Velocity Factor Research Articles

Investigation of Acoustic Waves generated by the Detonation Gun of a Zenith-M modernized Powerful Antihail Station

In this paper, a detonation gun of an antihail station was used to study acoustic waves as they propagated upward. The station's power was enhanced by placing a Hartmann resonance tube into the conical nozzle of the gun. Propagation speed, pressure-time waveform, and acoustic spectrum of the acoustic waves were determined. The propagation speed was approximately 890 m/s (Mach number ~2.6), and the initial (near-ground) intensity was 130-160 dB in the low-frequency range up to 200 Hz, where the energy distribution is relatively uniform. The results show that the antihail station can effectively influence atmospheric processes, either promoting rain precipitation or preventing hail formation.

Numerical Study of Bifurcation Structures in Reflected Shock-Wave/Laminar-Boundary-Layer Interaction Within an End-Wall Tube

Abstract The primary aim of this study is to analyze the unsteady characteristics of the interaction between a reflected shock wave and a laminar boundary layer in an end-wall shock tube. Our direct numerical simulations at shock Mach numbers of Ms = 1.9, 2.5, and 3.5 using a fifth-order WENO scheme and three-step Runge–Kutta time integration method revealed inhomogeneity and anisotropy in the shock bifurcation. Surprisingly, the upper and lower bifurcated structures maintain a notably asymmetric flow during the forward propagation of the reflected shock bifurcation. The inverse flow in the bifurcation resembles a crooked earthworm structure, exhibiting high-frequency oscillations indicative of instability. However, at higher shock intensities, the earthworm transforms into a stable strip-like configuration, facilitating the entrapment of inverse flow and leading to rapid bifurcation height growth and early convergence. Additionally, isolated islands with high density, temperature, and pressure emerge in the transitional region behind the bifurcated shocks, due to variations in wave propagation speed.

Study on Damage Characteristics and Physical Field Characteristics of Roadway Surrounding Rock Under Multiple Disturbances

ABSTRACTDuring the mining process, repetitive stress disturbances induced by mining activities can lead to alterations in the physical properties of coal, potentially resulting in rockburst occurrences within tunnels. To investigate the propagation rule of physical field characteristics and characteristics of failure in roadway surrounding rock under multiple disturbance damage caused by dynamic load, a combined experimental and theoretical analysis is conducted to study the weakening effect of rock mass under various disturbance circumstances. A model of roadway surrounding rock loosening and failure under multiple disturbances was proposed. The degree of damage is quantified by defining the weakening coefficient Di, A “weakening variable method” is proposed to confirm the main parameters of the Holmquist‐John‐son‐Cook (HJC) model under different disturbance conditions. The reliability of these findings was validated through a microseismic event at the Tangshan coal mine's 0250 working face in 2020, followed by numerical simulation studies. The results indicate that damaged coal weakens the intensity of stress waves at the same source velocity, with the strongest effect observed at interfaces between different damage zones. Furthermore, damaged coal exhibits a stronger weakening effect on stress wave propagation speed compared to undamaged coal in non‐interface areas. The study on roadway stability reveals that severely damaged coal‐rock samples significantly weaken stress waves; however, they also exhibit lower minimum energy for dynamic failure in roadway surrounding rock, indicating that low‐stress waves cause greater damage under severe damage conditions. The study investigates the impact of coal rock mass degradation on the stability of surrounding roadways under various disturbance conditions, which holds significant implications for the timely identification of potential instability risks in damaged coal bodies, optimization of support strategies, and ensuring mining safety.

Enhancing Fault Location Accuracy in Transmission Lines Using Transient Frequency Spectrum Analysis: An Investigation into Key Factors and Improvement Strategies

Fault location estimation in transmission lines is critical for power system reliability. Various methods have been developed for this purpose, among which transient frequency spectrum analysis (TFSA) stands out as a recent method based on travelling wave (TW) theory. TFSA determines the fault location by analyzing the frequency spectrum of transient currents and/or voltages at the instant of the fault, offering advantages such as independence from fault impedance and the ability to locate faults with one-side measurements. Despite its success in fault location, TFSA has several considerations that warrant detailed investigation. This study explores the effects of source inductance, series compensation, fault arc, and current transformer (CT) characteristics on transient frequencies. Additionally, the impact of noise on TFSA results is examined. The new proposed source inductance compensation method can reduce the error of 6.55% to 0.88%, where the same error can be reduced to 3.45% with the compensation method given in previous study. Strategies to enhance accuracy are discussed and compared to previous studies, including a proposed detection approach providing appropriate data size and precise wave propagation speed calculations. These findings contribute to a deeper understanding of TFSA’s limitations and inform practical improvements for fault location accuracy in power transmission systems.

