiments Index.

Time Reversal of Electromagnetic Waves

Abstract: We report the first experimental demonstration of time-reversal focusing with electromagnetic waves. An antenna transmits a 1-micros electromagnetic pulse at a central frequency of 2.45 GHz in a high-Q cavity. Another antenna records the strongly reverberated signal. The time-reversed wave is built and transmitted back by the same antenna acting now as a time-reversal mirror. The wave is found to converge to its initial source and is compressed in time. The quality of focusing is determined by the frequency bandwidth and the spectral correlations of the field within the cavity.

Propagation in and scattering from a matched metamaterial having a zero index of refraction.

Abstract: Planar metamaterials that exhibit a zero index of refraction have been realized experimentally by several research groups. Their existence stimulated the present investigation, which details the properties of a passive, dispersive metamaterial that is matched to free space and has an index of refraction equal to zero. Thus, unlike previous zero-index investigations, both the permittivity and permeability are zero here at a specified frequency. One-, two-, and three-dimensional source problems are treated analytically. The one- and two-dimensional source problem results are confirmed numerically with finite difference time domain (FDTD) simulations. The FDTD simulator is also used to treat the corresponding one- and two-dimensional scattering problems. It is shown that in both the source and scattering configurations the electromagnetic fields in a matched zero-index medium take on a static character in space, yet remain dynamic in time, in such a manner that the underlying physics remains associated with propagating fields. Zero phase variation at various points in the zero-index medium is demonstrated once steady-state conditions are obtained. These behaviors are used to illustrate why a zero-index metamaterial, such as a zero-index electromagnetic band-gap structured medium, significantly narrows the far-field pattern associated with an antenna located within it. They are also used to show how a matched zero-index slab could be used to transform curved wave fronts into planar ones.

Focusing of sound in a 3D phononic crystal.

Abstract: We present a combined experimental and theoretical study of phonon focusing phenomena in a pass band above the complete band gap in a 3D phononic crystal Wave propagation was found to depend dramatically on both frequency and incident direction This propagation anisotropy leads to very large negative refraction, which can be used to focus a diverging ultrasonic beam into a narrow focal spot with a large focal depth The experimental field patterns are well explained using a Fourier imaging technique, based on the 3D equifrequency surfaces calculated from multiple scattering theory

Experimental Observation of Nonlinear Traveling Waves in Turbulent Pipe Flow

Abstract: Transition to turbulence in pipe flow is one of the most fundamental and longest-standing problems in fluid dynamics. Stability theory suggests that the flow remains laminar for all flow rates, but in practice pipe flow becomes turbulent even at moderate speeds. This transition drastically affects the transport efficiency of mass, momentum, and heat. On the basis of the recent discovery of unstable traveling waves in computational studies of the Navier-Stokes equations and ideas from dynamical systems theory, a model for the transition process has been suggested. We report experimental observation of these traveling waves in pipe flow, confirming the proposed transition scenario and suggesting that the dynamics associated with these unstable states may indeed capture the nature of fluid turbulence.

Electric coupling to the magnetic resonance of split ring resonators

Abstract: We study both theoretically and experimentally the transmission properties of a lattice of split ring resonators (SRRs) for different electromagnetic (EM) field polarizations and propagation directions. We find unexpectedly that the incident electric field E couples to the magnetic resonance of the SRR when the EM waves propagate perpendicular to the SRR plane and the incident E is parallel to the gap-bearing sides of the SRR. This is manifested by a dip in the transmission spectrum. A simple analytic model is introduced to explain this interesting behavior.

Matrix analysis of microring coupled-resonator optical waveguides

Abstract: We use the coupling matrix formalism to investigate continuous-wave and pulse propagation through microring coupled-resonator optical waveguides (CROWs). The dispersion relation agrees with that derived using the tight-binding model in the limit of weak inter-resonator coupling. We obtain an analytical expression for pulse propagation through a semi-infinite CROW in the case of weak coupling which fully accounts for the nonlinear dispersive characteristics. We also show that intensity of a pulse in a CROW is enhanced by a factor inversely proportional to the inter-resonator coupling. In finite CROWs, anomalous dispersions allows for a pulse to propagate with a negative group velocity such that the output pulse appears to emerge before the input as in “superluminal” propagation. The matrix formalism is a powerful approach for microring CROWs since it can be applied to structures and geometries for which analyses with the commonly used tight-binding approach are not applicable.

