Wave Theory Research Articles

Introduction to Laura Marcus, Rhythm: The Measure of the Modern

ABSTRACT This Introduction to Laura Marcus's final monumental but unfinished work describes her wholly new understanding of the central importance of rhythm across the arts and sciences in the nineteenth and twentieth centuries. The turn to rhythm was formative in many fields and comprehended poetry, music, dance, sculpture, painting, photography, film, gymnastics, physics, education, psychology, physiology, thinking about race, class and gender, the past and the future, tradition and change. From wave theory to orthography rhythm shaped creative thought. We summarise the existing six chapters out of what were to be eight. 1. The discourses of wave theory. 2. Rhythm in modernity – aesthetics and science. 3. Dance theories of Steiner and Dalcroze – social and physiological. 4. Rhythm theory in modernist avant-garde periodicals. 5. The Bloomsbury Group, Frye and Woolf. 6. The cultural and political turn to native American rhythm.

The Rhetoric of Radicalism: The Anti-Colonial Inspiration Behind Osama bin Laden’s Ideology

ABSTRACT A current debate in the terrorism studies literature regards the continued value of Rapoport’s famous “wave theory” of modern terrorism and a new alternative known as “strain theory.” Wave theory assumes that international terrorism has occurred in distinct, temporal cycles while strain theory accounts for the learning behavior that occurs between waves by way of tactical adaption and therefore deemphasizes the distinctiveness of temporal waves. The present analysis contributes to the debate by analyzing Osama bin Laden’s ideology and justifications for violence, which are shown to owe a great debt to the anti-colonial rhetorical framework that inspired earlier forms of terrorism. By establishing a rhetorical connection between the works of Frantz Fanon, one of the most important figures of the anti-colonial period, and bin Laden’s written and spoken statements, the article challenges the historicization of modern terrorism as one that has unfolded in distinct waves, makes a cogent defense of strain theory, and contends that advocates of the new approach should extend their analysis beyond strategic and tactical choices to learned ideological and normative justifications for violence as well.

The stability analysis based on viscous theory of Faraday waves in Hele–Shaw cells

The linear instability of Faraday waves in Hele–Shaw cells is investigated with consideration of the viscosity of fluids after gap-averaging the governing equations due to the damping from two lateral walls and the dynamic behavior of contact angle. A new hydrodynamic model is thus derived and solved semi-analytically. The contribution of viscosity to critical acceleration amplitude is slight compared to other factors associated with dissipation, and the potential flow theory is sufficient to describe onset based on the present study, but the rotational component of velocity can change the timing of onset largely, which paradoxically comes from the viscosity. The model degenerates into a novel damped Mathieu equation if the viscosity is dropped with two damping terms referring to the gap-averaged damping and dissipation from dynamic contact angle, respectively. The former increases when the gap size decreases, and the latter grows as frequency rises. When it comes to the dispersion relation of Faraday waves, an unusual detuning emerges due to the imaginary part of the gap-averaged damping.

Numerical research on internal solitary waves in stratified fluid

Internal solitary waves are a common nonlinear large amplitude internal wave in nature, which can cause strong divergence and sudden strong currents in seawater during propagation, thus having great destructive effects on marine structures. The paper focuses on numerical wave generation based on three types of internal solitary wave theories. The waves are numerical simulated by RANS method in the paper. The numerical results of internal solitary wave theories are compared and analyzed. It shows that under the same numerical water tank scale and calculation conditions, the mKdV theory can obtain the largest wave amplitude, followed by the eKdV theory and the KdV theory. In addition, background currents will accelerate the propagation speed of internal solitary waves and increase their amplitude slightly.

Bridging the gap between annular and can-annular acoustic spectra.