A robust numerical method for the generation and propagation of periodic finite-amplitude internal waves in natural waters using high-accuracy simulations

Abstract. The design and implementation of boundary conditions for the robust generation and simulation of periodic finite-amplitude internal waves is examined in a quasi two-layer continuous stratification using a spectral-element-method-based incompressible flow solver. The commonly used Eulerian approach develops spurious, and potentially catastrophic small-scale numerical features near the wave-generating boundary in a non-linear stratification when the parameter A/(δc) is sufficiently larger than unity; A and δ are measures of the maximum wave-induced vertical velocity and pycnocline thickness, respectively, and c is the linear wave propagation speed. To this end, an Euler–Lagrange approach is developed and implemented to generate robust high-amplitude periodic deep-water internal waves. Central to this approach is to take into account the wave-induced (isopycnal) displacement of the pycnocline in both the vertical and (effectively) upstream directions. With amplitudes not restricted by the limits of linear theory, the Euler–Lagrange-generated waves maintain their structural integrity as they propagate away from the source. The advantages of the high-accuracy numerical method, whose minimal numerical dissipation cannot damp the above near-source spurious numerical features of the purely Eulerian case, can still be preserved and leveraged further along the wave propagation path through the robust reproduction of the non-linear adjustments of the waveform. The near- and far-source robustness of the optimized Euler–Lagrange approach is demonstrated for finite-amplitude waves in a sharp quasi two-layer continuous stratification representative of seasonally stratified lakes. The findings of this study provide an enabling framework for two-dimensional simulations of internal swash zones driven by well-developed non-linear internal waves and, ultimately, the accompanying turbulence-resolving three-dimensional simulations.

Nonlinear generalized piezothermoelasticity of spherical vessels made of functionally graded piezoelectric materials

The present study investigates the thermoelastic response of a heterogeneous piezoelectric sphere under thermal shock loading. Boundary conditions as well as loading are considered as symmetric; thus, the response of the sphere is expected to be symmetric. All of the properties of the thick-walled sphere, including mechanical, electrical and thermal properties, are considered dependent on the radial position, except for the relaxation time, which is considered a constant value along the radius. The governing equations of the sphere have been derived under heterogeneous anisotropic assumptions. The general form of the second law of thermodynamics, which is nonlinear in nature, and is called nonlinear energy equation is used. The number of the established equations is three, which includes the motion equation, energy equation and Maxwell electrostatic equation of Maxwell. These equations are obtained in terms of radial displacement, temperature difference and electric potential. The energy equation is derived based on Lord and Shulman theory with a single relaxation time. In the next step, by introducing dimensionless variables, the governing equations are provided in dimensionless presentation. Then these equations have been discretized using generalized differential quadrature method. Also, in order to follow the solution of the equations in time domain, Newmark method has been used. Since the system of equations is nonlinear, Picard algorithm is applied as a predictor-corrector mechanism to solve the nonlinear system of equations. Then numerical results are presented to investigate the propagation of mechanical, thermal and electric waves inside the heterogeneous sphere and also their reflection from the outer surface of the sphere. By examining the results, it can be seen that mechanical and thermal waves propagate with a limited speed, while the speed of electric wave propagation is infinite.

Time dependent black holes and gravitational wave in Einstein–Gauss–Bonnet theory with two scalar fields

In this paper, we investigate the time dependent black holes in the frame of Einstein–Gauss–Bonnet theory having two scalar fields and investigate the propagation of the gravitational wave (GW). In the reconstructed models, there often appear ghosts, which could be eliminated by imposing some constraints. We investigate the behavior of high-frequency gravitational waves by examining the effects of varying Gauss–Bonnet coupling during their propagation. The speed of propagation changes due to the coupling during the black hole formation process. The propagation speed of gravitational waves differs when they enter the black hole compared to when they exit.

