Wave Dispersion Research Articles

On the construction of various soliton solutions of two space-time fractional nonlinear models

Abstract In this article, we investigate a couple of nonlinear fractional models of eminent interests subsequently the conformable derivative sense is used to designate the fractional order derivatives. The given structures are transformed into nonlinear ordinary differential equations of integer order, and the extended simple equation technique is then employed to solve the resulting equations. Initially, the nonlinear space time fractional Klein–Gordon equation is considered emerging from quantum and classical relativistic mechanics, which have application in plasma physics, dispersive wave phenomena, quantum field theory, and optical fibres. Later, the (2 + 1)-dimensional time fractional Zoomeron equation is analysed which is convenient to explore the innovative phenomena related to boomerons and trappons. As a result, various new soliton solutions are successfully established. The reported results offer a key implementation for analysing the soliton solutions of nonlinear fractional models which are extremely encouraging arising in the recent era of science and engineering. The 3D simulations have been carried out to demonstrate dynamics of the various soliton solutions for a given set of parameters.

A Set of Accurate Dispersive Nonlinear Wave Equations

In this study, a set of accurate dispersive nonlinear wave equations is established, using the wave velocity and free surface elevation as variables. These equations improve upon previous equations in which the velocity potential is used as a variable by considering the rotational wave motion and by adding a second-order bottom slope term that applies to general situations, allowing the equations to consider the influence of rapidly changing, horizontal, two-dimensional bottom topographies. The problem of the inaccuracy of the integral calculations used in previous equations in nearshore areas is solved by approximating the integral calculations into differential calculations, and a set of coupled wave equations is established by keeping the free surface elevation and the horizontal velocity constant, thus allowing the calculation of nearshore wave-generated currents. The benefits of the current model are confirmed through comparisons with corresponding laboratory experimental findings and are illustrated through a comparison with the numerical outcomes of other pertinent models.

A class of fourth-order dispersive wave equations with exponential source

A class of fourth-order dispersive wave equations with exponential source

Exact solution of the propagation of ON-OFF signals by dispersive waves

Abstract The propagation of ON-OFF signals with dispersive waves is examined in this study.
An integral-form exact solution for a simple ON-OFF switching event is derived, which holds for any dispersion relation.
The integral can be exactly calculated for two types of dispersion relations.
Further, the analysis of these solutions shows that the ON-OFF signal propagates with the group velocity and that the boundary thickness of the signal increases with time, typically at a rate proportional to the square root of time, owing to dispersion.
Additionally, an approximate solution for a general dispersion relation is derived, and a for a higher-complexity ON-OFF switching pattern is constructed.

Acoustic wave propagation and scattering in visco-acoustic medium: Integral equation representation and De Wolf approximation

A visco-acoustic medium is an approximate representation of the absorption and attenuation characteristics of the actual earth medium, which will cause energy attenuation and velocity dispersion of seismic waves. The propagation law of scattered waves in viscoelastic media can be revealed through seismic wave forward simulation. However, the numerical simulation of scattered waves in a visco-acoustic medium using the De Wolf approximation method based on the Lippmann-Schwingr (L-S) equation has not been studied. Therefore, based on the Futterman dispersion relation, the mathematical expression of the integral equation of acoustic wave propagation and scattering in the visco-acoustic medium is derived. We combine the De Wolf approximation with the quality factor Q. The thin slab approximation and screen approximation methods are two realizations of the De Wolf approximation. The thin slab approximation and the screen approximation continuation operator in the viscous-acoustic medium are constructed and applied to the numerical simulation of the scattered wave field. The research results of the concave model and complex model indicate that due to the influence of medium viscosity, the energy of the deep reflected waves is weaker in the forward modeling records of the thin slab approximation method and screen approximation method, and the dominant frequency of seismic waves moves towards the low-frequency direction; Compared with the finite difference results, they only calculate one reflection, and there are no multiple wave signals in the seismic records. Finally, We discuss the thin slab approximation and the screen approximation method for detail around the division of the thickness of the thin slab, the selection of the reference frequency, and the non-uniformity of the medium.