In the literature on thermoacoustic instabilities in combustors, a distinction is typically made between annular and can-annular systems because these are the most common gas turbine architectures. In reality, however, annular combustors typically feature discretely symmetric elements, such as burner tubes, and can-annular combustors feature an azimuthally symmetric plenum at the turbine inlet. To better understand the general case in between the annular and can-annular extremes, we analyze the acoustic spectrum of an idealized can-annular combustion chamber with variable geometry, where the length of the axial gap distance beyond the ends of the cans-hence, the coupling strength-may be adjusted. For small gap sizes, the geometry approaches a set of isolated combustor cans, whereas for large gap sizes, it approaches that of pure annular systems. We present two theoretical models based on Bloch wave theory and validate them against finite-element simulations of the Helmholtz equation. We demonstrate that the azimuthal modes transform into the eigenmodes of an annular chamber as the gap is fully opened, and we show that below a certain frequency, all the modes in between the can-annular and annular limits can be classified by their axial and azimuthal mode orders.

Dynamic response of multi-unit floating offshore wind turbines to wave, current, and wind loads

Motion of a multi-unit wind-tracing floating offshore wind turbine (FOWT) to combined wave–current and wind is obtained in the frequency-domain. The linear diffraction wave theory with a Green function for small current speeds and the blade-element momentum method are used for the hydrodynamic and aerodynamic analysis, respectively. A finite-element method is coupled with the hydrodynamic and aerodynamic equations to obtain the elastic responses of the FOWT to the environmental loads. The wind-tracing FOWT consists of three 5 MW wind turbines installed at the corners of an equilateral triangular platform. The platform is connected to the seabed through a turret-bearing mooring system, allowing the structure to rotate and face the dominant wind direction; hence, the multi-unit FOWT is called the wind-tracing FOWT. In this study, rigid-body responses of the wind-tracing FOWT to waves and wind are compared with those to combined wave, current, and wind loads for several current speeds and various wave heading angles. For a chosen current speed and wave heading angle, hydro- and aeroelastic responses of the wind-tracing FOWT to combined waves, current, and wind are obtained and compared with those of the rigid structure. Discussion is provided on the effect of the wave–current interaction on the motion and elastic responses of the wind-tracing FOWT. The numerical results show that under the rated wind speed, the motion of the wind-tracing FOWT is mainly governed by the wave-induced hydrodynamic forces and moments and the presence of current results in larger elastic motion of the FOWT to the environmental loads.

Teaching acoustic and electromagnetic waves

Students have observational experience with waves by speaking and hearing, seeing, and feeling but their use of mathematics may be delayed until introductory physics at middle school, high school, and/or college. Students following a university physics or engineering bachelor’s degree are usually required to take a course on electromagnetic wave theory because of the foundational science and/or applications such as communications and observation. Regrettably, it is common that a mathematical description of various wave propagations may be acquired but without a thorough understanding of the underlying physics – especially in electromagnetics. Thus, we have tried to develop an introductory graduate level course that teaches electromagnetics and optic waves and its applications on the foundation of first understanding acoustics. This serves as a preparation for research or vocation. Topics include traveling waves, standing waves, wave impedance, radiation patterns, interference, interferometry, sonar and radar, imaging, waveguides in more. Examples of introducing the mathematics of solution first and then derivations of wave equation is presented. The goal is that mathematics should be a useful language to communicate physical information and that acoustic demonstrations should reinforce learning in multiple physical modalities.

Defect Detection in Grouting Sleeve Grouting Material by Piezoelectric Wave Method

The construction defects in grouting sleeves can jeopardize the safety of precast reinforced concrete structures. Thus, efficient and accurate defect detection is critical in engineering construction. In this paper, a defect detection method based on piezoelectric wave theory was proposed. Two piezoelectric ceramics were arranged within the grouting sleeve. One piezoelectric ceramic was affixed on the top of the steel bar, while the other was embedded in the grouting material, serving as the driver and sensor, respectively. The compactness defects, air cavity defects, steel anchoring defects, and water–binder ratio defects were set in the grouting sleeves, and the trends in time domain signals and signal evaluation indicators based on the wavelet packet total energy value (WPTEV) of different specimens were investigated. Based on the WPTEV, the evaluation index (EI) was proposed. In addition, the effect of the grouting material’s age on the piezoelectric wave signal was verified. Furthermore, the influence of grouting material defects on signals was simulated in ABAQUS, and the time domain signals and wavelet packet energy of sensor signals for specimens with varying defect dimensions were evaluated. The results showed that: (1) The defects in the grouting materials reduced the stress waves propagated through the grouting materials, resulting in a decrease in attenuation and an increasing trend in the signal; (2) The peak-to-peak values of piezoelectric ceramic sensors and the WPTEV of the signal increased with the degree of defects, and the WPTEV was more pronounced. For specimen M68, the WPTEV was 3.3 times that of the healthy specimen, however, the peak-to-peak value was only 2.3 times that of the healthy specimen; (3) The degree of defects was accurately determined by the defect evaluation index (EI) based on the WPTEV; (4) The signal was significantly attenuated with the increase in the age of the grouting material, especially in the first three days, and finally the signal achieved a stable value; (5) The numerical simulation indicated that the defects in the length and thickness of the air cavity in the grouting material were efficiently detected by the proposed piezoelectric arrangement in this study.

