High-frequency Wave Propagation Research Articles

Polarized High-frequency Wave Propagation Beyond the Nonlinear Schrödinger Approximation

Polarized High-frequency Wave Propagation Beyond the Nonlinear Schrödinger Approximation

Evaluation of Modified Frequency Dependent Equivalent Linear Method for Deconvolution Site Response Analysis

ABSTRACT Frequency-dependent equivalent linear (FD-EQL) site response analysis methods, developed as potential substitutes for the EQL procedure to better simulate the nonlinear soil response, have been reported to overpredict the high-frequency wave propagation. Modified procedures proposed to overcome this limitation have demonstrated to improve the fits with the nonlinear analysis results. The method has not yet been applied to perform a deconvolution analysis, where a conventional EQL analysis often fails to converge or provide reliable estimate. The conventional EQL procedure and one of the modified FD-EQL method, which uses an empirical factor f to interpolate the strain spectrum between the EQL and FD-EQL outputs, are used to perform a series of deconvolution analyses using an idealized 1000 m profile and twelve Kik-net downhole arrays. The residuals of recorded and deconvoluted motions are shown to increase with strain for the EQL method even when using the recommended frequency cut-off. For the FD-EQL method, the range of f recommended for convolution analyses is shown to provide unrealistic responses in performing deconvolution analyses. A new range that produces unbiased residuals for all strain amplitudes is proposed. Comparisons highlight that the modified FD-EQL yields reliable predictions of the within motion for all profiles and motion intensities, automatically suppressing the amplification of high-frequency noise typically accompanied in a deconvolution analysis.

Exponentially Convergent Multiscale Finite Element Method

We provide a concise review of the exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation. The ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis functions. Unlike most generalizations of the MsFEM in the literature, the ExpMsFEM does not rely on any partition of unity functions. In general, it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential convergence. Indeed, there are online and offline parts in the function representation provided by the ExpMsFEM. The online part depends on the right-hand side locally and can be computed in parallel efficiently. The offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix; they are all independent of the right-hand side, so the stiffness matrix can be used repeatedly in multi-query scenarios.

Approximation of High-Frequency Wave Propagation in Dispersive Media

Approximation of High-Frequency Wave Propagation in Dispersive Media

Simulation of electromagnetic high-frequency wave propagation processes in multilayer geo-structures

The paper describes the research findings on georadar detection of hydraulic fractures in hydrocarbon reservoirs. Numerical and physical modeling enables studying effect exerted by the electromagnetic properties of the created fracture fill and by the properties of the enclosing formation on the coefficient of high-frequency EM wave reflection from the interface.

A Survey on Modelling of Automotive Radar Sensors for Virtual Test and Validation of Automated Driving.

Radar sensors were among the first perceptual sensors used for automated driving. Although several other technologies such as lidar, camera, and ultrasonic sensors are available, radar sensors have maintained and will continue to maintain their importance due to their reliability in adverse weather conditions. Virtual methods are being developed for verification and validation of automated driving functions to reduce the time and cost of testing. Due to the complexity of modelling high-frequency wave propagation and signal processing and perception algorithms, sensor models that seek a high degree of accuracy are challenging to simulate. Therefore, a variety of different modelling approaches have been presented in the last two decades. This paper comprehensively summarises the heterogeneous state of the art in radar sensor modelling. Instead of a technology-oriented classification as introduced in previous review articles, we present a classification of how these models can be used in vehicle development by using the V-model originating from software development. Sensor models are divided into operational, functional, technical, and individual models. The application and usability of these models along the development process are summarised in a comprehensive tabular overview, which is intended to support future research and development at the vehicle level and will be continuously updated.

Various forms of lumps and interaction solutions to generalized Vakhnenko Parkes equation arising from high-frequency wave propagation in electromagnetic physics

This article retrieves multiple lump, periodic cross kink, rogue wave, multiwave, breathers, M-shaped and interactional solutions for generalized Vakhnenko Parkes (gVP) equation via appropriate transformations. This leads to a transformed equation for which it is straightforward to evaluate the exact solutions. The gVP equation gives a description of high-frequency waves in the relaxation medium possessing periodic and solitary traveling wave solutions some of which are loop-like in nature. These types of solutions have been observed in wave propagations, rogue waves and many other physical systems. We also interpret some of our solutions in distinct dimensions via 3D, 2D, contours and density profiles.

