Wave Representation Research Articles

Spatial reconstruction of sound fields using local and data-driven functions.

Sound field analysis methods make it possible to characterize and reconstruct a sound field from a limited set of observations. Classical approaches rely on the use of analytical basis functions to model the sound field throughout the observed domain. When the complexity of the sound field is high, for example, in a room at mid and high frequencies, propagating wave representations can be suboptimal due to model discrepancy. We examine the use of local representations to alleviate this model discrepancy and explore data-driven approaches to obtain suitable models. Specifically, local representations are used to reconstruct the sound field over a large spatial aperture in a room. The performance of local models is compared against conventional plane wave reconstructions and the use of data-driven local functions is examined. Dictionary learning and principal component analysis are used to obtain functions from extensive spatial measurements in an empty room. The results indicate that local partitioning models conform to fields of high spatial complexity. Dictionary learning generalizes across different rooms and frequencies-conferring potential for modelling complex sound fields based on their local and statistical properties.

Transformation of Water Wave Spectra into Time Series of Surface Elevation

Spectral wave modelling is widely used to simulate large-scale wind–wave processes due to its low computation cost and relatively simpler formulation, in comparison to phase-resolving or hydrodynamic models. However, some applications require a time-domain representation of sea waves. This article proposes a methodology to transform the wave spectrum into a time series of water surface elevation for applications that require a time-domain representation of ocean waves. The proposed method uses a generated phase spectrum and the inverse Fourier transform to turn the wave spectrum into a time series of water surface elevation. The consistency of the methodology is then verified. The results show that it is capable of correctly transforming the wave spectrum, and the significant wave height of the resulting time series is within 5% of that of the input spectrum.

AGNES in irreversible systems: The indium case

• In 3+ /In 0 irreversibility is by-passed due to the lability of In hydroxy species. • AGNES conditions are met in the Nernstian region of the foot of an SSCP wave. • They can be recognized as a linear segment when plotting ln (τ/τ*) vs E d. Free indium concentrations can be determined using AGNES (Absence of Gradients and Nernstian Equilibrium Stripping) with no relevant hindrance from the irreversibility of the In 3+ /In° redox couple at a mercury electrode. The electroactivity, high lability and mobility of the In hydroxy species help in reaching AGNES conditions for a relatively moderate ratio (deposition time):(gain), which decreases with increasing pH due to the growing contribution of the hydroxy species. In the related technique SSCP (Scanned Stripping ChronoPotentiometry), points corresponding to more positive deposition potentials are said to be “at the foot of the wave”. Some of these points can reach equilibrium along the fixed SSCP deposition time, so that these points are effectively AGNES experiments, and free metal ion concentrations (such as those of free indium) can also be computed from them provided sufficiently accurate data are available. A new representation of the SSCP wave allows for the diagnosis of the potential region where AGNES conditions are fulfilled.

Vertical coordinate and resolution dependence of the second moment turbulent closure models and their limitations

Coordinate and resolution dependence of three second moment turbulent closure models are studied using one-dimensional Navy Coastal Ocean Model (NCOM) experiments and large eddy simulations at Ocean Station Papa. Our results suggest that finer resolution near the base of the mixed layer is critical for better model performance. A mixed layer enhanced vertical grid is proposed that outperforms both the uniform and the stretched grids with significantly fewer vertical layers used. For the new grid, the model accuracy is strongly dependent on the resolution near the base of the mixed layer, and not affected much by the total number of vertical layers used. However, given the success of the new grid, the lack of representation for the near inertial gravity waves below the mixed layer has hampered the ability of second moment turbulent closure models on accurate representation of turbulent mixing in the water column. While both the Langmuir circulation and the variation of surface heat fluxes are shown to be able to significantly change the strength of the near inertial waves, they have negligible effect on the eddy viscosity in the transition layer.

Singular value decomposition and similarity renormalization group evolution of nuclear interactions