Efficient Mid-Infrared Soliton Self-Frequency Shift and Dispersive Wave in a Chalcogenide Fiber

Efficient Mid-Infrared Soliton Self-Frequency Shift and Dispersive Wave in a Chalcogenide Fiber

Effect of bathymetry data on tsunami wave ray tracing in the western Banten sea

The lack of tsunami wave warning during the Anak Krakatau collapse in 2018 resulted in devastating damage to coastal areas. The tsunami wave arrived in the coastal areas approximately half an hour after the collapse. As a tsunami wave can travel abruptly, an early warning system should warn faster. However, a warning system based on a sophisticated hydrodynamic model in real-time would take time to conduct the numerical tsunami wave simulation. Hence, this study proposes a fast and reliable estimation of tsunami wave propagation through a classic ray tracing analysis. We use two ray-tracing methods to investigate the tsunami wave propagation from Anak Krakatau to the western Banten Sea. The first method follows Snell’s law, considering dispersive waves, and the second assumes non-dispersive waves based on the ray tracing equations, considering the Earth’s sphericity. Both methods are quantitatively evaluated by comparing the travel time measured at Anyer and Marina Jambu. This study finds that non-dispersive wave tracing performs a shorter computational time and slightly better prediction of tsunami wave propagation than dispersive-based wave tracing, with a relative absolute difference of the travel time of 17.9–26.7% in Anyer and 3.6–5.2% in Marina Jambu. This study also confirms the importance of bathymetry validity in wave ray tracing. Two regional bathymetry datasets with a mean difference of less than 5 m result in different wave ray tracing, in which one dataset does not produce the wave ray path toward the Panaitan Island. Based on bathymetric surveys in Anyer and Marina Jambu, the national bathymetry data (BATNAS) has shown its superiority to being used as a bathymetry in the ray-tracing process, with correlations of 81% and 93% in both areas compared to other available bathymetry datasets. We summarize that reliable bathymetry data and the non-dispersive ray tracing method can be used as an initial estimation of tsunami wave propagation efficiently.

Supercontinuum generation optimization in a dispersion-varying chalcogenide fiber

We experimentally demonstrate that a variable longitudinal dispersion profile can enhance supercontinuum generation in a chalcogenide tapered fiber, compared to tapered fibers with a standard, constant dispersion profile. For this purpose, nonlinear As2S3 tapered fibers are compared experimentally and numerically based on their dispersion profile. The optimal taper with non-uniform dispersion profile simultaneously enhances the energy transfer to both dispersive waves and Raman solitons towards shorter and longer wavelengths, respectively. The generated supercontinuum spans within the spectral range of 1.20-2.98 μm with an out-of-pump power enhancement of 4.3 dB at shorter wavelengths, 2.5 dB at longer wavelengths, and a bandwidth extension of 262 nm, compared to the supercontinuum generated with an optimal but constant dispersion profile.

Flexural pulse wave velocity in blood vessels.

Arteriosclerosis is a major risk factor for cardiovascular disease and results in arterial vessel stiffening. Velocity estimation of the pulse wave sent by the heart and propagating into the arteries is a widely accepted biomarker. This symmetrical pulse wave propagates at a speed which is related to the Young's modulus through the Moens Korteweg (MK) equation. Recently, an antisymmetric flexural wave has been observed in vivo. Unlike the symmetrical wave, it is highly dispersive. This property offers promising applications for monitoring arterial stiffness and early detection of atheromatous plaque. However, as far as it is known, no equivalent of the MK equation exists for flexural pulse waves. To bridge this gap, a beam based theory was developed, and approximate analytical solutions were reached. An experiment in soft polymer artery phantoms was built to observe the dispersion of flexural waves. A good agreement was found between the analytical expression derived from beam theory and experiments. Moreover, numerical simulations validated wave speed dependence on the elastic and geometric parameters at low frequencies. Clinical applications, such as arterial age estimation and arterial pressure measurement, are foreseen.

Propagation and dispersion of Bloch waves in periodic media with soft inclusions

We investigate the behavior of waves in a periodic medium containing small soft inclusions or cavities of arbitrary shape, such that the homogeneous Dirichlet conditions are satisfied at the boundary. The leading terms of Bloch waves, their dispersion relations, and low frequency cutoff are rigorously derived. Our approach reveals the existence of exceptional wave vectors for which Bloch waves are comprised of clusters of perturbed plane waves that propagate in different directions. We demonstrate that for these exceptional wave vectors, no Bloch waves propagate in any one specific direction.

