Different Types Of Waves Research Articles

Three-dimensional investigation of liquid film structure at the initial area of annular-dispersed flow

Initial stage of downward flow of gas-sheared liquid film in a vertical rectangular duct was studied using brightness-based laser-induced fluorescence technique. Measurements were resolved along both longitudinal and transverse coordinates and time. The initial high-frequency waves which are formed at the inlet were found to be two-dimensional. These waves are promptly broken into localised horseshoe-shaped waves which merge downstream to form large-scale quasi-2D disturbance waves. Peculiarities of three-dimensional evolution of waves of different types were studied in a wide range of flow parameters.

Usage Autocorrelation Function in the Capacity of Indicator Shape of the Signal in Acoustic Emission Testing of Intricate Castings

The article contains information about acoustic emission signals analysing using autocorrelation function. Operation factors were analysed, such as shape of signal, the origins time and carrier frequency. The purpose of work is estimating the validity of correlations methods analysing signals. Acoustic emission signal consist of different types of waves, which propagate on different trajectories in object of control. Acoustic emission signal is amplitude-, phase- and frequency-modeling signal. It was described by carrier frequency at a given point of time. Period of signal make up 12.5 microseconds and carrier frequency make up 80 kHz for analysing signal. Usage autocorrelation function like indicator the origin time of acoustic emission signal raises validity localization of emitters.

Propagation of surface plasmon–polaritons at the boundary of a metal–dielectric with thermal optical nonlinearity

Media with thermal defocusing nonlinearity and bordering material with high thermal conductivity are investigated. The problem of creating a fixed optical waveguide at the boundary of a metal–dielectric with thermal nonlinearity is solved. The possibility of different types of waves propagating in such a wave guide is considered.

A description of piezoelectric effect in non‐polar materials taking into account the quadrupole moments

A method of the description of piezoelectric effect in non‐polar materials is suggested. This method is based on the model of unit cell possessing a non‐zero quadrupole moment and the zero dipole moment. The suggested theory contains several additional material tensors. A comparison of the suggested theory with the classical theory of piezoelectricity is carried out. The structure of the additional material tensors is determined for the crystal lattice with the hexagonal crystal symmetry of quartz. An analysis of dispersion relations is carried out. This analysis reveals that the quadrupole moment tensor has a qualitative influence on the behavior of solution. Namely, the quadrupole moments cause rather the redistribution of energy between the waves of different type than the wave damping. A method of determination of the additional material moduli is suggested. The method consists in using the dispersion relations containing the unknown material moduli and the experimental data on attenuation factor versus frequency.

Application of modelling by study of migration transformation in seismic works

The article highlights application of modelling by making seismic images through migration transformation. It describes the essence of genesis of the seismic waves of different types on the heterogenous geological terrain and provides a simplified algorithm of the account of factors corrupting the seismic record.

Interaction of Transverse Plane Waves in Nanocomposites

The interaction of nonlinear harmonic plane elastic waves in a Murnaghan material is studied theoretically. A solution that describes the interaction of horizontally and vertically polarized harmonic transverse waves is found using the perturbation method. Pumping of energy between transverse waves of different types is described. Numerical results are obtained for five types of nanocomposites

Velocity analysis with vertical seismic profile data using migration of surface-related multiples

We have developed an original method for migration velocity analysis for vertical seismic profile (VSP) data. The method is based on VSP imaging with the primary reflected data and surface-related multiples. Velocity updates are carried out by matching the images obtained by these two types of waves. To do it automatically, we have introduced an objective function of the crosscorrelation type and developed a gradient-based maximization algorithm. On synthetic walk-away VSP data sets, we found that maximization of the crosscorrelation of the images provided by the two different types of waves allowed the retrieval of the interval velocities below the borehole receivers — a problem that was considered to be challenging with a VSP acquisition. Also, the possibility of the lateral velocity gradient reconstruction was developed on a simple synthetic model. On the real walk-away VSP data set from the North Sea, we found that the method could also be used for estimation of effective anisotropy parameters below the borehole receivers. In all of our examples, the velocity model refinement based on the presented method led to significant improvements of the seismic images.