New Breather and Multiple-Wave Soliton Dynamics for Generalized Vakhnenko–Parkes Equation With Variable Coefficients

Abstract In investigation is the generalized Vakhnenko–Parkes equation with time-dependent coefficients, which is a new nonlinear model connecting to high-frequency wave propagation in relaxing media with variable perturbations. An extended Hirota bilinear method is proposed to construct soliton, breather, and multiple-wave soliton solutions for the equation. Our research shows that the soliton solutions can degenerate into existing single soliton solutions while the breather and multiple-wave soliton solutions are first obtained. By utilizing the two free functions involved in the solutions, the dynamics of some novel excited breathers and multiple-wave solitons are demonstrated. Our results confirm that the generalized Vakhnenko–Parkes equation possesses rich solution structures and interesting dynamical features, which may be depict various nonlinear wave behaviors of high-frequency waves.

Investigation of critical delamination characteristics in composite plates combining cubic spline piezo-layerwise mechanics and time domain spectral finite elements

The scope of the present work is to elucidate the reverberations of propagating guided waves through delaminated regions confined in composite plate structures. As it is well known, delamination between consequent plies is the most common type of damage in composite structures. A mean of investigation of delamination cracks is through guided wave propagation. It has been observed that either type of guided waves (antisymmetric or symmetric) has different repercussions inside and outside the delaminated area. Inside this work is used a well-established numerical tool developed by the authors. By making good use of its reported numerical capabilities, the authors used the Hermitian Cubic Splined Layerwise mechanics to incorporate the delamination and the physical presence of piezoelectric actuators. The two mentioned aspects were then integrated into a time domain spectral finite element. The outcome was the development of a multinode explicit layerwise finite element, able of modelling the physical presence of active piezoelectric sensors, the existence of delamination cracks through the thickness and the excitation of each fundamental wave mode separately (A0 &S0). The calculated semi-diagonal mass matrix, due to the collocation of the nodes with the grid points of Gauss–Lobatto–Legendre quadrature, boosts the speed of numerical time integration, while the use of high order polynomials as shape functions, conduce to a vast reduction of the mesh size, enabling the thorough investigation and simulation of high frequency wave propagation.

The solar eclipse effect on diffusion processes of O+ + O2 → O2+ + O reaction for the upper ionosphere over Kharkov

The Sun is the most effective factor in determining all processes in the ionosphere. For this reason, examining the effect of solar eclipses on the earth ionosphere provides a very important source of information about sudden and medium-scale changes in the ionosphere structure during a solar eclipse. In this study, the effect of solar eclipse on March 29, 2006 in Kharkov on self-diffusion of O+ + O2 ? O2+ + O reaction was investigated depending on the altitude (202, 252, and 303 km). As a result of the investigation, the minimum value of self-diffusion coefficient was seen at three altitudes on March 29, 2006 at the time of full covering in the solar. Self-diffusion coefficients were found to increase with increasing altitude. The results of the experimental study conducted to examine the effect of the eclipse on the ionosphere using high frequency wave propagation in Turkey where it was seen total eclipse on March 29, 2006 and the result that we obtained in this research are consistent with each other.

Loop-like kink breather and its transition phenomena for the Vakhnenko equation arising from high-frequency wave propagation in electromagnetic physics

We report a novel type of breather by studying the Vakhnenko equation (VE) describing high-frequency wave (HFW) propagation in electromagnetic physics. By extending the bilinear function into a mixed exponential and trigonometric cosine function in Hirota bilinear method, an analytical multiple-valued function solution is constructed, which is a verified loop-like kink breather. The propagation control and evolution based on the parameter are investigated for the breather. Several interesting transition phenomena are revealed, such as, the transitions from the soliton to breather, from the single loop to the double loops, and from the leaping background waves to the flat ones. The results are helpful to understand the compressed mechanism to pulses in ultrafast optics.

Thin-layer solutions of the Helmholtz equation

This paper gives a brief overview of some configurations in which high-frequency wave propagation modelled by Helmholtz equation gives rise to solutions that vary rapidly across thin layers. The configurations are grouped according to their mathematical structure and tractability and one of them concerns a famous open problem of mathematical physics.

