Traveling-wave Research Articles

Fault location method for new distribution networks based on waveform matching of time–frequency travelling waves

AbstractSome existing fault location methods for distribution networks rely too much on the local wave head information of the time or frequency domain signals, making it difficult to adapt to the increasingly complex structure and operating conditions of the distribution network after the new energy access. For improvement, the travelling wave (TW) time and frequency ranges that can effectively avoid waveform distortion caused by new energy access are analysed. The one‐to‐one matching relationship between the TW waveforms in these ranges and the fault positions is revealed. A fault TW time–frequency matrix with specific time and frequency windows is constructed, and a new distribution network fault location method is proposed based on the matching technique of waveform features, which realises the accurate fault location by exploring the proportionality between the cumulative trend of the matrix energy amplitude deviation and the fault point position. Simulation test results show that the proposed method is not affected by the complex structure of distribution networks such as new energy access and overhead‐cable line mixing on fault location and flexibly transforms the fault location problem into a time–frequency TW waveform matching problem, which improves the accuracy and robustness of the fault location for new distribution networks to a degree.

Innovative W-Band Through-Wall Radar With Sector Scanning: Utilizing Traveling Wave Tubes for Enhanced Penetration

Innovative <i>W</i>-Band Through-Wall Radar With Sector Scanning: Utilizing Traveling Wave Tubes for Enhanced Penetration

A venting resonator emitting monochromatic periodic traveling waves in dispersive media

Dynamically stable traveling periodic waves are notoriously difficult to realize experimentally. Manifestations of such waves inherently become unstable in any dispersive medium, whether it be at continuum length scales in fluid mechanics, in electrodynamics, or in nonlinear optics. Here, a simple experimental system is proposed where Stokes waves are emitted from a resonator whose cavity accommodates standing waves of same wavelength that is emitted out. A single characteristic wavelength is found for each driving frequency despite the coexistence of standing and traveling waves, external noise, and potentially parasitic reflections. The system's response is shown to be reliable at very small values of quality factor. A unique utility of this model system is suggested in that such a venting resonator can be used as an inhibitor of modulation instability in dispersive medium where an engineering application demands stable periodic traveling waves. Some parallels are drawn with other unbounded resonators found in society, whereby their leakiness is central to their application, such as the role of air-filled cavity to achieve impedance matching in stringed musical instruments, or energy harvesting from oscillating fluid columns in nature.

Novel soliton solutions and phase plane analysis in nonlinear Schrödinger equations with logarithmic nonlinearities

This paper investigates a generalized form of the nonlinear Schrödinger equation characterized by a logarithmic nonlinearity. The nonlinear Schrödinger equation, a fundamental equation in nonlinear wave theory, is applied across various physical systems including nonlinear optics, Bose–Einstein condensates, and fluid dynamics. We specifically explore a logarithmic variant of the nonlinear Schrödinger equation to model complex wave phenomena that conventional polynomial nonlinearities fail to capture. We derive four distinct forms of the nonlinear Schrödinger equation with logarithmic nonlinearity and provide exact solutions for each, encompassing bright, dark, and kink-type solitons, as well as a range of periodic solitary waves. Analytical techniques are employed to construct bounded and unbounded traveling wave solutions, and the dynamics of these solutions are analyzed through phase portraits of the associated dynamical systems. These findings extend the scope of the nonlinear Schrödinger equation to more accurately describe wave behaviors in complex media and open avenues for future research into non-standard nonlinear wave equations.

Parametric study of traveling wave motion in energy absorption mode

There are two modes of traveling wave motion, traveling wave propulsion and traveling wave energy absorption. In this paper, a two-dimensional flexible traveling wave plate is taken as the research object. The characteristic length and characteristic parameter of traveling wave motion are determined by numerical simulation, and the parametric study of the traveling wave motion in energy absorption mode is conducted. The effects of dimensionless amplitude and dimensionless wave velocity on the energy absorption characteristics of flexible traveling wave plate are analyzed, and the mechanism of traveling wave energy absorption is revealed. The results show that the larger the dimensionless amplitude is, the stronger the work capacity of the traveling wave plate becomes, while the absolute amplitude or absolute wavelength has little effect on the work capacity of the traveling wave plate. Under different waveforms, the work capacity of the traveling wave plate increases first and then decreases as the dimensionless wave velocity increases. Within the parameter range studied in this article, when the dimensionless amplitude is 0.2 and the dimensionless wave velocity is 0.5, the traveling wave plate can achieve an energy absorption efficiency of about 40 %.