On wave propagation in a random micropolar thermoelastic medium, second moments, and associated Green’s tensor

The couple stress theory developed by Eringen comprises granular materials as also composite fibrous materials. As such, micropolar materials present an inclusive model of composite materials. This article endeavors to study aspects of wave propagation in a random weakly thermal micropolar elastic medium. The smooth perturbation technique has been employed. The classical thermoelasticity has been used. Six different types of waves have been observed to propagate in the random interacting medium. Dispersion equations have been derived. The effects due to random variations of micropolar elastic and thermal parameters have been observed. Change of phase speed occurs on account of randomness. Attenuation coefficients for high-frequency waves have been computed. Second moment properties have been discussed with application to wave propagation in the random micropolar elastic medium. 36 + 1 components of the associated Green’s tensor have been computed. Integrals involving correlation functions have been transformed to radial forms. A special type of correlation function has been used to approximately measure effects of random variations of parameters.

Exact traveling wave solutions of the van der Waals normal form for fluidized granular matter

Analytical solutions of the van der Waals normal form for fluidized granular media have been done to study the phase separation phenomenon by using two different exact methods. The Painlevé analysis is discussed to illustrate the integrability of the model equation. An auto-Bäcklund transformation is presented via the truncated expansion and symbolic computation. The results show that the exact solutions of the model introduce solitary waves of different types. The solutions of the hydrodynamic model and the van der Waals equation exhibit a behavior similar to the one observed in molecular dynamic simulations such that two pairs of shock and rarefaction waves appear and move away, giving rise to the bubbles. The dispersion properties and the relation between group and phase velocities of the model equation are studied using the plane wave assumption. The diagrams are drawn to illustrate the physical properties of the exact solutions, and indicate their stability and bifurcation.

Identification and Extraction of Surface Waves from Three‐Component Seismograms Based on the Normalized Inner Product

Abstract Identification of different wave types in a seismogram is an important step for the understanding of wave propagation phenomena. Because in most seismograms, different types of waves with different frequencies may appear simultaneously, separation of waves is more effectively achieved when a time–frequency analysis is performed. In this work, we propose a new time–frequency analysis procedure to identify and extract Rayleigh and Love waves from three‐component seismograms. Exploiting the advantage of the absolute phase preservation by the Stockwell transform, we construct time–frequency filters to extract waves based on the normalized inner product (NIP). Because the NIP is the time–frequency counterpart of the correlation, Rayleigh and Love waves can be identified depending on the NIP between the Stockwell transforms of the horizontal and vertical displacement components. The novelty and advantage of the proposed procedure is that it does not require specifying a priori the direction of propagation of the surface waves, but instead such direction is determined. Furthermore, it is shown that the NIP is a more stable parameter in the time–frequency domain when compared to the instantaneous reciprocal ellipticity, and thus it avoids smoothing (and with it, altering) the data. The procedure has been successfully tested with real signals, specifically to extract Rayleigh and Love waves from seismograms of one aftershock of the 1999 Chi‐Chi earthquake. With the proposed procedure, we found different directions of propagation for retrograde and prograde Rayleigh waves, which might suggest that they are generated by different mechanisms.

Enhanced transmission band in periodic media with loss modulation

We study the propagation of waves in a periodic array of absorbing layers. We report an anomalous increase of wave transmission through the structure related to a decrease of the absorption around the Bragg frequencies. The effect is first discussed in terms of a generic coupled wave model extended to include losses, and its predictions can be applied to different types of waves propagating in media with periodic modulation of the losses at the wavelength scale. The particular case of sound waves in an array of porous layers embedded in air is considered. An experiment designed to test the predictions demonstrates the existence of the enhanced transmission band.

On the traveling waves governed by the Camassa–Holm equation

The Camassa–Holm equation admits undistorted traveling waves that are either smooth or exhibit peaks or cusps. All three wave types can be periodic or solitary. Also waves of different types may be combined. In the present paper it is shown that, apart from peaks and cusps, the traveling waves governed by the Camassa–Holm equation can be found from some simpler equation. In the case of peaked solutions, this reduced equation is even linear. The governing equation of traveling waves in its original form can be interpreted as a nonlinear combination of the reduced equation and its first integral. For a small range of the integration constant, the reduced equation admits bounded solutions, which then are directly inherited by the Camassa–Holm equation. In general, the solutions of the reduced equation are unbounded and cannot be considered to represent traveling waves. The full equation, however, has a nonlinearity in the highest derivative, which is characteristic for the Camassa–Holm and some other equations. This nonlinear term offers the possibility of constructing bounded traveling waves from the unbounded solutions of the reduced equation. These waves necessarily have discontinuities in the slope and are, therefore, solutions only in a generalized sense.