Maxwell equations in a curved spacetime: Spin optics approximation

We study propagation of high-frequency electromagnetic waves in a curved spacetime. We demonstrate how a modification of the standard geometric optics allows one to include the helicity dependent corrections into the equations of motion of circularly polarized beams of radiation. As a result, polarized light rays are still null but not geodesic curves. To achieve these results we construct null frames associated with a set of (non-geodesic) null rays and use these frames for description of the high-frequency wave propagation. We call this approach spin optics approximation. It is completely covariant and it can be used in an arbitrary time-dependent gravitational field.

The surrogate matrix methodology: Accelerating isogeometric analysis of waves

The surrogate matrix methodology delivers low-cost approximations of matrices (i.e., surrogate matrices) which are normally computed in Galerkin methods via element-scale quadrature formulas. In this paper, the methodology is applied to a number of model problems in wave mechanics treated in the Galerkin isogeometric setting. Herein, the resulting surrogate methods are shown to significantly reduce the assembly time in high frequency wave propagation problems. In particular, the assembly time is reduced with negligible loss in solution accuracy. This paper also extends the scope of previous articles in its series by considering multi-patch discretizations of time-harmonic, transient, and nonlinear PDEs as particular use cases of the methodology. Our a priori error analysis for the Helmholtz equation demonstrates that the additional consistency error introduced by the presence of surrogate matrices is independent of the wave number. In addition, our floating point analysis establishes that the computational complexity of the methodology compares favorably to other contemporary fast assembly techniques for isogeometric methods. Our numerical experiments demonstrate clear performance gains for time-harmonic problems, both with and without the presence of perfectly matched layers. Notable speed-ups are also presented for a transient problem with a compressible neo-Hookean material.

Oblique and vertical incidence ionogram simulations with the presence of Es layer

The methodology making available an analysis of high frequency (HF) wave propagation in ionosphere with the presence of sporadic E layer (Es) is presented. A numerical ray tracing code is exploited to estimate the ray-paths through ionosphere comprising E, Es, F1 and F2 layers. A number of vertical and oblique sounding ionograms were emulated in the frame of NIM-RT propagation model. Fairly good resemblance between measured and simulated ionograms with the presence of Es layer was achieved. Numerical modelling provides an assessment of a number of parameters defining Es layer features including virtual height of the layer and its transparency.

A numerical study of the pollution error and DPG adaptivity for long waveguide simulations

High-frequency wave propagation has many important applications in acoustics, elastodynamics, and electromagnetics. Unfortunately, the finite element discretization for these problems suffers from significant numerical pollution errors that increase with the wavenumber. It is critical to control these errors to obtain a stable and accurate method. We study the effect of pollution for very long waveguide problems in the context of robust discontinuous Petrov–Galerkin (DPG) finite element discretizations. Our numerical experiments show that the pollution primarily has a diffusive effect causing energy loss in the DPG method while phase errors appear less significant. We report results for 3D vectorial time-harmonic Maxwell problems in waveguides with more than 8000 wavelengths. Our results corroborate previous analysis for the Galerkin discretization of the Helmholtz operator by Melenk and Sauter (2011). Additionally, we discuss adaptive refinement strategies for multi-mode fiber waveguides where the propagating transverse modes must be resolved sufficiently. Our study shows the applicability of the DPG error indicator to this class of problems. Finally, we illustrate the importance of load balancing in these simulations for distributed-memory parallel computing.

Using Ultrasonic Waves to Determine the Microstructure of Snow

High frequency (ultrasonic) acoustic wave propagation measurements were inverted to determine important near-surface parameters of snow including porosity, tortuosity, and pore geometry, using a newly-designed, oblique-reflection transducer apparatus. Acoustic signals interact with the physical structure of porous media, are particularly sensitive to porosity and tortuosity, and can be used to measure physical properties in a non-destructive manner. Given the fragile nature of freshly fallen snow, non-contact, non-destructive characterization methods made possible via acoustic signals, are desirable. High frequency wave propagation methods can be used to determine in situ near surface micro-pore geometry parameters in snow using methods demonstrated on cohesive porous materials including manufactured foams, porous metals, and sintered glass beads. Here, we conducted high frequency, oblique-angle and near vertical reflection measurements on snow samples to demonstrate the feasibility of acoustic response detection. We compared the acoustically derived snow physical parameters, including porosity and tortuosity, with values determined from X-ray micro-computed tomography (μCT) and gravimetric methods. Preliminary results using different snow types, and following the methods from previous work for cohesive porous media (i.e. fused glass beads) show good agreement between values of porosity determined from the acoustic measurements and the values determined from μCT image analysis.