Experimental detection of mechanical deformations exploiting electromechanical effects

The present paper discusses experimental results concerning the deformation-induced generation of electric potential difference in steel specimens. According to our observations, voltages in the order of 10 microVolts can be measured between points on the surfaces of steel bodies during mechanical deformation. Three different experimental set-ups were used to determine the properties of the phenomenon, carefully excluding the influence of possible external electromagnetic fields. In order to exclude thermoelectric effects, a special steel specimen was fabricated. Further experimental campaigns were conducted with long, thin metallic rods in two different set-ups: the generation of voltage was measured during the traveling of longitudinal shock waves and during bending vibrations of the specimens. The results indicate that the variation of the magnetization of the material – the magnetoelastic effect – plays an important role in the phenomenon, but thermoelectricity also contributes to the measurable voltage signals. The electromechanical effect identified in the present paper may have several applications in measurement technology. The most relevant advantage of the applied measurement methods is that these are essentially sensor-free, since the mechanical vibrations can be detected by simply soldering, welding, or pressing copper wires to the examined steel specimen.

New Exact Solutions for Generalized of Combined with Negative Calogero-Bogoyavlenskii Schiff and Generalized Yu–Toda–Sassa–Fukuyama Equations

In this paper, we present generalized model of combined Calogero-Bogoyavlenskii Schiff and negative-order Calogero-Bogoyavlenskii Schiff G(CBS-nCBS) equation and generalized Yu–Toda–Sassa–Fukuyama g(YTSF) equation. We apply the extended hyperbolic function method, to solve generalized models. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions solutions of these equations from the method with the aid of the computer program Maple.

Numerical investigation on the VIV response of the flexible cylindrical structures subjected to non-linearly varying shear flow

Vortex-induced vibration (VIV) of flexible cylinders is an important phenomenon in ocean structures, which may cause fatigue damage and structural failure of offshore structures. Much literature has extensively explored VIV of flexible cylinders under various flow conditions, such as uniform and linearly varying shear flow. However, real scenarios in most cases involve non-uniform, non-linearly varying shear flow profiles. Hence, it is important to investigate the VIV response of the flexible cylindrical structures subjected to non-linearly varying shear flow profiles. This study employs a wake oscillator model (WOM) that simulates the VIV response of the flexible cylinder under the action of non-linearly varying shear flow velocity profiles. The flexible cylinder subjected to linearly varying sheared flow velocity profiles not only overpredicts but also underpredicts the VIV responses compared to the non-linearly varying sheared flow profile, which represents the real scenario. The VIV mode number for the flexible cylinder subjected to non-linear shear flow was found to have a non-linear relationship with that of linear shear flow. The VIV response of the flexible cylinder subjected to a linearly varying shear flow profile exhibits more travelling wave behaviour compared to non-linear shear flow. The location of the maximum VIV response of the structure having the same aspect ratio (L/D) and shear parameter (β), was different for linear and non-linear flow profiles across the span. The time and frequency domain responses showed a shift in the frequency band. The results obtained from the numerical simulations give better insights into the vibrational behaviour of flexible cylinders in realistic flow environments.

Considerable traveling wave solutions of a generalized Hietarinta-type equation

Considerable traveling wave solutions of a generalized Hietarinta-type equation

Phase-controlled pattern-tunable optical traveling wave antenna array

An optical phased array is designed based on equally spaced identical Au waveguides serving as optical traveling wave antennas (OTWAs). Phased surface plasmon polaritons are fed through the Au waveguides and partly radiate out at the terminals. The simulation results indicate that the pattern maximum of a 7-element OTWA array can be dynamically steered over a range of up to 60.6° by changing the excitation phase differences between the elements, and the main lobe is narrowed compared to the single-element case. A theoretical analysis about the tunable pattern by the pattern multiplication principle is carried out, which is basically consistent with the simulations. Such an OTWA array should have potential applications in nano-optics due to its ability to steer the pattern without mechanical motion.

Travelling waves with continuous profile for hyperbolic Keller-Segel equation

Abstract This work describes a hyperbolic model for cell-cell repulsion with population dynamics. We consider the pressure produced by a population of cells to describe their motion. We assume that cells try to avoid crowded areas and prefer locally empty spaces far away from the carrying capacity. Here, our main goal is to prove the existence of travelling waves with continuous profiles. This article complements our previous results about sharp travelling waves. We conclude the paper with numerical simulations of the PDE problem, illustrating such a result. An application to wound healing also illustrates the importance of travelling waves with a continuous and discontinuous profile.