Research on Detection of Switch Rail Defects Based on Pulse Reflection Method of the Dominant Mode

Guided wave structural health monitoring offers a promising way for continuous surveillance and identification of structural damage. However, due to the variable cross-section properties of the switch rail in the longitudinal direction, there are different modes present on different cross-sections, so the guided wave signals excited are very complex. The traditional baseline subtraction method can be used to extract defect echo features, but it is prone to false positives due to the influence of external factors such as field temperature change and environmental noise. This paper proposes a switch rail defect detection method based on the pulse reflection method of the dominant mode. Initially, eight typical cross-sections are chosen based on the cross-sectional dimensions of the switch rail. Semi-analytical finite element(SAFE) method is utilized to solve the dispersion curves and wave structure matrix of guided waves in the switch rail. According to the 3σ rule, the dominant mode whose node amplitude is much higher than other modes is selected, and the excitation signal is applied at the maximum value of the mode, which successfully excites the dominant mode. Through simulation and experimental validation, the reflected waves of the dominant mode at the defect are observable and visible, and the pulse reflection method can be used to detect the defects at the switch rail foot with a positioning error of less than 10 cm. The pulse reflection method of the dominant mode proposed in this paper, which has high detection efficiency and is not affected by the ambient temperature, provides a new idea and way to detect defects of the switch rail based on the ultrasonic guided wave method.

The Multi-parameter Test of Gravitational Wave Dispersion with Principal Component Analysis

In this work, we consider a conventional test of gravitational wave (GW) propagation which is based on the phenomenological parameterized dispersion relation to describe potential departures from General Relativity (GR) along the propagation of GWs. But different from tests conventionally performed previously, we vary multiple deformation coefficients simultaneously and employ the principal component analysis (PCA) method to remedy the strong degeneracy among deformation coefficients and obtain informative posteriors. The dominant PCA components can be better measured and constrained, and thus are expected to be more sensitive to potential departures from the waveform model. Using this method we analyze ten selected events and get the result that the combined posteriors of the dominant PCA parameters are consistent with GR within 99.7% credible intervals. The standard deviation of the first dominant PCA parameter is three times smaller than that of the original dispersion parameter of the leading order. However, the multi-parameter test with PCA is more sensitive to not only potential deviations from GR but also systematic errors of waveform models. The difference in results obtained by using different waveform templates hints that the demands of waveform accuracy are higher to perform the multi-parameter test with PCA. Whereas, it cannot be strictly proven that the deviation is indeed and only induced by systematic errors. It requires more thorough research in the future to exclude other possible reasons in parameter estimation and data processing.

Impact of clutter waves on surface-wave analysis under short alignment and a clutter waves removal method

Active source surface-wave exploration has become one of the common methods for obtaining shallow urban subsurface structures. The method offers the advantages of being non-destructive, easy to operate, and providing reliable results. Obtaining accurate dispersion curves is a key factor for the successful application of this method. Currently, most researchers believe that surface wave energy constitutes a large proportion of the seismic records, while the energy of other seismic waves (such as body waves) is relatively small. Therefore, there is no need to remove clutter waves other than surface waves when calculating surface wave dispersion. However, this paper compares the effects of dispersion imaging obtained with and without clutter wave removal through numerical simulations and field tests. The results indicate that when the measurement alignment is short (generally less than 20 m), clutter waves can cause varying degrees of “distortion” in the dispersion curves, deviating from the real dispersion curves. Conversely, after removing clutter waves, the “distortion” can be corrected, leading to more accurate dispersion imaging. Therefore, we recommend conducting clutter removal processing when the measurement alignment is short. This paper proposes a stable and feasible clutter wave removal method that can effectively suppress clutter interference and improve the accuracy of dispersion imaging. The research in this paper provides an alternative and optimized solution for the pre-processing of near-surface active source surface-wave exploration.