One of the main challenges for ab initio nuclear many-body theory is the growth of computational and storage costs as calculations are extended to heavy, exotic, and structurally complex nuclei. Here, we investigate the factorization of nuclear interactions as a means to address this issue. We perform Singular Value Decompositions of nucleon-nucleon interactions in partial wave representation and study the dependence of the singular value spectrum on interaction characteristics like regularization scheme and resolution scales. We develop and implement the Similarity Renormalization Group (SRG) evolution of the factorized interaction, and demonstrate that this SVD-SRG approach accurately preserves two-nucleon observables. We find that low-resolution interactions allow the truncation of the SVD at low rank, and that a small number of relevant components is sufficient to capture the nuclear interaction and perform an accurate SRG evolution, while the Coulomb interaction requires special consideration. The rank is uniform across all partial waves, and almost independent of the basis choice in the tested cases. This suggests an interpretation of the relevant singular components as mere representations of a small set of abstract operators that can describe the interaction and its SRG flow. Following the traditional workflow for nuclear interactions, we discuss how the transformation between the center-of-mass and laboratory frames creates redundant copies of the partial wave components when implemented in matrix representation, and we discuss strategies for mitigation. Finally, we test the low-rank approximation to the SRG-evolved interactions in many-body calculations using the In-Medium SRG. By including nuclear radii in our analysis, we verify that the implementation of the SRG using the singular vectors of the interaction does not spoil the evolution of other observables.

Holographic tomography of dynamic three-dimensional acoustic vortex beam in liquid

Acoustic vortex beams have attracted significant research interest in the last decade. The orbital angular momentum provides an additional degree-of-freedom, hence attracting attention in physics and technology. Generation and measurement are important parts of acoustic vortex research. For the production of acoustic vortices, it is convenient and less costly to use passive materials. Moreover, a point-by-point scanning procedure with a hydrophone still remains the commonly used method and is cumbersome to measure a three-dimensional acoustic field. However, an acoustic vortex field is usually three-dimensional, dynamic, and complex. Thus, the demand for imaging methods for complex pressure distributions has emerged. Herein, we introduced an improved hybrid single-arm coiling slit to generate an acoustic vortex with a deep potential well and infirm focusing. In addition, we proposed a method for holographic reconstruction and visualization of a three-dimensional acoustic field, which does not destroy the acoustic field information. The spatial-temporal properties of the acoustic vortex in the experiment closely match that of theoretical prediction. This study provides a reference for the manipulation and representation of a three-dimensional underwater acoustic wave.

Sensitivity of low‐tropospheric Arctic temperatures to assimilation of AIRS cloud‐cleared radiances: Impact on midlatitude waves

AbstractIn this work it is shown that the prediction of individual midlatitude waves in a global forecast framework may benefit from the assimilation of cloud‐cleared radiances (CCRs) from the Atmospheric Infrared Sounder (AIRS). The assimilation of CCRs, relative to clear‐sky radiances, provides more information in high‐latitude areas affected by broken low‐level stratus clouds, which are common over north polar latitudes during the summer and autumn seasons. This added information in cloudy regions produces slightly lower low‐level temperatures and lower mid‐tropospheric heights (through hydrostatic adjustment) over the Arctic and part of northeastern Siberia. In areas that are both dynamically unstable (with the potential for rapid error growth) and data void (as observed by clear‐sky radiances), the assimilation of CCRs provides valuable information that can improve the representation of individual baroclinic waves and their subsequent forecasts. The assimilation of AIRS CCRs slightly modifies the geopotential height gradients between the Arctic and the midlatitudes, leading to improvements in the forecast of individual baroclinic waves, as is shown through three case‐studies. The set of observing system experiments (OSEs) is performed with the NASA Goddard Earth Observing System (GEOS) data assimilation and forecast system during boreal autumn 2014. AIRS CCRs are thinned to approximately one quarter the density of operationally assimilated AIRS radiances, consistent with their higher information content. Global 6‐hourly analyses are produced from 01 September to 10 November 2014 and seven‐day forecasts are initialized at 0000 UTC daily. Since the CCR methodology is widely applicable, these findings are also relevant to other infrared sensors.

Seismometers as infrasound sensors

An experiment was conducted in West-Central Mississippi in which five explosive charges were detonated. The TNT equivalent sizes of the charges ranged from 0.57 to 10.91 kg (1.25 to 24 lb). Among the arrays of sensors deployed, seismometers were deployed near microphones at distances of 0.5, 2.1, and 8.4 km from the source. The blast wave at these distances had decayed in amplitude to an acoustic wave. The coherence between the seismometer and microphone signals showed that the seismometer provided reasonable representation of the acoustic wave over a limited frequency band. This band changed with distance from the source. In addition, two 3-component seismometers were deployed near each other 8.4 km from the source. These seismometers were of different types, one having a resonance frequency of 1 Hz and the other 4.5 Hz. The signals from the horizontal components of these seismometers were analyzed to determine their effectiveness as vector sensors. The results showed that the back-azimuth determined from the seismometers agreed reasonably well with ground truth for the first arrival of the acoustic wavefront, however the results degraded as the trailing part of the wavefront passed. Permission to publish was granted by the Director, Geotechnical and Structures Laboratory.