Love waves propagation in layered viscoelastic waveguides characterized by a Zener model

This paper describes a theory of surface Love waves propagating in lossy waveguides consisting of a viscoelastic layer deposited on a semi-infinite elastic substrate. The Zener model to describe the viscoelastic behavior of a medium is used. This simple model captures both the relaxation and retardation. A new form of the unsteady momentum equation for viscoelastic waveguides has been established. By using appropriate boundary conditions, an analytical expression for the complex dispersion equation of Love waves has been deduced. The influence of the loss factor and the ratio of shear moduli of the surface layer on the dispersion curves of Love waves velocity and attenuation is analyzed numerically. The numerical solutions show the dependence of the velocity change and the wave attenuation in terms of the loss factor and the ratio of shear moduli. The obtained results show that the change in the ratio of shear moduli can represent a hardening or softening effect of the surface layer. These effects depend on the loss factor value of the surface layer. In addition, these results are novel, fundamental and can be applied in the characterization of the viscoelastic properties of soft biomaterials and tissues, in nondestructive testing of materials, in geophysics and seismology. Thus, the obtained complex dispersion equation can be very useful to interpret the experimental measurements of Love waves properties in viscoelastic waveguides.

Periodicity, Elliott waves, and fractals in the NFT market

Non-fungible tokens (NFTs) are unique digital assets that exist on a blockchain and have provided new revenue streams for creators. This research investigates NFT market inefficiencies to identify claimed cyclic behavior and cryptocurrency influences on NFT prices. The research found that while linear models are not useful in modeling NFT price series, models that extract periodic behavior can provide explanations and predictions of price behavior. The investigation of autocycles in cryptocurrency and NFT markets did not support the existence of Elliott Wave behavior in any of these blockchain enabled assets. Rather NFT price behavior is strongly tied to the underlying asset and its community of fans. These fans commit to periodic bouts of idiosyncratic trading which cools for a while, and then restarts. The research found no evidence supporting whole market effects across the full price series of individual NFTs. The research strongly supports prior findings that the offsetting movements significantly influence NFT prices and trading volume in Bitcoin and Ether. The research found NFT markets exhibit characteristics resembling a social media platform rather than more traditional asset markets like stock exchanges. It found that traditional linear econometric models cannot predict or explain NFT price series, only that NFT price and volume were weakly correlated. Fractal models consistent with Elliott wave theory do explain some of NFT price behavior, but are not consistent or stable over time. This research confirmed prior research findings that Bitcoin and Ether price movements are correlated with general NFT price and volume series in periods of between 24 and 48 h, with significant numbers of trades into and out of cryptocurrencies at 2 and 8 h.

Experimental study on surface wave interaction with submerged tensioned barriers using IoT image processing

The present study investigated experimentally the dynamic interactions between surface waves and submerged vertical tensioned barriers with full and partial penetrations. The range of tension for the barrier was set within the flexible membrane regime in the experiments which measurements have not been reported in the literature so far. In addition, an extensive Internet of Things (IoT) system with five GoPro cameras was developed for the measurements to quantify both the surface wave transformation as well as dynamic response of the barrier. The cameras were synchronized through the IoT system to cover the entire wave flume, and the recorded videos were converted to spatial and temporal data using image processing techniques. The experimental results were found to agree with the analytical predictions based on the linear wave theory reasonably well. In particular, the measured reduction in the tensioning effect on the wave transmission and reflection with decreased barrier length was in close argument with the predictions. Similar good agreement was also observed for the dynamic response of the tensioned barrier during the wave interaction. However, additional energy loss was noted in the experiments possibly due to energy dissipation at the boundary ends of the experimental barrier and wave-induced flow separation with partial penetration which are not considered in the analytical analysis.