HISOL: High-energy soliton dynamics enable ultrafast far-ultraviolet laser sources

Ultrafast laser sources in the far ultraviolet (100–300 nm) have been the subject of intense experimental efforts for several decades, driven primarily by the requirements of advanced experiments in ultrafast science. Resonant dispersive wave emission from high-energy laser pulses undergoing soliton self-compression in a gas-filled hollow capillary fiber promises to meet several of these requirements for the first time, most importantly by combining wide-ranging wavelength tuneability with the generation of extremely short pulses. In this Perspective, we give an overview of this approach to ultrafast far-ultraviolet sources, including its historical origin and underlying physical mechanism, the state of the art and current challenges, and our view of potential applications both within and beyond ultrafast science.

Electroelastic wave dispersion in the rotary piezoelectric NEMS sensors/actuators via nonlocal strain gradient theory

This article introduces a computational means for investigating the electroelastic nonlinear wave dispersion traits of the nano-dimension sandwich pipe, which is composed of a core formed of a bi-directional functionally graded (Bi-FG) material, together with a piezoelectric sensor/actuator. A combination of Hamilton’s principle, first-order shear deformation, along with Von-Karman nonlinearity, is used for modeling and obtaining the nonlinear governing equations of the nano-sized sandwich pipe connected to a piezoelectric part. The nonlinear governing equations to obtain the nonlinear phase velocity of the current system are determined using a combination of analytical and multiple scales approaches. Due to some computational cost for choosing the precise values of both the nonlocality factor and length scale of the nanopipe in the laboratory, for the first time in this research, with the aid of COMSOL multi-physics finite element simulation, the results are verified, and new outcomes for obtaining the exact functions for nonlocal and length scale factors is presented. In addition, an artificial neural network (ANN) is utilized in this study for the prediction of the results. The mathematical and finite element results were used to train the ANN. A newly presented optimization algorithm is exploited for the first time for optimizing the ANN parameters concluding higher accuracy of the ANN predictions. Consequently, to explore the influences of the location of the piezoelectric patch, nonlocality and length scale factors, and applied voltage parameter on the phase velocity characteristics of the nano-dimension sandwich pipe made of a Bi-FG core and electrically patch, an effort is performed. As an applicable result that can be useful in the related nano-industries, the current work presents exact nonlocal and length scale functions for different conditions.

A SHORT SOLUTION OF THE LOCAL FRACTIONAL (2+1)-DIMENSIONAL DISPERSIVE LONG WATER WAVE SYSTEM

In this paper, a local fractional Riccati differential equation method is applied. A new travelling wave solution to the nonlinear local fractional [Formula: see text]-dimensional dispersive long water wave system is investigated. After travelling wave transformation, the governing model studied is converted into nonlinear ordinary differential equation. Some properties with the strain conditions are also reported.

THE EFFECT OF LINAGLIPTIN ON ARRHYTHMIA IN PATIENTS WITH TYPE 2 DIABETES MELLITUS

OBJECTIVE: Linagliptin is a dipeptidyl peptidase-4 (DPP-4) inhibitor that prevents the inactivation of incretin hormones and also stimulates the release of glucose-dependent insulin. Electrocardiographic abnormalities such as P wave dispersion and QT dispersion are associated with ventricular tachyarrhythmias and atrial fibrillation, respectively. In this study, we seek to determine if the introduction of linagliptin has any impact on the P wave dispersion and QT dispersion in individuals with Type 2 diabetes mellitus (Type 2 DM). MATERIAL AND METHODS: The study included 60 random patients (28 females- 46.7 % , 18 hypertension- 30 %, 16 smokers- 26.7 % ) who were admitted to the Training and Research Hospital internal medicine policlinic between October 2019 and May 2021 and who started linagliptin. The patients' electrocardiograms were taken at the start and the conclusion of the sixth month. Echocardiography was performed at treatment initiation and at the 6th month. RESULTS: When basal and 6th month electrocardiograms were compared, significant changes were observed in P wave dispersion (0.0435 ± 0.014 - 0.0312 ± 0.011 p<0.01), QT interval dispersion (0.0496 ± 0.01 - 0.0402 ± 0.01 p<0.01) and QTc interval dispersion (0.051 ± 0.01 - 0.038 ± 0.14 p<0.01). CONCLUSIONS: We demonstrated in this study that linagliptin had no detrimental effects on heart rhythm. Our study will be a guide for longer follow-up studies.