Laser Transverse Modes with Ray-Wave Duality: A Review

We present a systematic overview on laser transverse modes with ray-wave duality. We start from the spectrum of eigenfrequencies in ideal spherical cavities to display the critical role of degeneracy for unifying the Hermite–Gaussian eigenmodes and planar geometric modes. We subsequently review the wave representation for the elliptical modes that generally carry the orbital angular momentum. Next, we manifest the fine structures of eigenfrequencies in a spherical cavity with astigmatism to derive the wave-packet representation for Lissajous geometric modes. Finally, the damping effect on the formation of transverse modes is generally reviewed. The present overview is believed to provide important insights into the ray-wave correspondence in mesoscopic optics and laser physics.

The DeRisk database: Extreme design waves for offshore wind turbines

The estimation of extreme loads from waves is an essential part of the design of offshore wind turbines. Standard design codes suggest either to use simplified methodologies based on regular waves, or to perform fully-nonlinear computations. The former may not provide an accurate representation of the real extreme waves, while the latter is too computationally intensive for fast design iterations. Here, we address these limitations by using the fully-nonlinear solver OceanWave3D to establish the DeRisk database, a large dataset of extreme wave kinematics in a two-dimensional domain. From the database, which is open and freely available, a designer can easily extract fully-nonlinear wave kinematics for a wave condition and water depth of interest by identifying a suitable computation in the database and, if needed, by Froude-scaling the kinematics. This will ultimately enable quicker estimations of nonlinear wave loads, speeding up design evaluations. The database sea states cover a range of nondimensional depth of about h∗∈[3.0⋅10−3,6.5⋅10−2] and of nondimensional significant wave height of HS∗∈[1.0⋅10−3,8.0⋅10−3], where h∗=h/(gTP2)[−] and HS∗=HS/(gTP2)[−].The fully-nonlinear solver is validated against the DeRisk model-scale experiments, where a number of long-crested sea state realizations are generated at two different water depths, 33.0[m] and 20.0[m], and the induced force on a stiff monopile with a diameter of D=7.0[m] is measured.Comparison with the experiments shows that the database predicts maximum crest elevations at both depths very accurately. Predictions of the in-line force, obtained by application of the Rainey slender body force model with the database wave kinematics, are accurate for milder storms. However, for stronger storms, where slamming loads from breaking waves dominate, the force computations from the database kinematics provide slightly nonconservative force estimates compared with the standard methodologies such as the embedded stream function and the WiFi JIP model. This discrepancy is mainly due to the lack of a slamming load model in the applied force model. A procedure to add slamming loads to OceanWave3D and to the DeRisk database is currently being developed.

Tomography of dark-field scatter including single-exposure Moiré fringe analysis with X-ray biprism interferometry-A simulation study.

In this work, we present tomographic simulations of a new hardware concept for X-ray phase-contrast interferometry wherein the phase gratings are replaced with an array of Fresnel biprisms, and Moiré fringe analysis is used instead of "phase stepping" popular with grating-based setups. Projections of a phantom consisting of four layers of parallel carbon microfibers is simulated using wave optics representation of X-ray electromagnetic waves. Simulated projections of a phantom with preferential scatter perpendicular to the direction of the fibers are performed to analyze the extraction of small-angle scatter from dark-field projections for the following: (1) biprism interferometry using Moiré fringe analysis; (2) grating interferometry using phase stepping with eight grating steps; and (3) grating interferometry using Moiré fringe analysis. Dark-field projections are modeled as projections of voxel intensities represented by a fixed finite vector basis set of scattering directions. An iterative MLEM algorithm is used to reconstruct, from simulated projection data, the coefficients of a fixed set of seven basis vectors at each voxel representing the small-angle scatter distribution. Results of reconstructed vector coefficients are shown comparing the three simulated imaging configurations. The single-exposure Moiré fringe analysis shows not only an increase in noise because of one-eighth the number of projection samples but also is obtained with less dose and faster acquisition times. Furthermore, replacing grating interferometry with biprism interferometry provides better contrast-to-noise. The simulations demonstrate the feasibility of the reconstruction of dark-field data acquired with a biprism interferometry system. With the potential of higher fringe visibility, biprism interferometry with Moiré fringe analysis might provide equal or better image quality to that of phase stepping methods with less imaging time and lower dose.