Numerical study on local scour characteristics around submarine pipelines in the Yellow River Delta silty sandy soil under waves and currents

AbstractDue to their high reliability and cost‐efficiency, submarine pipelines are widely used in offshore oil and gas resource engineering. Due to the interaction of waves, currents, seabed, and pipeline structures, the soil around submarine pipelines is prone to local scour, severely affecting their operational safety. With the Yellow River Delta as the research area and based on the renormalized group (RNG) k‐ε turbulence model and Stokes fifth‐order wave theory, this study solves the Navier–Stokes (N–S) equation using the finite difference method. The volume of fluid (VOF) method is used to describe the fluid‐free surface, and a three‐dimensional numerical model of currents and waves–submarine pipeline–silty sandy seabed is established. The rationality of the numerical model is verified using a self‐built waveflow flume. On this basis, in this study, the local scour development and characteristics of submarine pipelines in the Yellow River Delta silty sandy seabed in the prototype environment are explored and the influence of the presence of pipelines on hydrodynamic features such as surrounding flow field, shear stress, and turbulence intensity is analyzed. The results indicate that (1) local scour around submarine pipelines can be divided into three stages: rapid scour, slow scour, and stable scour. The maximum scour depth occurs directly below the pipeline, and the shape of the scour pits is asymmetric. (2) As the water depth decreases and the pipeline suspension height increases, the scour becomes more intense. (3) When currents go through a pipeline, a clear stagnation point is formed in front of the pipeline, and the flow velocity is positively correlated with the depth of scour. This study can provide a valuable reference for the protection of submarine pipelines in this area.

Toward the response of coastal bridges with updated RC shear key properties under the multi-hazard action of earthquakes and tsunamis

Coastal bridges are significantly endangered by the combined effects of earthquakes and tsunamis. The accurate prediction of bridge responses in such scenarios is vital to ensure their security. Reinforced concrete (RC) shear keys, which serve as sacrificial bridge components, can effectively mitigate inertial loads from superstructures, and thus safeguard pier columns. Previous research has shown that their mechanical properties can differ considerably under cyclic and persistent impacts. Therefore, this study focused on the seismic-tsunami responses of a simple-support coastal bridge equipped with RC shear keys. A horizontal failure shear key was incorporated because of its distinct performance observed previously. The OpenSees platform was employed to conduct the numerical work, with an updated material framework developed to modify the shear key behavior before the tsunami analysis. Natural ground motion records were selected to demonstrate the dynamic analysis, and the records were scaled using spectral accelerations (Sa) to account for the various damage states of shear keys resulting from superstructure collisions. The tsunami wave impact was modeled using the second-order solitary wave theory, with different wave conditions employed to consider the immersed conditions. The calculation results were compared for the bridges with and without updated shear key properties, showing distinctions in terms of time-history and maximum responses at certain seismic levels. Based on the analysis results, this study is expected to provide a reliable estimation of the seismic-tsunami responses of coastal bridges.

Fluid Oscillation‐Driven Bi‐Directional Air Turbine Triboelectric Nanogenerator for Ocean Wave Energy Harvesting

AbstractOcean wave energy is one of the important renewable energy sources. However, random, low‐frequency, and micro‐amplitude characteristics of ocean waves make it difficult for traditional electromagnetic generators to collect wave energy efficiently. The emergence of triboelectric nanogenerator (TENG) provides an extremely effective technical means for the collection of low‐frequency and micro‐amplitude wave energy. In this work, a non‐contact turntable‐structured oscillating water column TENG (OWC‐TENG) is designed by combining an OWC wave energy conversion mechanism with a TENG for the first time. The OWC is optimized through simulation experiments according to the principles of ship hydrostatics and wave theory. The output performances of the OWC‐TENGs with different structural parameters under different water wave excitation conditions are then tested. The TENG delivers a maximum output current of 55.45 µA and an output power of 5.28 mW, which corresponds to a power density of 114.8 W m−3, enabling a stable power supply for small sensors at sea. This work provides a new solution to the efficient collection of low‐frequency micro‐amplitude ocean wave energy for powering various offshore equipments, presenting broad application prospects in ocean blue energy development and offshore Internet of Things.