High-frequency Wave Propagation Along a Spicule Observed by CLASP

Abstract The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) sounding rocket experiment, launched in 2015 September, observed the hydrogen Lyα line (121.6 nm) in an unprecedented high temporal cadence of 0.3 s. CLASP performed sit-and-stare observations of the quiet Sun near the limb for 5 minutes with a slit perpendicular to the limb and successfully captured an off-limb spicule evolving along the slit. The Lyα line is well suited for investigating how spicules affect the corona because it is sensitive to higher temperatures than other chromospheric lines, owing to its large optical thickness. We found high-frequency oscillations of the Doppler velocity with periods of 20–50 s and low-frequency oscillation of periods of ∼240 s on the spicule. From a wavelet analysis of the time sequence data of the Doppler velocity, in the early phase of the spicule evolution, we found that waves with a period of ∼30 s and a velocity amplitude of 2–3 km s−1 propagated upward along the spicule with a phase velocity of ∼470 km s−1. In contrast, in the later phase, possible downward and standing waves with smaller velocity amplitudes were also observed. The high-frequency waves observed in the early phase of the spicule evolution would be related with the dynamics and the formation of the spicules. Our analysis enabled us to identify the upward, downward, and standing waves along the spicule and to obtain the velocity amplitude of each wave directly from the Doppler velocity for the first time. We evaluated the energy flux by the upward-propagating waves along the spicule, and discussed the impact to the coronal heating.

Gravitational lensing beyond geometric optics: II. Metric independence

Typical applications of gravitational lensing use the properties of electromagnetic or gravitational waves to infer the geometry through which those waves propagate. Nevertheless, the optical fields themselves - as opposed to their interactions with material bodies - encode very little of that geometry: It is shown here that any given configuration is compatible with a very large variety of spacetime metrics. For scalar fields in geometric optics, or observables which are not sensitive to the detailed polarization content of electromagnetic or gravitational waves, seven of the ten metric components are essentially irrelevant. With polarization, five components are irrelevant. In the former case, this result together with diffeomorphism invariance allows essentially any geometric-optics configuration associated with a particular spacetime to be embedded into any other spacetime, at least in finite regions. Going beyond the geometric-optics approximation breaks some of this degeneracy, although much remains even then. Overall, high-frequency wave propagation is shown to be insensitive to compositions of certain conformal, Kerr-Schild, and related transformations of the background metric. One application is that new solutions for scalar, electromagnetic, and gravitational waves may be generated from old ones. In one example described here, the high-frequency scattering of a plane wave by a point mass is computed by transforming a plane wave in flat spacetime.

Ionospheric high frequency wave propagation using different IRI hmF2 and foF2 models

High frequency (HF) electromagnetic wave propagation is commonly used in long-distance communication and detection. The ionosphere is a highly variable medium affecting this propagation. However, mean climatological conditions are useful in order to determine a “base level” for the design and operation of systems using HF waves that propagate in the ionosphere. Important variables that determine these conditions are the ionosphere peak height, hmF2, and F2 critical frequency, foF2. In the present work the effect of different hmF2 and foF2 model options in IRI-2016 and its spatial variability are analyzed through the analysis of the ground range and reflection height of HF ray paths using a numerical ray tracing method. The model options are M(3000)F2, AMTB and SDMF2 for hmF2, and URSI and CCIR for foF2. We perform this study for a quiet day, April 26 at 12 LT, and solar activity maximum conditions. Ground range and reflection height variation between values obtained with the different model options are on average not greater than ~40%, but can be higher for a Pedersen ray case. These variations are in general much stronger than those obtained when Earth's magnetic field is neglected in ray path assessments. However, while the magnetic field effect is of “physical” origin that has always the same sign, the effect of changing a model used for certain parameter's estimation depends on the model performance which may vary with location and time.