Inverse problems: seeing the unseen

This survey article deals mainly with two inverse problems and the relation between them. The first inverse problem we consider is whether one can determine the electrical conductivity of a medium by making voltage and current measurements at the boundary. This is called electrical impedance tomography and also Calderón’s problem since the famous analyst proposed it in the mathematical literature (Calderón in On an inverse boundary value problem. Seminar on numerical analysis and its applications to continuum physics (Rio de Janeiro, 1980), Soc Brasil Mat. Rio de Janeiro, pp. 65–73, 1980). The second is on travel time tomography. The question is whether one can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as a geometry problem, the boundary rigidity problem. Can we determine a Riemannian metric of a compact Riemannian manifold with boundary by measuring the distance function between boundary points? These two inverse problems concern visibility, that is whether we can determine the internal properties of a medium by making measurements at the boundary. The last topic of this paper considers the opposite issue: invisibility: Can one make objects invisible to different types of waves, including light?

Dispersion properties of vortex-type monatomic lattices

The paper presents a systematic study of dispersive waves in an elastic chiral lattice. Chirality is introduced through gyroscopes embedded into the junctions of a doubly periodic lattice. Bloch–Floquet waves are assumed to satisfy the quasi-periodicity conditions on the elementary cell. New features of the system include degeneracy due to the rotational action of the built-in gyroscopes and polarisation leading to the dominance of shear waves within a certain range of values of the constant characterising the rotational action of the gyroscopes. Special attention is given to the analysis of Bloch–Floquet waves in the neighbourhoods of critical points of the dispersion surfaces, where standing waves of different types occur. The theoretical model is accompanied by numerical simulations demonstrating directional localisation and dynamic anisotropy of the system.

Detection of microseismic compressional (P) body waves aided by numerical modeling of oceanic noise sources

Among the different types of waves embedded in seismic noise, body waves present appealing properties but are still challenging to extract. Here we first validate recent improvements in numerical modeling of microseismic compressional (P) body waves and then show how this tool allows fast detection and location of their sources. We compute sources at ~0.2 Hz within typical P teleseismic distances (30–90°) from the Southern California Seismic Network and analyze the most significant discrete sources. The locations and relative strengths of the computed sources are validated by the good agreement with beam‐forming analysis. These 54 noise sources exhibit a highly heterogeneous distribution, and cluster along the usual storm tracks in the Pacific and Atlantic oceans. They are mostly induced in the open ocean, at or near water depths of 2800 and 5600 km, most likely within storms or where ocean waves propagating as swell meet another swell or wind sea. We then emphasize two particularly strong storms to describe how they generate noise sources in their wake. We also use these two specific noise bursts to illustrate the differences between microseismic body and surface waves in terms of source distribution and resulting recordable ground motion. The different patterns between body and surface waves result from distinctive amplification of ocean wave‐induced pressure perturbation and different seismic attenuation. Our study demonstrates the potential of numerical modeling to provide fast and accurate constraints on where and when to expect microseismic body waves, with implications for seismic imaging and climate studies.

Saturn's ULF wave foreshock boundary: Cassini observations

Even though the solar wind is highly supersonic, intense ultra-low frequency (ULF) wave activity has been detected in regions just upstream of the bow shocks of magnetized planets. This feature was first observed ahead of the Earth's bow shock, and the corresponding region was called the ULF wave foreshock, which is embedded within the planet's foreshock. The properties as well as the spatial distribution of ULF waves within the Earth's foreshock have been extensively studied over the last three decades and have been explained as a result of plasma instabilities triggered by solar wind ions backstreaming from the bow shock. Since July 2004, the Cassini spacecraft has characterized the Saturnian plasma environment including its upstream region. Since Cassini's Saturn orbit insertion (SOI) in June 2004 through August 2005, we conducted a detailed survey and analysis of observations made by the Vector Helium Magnetometer (VHM). The purpose of the present study is to characterize the properties of waves observed in Saturn's ULF wave foreshock and identify its boundary using single spacecraft techniques. The amplitude of these waves is usually comparable to the mean magnetic field intensity, while their frequencies in the spacecraft frame yields two clearly different types of waves: one with frequencies below the local proton cyclotron frequency (ΩH+) and another with frequencies above ΩH+. All the wave crossings described here, clearly show that these waves are associated to Saturn's foreshock. In particular, the presence of waves is associated with the change in θBn to quasi-parallel geometries. Our results show the existence of a clear boundary for Saturn's ULF wave foreshock, compatible with θBn∼45° surfaces.