Multimodal surface wave inversion with automatic differentiation

Summary Investigating subsurface shear-wave velocity (vs) structures using surface wave dispersion data involves minimizing a misfit function that is commonly solved through gradient-based optimization. Sensitivity kernels for model updates are commonly estimated using numerical differentiation, variational methods or implicit functions which however, may involve numerical instability and computational challenges when dealing with complex velocity models and large datasets. In this study, we propose a novel surface wave inversion framework in which error-free gradients are calculated by automatic differentiation (AD) and forward modeling is implemented by convenient computational graphs in the state-of-the-art deep learning framework. The AD-based inversion approach is first validated using two synthetic datasets. Then the subsurface structures at three distinct locations, namely the Great Plains and the Long Beach in the US and Tong Zhou in China, are also derived using this method with seismic ambient noise data, which show nice consistency with those obtained using traditional methods. With the significantly improved computational efficiency, a great number of initial models can be inverted simultaneously to mitigate the impact of local minima and to estimate the uncertainty in the invert models. We have developed a new surface wave inversion package named ADsurf based on automatic differentiation and computational graphs in the deep learning framework, and its computational efficiency is also compared with the traditional finite-difference based gradient estimation approach. While a great number of intriguing studies on the geophysical inverse problems have been conducted recently using deep learning for end-to-end mapping, the use of AD provided in the in the deep learning frameworks to assist and expedite the gradient computations are still underexploited in geophysics. Thus, it is expected that various geophysical inverse problems in many different areas beyond the surface wave inversion can also be tackled with this new paradigm in the future.

Mathematical and Physical Characteristics of the Phase Spectrum of Earthquake Ground Motions

This study presents a rigorous investigation into the mathematical and physical properties inherent in the Fourier phase spectrum of earthquake ground motions. This exploration includes a detailed examination of the probability distribution of phase angles and differences, elucidated through two novel numerical experiments utilizing the reduction ad absurdum approach. Moreover, the study scrutinizes the physical attributes of earthquake ground motion’s phase spectrum, employing the circular frequency-dependent phase derivative as a key analytical factor. In a novel approach, the research delves into the relationship between circular frequency-dependent phase derivatives and Fourier amplitudes, shedding light on essential connections within earthquake phenomena, particularly addressing non-stationarity. Expanding the scope, the study comprehensively examines the influence of source, propagation path, and site on both the phase spectrum and accelerogram. Employing the control variate technique facilitates this analysis, providing valuable insights into the underlying physical mechanisms governing earthquake wave behavior. The findings highlight the temporal properties of the phase spectrum, attributing its complexity to the temporal heterogeneity in energy release during the fault rupture and dispersion of earthquake waves. This novel approach not only enhances the understanding of earthquake dynamics, but also underscores the significance of considering temporal variations in earthquake events.

Inversion of shear wave slowness and attenuation from dipole acoustic logging data based on an equivalent tool theory

The presence of a sonic logging tool affects the propagation characteristics of dipole-flexural wave in a fluid-filled borehole. As a result, the tool effect should be considered during the processing and inversion of the dipole-flexural wave for acoustic properties of shear wave. We show that the presence of the tool not only changes the slowness dispersion of the flexural wave but also results in a shift of its frequency-dependent attenuation toward lower frequencies. Equivalent tool theory (ETT) can realistically model the effect of an acoustic tool on guided wave propagation. With the ETT framework, we develop a unified workflow for estimating both the shear wave slowness and attenuation from dipole array acoustic waveforms. The workflow is an extension of the model-based dispersive processing of dipole logging data. The proposed workflow involves two inversion procedures. By matching the actual dispersion data with the theoretical dispersion predicted by the ETT, we can invert the shear wave slowness and tool parameters. With the estimated shear wave slowness and other borehole parameters, we further calculate the partition coefficients of flexural waves using the ETT. Based on the concept of energy partitioning, we formulate a linear optimization problem and invert for the shear wave attenuation from the frequency-dependent dipole attenuation. We use synthetic and field data to demonstrate the effectiveness and applicability of the developed method. The results show that it is important to incorporate the tool effect when processing dipole acoustic logging data for shear wave slowness and attenuation, especially in a fast formation.