Towards a locally constructed multi-element ultrasound imaging transducer for resource poor environments

This paper investigates techniques and materials for making a multi-element ultrasound imaging transducer with craft-based techniques available in resource poor environments. The transducer housing can be conveniently divided into three parts: the body supporting the piezoelectric (PZT) elements and other components; the matching layer between the PZT elements and the human body; and the backing layer behind the PZT elements. Low-cost 3D printing systems based on photopolymers were found to be suitable for manufacturing the body. Finite Element Modelling (FEM) showed that the material characteristics of the backing layer and the thickness of the matching layer were much less critical than predicted by ultrasound plane wave theory and transmission line theory, respectively. The backing and matching layers are normally made from epoxy-tungsten composites that are pourable in the uncured state. However, the composite required for the backing layer was putty-like when uncured. When the tungsten was allowed to settle under gravity during curing, a 20 % by volume uncured tungsten-epoxy composite gave a 30 % by volume concentration of tungsten at the bottom when cured at 20–30 °C. These findings, when coupled with the findings from the FEM modelling, suggests that constructing a multi-element ultrasound imaging transducer using craft-based techniques is feasible.

How Fast are Elastic Domino Waves?

The paper is concerned with the problem of toppling propagation velocity in elastic, domino-like mechanical systems. We build on the work of Efthimiou and Johnson, who developed the theory of perfectly elastic collisions of thin rigid dominoes on a frictional foundation. This theory has been criticised for the lack of correspondence with the experimental observations, in particular, prediction of infinite propagation velocity for zero spacing between dominoes, as well as the inability to represent the collective nature of collisions in real domino systems. In our work we consider a more realistic scenario of dominoes of finite stiffness and obtain a theory of fast elastic domino waves, taking into account a limit velocity of the perturbation propagation in the system of dominoes. Moreover, finite collision time allows to extract dynamic quantities of collisions and establish upper and lower borders for domino separations where the theory could still be applied. Our discrete element simulations support our theoretical findings and shed light on the nature of collective interactions in the nearly-elastic domino chains.Graphical abstract

Influence of water coupling coefficient on the blasting effect of red sandstone specimens

This study investigates the impact of different water coupling coefficients on the blasting effect of red sandstone. The analysis is based on the theories of detonation wave and elastic wave, focusing on the variation in wall pressure of the blasting holes. Using DDNP explosive as the explosive load, blasting tests were conducted on red sandstone specimens with four different water coupling coefficients: 1.20, 1.33, 1.50, and 2.00. The study examines the morphologies of the rock specimens after blasting under these different water coupling coefficients. Additionally, the fractal dimensions of the surface cracks resulting from the blasting were calculated to provide a quantitative evaluation of the extent of rock damage. CT scanning and 3D reconstruction were performed on the post-blasting specimens to visually depict the extent of damage and fractures within the rock. Additionally, the volume fractal dimension and damage degree of the post-blasting specimens are calculated. The findings are then combined with numerical simulation to facilitate auxiliary analysis. The results demonstrate that an increase in the water coupling coefficient leads to a reduction in the peak pressure on the hole wall and the crushing zone, enabling more of the explosion energy to be utilized for crack propagation following the explosion. The specimens exhibited distinct failure patterns, resulting in corresponding changes in fractal dimensions. The simulated pore wall pressure–time curve validated the derived theoretical results, whereas the stress cloud map and explosion energy-time curve demonstrated the buffering effect of the water medium. As the water coupling coefficient increases, the buffering effect of the water medium becomes increasingly prominent.