Quantifying elasticity and viscosity from measurement of shear wave speed dispersion

Abstract: The propagation speed of shear waves is related to frequency and the complex stiffness (shear elasticity and viscosity) of the medium. A method is presented to solve for shear elasticity and viscosity of a homogeneous medium by measuring shear wave speed dispersion. Harmonic radiation force, introduced by modulating the energy density of incident ultrasound, is used to generate cylindrical shear waves of various frequencies in a homogeneous medium. The speed of shear waves is measured from phase shift detected over the distance propagated. Measurements of shear wave speed at multiple frequencies are fit with the theoretical model to solve for the complex stiffness of the medium. Experiments in gelatin phantoms show promising results validated by an independent method. Practical considerations and challenges in possible medical applications are discussed.

Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory

Abstract: In part I of this work (Bona J L, Chen M and Saut J-C 2002 Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and the linear theory J. Nonlinear Sci. 12 283–318), a four-parameter family of Boussinesq systems was derived to describe the propagation of surface water waves. Similar systems are expected to arise in other physical settings where the dominant aspects of propagation are a balance between the nonlinear effects of convection and the linear effects of frequency dispersion. In addition to deriving these systems, we determined in part I exactly which of them are linearly well posed in various natural function classes. It was argued that linear well-posedness is a natural necessary requirement for the possible physical relevance of the model in question. In this paper, it is shown that the first-order correct models that are linearly well posed are in fact locally nonlinearly well posed. Moreover, in certain specific cases, global well-posedness is established for physically relevant initial data. In part I, higher-order correct models were also derived. A preliminary analysis of a promising subclass of these models shows them to be well posed.

Dispersion Relation of Electromagnetic Waves in One-Dimensional Plasma Photonic Crystals

Abstract: The dispersion relation of electromagnetic waves in one-dimensional plasma photonic crystals is studied. The plasma photonic crystal is a periodic array composed of alternating thin plasma and dielectric material. The dispersion relation is obtained by solving a Maxwell wave equation using a method analogous to Kronig-Penny’s problem in quantum mechanics, and it is found that the frequency gap and cut-off appear in the dispersion relation. The frequency gap is shown to become larger with the increase of the plasma density as well as plasma width.

Linear and nonlinear wave propagation in negative refraction metamaterials

Abstract: We discuss linear and nonlinear optical wave propagation in a left-handed medium (LHM) or medium of negative refraction (NRM). We use the approach of characterizing the medium response totally by a generalized electric polarization (with a dielectric permittivity {tilde {var_epsilon}}(w, {rvec k})) that can be decomposed into a curl and a non-curl part. The description has a one-to-one correspondence with the usual approach characterizing the LHM response with a dielectric permittivity {var_epsilon}<0 and a magnetic permeability {mu}<0. The latter approach is less physically transparent in the optical frequency region because the usual definition of magnetization loses its physical meaning. Linear wave propagation in LHM or NRM is characterized by negative refraction and negative group velocity that could be clearly manifested by ultra-short pulse propagation in such a medium. Nonlinear optical effects in LHM can be predicted from the same calculations adopted for ordinary media using our general approach.

Near Field Characteristics of Landslide Generated Impulse Waves

Abstract: Landslide generated impulse waves were investigated in a two-dimensional physical laboratory model based on the generalized Froude similarity. The recorded wave profiles were extremely unsteady and nonlinear. Four wave types were determined: weakly nonlinear oscillatory wave, non-linear transition wave, solitary-like wave and dissipative transient bore. Most of the generated impulse waves were located in the intermediate water depth wave regime. Nevertheless the propagation velocity of the leading wave crest closely followed the theoretical approximations for a solitary wave. Between 4 and 50% of the kinetic slide impact energy propagated outward in the impulse wave train. The applicability ranges of the classical nonlinear wave theories to landslide generated impulse waves were determined. The main wave characteristics were related to the landslide parameters driving the entire wave generation process. The slide Froude number was identified as the dominant parameter. The physical model results were compared to the giant rockslide generated impulse wave which struck the shores of the Lituya Bay, Alaska, in 1958.