The impact of relaxation on isothermal acoustic traveling waves: A new solvable model based on Navier–Stokes–Maxwell theory

An analysis of isothermal acoustic traveling waves in a particular sub-class of Maxwell fluids, specifically, those which behave like perfect gases and wherein the shear viscosity is proportional to the square of the mass density, is presented. Exact solutions are derived and analyzed, shock thickness results are computed, and the thermodynamic consistency of the isothermal assumption is verified vis-à-vis the Mach number values considered. It is shown that, within the range where both yield dispersed shock profiles, the Maxwell case leads to significantly smaller shock thicknesses and more asymmetric solution profiles than those admitted by the corresponding Newtonian (fluid) case.

Multicriteria evaluations for sand production potentials: a case study from a producing oil field in the Niger Delta Basin (Nigeria)

Geomechanical evaluation of three wells in an onshore Niger Delta Oil Field in which some reservoirs have histories of free water production was carried out to predict their potential for sand production. The mechanical characteristics of the reservoirs, such as the Poisson ratio (v), shear modulus (G), elastic modulus (E), bulk modulus (Kb), and bulk compressibility, were calculated using petrophysical parameters such as s-velocity (Vs), p-velocity (Vp), gamma ray index (IGR), the volume of shale (Vsh), porosity (), and pseudo factor (q) derived from wireline logs (Cb). Five geomechanical techniques—porosity, acoustic wave travel time, sand production index, Schlumberger sand production index, and shear modulus to bulk compressibility ratio (G/Cb) were used to forecast the potential for sand production in the reservoirs. The porosity values varied from 14 to 27%, which is below the threshold value of 30% for sand production. The acoustic wave travel time ranged from 81.59 to 89.91s/ft, which is below the threshold value of 104s/ft for sand production. The threshold value for the sand production index was &lt; 2.9 ×106psi. The values for the sand production index fell between 11x 106psi and 12.4 x 106psi, which is below the limits for the onset of sanding. The G/Cb values in the reservoirs across the three wells fell between 1.15 x 1012psi2 and 1.43 x 1012psi2 while the threshold value for the Schlumberger sand production index fell between 1.15 x 1012psi2 and 1.43 x 1012psi2. Only the Schlumberger criterion predicted the potential for likely sand production.

Construction and experimental verification of wave velocity model for source location in goaf overlying rock strata

The geological structure of the goaf overlying rock is complex, a consequence of coal mining that has modified the original stratified structure of the sedimentary strata. To enhance the accuracy of microseismic source location in such intricate geological formations, a wave velocity model for the “three zones” goaf was constructed based on natural divisions within the strata using Snell's law and assuming a homogeneous medium. The model took into account the effects of rock deformation and fracture development, enabling the derivation of formulas for microseismic wave propagation path and travel time calculation. Additionally, the concept of equivalent wave velocity was defined. An indoor simulation test using similar materials was conducted to establish a geological model of the goaf. By comparing the errors between the theoretical and measured values of equivalent wave velocity, assessing the locating effects before and after implementing the wave velocity model of the goaf, and verifying the feasibility of the model, it was demonstrated that establishing a wave velocity model based on the characteristics of the strata structure was crucial for improving the accuracy of the microseismic source location. Notably, as the propagation path of microseismic waves in the goaf increased, the equivalent wave velocity decreased. The wave velocity structure in the goaf exhibited nonuniformity, with the relative error between the theoretical and measured values of equivalent wave velocity being limited to 10 %. The incorporation of this established wave velocity model into the location method resulted in a substantial 58.57 % increase in locating accuracy.

Minimal wave speed and spreading speed in predator-prey systems with stage structure

This article studies the minimal wave speed of traveling wave solutions as well as spreading speed in predator-prey systems. The model divides the prey into the immaturity and maturity, and the predator feeds on the immature individuals. For the traveling wave solutions connecting the predator-free equilibrium with the coexistence state, we consider two different diffusion modes. For both modes, the minimal wave speed is shown by presenting the existence or nonexistence of nontrivial traveling wave solutions for all wave parameters. When the diffusion is local, the minimal wave speed is the spreading speed of the corresponding initial value problem, in which the initial condition implies that the predator is the invader while the prey is the aborigine in the whole habitat. Under the persistence assumption in the corresponding kinetic systems, our conclusion coincides with the fact that the diffusion of the prey may have less effect on the invasion ability of the predator.

Propagation dynamics of a nonlocal dispersal Zika transmission model with general incidence

In this paper, we are interested in propagation dynamics of a nonlocal dispersal Zika transmission model with general incidence. When the threshold is greater than one, we prove that there is a wave speed such that the model has a traveling wave solution with speed , and there is no traveling wave solution with speed less than . When the threshold is less than or equal to one, we show that there is no nontrivial traveling wave solution. The approaches we use here are Schauder's fixed point theorem with an explicit construction of a pair of upper and lower solutions, the contradictory approach, and the two‐sided Laplace transform.

