Wave Theory Research Articles

Numerical simulation and experimental investigation of the propagation law of plasma pulse shock waves

Abstract Plasma pulse shock wave rock-breaking technology represents a novel approach to rock fracturing. Present research on this subject largely addresses rocks and electrodes, yet often neglects the critical influence of shock waves in the rock-breaking process. Therefore, it is necessary to further study the propagation law of the shock wave and its reflection and transmission. This paper undertakes experimental simulations using the RHT rock model to explore the propagation process of plasma pulse shock waves based on two variables: the medium and the shape of the electrode. Integrated with one-dimensional stress wave theory, the study examines the impact of four specific parameters—dielectric thickness, surrounding rock height, surrounding rock density, and surrounding rock porosity—on the reflection and transmission rates of shock waves. Pressure data collected from experimental platform are utilized to validate the study’s conclusions. The findings indicate that the propagation behaviors of shock waves differ significantly between water and air mediums. The shape of the electrode causes significant differences in the pressure exerted by the shock wave at the same location. Both the thickness of the dielectric and the porosity of the surrounding rock show a positive correlation with the reflection coefficient and a negative correlation with the transmission coefficient, while the density of the surrounding rock exhibits an inverse relationship. The height of the surrounding rock is irrelevant to both reflection and transmission coefficients.

Interplay of Spin Nernst Effect and Entanglement Negativity in Layered Ferrimagnets: A Study via Exact Diagonalization

In this paper, we analyzed the influence of the spin Nernst effect on quantum correlation in a layered ferrimagnetic model. In the study of three-dimensional ferrimagnets, the focus is on materials with a specific arrangement of spins, where the neighboring spins are parallel and the others are antiparallel. The anisotropic nature of these materials means that the interactions between spins depend on their relative orientations in different directions. We analyzed the effect of magnon bands induced by the coupling parameters on entanglement negativity. The influence of the coupling parameters of the topologic phase transition on quantum entanglement is investigated as well. Numerical simulations using the Lanczos algorithm and exact diagonalization for different lattice sizes are compared with the results of spin wave theory.

On the transverse-traceless gauge condition when matter is presented

The transverse-traceless gauge condition is an important concept in the theory of gravitational waves. It is well known that a vacuum is one of the key conditions to guarantee the existence of the transverse-traceless gauge. Although it is thin, the interstellar medium is ubiquitous in the Universe. Therefore, it is important to understand the concept of gravitational waves when matter is presented. Bondi–Metzner–Sachs theory has solved the gauge problem related to gravitational waves. But it does not help with cases when the gravitational wave propagates in matter. This paper discusses possible extensions of the transverse-traceless gauge condition to Minkowski perturbation with matter presented.

Metasurface absorber for millimeter waves: a deep learning-optimized approach for enhancing the isolation of wideband dual-port MIMO antennas

In this communication, the concept of metasurface absorber is utilized to enhance the isolation in the dual port multiple-input multiple-output (MIMO) antenna specially designed for a wideband millimeter wave operation. The frequency of operation of the designed module is 32.5–42.5 GHz with sufficient gain attributes. The designed metasurface array consists of two circular rings on two different layers. The concept of deep learning is utilized to optimize the dimensional configuration of the metasurface to achieve the maximum absorption of electromagnetic waves in the band of interest. The suppression of mutual coupling by double-ring metasurface is analyzed with the help of the wave theory concept. In contrast to previous decoupling methods using metasurfaces, the suggested metasurface is intended to be in the same plane as the array. The findings demonstrate the capability of effectively separating antenna elements in wideband MIMO antenna without compromising the geometrical complexity. Diversity metrics such as envelope correlation coefficient (ECC), mean effective gain (MEG), channel capacity loss (CCL), and total active reflection coefficient (TARC) for the proposed frequency range are also used to evaluate the performance of the constructed MIMO antenna. The wideband characteristics with a compact configuration make the design MIMO module a suitable candidate for mm-wave applications. The congruence between simulation and measurement confirms the validity of the suggested design.