Nonlinear surface waves in left-handed materials.

Abstract: We study both linear and nonlinear surface waves localized at the interface separating a left-handed (LH) medium (i.e., a medium with both negative dielectric permittivity and negative magnetic permeability) and a conventional [or right-handed (RH)] dielectric medium. We demonstrate that the interface can support both TE- and TM-polarized surface waves-surface polaritons, and we study their properties. We describe the intensity-dependent properties of nonlinear surface waves in three different cases, i.e., when both the LH and RH media are nonlinear and when either of the media is nonlinear. In the case when both media are nonlinear, we find two types of nonlinear surface waves, one with the maximum amplitude at the interface, and the other one with two humps. In the case when one medium is nonlinear, only one type of surface wave exists, which has the maximum electric field at the interface, unlike waves in right-handed materials where the surface-wave maximum is usually shifted into a self-focusing nonlinear medium. We discuss the possibility of tuning the wave group velocity in both the linear and nonlinear cases, and show that group-velocity dispersion, which leads to pulse broadening, can be balanced by the nonlinearity of the media, so resulting in soliton propagation.

Heating and current drive by electron cyclotron waves

Abstract: The physics model of electron cyclotron heating (ECH) and current drive (ECCD) is becoming well validated through systematic comparisons of theory and experiment. This work has shown that ECH and ECCD can be highly localized and robustly controlled in toroidal plasma confinement systems, leading to applications including stabilization of magnetohydrodynamic instabilities like neoclassical tearing modes, control and sustainment of desired profiles of current density and plasma pressure, and studies of localized transport in laboratory plasmas. The experimental work was supported by a broad base of theory based on first principles which is now well encapsulated in linear ray tracing codes describing wave propagation, absorption, and current drive and in fully relativistic quasilinear Fokker–Planck codes describing in detail the response of the electrons to the energy transferred from the wave. The subtle balance between wave-induced diffusion and Coulomb relaxation in velocity space provides an understandin...

Using a Three-Dimensional Smoothed Particle Hydrodynamics Method for Wave Impact on a Tall Structure

Abstract: The impact of a single wave generated by a dam break with a tall structure is modeled with a three-dimensional version of the smoothed particle hydrodynamics method. The method is used to analyze the propagation of a long wave and the force it exerts on a tall structure located in a region with vertical boundaries. Velocities and forces obtained from a numerical model are shown to be in good agreement with laboratory measurements. The effect of having a dry bed in front of the dam prior to the dam break versus a wet bed in the experiment is discussed.

Channel model for wireless communication around human body

Abstract: A channel model for a wireless body area network at 400 MHz, 900 MHz and 2.4 GHz is derived. The electromagnetic wave propagation around the body is simulated with a finite-difference time-domain simulator. Creeping waves were identified as the propagation path around the body. Its impact on the delay spread in an indoor environment is discussed.

On the nature of EIT waves, EUV dimmings and their link to CMEs

Abstract: EIT waves and extreme-ultraviolet (EUV) dimmings attract particular attention as they frequently accompany Coronal Mass Ejections (CMEs) We present several examples of EIT waves and EUV dimmings with particular morphologies previously unreported in the literature We report for the first time an EIT wave in the Fe XV (284 A) bandpass of the SOHO/EIT instrument The observations of this event confirm previous results that an EIT wave is a purely coronal phenomenon that does not propagate in the transition region plasma Two EIT wave events initiated close to the solar limb are investigated, thus per- mitting us to see simultaneously the wave and the magnetic configuration of the CME These observations suggest that EIT wave can be regarded as a bimodal phenomenon The wave mode represents a wave-like propagating disturbance Its char- acteristic features are propagation of a bright front to large distances from dimming sites and quasi-circular appearance The eruptive mode is the propagation of a dimming and of an EIT wave as a result of successive opening of magnetic field lines during the CME lift-off It can be identified by noting the expansion of a dimming and the appearance of another dimming ahead of a bright front We reveal the temperature structure of the EUV dimmings that appeared after the classical EIT wave event on May 12, 1997, using differential emission measure (DEM) maps obtained through the analysis of images in four EIT bandpasses The part of the CME mass contained in the low corona observed by the EIT is estimated to be about 10 15 g It appears that around 50% of this total CME mass in the low corona is contained outside of transient coronal holes It is shown that at present it is difficult to reconcile all the observational facts into a coherent physical model In particular, the physical nature of the wave mode of EIT waves remains elusive