Resolved Convection Improves the Representation of Equatorial Waves and Tropical Rainfall Variability in a Global Nonhydrostatic Model

AbstractNumerical weather and climate models continue to struggle with simulating equatorial waves and tropical rainfall variability. This study presents a potential remedy—high‐resolution global models with explicitly resolved convection. A series of global nonhydrostatic simulations was produced with horizontal cell spacings between 3.75 and 480 km; the share of resolved precipitation in these simulations ranged from 88% to 2%. The simulations in which convection was mostly resolved produced much more realistic equatorial waves than the simulations in which convection was mostly parameterized. Consequently, the simulations with resolved convection produced more realistic precipitation patterns and precipitation variances. The results demonstrate that high‐resolution global models with explicitly resolved convection are a promising tool to improve tropical weather forecasts and climate projections.

The Solution of the Problem of Scattering by a Semitransparent Half-Plane Using the Malyuzhinets Method

The rigorous solution of the problem of scattering of a plane electromagnetic wave by the semitransparent half-plane is presented. The solution is obtained using the method of the Sommerfeld—Malyuzhinets integral for two polarizations of the incident field. The analytical representation of the cylindrical wave scattered by the edge of the semitransparent half-plane is obtained with the use of the rigorous solution mentioned above. The accuracy of this analytical representation is tested by the comparison of numerical results obtained using the Wiener—Hopf method.

Toward Transient Subgrid-Scale Gravity Wave Representation in Atmospheric Models. Part I: Propagation Model Including Nondissipative Wave–Mean-Flow Interactions

AbstractCurrent gravity wave (GW) parameterization (GWP) schemes are using the steady-state assumption, in which an instantaneous balance between GWs and mean flow is postulated, thereby neglecting transient, nondissipative interactions between the GW field and the resolved flow. These schemes rely exclusively on wave dissipation, by GW breaking or near critical layers, as a mechanism leading to forcing of the mean flow. In a transient GWP, without the steady-state assumption, nondissipative wave–mean-flow interactions are enabled as an additional mechanism. Idealized studies have shown that this is potentially important, and therefore the transient GWP Multiscale Gravity Wave Model (MS-GWaM) has been implemented into a state-of-the-art weather and climate model. In this implementation, MS-GWaM leads to a zonal-mean circulation that agrees well with observations and increases GW momentum-flux intermittency as compared with steady-state GWPs, bringing it into better agreement with superpressure balloon observations. Transient effects taken into account by MS-GWaM are shown to make a difference even on monthly time scales: in comparison with steady-state GWPs momentum fluxes in the lower stratosphere are increased and the amount of missing drag at Southern Hemispheric high latitudes is decreased to a modest but nonnegligible extent. An analysis of the contribution of different wavelengths to the GW signal in MS-GWaM suggests that small-scale GWs play an important role down to horizontal and vertical wavelengths of 50 km (or even smaller) and 200 m, respectively.

Thermoacoustic wave generation in multilayered thermophones with cylindrical and spherical geometries

A thermoacoustic sound generation model, based on the classical balance equations of the continuum mechanics, is here developed for the cylindrical and the spherical thermoacoustic wave generation. In both geometries, the model considers an arbitrary multilayered structure, where each layer can be fluid or solid and it is characterized by the fully coupled thermo-visco-acoustic response. It means that the viscous behavior and the thermal conduction are considered in each layer. The model is based on a unified representation of cylindrical or spherical thermoacoustic waves, which is valid for both fluid and solid phases. Thanks to the continuity of temperature, particle velocity, normal stress, and heat flux between adjacent layers, the model can be implemented by means of a versatile matrix approach, allowing flexible analysis and design of cylindrical or spherical thermophones. Any thermoacoustic variable can be determined at any position, any frequency, and for any input power. The results are compared with the models already existing in the literature, and the underlying physics is thoroughly discussed. The analysis is focused on a better understanding of the thermoacoustic generation with application to the state of the art of the thermophone technology.

On ab initio-based, free and closed-form expressions for gravitational waves

We introduce a new approach for finding high accuracy, free and closed-form expressions for the gravitational waves emitted by binary black hole collisions from ab initio models. More precisely, our expressions are built from numerical surrogate models based on supercomputer simulations of the Einstein equations, which have been shown to be essentially indistinguishable from each other. Distinct aspects of our approach are that: (i) representations of the gravitational waves can be explicitly written in a few lines, (ii) these representations are free-form yet still fast to search for and validate and (iii) there are no underlying physical approximations in the underlying model. The key strategy is combining techniques from Artificial Intelligence and Reduced Order Modeling for parameterized systems. Namely, symbolic regression through genetic programming combined with sparse representations in parameter space and the time domain using Reduced Basis and the Empirical Interpolation Method enabling fast free-form symbolic searches and large-scale a posteriori validations. As a proof of concept we present our results for the collision of two black holes, initially without spin, and with an initial separation corresponding to 25–31 gravitational wave cycles before merger. The minimum overlap, compared to ground truth solutions, is 99%. That is, 1% difference between our closed-form expressions and supercomputer simulations; this is considered for gravitational (GW) science more than the minimum required due to experimental numerical errors which otherwise dominate. This paper aims to contribute to the field of GWs in particular and Artificial Intelligence in general.