Shear wave speed, dispersion slope and anisotropy evaluation using cardiac shear wave elastography in patients with Fabry disease

Abstract Background Cardiac shear wave imaging has been proposed to investigate left ventricular myocardial alterations non-invasively. Dispersion slope and anisotropy are fundamental properties that have not been studied in Fabry disease (FD) patients yet. Purpose The aim of this study was to determine and compare shear wave propagation speed, dispersion slope and fractional anisotropy in FD patients and healthy controls. Methods We prospectively included 20 FD patients and 20 healthy controls (HC). Shear wave speed, dispersion slope and fractional anisotropy were measured non-invasively in anteroseptal basal segment using an ultrasound for cardiac shear wave imaging. Echocardiography, electrocardiogram and laboratory evaluations were performed. Results Shear wave propagation speed was higher in FD patients than in HC group (1.46 ± 0.12 m/s and 1.36 ± 0.17 m/s, p = 0.03). No difference was found in dispersion slope (11.4 m/s/kHz in FD group and 11.3 m/s/kHz in HC group, p = 0.6). Fractional anisotropy was 0.05 ± 0.04 in FD group and 0.05 ± 0.04 in HC group, p = 0.4. Conclusion Shear wave speed was higher in FD patients compared to control group. Dispersion slope and fractional anisotropy in FD group did not reveal significant difference to the control group.

Comprehensive analysis of wave interactions and resulting spall damage in layered heterogeneous medium under impact

The effect of dynamic spall damage on the response of layered medium subjected to one-dimensional impact involving an impactor and a multi-layered target is investigated. The study examines the damage caused by elastic waves below the Hugoniot Elastic Limit (HEL) during impact events. Analytical expressions of stress and particle velocity derived from mass and momentum conservation principles are utilized to solve the wave interactions within the impactor-target system, considering reflections, transmissions, and wave interactions between layers. These analytical expressions, integrated into a computational framework, facilitate the monitoring of material responses following each wave interaction, thereby analysing the impact response of the layered medium. Wave interactions, resulting in tensile stresses, that can cause damage to the target have been identified. A strain-based damage initiation and evolution law is incorporated into the developed computer program to predict damage in each layer of a medium. Damage alters the medium’s impact behaviour by decreasing stress magnitude and inducing temporal delays in the response due to attenuated wave propagation speed. The occurrences of tensile stress are explored, analysing spatial and temporal variations of multiple damage incidents within the layered medium. The tension at the interface between two layers can induce damage in one or both adjacent layers, leading to debonding between layers. The effect of damage on the impact response of the medium is analysed by comparing the results for the damaged and undamaged target scenarios. The impact behaviour of a single-layer and a multi-layer target obtained from the present model, in terms of stress and particle velocity, is verified through Finite Element simulations of the identical impact problems, where the damage evolution criterion is incorporated using a VUMAT subroutine. The outcomes derived from this study align closely with Finite Element (FE) results.

Probing the speed of scalar induced gravitational waves from observations

The propagation speed of gravitational waves is a fundamental issue in gravitational theory. According to general relativity, gravitational waves propagate at the speed of light. However, alternative theories of gravity propose modifications to general relativity, including variations in the speed of gravitational waves. In this paper, we investigate scalar-induced gravitational waves that propagate at speeds different from the speed of light. First, we analytically calculate the power spectrum of scalar induced gravitational waves based on the speed and spectrum of primordial curvature perturbations. We then explore several scalar power spectra, deriving corresponding fractional energy densities, including monochromatic spectrum, scale-invariant spectrum, and power-law spectrum. Finally, we constrain scalar-induced gravitational waves and evaluate the signatures of their speed from the combination of CMB+BAO and gravitational wave observations. Our numerical results clearly illustrate the influence of the speed of scalar-induced gravitational waves.