The analysis of traveling wave solutions and dynamical behavior for the stochastic coupled Maccari's system via Brownian motion

The stochastic coupled Maccari's system (MS) is a kind of important nonlinear partial differential equations to describe fluid flow, plasma physics, nonlinear optics and so on. In this article, the dynamical behavior and some new exact traveling wave solutions of the system are investigated. By means of complex traveling wave transformation, the system is transformed into a nonlinear ordinary differential equation. The dynamical behavior of the system as well as its perturbation case are illustrated by bifurcation theory. And then, some new stochastic traveling wave solutions of the system are extracted based on the theory of polynomial complete discrimination system. To show the effect of stochastic factor on the solutions, their structures under different Brownian motion amplitudes are compared by several sets of graphs. The results obtained in this paper have supplemented the study of the system, and the technique used to exploit the traveling wave solutions are effective.

Atmospheric pressure-induced three-dimensional surface wave propagation in the compressible ocean: Effect of static compression

Under the assumptions of linearized water wave theory, we build a three-dimensional mathematical model that couples atmospheric pressure waves and surface ocean waves, including water compressibility and its static part, to simulate Meteotsunami propagation in the ocean. The solution uses the Laplace–Fourier double transformation technique, emphasizing axisymmetry of the mathematical problem and rigorous treatment of a fairly complicated dispersion relation while using inverse transformations. A novel derivation of the axisymmetric atmospheric pressure front is shown. The impact of water compressibility is shown through a comparative graphical representation against the incompressible case. Faster travel of free-surface waves is observed in the incompressible ocean, followed by the cases with and without static compression of the compressible ocean, respectively. The static compression shifts the phase of the acoustic-gravity modes. The locked wave is hardly influenced by the water compressibility and is entangled with the moving pressure front. The model is validated with the observational pressure data and agrees well with our computed pressure profile. Then, the locked wave profile generated from our model agrees well with the deep-ocean assessment and reporting of tsunami data.

Spatiotemporal resonance in mouse primary visual cortex

Human primary visual cortex (V1) responds more strongly, or resonates, when exposed to ∼10, ∼15-20, and ∼40-50Hz rhythmic flickering light. Full-field flicker also evokes the perception of hallucinatory geometric patterns, which mathematical models explain as standing-wave formations emerging from periodic forcing at resonant frequencies of the simulated neural network. However, empirical evidence for such flicker-induced standing waves in the visual cortex was missing. We recorded cortical responses to flicker in awake mice using high-spatial-resolution widefield imaging in combination with high-temporal-resolution glutamate-sensing fluorescent reporter (iGluSnFR). The temporal frequency tuningcurves in the mouse V1 were similar to those observed in humans, showing a banded structure with multiple resonance peaks (8, 15, and 33Hz). Spatially, all flicker frequencies evoked responses inV1 corresponding to retinotopic stimulus location, but some evoked additional peaks. These flicker-induced cortical patterns displayed standing-wave characteristics and matched linear wave equationsolutions in an area restricted to the visual cortex. Taken together, the interaction of periodic traveling waves with cortical area boundaries leads to spatiotemporal activity patterns that may affect perception.

An approximation method to determine the travel time in total focusing imaging of carbon fiber-reinforced laminates

Abstract It is critical to accurately determine the propagation time in testing objects for ultrasonic array imaging using the Total Focusing Method (TFM). However, it poses challenges for the calculation of wave propagation time in carbon fiber reinforced polymer (CFRP) laminates because of the material anisotropy and inhomogeneity. This paper introduces a novel approach for computing ultrasonic wave travel time to enhance the TFM image of CFRP laminates. This method, termed the layer-by-layer acoustic travel time approximation (L-L TravelTimeAppro), considers the anisotropy within each monolayer and the heterogeneity of CFRP. It approximates the propagation path as straight throughout the material and computes the wave propagation duration utilizing the group velocity in each ply. The application of this method to TFM imaging is referred to as TravelTimeAppro-TFM. Experiments were conducted in a specially designed CFRP laminate. Subsequently, TFM imaging was processed by using propagation time calculated by isotropic, Dijkstra, and L-L TravelTimeAppro methods, respectively. The results indicate that TravelTimeAppro-TFM outperforms isotropic-TFM in terms of imaging amplitude gain with a maximum gain of 4.67 dB. Furthermore, it offers superior computational efficiency compared to Dijkstra-TFM.