Seismic Fragility Analysis of Offshore Wind Turbines Considering Site-Specific Ground Responses

This study investigated the seismic performance and assessed the seismic fragility of an existing pentapod suction-bucket-supported offshore wind turbine, focusing on the amplification of earthquake ground motions. A simplified suction bucket–soil interaction model with nonlinear spring elements was employed within a finite element framework, linking the suction bucket and soil to hypothetical points on the OWT structures at the mudline. Unlike conventional approaches using bedrock earthquake records, this study utilized free-field surface motions as input, derived from bedrock ground motions through one-dimensional wave theory propagation to estimate soil-layer-induced amplification effects. The validity of the simplified model was confirmed, enabling effective assessment of seismic vulnerability through fragility curves. These curves revealed that the amplification effect increases the vulnerability of the OWT system, raising the probability of exceeding damage limit states such as horizontal displacement of the tower top, tower stress, and horizontal displacement at the mudline during small to moderate earthquakes, while decreasing this likelihood during strong earthquakes. Comparisons between the Full Model and the simplified Spring Model reveal that the simplified model reduces computational time by approximately 75%, with similar seismic response accuracy, making it a valuable tool for rapid seismic assessments. This research contributes to enhancing seismic design practices for suction-bucket-supported offshore wind turbines by employing a minimalist finite element model approach.

Evolution of arbitrary temporal ocean floor motion-induced surface waves over a trench

The scattering of surface water waves generated through an arbitrary temporal motion of a portion of the ocean floor within a trench and from the sudden depth change at the wall of the trench is studied under the assumption of linearized water wave theory and a weakly compressible ocean that includes static oceanic background compression. The Fourier transformation and eigenfunction expansion techniques are deployed to find the surface displacement and pressure profiles with the help of appropriate matching conditions between regions of different depths. The difficulties of numerical computation owing to large oscillations of the displacement potential function around specific frequencies are overcome using adequate non-uniform finer meshing. Apart from the time-domain propagation of tsunami waves away from the origin, standing wave formations are observed within the trench region, supported by significantly large pressure fluctuations in time. These standing waves or the pressure fluctuations are higher when the ocean depth is large. The change in tsunami speed due to sudden depth change is readily visible in the time-domain simulations. Ocean compressibility results in fluctuations in the envelope of the propagating wavefront. Both the two-dimensional and axisymmetric three-dimensional solutions are presented. In comparison, the propagating surface wavefront for the latter case evolves with a sharper slope, which is additionally illustrated by the animation movies.

Exploration of novel solitary waves in presence of higher order polynomial nonlinearity and spatio-temporal dispersion via itô calculus

This study investigates highly stochastic solitary waves inside the structure of nonlinear Schrödinger equation of eighth-order, characterized by heightened polynomial nonlinearity and influenced by multiplicative white noise modeled in the Itô sense. To discern the influence of white noise on the governing model, the bright and dark soliton profiles are generated by using the Sardar sub-equation and G′/(bG′+G+a)-expansion methods. Our approach yields diverse solutions, encompassing singular solitary waves, breather, periodic, and dark–bright solitons. Visual representations through 3D and 2D graphs with relevant parameter values enhance the comprehension of results. The distinctive nature of our methods, untested in this context, results in novel soliton solutions, underscoring their efficacy. This research not only deepens understanding in soliton wave theory but also demonstrates its practical relevance for solving nonlinear complexities in engineering and scientific fields.

Sun Glints and Underwater Caustics in Remote Sensing of Seas and Oceans

The Sun glints that are observed on the water surface have different radiances, shapes, and color shades, depending on the positions of the Sun and the observer, the water surface statement, and the transparency of the water and atmosphere. The texture, radiance, and color characteristics of Sun glints carry information about the state of the water and atmosphere. Therefore, Sun glints play an important role in remote sensing of seas and oceans, being a useful signal in some problems and noise in others. Bright stripes (underwater caustics) on the bottom of the water basin that are caused by the waves are also an indicator of the water surface shape. The application of the wave theory of light is used to study the intensity distribution in the vicinity of the caustic (i. e., where the geometric-optical approximation is inapplicable), which arises when light is refracted on a wavy water surface.A formula, which determines the parameters of the waves from the width of the caustic zone is obtained. The correctness of the method has been verified by experiments carried out in the pool. Also, here we give a brief overview of our investigations related to sun glints and underwater caustics.

Hydrodynamic response of a submerged elliptic disc to surface water waves

The impact of an elliptic disc submerged in water of infinite depth on radiation and scattering phenomena is analyzed employing linear water wave theory. The problem is tackled by reducing it into two-dimensional hypersingular integral equations over the surface of the disc. Utilizing a spectral method, where the hypersingularity is evaluated analytically, we obtain numerical solutions for the integral equations. This study presents numerical findings concerning various hydrodynamic parameters relevant to disc scattering and radiation. Initially it compares numerical outcomes with those of a circular disc, before conducting a comprehensive parametric investigation for the elliptic disc. The primary focus is on investigating how the submerged depth and the geometry of the disc impact physical quantities such as added mass, damping coefficient, surface elevation, differential cross-section, and exciting forces. The results reveal a noticeable change in the pressure field around the disc as it approaches the free surface, leading to resonance. Due to the geometry of the submerged rigid elliptic disc, notable alterations in wave profile are noted in the results for both radiation and scattering problems. Furthermore, the radiation problem results reveal significant variations in the added mass and the damping coefficient for non-circular bodies, particularly with a high ratio of the semi-major axis to the semi-minor axis. Overall, this investigation provides a significant benchmark and valuable insights into potential applications in ocean energy and indicates a new design idea of an elliptic base oscillator alongside the commonly used circular designs.