Study on ground-penetrating radar wave field characteristics for earth dam disease considering the medium randomness

Ground-Penetrating Radar (GPR) has been widely used for non-destructive testing of earth dam disease. However, the forward simulation of GPR for earth dam disease often employs layered homogeneous models, neglecting the influence of medium randomness on its wave field characteristics. Therefore, considering the randomness of the medium, a geoelectrical model for earth dam disease is established, which is based on the mixed-type autocorrelation function and the finite element time-domain method. The influence of random medium model parameters on the single-channel wave of GPR is analyzed. The electromagnetic wave propagation characteristics under different medium models are explored. The forward simulation of GPR for earth dam disease such as panel voiding, concentrated seepage, and loosening are performed. The differences in propagation characteristics for earth dam disease between uniform medium model and random medium model are compared. Compared to the calculation results of the uniform medium model, the propagation speed and amplitude of electromagnetic waves in the random medium model changes, and a number of diffraction waves are present. When performing forward simulation of GPR for earth dam disease, considering medium randomness can deepen the understanding of the GPR section view and help improve the accuracy of image interpretation.

Upstream influence of midlatitude jet stream biases in boreal summer

AbstractClimate models exhibit biases in the mean state and in variability across different regions of the Earth. For example, atmosphere‐only models have a poleward bias in summertime jet streams across the Northern Hemisphere (NH). This can result from many processes, including misrepresentation of Rossby waves that can propagate in different directions and thereby interact with jet streams. However, Rossby‐wave biases can result from biased background state of the climate system as well. The propagation speed of Rossby waves depends on jet stream strength, thus a poleward displacement of the jet stream can hinder westward propagation of Rossby waves at higher latitudes and displace eastward propagating Rossby waves (downstream development). These biases then impact other regions resulting in biased atmospheric circulation across the NH. Indeed, in this study we confirm this via regional nudging experiments within the Norwegian Earth System Model. Namely, nudged horizontal winds over the North Pacific can improve Rossby wave statistics and thereby atmospheric circulation over Eurasia (i.e., upstream). However, nudging over the North Atlantic has little effect on boreal summer atmospheric circulation. This implies that improving biases over the North Pacific is crucial for a better representation of modelled boreal summer circulation over Eurasia.

The modeling of acoustic black hole beam by spectral element method

A technique developed in recent decades for the passive control of vibrations and noise is the Acoustic Black Hole (ABH). The structural ABH effect is achieved by incorporating a local modification in the thickness of a thin structure, typically a beam or a plate, with a variation in thickness according to a spatial power law. The combination of the variation in the thickness power law and a local increase in damping, provided by the concomitant application of layers of viscoelastic material, produces a significant reduction in the wave propagation speed and an increase of attenuation properties. As an elastic wave propagates within an ABH, its propagation speed decreases smoothly and continuously, in theoretical case, when the structure's thickness disappears at the end of the ABH, the wave speed drops to zero. For practical applications, ABH is typically combined with dissipative materials to obtain significantly higher structural loss factors. This work aims to establish a numerical approach for modeling and designing a beam-type structural one-dimensional ABH device for vibration control device using the Spectral Element Method (SEM) and verified by the Finite Element Method (FEM). Examples are performed, and the results are compared with those found in the literature.

Estimation of ground vibration emission increase with respect to velocity in high-speed railways

During the design of a new line, it is often necessary to estimate railway vibration emissions at a given future speed from experimental data in similar circumstances, but at a different speed. Future levels are usually estimated according to a logarithmic evolution law with respect to speed, a typical one being that in USA FTA Report nº0123 "Transit Noise and Vibration Impact Assessment Manual", a de facto standard in the sector. Also, it is known that for high-speed lines a drastic increase in vibrations is observed when railway speed is higher than the propagation speed of surface Rayleigh waves. This phenomenon, known as trans-Rayleigh boom, produces a sharp discontinuity in the evolution of vibration emissions. However, vibration levels observed in the vicinity of a high-speed line have shown values well above the prediction rule suggested in FTA Manual, which could not be explained by a trans-Rayleigh boom. A more accurate extrapolation method based on local rail roughness measurements is capable of producing improved predictions compared to FTA rule of thumb. This contribution shows the details of the method suggested, and the improvement in the prediction (with respect to FTA extrapolation law) obtained in the specific case of a high-speed railway.