The effect of loss/gain and Hamiltonian perturbations of the Ablowitz—Ladik lattice on the recurrence of periodic anomalous waves

Using the finite gap method, in this paper we extend the recently developed perturbation theory for anomalous waves (AWs) of the periodic nonlinear Schrödinger (NLS) type equations to lattice equations, using as basic model the Ablowitz–Ladik (AL) lattices, integrable discretizations of the focusing and defocusing NLS equations. We study the effect of physically relevant perturbations of the AL equations, like linear loss, gain, and/or Hamiltonian corrections, on the AW recurrence, in the simplest case of one unstable mode. We show that these small perturbations induce O(1) effects on the periodic AW dynamics, generating three distinguished asymptotic patterns. Since dissipation and higher order Hamiltonian corrections can hardly be avoided in natural phenomena involving AWs, we expect that the asymptotic states described analytically in this paper will play a basic role in the theory of periodic AWs in natural phenomena described by discrete systems. The quantitative agreement between the analytic formulas of this paper and numerical experiments is excellent.

Generation and Evolution of Internal Solitary Waves in a Coastal Plain Estuary

Abstract Large-amplitude internal solitary waves were recently observed in a coastal plain estuary and were hypothesized to evolve from an internal lee wave generated at the channel–shoal interface. To test this mechanism, a 3D nonhydrostatic model with nested domains and adaptive grids was used to investigate the generation of the internal solitary waves and their subsequent nonlinear evolution. A complex sequence of wave propagation and transformation was documented and interpreted using the nonlinear wave theory based on the Korteweg–de Vries equation. During the ebb tide a mode-2 internal lee wave is generated by the interaction between lateral flows and channel–shoal topography. This mode-2 lee wave subsequently propagates onto the shallow shoal and transforms into a mode-1 wave of elevation as strong mixing on the flood tide erases stratification in the bottom boundary layer and the lower branch of the mode-2 wave. The mode-1 wave of elevation evolves into an internal solitary wave due to nonlinear steepening and spatial changes in the wave phase speed. As the solitary wave of elevation continues to propagate over the shoaling bottom, the leading edge moves ahead as a rarefaction wave while the trailing edge steepens and disintegrates into a train of rank-ordered internal solitary waves, due to the combined effects of shoaling and dispersion. Strong turbulence in the bottom boundary layer dissipates wave energy and causes the eventual destruction of the solitary waves. In the meantime, the internal solitary waves can generate elevated shear and dissipation rate in local regions. Significance Statement In the coastal ocean nonlinear internal solitary waves are widely recognized to play an important role in generating turbulent mixing, modulating short-term variability of nearshore ecosystem, and transporting sediment and biochemical materials. However, their effects on shallow and stratified estuaries are poorly known and have been rarely studied. The nonhydrostatic model simulations presented in this paper shed new light into the generation, propagation, and transformation of the internal solitary waves in a coastal plain estuary.

Predicting the Arrival Time of an Interplanetary Shock Based on DSRT Spectrum Observations for the Corresponding Type II Radio Burst and a Blast Wave Theory

Since fast head-on coronal mass ejections and their associated shocks represent potential hazards to the space environment of the Earth and even other planets, forecasting the arrival time of the corresponding interplanetary shock is a priority in space weather research and prediction. Based on the radio spectrum observations of the 16-element array of the Daocheng Solar Radio Telescope (DSRT), the flagship instrument of the Meridian Project of China, during its construction, this study determines the initial shock speed of a type II solar radio burst on 2022 April 17 from its drifting speed in the spectrum. Assuming that the shock travels at a steady speed during the piston-driven phase (determined from the X-ray flux of the associated flare) and then propagates through interplanetary space as a blast wave, we estimate the propagation and arrival time of the corresponding shock at the orbit of the Solar Terrestrial Relations Observatory-A (STEREO-A). The prediction shows that the shock will reach STEREO-A at 14:31:57 UT on 2022 April 19. The STEREO-A satellite detected an interplanetary shock at 13:52:12 UT on the same day. The discrepancy between the predicted and observed arrival time of the shock is only 0.66 hr. The purpose of this paper is to establish a general method for predicting the shock’s propagation and arrival time from this example, which will be utilized to predict more events in the future based on the observations of ground-based solar radio spectrometers or telescopes like DSRT.