Mathematical model and its solution for water-altering-gas (WAG) injection process incorporating the effect of miscibility, gravity, viscous fingering and permeability heterogeneity

AbstractThe oil recovery from the water-alternating-gas (WAG) injection process is significantly impacted by gravity, viscous fingering, and the permeability heterogeneity of the reservoir. Therefore, the combined effect of these parameters cannot be neglected in the WAG injection process. This article presents the development of a mathematical model of oil recovery and its solution for the WAG injection process that takes into account the combined effects of miscibility change, viscous fingering, gravity, and permeability heterogeneity in an inclined stratified reservoir. First, the governing equations and fractional flow functions were explained in relation to the effects of gravity, permeability heterogeneity, viscous fingering, and miscibility change in an inclined stratified porous medium. Then, a mathematical model was developed using fractional flow functions and conservation equations for both injected water and solvent. The model was generated in the form of a quasi-linear first-order partial differential equation, which was solved analytically in two dimensions (2-D) utilizing vector calculus. Next, this model was solved analytically by applying wave theory to practical constant pressure boundary conditions, which generate distinct waves at different times to provide pressure and saturation at the displacement front location. The total volumetric flux and breakthrough time are calculated from the analytical solution at various times. The presented analytical solutions can be used to predict different parameters for stratified porous media in a fast and efficient way. Finally, the results of analytical solution validated with high-resolution numerical simulation for a wide range of permeability heterogeneity, which shows excellent agreement for breakthrough time, saturation, and pressure versus displacement location of different waves at different times. This analytical solution will save time and money by offering guidance to engineers for analyzing the saturation and pressure distribution at different times and predicting oil recovery. It will also improve the understanding of the physics underlying the multiphase flow WAG injection process in heterogeneous reservoirs.

Advancing pure ray tracing for the simulation of volume holographic optical elements: innovations in diffractive waveguide-based augmented reality systems

As augmented reality (AR) glasses technology evolves, volume holographic diffractive waveguide designs are increasingly adopted to enhance portability and performance. Traditionally, these systems require separate geometric and wave optics approaches to handle ray propagation and holographic element diffraction, adding significant complexity to the design process. This study presents an innovative pure ray tracing simulation method that integrates geometric and wave optics seamlessly. By incorporating Kogelnik's coupled wave theory, our model accurately predicts the diffraction behavior of volume holographic optical elements (VHOEs) and converts this information into ray data for tracing, enabling exact AR imaging simulations. Applied to the design of volume holographic waveguide AR glasses, human vision simulations, and experiments validated this method's reliability, demonstrating its versatility and effectiveness. This model improves design efficiency and promotes innovative advancements in cross-theoretical optical system design, positioning it as a crucial tool for future AR glasses development.

Dynamic Linguistics

Abstract As opposed to static approaches, the dynamic approach (DA) emphatically distances itself from the routinised use of the concept of language (as in the English, French or Quechua language), the sole reliance on the dichotomised model of language history explained by vertical change (the Stammbaum approach) and horizontal change (the contact approach), and the eccentrification of creole language emergence. The notion of a DA to language surfaced at several points in time, reaching two climaxes, namely the advent of Wave Theory (Schmidt 1872) and the incorporation of variation in the machinery of a modular approach to grammar (Bailey 1973; Bickerton 1971; Seuren 1982). In a nutshell, the DA advocates for the polylectal nature of linguistic competence (in the transformationalist/generative semantic sense), the fluid nature of language variation over time and space, as well as for the notions of functionality and the Principle of Semantic Transparency as guiding forces throughout the history of languoids.1 In this article, the basic tenets of this approach are outlined, embedded in a historical frame within the advent of Generative Semantics and variation-centred approaches to language. These tenets are illustrated with case studies from languoids used in Northwestern Amazonia, Balgo in Western Australia, as well as Senegambia in West Africa.

Kernel polynomial method for linear spin wave theory

Calculating dynamical spin correlations is essential for matching model magnetic exchange Hamiltonians to momentum-resolved spectroscopic measurements. A major numerical bottleneck is the diagonalization of the dynamical matrix, especially in systems with large magnetic unit cells, such as those with incommensurate magnetic structures or quenched disorder. In this paper, we demonstrate an efficient scheme based on the kernel polynomial method for calculating dynamical correlations of relevance to inelastic neutron scattering experiments. This method reduces the scaling of numerical cost from cubic to linear in the magnetic unit cell size.