A Simple and Robust CryoSat‐2 Radar Freeboard Correction Method Dedicated to TFMRA50 for the Arctic Winter Snow Depth and Sea Ice Thickness Retrieval

AbstractCryoSat‐2 has been successful in observing sea ice thickness from space by providing ice freeboard information. The initial estimate of the ice freeboard, called radar freeboard, is obtained by analyzing the observed waveform using a retracker. A series of corrections are needed to convert the radar freeboard to the ice freeboard. Those are the physical effects (e.g., changes in wave propagation speed and the distribution of scattering at snow and ice surfaces, etc.) and the bias of the retracker; however, traditionally, only the wave speed correction has been applied due to lack of enough information to perform the complete correction. Here, an alternative correction method for the CryoSat‐2 radar freeboard derived using the Threshold First‐Maximum Retracker Algorithm with a 50% threshold (TFMRA50) is proposed. Snow depth was used as a predictor for the correction, similar to the traditional wave speed correction, but the coefficients were empirically determined by performing a direct comparison of the radar freeboard from CryoSat‐2 and the ice freeboard from airborne observations. Consequently, this new empirical correction treats the physical effects and the retracker bias as a whole, which have been difficult to separate in the retrieval process. In this paper, we demonstrate that the retrieval accuracy of snow and ice variables and the consistency of the two independent retrieval methods are improved when the new correction is applied. The result of this study emphasizes the importance of compatibility between the retracker and the freeboard correction method.

A cortical field theory – dynamics and symmetries

We characterise cortical dynamics using partial differential equations (PDEs), analysing various connectivity patterns within the cortical sheet. This exploration yields diverse dynamics, encompassing wave equations and limit cycle activity. We presume balanced equations between excitatory and inhibitory neuronal units, reflecting the ubiquitous oscillatory patterns observed in electrophysiological measurements. Our derived dynamics comprise lowest-order wave equations (i.e., the Klein-Gordon model), limit cycle waves, higher-order PDE formulations, and transitions between limit cycles and near-zero states. Furthermore, we delve into the symmetries of the models using the Lagrangian formalism, distinguishing between continuous and discontinuous symmetries. These symmetries allow for mathematical expediency in the analysis of the model and could also be useful in studying the effect of symmetrical input from distributed cortical regions. Overall, our ability to derive multiple constraints on the fields — and predictions of the model — stems largely from the underlying assumption that the brain operates at a critical state. This assumption, in turn, drives the dynamics towards oscillatory or semi-conservative behaviour. Within this critical state, we can leverage results from the physics literature, which serve as analogues for neural fields, and implicit construct validity. Comparisons between our model predictions and electrophysiological findings from the literature — such as spectral power distribution across frequencies, wave propagation speed, epileptic seizure generation, and pattern formation over the cortical surface — demonstrate a close match. This study underscores the importance of utilizing symmetry preserving PDE formulations for further mechanistic insights into cortical activity.

Estimating the In Situ Stratification via Remotely Sensed Internal Wave Speeds

Abstract This work tests a methodology for estimating the ocean stratification gradient using remotely sensed, high temporal and spatial resolution field measurements of internal wave propagation speeds. The internal wave (IW) speeds were calculated from IW tracks observed using a shore-based, X-band marine radar deployed at a field site on the south-central coast of California. An inverse model, based on the work of Kar and Guha, utilizes the linear internal wave dispersion relation, assuming a constant vertical density gradient is the basis for the inverse model. This allows the vertical gradient of density to be expressed as a function of the internal wave phase speed, local water depth, and a background average density. The inputs to the algorithm are the known cross-shore bathymetry, the background ocean density, and the remotely sensed cross-shore profiles of IW speed. The estimated density gradients are then compared to the synchronously measured vertical density profiles collected from an in situ instrument array. The results show a very good agreement offshore in deeper water (∼50–30 m) but more significant discrepancies in shallow water (20–10 m) closer to shore. In addition, a sensitivity analysis is conducted that relates errors in measured speeds to errors in the estimated density gradients. Significance Statement The propagation speed of ocean internal waves inherently depends on the vertical structure of the water density, which is termed stratification. In this work, we evaluate and test with real field observations a technique to infer the ocean density stratification from internal wave propagation speeds collected from remote sensing images. Such methods offer a way to monitor ocean stratification without the need for extensive in situ measurements.