Scattering of acoustic waves by a sector

In this work we study the problem of diffraction of an acoustic plane wave by a plane angular sector with the Dirichlet boundary condition on its surface. By means of incomplete separation of variables, with the aid of Watson–Bessel integral representation the problem is reduced to an infinite system of linear summation equations of the second kind. Exploiting the reduction of the integral representation to that of the Sommerfeld type, a consequent procedure is then developed in order to describe different components in the far field asymptotics. To that end, the analytic properties and singularities of the integrand in the Sommerfeld integral are carefully studied. The latter plays a crucial role when evaluating the Sommerfeld integral by means of the saddle point technique because these singularities are captured in the process of deformation of the Sommerfeld contours into the steepest descent paths. The corresponding asymptotic contributions of the singularities lead to the description of the different types of waves in the far field asymptotics. These are the waves reflected from the sector, the waves from the edges including those multiply diffracted from one edge to another. The spherical wave from the vertex of the sector is specified by the saddle points. The singularities migrate, provided the observation point moves, and may coalesce with each other and with the saddle points, which requires more accurate asymptotic evaluation of the Sommerfeld integral in terms of the transition special functions closely related to the Fresnel integral.

Modelo de propagación de ondas solitarias en el corazón

In cardiac electrical activity, different types of waves meander through the heart. We present a model of the electrical activity of the heart that proposes that the homogeneous wave fronts propagating through the heart are in fact solitons. We use a general set of reaction-diffusion equations known as the Barrio-Varea-Aragón-Maini (BVAM) model[1] that presents a wealth of non-linear bifurcations, and we are able to follow the route to chaos, using a mapping of the amplitude equations to the dynamics of the complex Ginzburg-Landau equation. We study the dynamics of wave fronts numerically in the BVAM model to describe the mechanisms leading to heart fibrillation and compare the findings with experimental data.

Ultrasonography and Optical Low-Coherence Interferometry Compared in the Chicken Eye

To compare ocular biometry [anterior chamber depth (ACD), lens thickness (LT), vitreous chamber depth (VCD), and axial length (AL)] using A-scan ultrasonography and optical low-coherence interferometry (OLCI) in the chicken eye. Two-week-old chicks (n = 42) were measured. Bland-Altman plots and repeatability and correlation analyses were calculated for both methods. There was a high correlation between both methods for ACD (r = 0.6144, p < 0.0001), VCD (r = 0.9595, p < 0.0001), and AL (r = 0.9290, p < 0.0001) but not for LT (r = 0.1604, p = 0.144). Measurements by OLCI were more consistent (smaller coefficients of variation and higher intraclass correlation). Bland-Altman plots showed that ultrasound provided larger values for LT, VCD, and AL but not for ACD [differences between ultrasound and OLCI (mean ± SD): ACD = -0.11 ± 0.12 mm; LT = 0.10 ± 0.09 mm; VCD = 0.25 ± 0.08 mm; AL = 0.50 ± 0.16 mm]. A high correlation between both techniques was found for three of the four parameters (ACD, VCD, and AL). However, as the absolute values were different, both techniques cannot replace each other mainly because (1) one is non-contact and the other contact and can induce a minor indentation of the cornea and (2) each device uses different types of waves that cross the ocular interfaces differently. While consistency and repeatability were better by OLCI, a disadvantage is that, different from humans, it can only be used in anesthetized chicks.

Performance of convolutional perfectly matched layers for pseudospectral time domain poroviscoelastic schemes

This paper presents an implementation of the convolutional perfectly matched layer for the velocity–stress formulation of poroviscoelastic equations in anisotropic media, with high-order time and space formulations. After its introduction by Bérenger in 1994 for Maxwell's equation, the perfectly matched layer (PML) quickly became the standard approach to absorb outgoing waves on a numerical mesh. Subsequent developments include generalization and formulation in terms of a convolutional operator and auxiliary differential equations that improve efficiency and allow for the implementation of high-order time integration schemes. In this work, a fourth-order Runge–Kutta scheme is employed. Also, with the convolutional formulation, the wavefields need not be split as in the original formalism. Such unsplit PMLs allow for the implementation with a pseudospectral operator as presented in this paper. Although efforts have been deployed for the optimization of PML parameters, such an approach is not always tractable, especially for seismic wave propagation because different types of waves interact with the medium. Hence, the performance of the implementation is evaluated through a series of numerical experiments. Tests are performed for waves impinging on the PML interface both at normal and grazing incidence, for both isotropic and anisotropic media. The results highlight the advantage of the convolutional formulation for waves at grazing incidence and show that anisotropic media require a larger number of absorbing layers to achieve performances comparable to those obtained in isotropic media.