Finite‐difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid

Abstract: We describe the application of the rotated staggered-grid (RSG) finite-difference technique to the wave equations for anisotropic and viscoelastic media. The RSG uses rotated finite-difference operators, leading to a distribution of modeling parameters in an elementary cell where all components of one physical property are located only at one single position. This can be advantageous for modeling wave propagation in anisotropic media or complex media, including high-contrast discontinuities, because no averaging of elastic moduli is needed. The RSG can be applied both to displacement-stress and to velocity-stress finite-difference (FD) schemes, whereby the latter are commonly used to model viscoelastic wave propagation. With a von Neumann-style anlysis, we estimate the dispersion error of the RSG scheme in general anisotropic media. In three different simulation examples, all based on previously published problems, we demonstrate the application and the accuracy of the proposed numerical approach.

Generation of Mesoscale Gravity Waves in Upper-Tropospheric Jet–Front Systems

Abstract: Multiply nested mesoscale numerical simulations with horizontal resolution up to 3.3 km are performed to study the generation of mesoscale gravity waves during the life cycle of idealized baroclinic jet–front systems. Long-lived vertically propagating mesoscale gravity waves with horizontal wavelengths ∼100–200 km are simulated originating from the exit region of the upper-tropospheric jet streak, in a manner consistent with past observational studies. The residual of the nonlinear balance equation is found to be a useful index in diagnosing flow imbalance and predicting wave generation. The imbalance diagnosis and model simulations suggest that balance adjustment, as a generalization of geostrophic adjustment, is likely responsible for generating these mesoscale gravity waves. It is hypothesized that, through balance adjustment, the continuous generation of flow imbalance from the developing baroclinic wave will lead to the continuous radiation of gravity waves.

Shoaling of subharmonic gravity waves

Abstract: [1] In this paper the energy budget of wave group-induced subharmonic gravity waves in the nearshore region is examined on the basis of the energy equation for long waves in conjunction with analyses of a high-resolution laboratory data set of one-dimensional random wave propagation over a barred beach. The emphasis is on the growth of forced subharmonics and the deshoaling of the reflected free waves in the shoaling zone. The incident lower-frequency subharmonics are nearly fully reflected at the shoreline, but the higher-frequency components appear to be subject to a significant dissipation in a narrow inshore zone including the swash zone. The previously reported phase lag of the incident forced waves behind the short-wave groups is confirmed, and its key role in the transfer of energy between the grouped short waves and the shoaling bound waves is highlighted. The cross-shore variation of the local mean rate of this energy transfer is determined. Using this as a source function in the wave energy balance allows a very accurate prediction of the enhancement of the forced waves in the shoaling zone, where dissipation is insignificant. The phase lag appears to increase with increasing frequency, which is reflected in a frequency-dependent growth rate, varying very nearly from the free-wave variation ∼ h -1/4 (Green's law) for the lower frequencies to the shallow-water equilibrium limit for forced subharmonics ∼h -5/2 for the higher frequencies. This observed frequency dependence is tentatively generalized to a dependence on a normalized bed slope, controlling whether a so-called mild-slope regime or a steep-slope regime prevails, in which enhanced incident forced waves dominate over breakpoint-generated waves or vice versa.