Investigation of Backpressure Wave Propagation Properties during Gas Kicks in Managed Pressure Drilling

Summary It is often essential to provide backpressure to the wellbore by changing the opening size of the choke valve when a gas kick is detected during managed pressure drilling (MPD), which maintains the pressure in the bottom of the hole. In this study, a mathematical model was developed to explain how backpressure waves spread and weaken in a wellbore during MPD when there is a gas-liquid two-phase flow. The model is founded on a two-phase flow model, which thoroughly accounts for the gravity, shear force, and interphase interactions between the gas and liquid phases. The small perturbation theory was used to compute the backpressure wave’s propagation speed and attenuation coefficient. The outcome showed satisfactory agreement with other scholars’ experimental results. The model was used to study the impacts of the following variables on the backpressure wave propagation properties: void fraction, temperature, pressure, interphase resistance, shear force, density, invading gas composition, displacement of the drilling fluid, rate of intrusion of gas, gas-liquid surface tension, and drilling fluid viscosity. By using an example well, the laws of pressure wave propagation speed, attenuation coefficient, and propagation time with well depth were analyzed. Through evaluative methods in the field of economic management, the principal control variables governing the propagation of backpressure waves were determined. The conclusion is that, in terms of operational feasibility, lower drilling fluid density and reduced drilling fluid displacement are advantageous for a faster propagation of backpressure waves to the bottom of the well.

Nonlinear wave model of towed system and numerical method for its calculation

Towed systems have found wide practical applications. Notable underwater systems for the long-distance extraction of minerals (concretions) from the ocean floor extend over 5-10 km. The existing mathematical models for solving dynamic problems of such systems in various environments are not entirely accurate regarding the diversity of wave processes. This necessitates the development of refined wave models. This article presents a new quasi-linear mathematical model describing the nonlinear four-mode dynamics of a towed system in a spatially inhomogeneous field of mass and surface forces. It is described by a nonlinear system of twelve first-order partial differential equations. The principles of boundedness and hyperbolicity are satisfied. The validation of the two-mode reduction of the model is based on the numerical solution of the problem of the propagation of two waves: longitudinal and configurational. Using a numerical algorithm and a program based on the finite difference method, a comparison of two difference schemes – Crank-Nicolson and Euler – was conducted. The main limitations for applying the finite difference method used for numerical modeling of wave propagation and reflection in a towed system are the peculiarities of the defining quasi-linear equations, which are related to the necessity of simultaneous computation of variables responsible for fast and slow processes. For such systems of equations, the term "singularly perturbed system of equations" is used. These perturbations result from the significant differences in the propagation speeds of longitudinal and configurational waves at the physical level. Consequently, it is necessary to employ special time-stepping regularization and filtering methods for numerical results. This imposes certain restrictions on the ability to model real processes and on the accuracy of the obtained results, necessitating the use of implicit difference schemes and high-frequency filtering.

Research on the dynamics of flame propagation and overpressure evolution in full-scale residential gas deflagration

To determine the effect of ignition height on indoor flame spread behavior and overpressure development, a comprehensive full-scale deflagration testing facility was established. Extensive experimental research was conducted within this facility. The findings indicate that indoor flame reignition and the occurrence of secondary explosions are most pronounced with intermediate ignition. Furthermore, the explosion overpressure generated during the reverse turn of shock wave propagation is greater than that produced by the forward turn. In comparison to the peak overpressure Pext in the master bedroom for top, middle, and bottom ignition, the peak overpressure Pext in the second bedroom increased by approximately 14.48 %, 15.04 %, and 19.20 %, respectively. When comparing middle ignition to top ignition, the propagation speed of shock waves in the kitchen balcony, restroom, second bedroom, and master bedroom was enhanced by 34.21 %, 40.85 %, 40.70 %, and 34.65 %, respectively. Furthermore, when comparing middle ignition to bottom ignition, the propagation speed of shock waves in these areas experienced a significant increase of 126.32 %, 124.39 %, 123.26 %, and 113.86 %, respectively. These research findings provide a theoretical foundation and empirical data to support the investigation and analysis of the causes of indoor gas explosion incidents.