Degradation performance analysis and operation optimization of rotary-traveling wave oscillators for RF-CMOS applications

In this work, the impact of the parasitic effects caused by discontinuities on Resonant Rotary Traveling Wave Oscillators (RTWO) for RF-CMOS applications, is analyzed and modeled. By using experimental data in addition to the full wave representation, semi-empirical models are obtained for different discontinuities contained in an RTWO. Then, using the proposed models and 180 nm CMOS process parameters, an RTWO was designed with an operating frequency of 20 GHz, whilst the impact of the discontinuities was quantified in its output signal. The results show that the impact of the parasitic elements due to these discontinuities present a filtering effect leading to a distortion of the magnitude and number of harmonics in the output signal, with a reduction of 13.8% when the effects of the geometrical discontinuities were included. In order to mitigate the parasitic effects due to discontinuities, the use of topological (layout) methods in stack paths and the Möbius connection are proposed. Additionally, a process variation analysis was conducted and the results show that the operation frequency could vary in a range from 17.21 GHz to 18.91 GHz; while the output voltage could fluctuate between 1.17 V and 1.91 V depending on the process, bias voltage and temperature (PVT) conditions. These effects must be taken into account in the design of RTWOs to avoid inefficient tuning stages, especially for high frequency applications, and for advanced technologies where the impact of the analyzed discontinuities is increased.

Surface wave scattering by multiple flexible fishing cage system

A study of the wave dynamics around a multiple cylindrical fishing cage system is carried out under the assumption of linear water wave theory and small-amplitude wave response. The Fourier–Bessel series expansion of the velocity potential is derived for the regions enclosed under the open-water and cage systems and the immediate vicinity. The scattering between the cages is accounted for by employing Graf's addition theorem. The porous flexible cage system is modeled using Darcy's law and the three-dimensional membrane equation. The edges of the cages are moored along their circumferences to balance its position. The unknown coefficients in the potentials are obtained by employing the matched eigenfunction method. In addition, the far-field scattering coefficients for the entire system are obtained by expanding the Bessel and Hankel functions in the plane wave representation form. Numerical results for the hydrodynamic forces, scattering coefficients, and power dissipation are investigated for various cage and wave parameters. The time simulation for the wave scattering from the cage system is investigated. The study reveals that wave loading on the cage system can be significantly reduced by the appropriate spatial arrangement, membrane tension, and porous-effect parameter. Moreover, the far-field results suggest that the cage system can also be used as a breakwater.

MACLAURIN SERIES METHOD FOR FRACTAL DIFFERENTIAL-DIFFERENCE MODELS ARISING IN COUPLED NONLINEAR OPTICAL WAVEGUIDES

Fractal Calculus is designed to reveal the study of waves. Most of the waves are very grim to model correctly. Fractal representation of waves helps to better understand complex wave phenomena. In this paper, a Maclaurin series method (MSM) is proposed to obtain the exact and approximate solutions of fractal nonlinear differential-difference models produced by coupled nonlinear optical waveguides. The method is very simple, easy to understand, and minimizes calculation compared to existing approximate methods.

A Computational Model for Simulation of Shallow Water Waves by Elastic Deformations in the Topography

We propose a coupled model to simulate shallow water waves induced by elastic deformations in the bed topography. The governing equations consist of the depth-averaged shallow water equations including friction terms for the water freesurface and the well-known second-order elastostatics formulation for the bed deformation. The perturbation on the free-surface is assumed to be caused by a sudden change in the bottom beds. At the interface between the water flow and the bed topography, transfer conditions are implemented. Here, the hydrostatic pressure and friction forces are considered for the elastostatic equations whereas bathymetric forces are accounted for in the shallow water equations. The focus in the present study is on the development of a simple and accurate representation of the interaction between water waves and bed deformations in order to simulate practical shallow water flows without relying on complex partial differential equations with free boundary conditions. The effects of location and magnitude of the deformation on the flow fields and free-surface waves are investigated in details. Numerical simulations are carried out for several test examples on shallow water waves induced by sudden changes in the bed. The proposed computational model has been found to be feasible and satisfactory.