Introduction to Hydrocodes

Abstract: Dynamic Behavior of Materials and Structures, Wave Propagation and Impact, Shock Waves in Solids, Numerical Modeling of Fast, Transient Phenomena, How Does a Hydrocode Really Work?, Alternatives to Purely Lagrangian Computations, Experimental Methods for Material Behavior at High Strain Rates, Practical Aspects of Numerical Simulation of Dynamics Events

Ince-Gaussian modes of the paraxial wave equation and stable resonators

Abstract: We present the Ince-Gaussian modes that constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation in elliptic coordinates and that are transverse eigenmodes of stable resonators. The transverse shape of these modes is described by the Ince polynomials and is structurally stable under propagation. Ince-Gaussian modes constitute the exact and continuous transition modes between Laguerre- and Hermite-Gaussian modes. The expansions between the three families are derived and discussed. As with Laguerre-Gaussian modes, it is possible to construct helical Ince-Gaussian modes that exhibit rotating phase features whose intensity pattern is formed by elliptic rings and whose phase rotates elliptically.

Symmetry of steady periodic surface water waves with vorticity

Abstract: For large classes of vorticities we prove that a steady periodic gravity water wave with a monotonic profile between crests and troughs must be symmetric. The analysis uses sharp maximum principles for elliptic partial differential equations.

Propagation of electromagnetic waves at MHz frequencies through seawater

Abstract: The nature of the ocean environment and its vast size has necessitated the development of sophisticated equipment and techniques for various underwater applications including diver-to-diver communications, ROV/AUV docking, communications and oil and gas explorations. To facilitate scientific exploration a wide variety of systems and vehicles have been developed to operate within the shallow continental shelf region or in deep oceans. For successful underwater electromagnetic (EM) wave operation, knowledge is required of the wave transmission properties of seawater over all distances both short and long. This information is required for such activities such as: sensor systems, imaging, position fixing, measurement of speed, obstacle detection and avoidance, guidance, communication of data/voice and remote control. This paper presents a new approach of EM wave propagation through seawater. The experimental results conducted in the laboratory and the real environment of seawater is presented.

Partial focusing of radiation by a slab of indefinite media

Abstract: Negative refraction can occur at the interface between vacuum and an indefinite medium—an anisotropic medium for which not all elements of the permittivity and permeability tensors have the same sign. We show experimentally and via simulations that a metamaterial composed of split ring resonators, designed to provide a permeability equal to −1 along the longitudinal axis, will redirect s-polarized electromagnetic waves from a nearby source to a partial focus. The dispersion characteristics of indefinite media prohibit the possibility of true aplanatic points for a planar slab; however, by contouring the surfaces aplanatic points may be realized, as well as other geometrical optical behavior.

Coseismic and postseismic velocity changes measured by repeating earthquakes

Abstract: [1] Repeating earthquakes that rupture approximately the same fault patch and have nearly identical waveforms are a useful tool for measuring temporal changes in wave propagation in the Earth's crust. Since source and path effects are common to all earthquakes in a repeating earthquake sequence (multiplet), differences in their waveforms can be attributed to changes in the characteristics of the medium. We have identified over 20 multiplets containing between 5 and 40 repeating events in the aftershock zones of the 1989 Loma Prieta and 1984 Morgan Hill, California, earthquakes. Postmain shock events reveal delays of phases in the early S wave coda of as much as 0.2 s relative to premain shock events. The delay amounts to a path-averaged coseismic velocity decrease of about 1.5% for P waves and 3.5% for S waves. Since most of the multiplets are aftershocks and follow Omori's law, we have excellent temporal sampling in the immediate postmain shock period. We find that the amplitude of the velocity decrease decays logarithmically in time following the main shock. In some cases it returns to the premain shock values, while in others it does not. Similar results are obtained for the Morgan Hill main shock. Because the fractional change in S wave velocity is greater than the fractional change in P wave velocity, it suggests that the opening or connection of fluid-filled fractures is the underlying cause. The magnitude of the velocity change implies that low effective pressures are present in the source region of the velocity change. Our results suggest that the changes are predominantly near the stations and shallow, but we cannot exclude the possibility that changes occur at greater depth as well. If the variations are shallow, we may be detecting the lingering effects of nonlinearity during main shock strong ground motion. If the variations are deep, it suggests that pore pressures at seismogenic depths are high, which would likely play a key role in the earthquake process.