Axisymmetric forced vibration of the hydro-elastic system consisting of a pre-strained highly elastic plate and compressible viscous fluid

The paper studies the axisymmetric harmonic forced vibration of the hydro-elastic system composed of an initially strained plate made of highly elastic material, a compressible viscous fluid layer, and a rigid wall restricting the fluid flow. It is assumed that the plate is in contact with the fluid layer after the appearance of the finite axisymmetric homogeneous initial strains within which are caused by the stretching of the plate by uniformly distributed radial forces acting at infinity. Also, it is assumed that after this contact, the point located time-harmonic force begins to act on the free-face plane of the plate. Within this framework, the steady-state forced vibration of the hydro-elastic system under consideration is studied by employing the eq. and relations of the so-called three-dimensional linearized theory of elastic waves in bodies with finite initial strains to describe the motion of the plate and by employing the linearized Navier-Stokes eq. to describe the flow of the fluid. The corresponding mathematical problem is solved by employing the Hankel integral transform method, and the originals of the sought values are found numerically by employing the algorithms and PC programs composed by the authors. Numerical results are presented and discussed on the frequency response of the normal stress acting on the interface plane between the plate and fluid layer. According to these discussions, corresponding conclusions on the influence of the problem parameters on the frequency response of the interface stress are made. In particular, it is established that in the axisymmetric forced vibration case, the resonance-type phenomenon appears due to the fluid viscosity.

Modulation instability, and dynamical behavior of solitary wave solution of time M- fractional clannish random Walker's Parabolic equation via two analytic techniques

The theory of solitary waves or solitons is crucial in nonlinear models due to their ability to propagate without distortion, making them essential in fields like physics, biology, engineering, and mathematics. This study explores solitary waves in the time fractional Clannish Random Walker's Parabolic equation using two effective approaches: polynomial expansion technique (PET) and unified technique (UT). This model is particularly significant in areas such as ecology, sociology, and urban planning, where understanding individual interactions within spatial contexts is vital. By solving this equation, we gain insights into group formation and navigation, enhancing our comprehension of emergent patterns and system design. The application of PET and UT allows us to derive various solutions, including exponential, hyperbolic, and trigonometric forms. Utilizing the Maple programming language, we visualize novel phenomena, such as kink waves, anti-kink waves, and periodic lump waves. This research demonstrates that the proposed methodologies can yield precise soliton solutions, contributing valuable insights to nonlinear science and engineering applications.

Evolving visitors/tourists’ demands, preference and future expectations, related to 7PS sustainability during and after the pandemic through the X.0 wave/tomorrow age theory (when X.0=5.0)

PurposeThis study explores evolving tourist preferences post-COVID-19, focusing on the growing demand for sustainable tourism. Using the X.0 wave/tomorrow age theory when X.0 = 5.0, it identifies transformative trends influencing the tourism industry's adaptation to new sustainability expectations.Design/methodology/approachA mixed-methods approach combines extensive surveys and interviews with diverse tourist profiles to examine behaviors and preferences. The seven pillars of sustainability (7PS) model frames the analysis.FindingsTourism is shifting toward sustainable practices, emphasizing cultural differences, environmental stewardship, social engagement, economic resilience, technological infrastructure, educational methods and political supports. The integration of X.0 wave theory with SME 5.0 concepts highlights the importance of responsible tourism aligned with evolving tourist expectations.Originality/valueThis study pioneers the application of the X.0 wave/tomorrow age theory to tourism, offering a novel framework for sustainable practices. It provides insights for making tourism resilient, ecologically sound and socially responsible, meeting post-pandemic visitor demands.

Velocity field measurements under Very Large Floating Structures interacting with surface waves

Increasing utilization of ocean space and a global push for renewable energy solutions has spurred interest in wave behavior around Very Large Floating Structures, like floating photovoltaic (PV) systems. Flexible PV modules may be more suitable for the varying wave conditions found in offshore environments. However, while viscoelastic models are commonly used for wave prediction, they show notable discrepancies with experiments, likely due to untested assumptions of inviscid flow. This experimental study aims to fill that gap by investigating both the wave characteristics and velocity fields underneath flexible and rigid structures using simultaneous Particle Image Velocimetry (PIV) and wave elevation measurements. Wave attenuation is observed for short wavelengths over the flexible structure length. The 2nd order Stokes wave theory provides a good approximation of the wave-induced horizontal velocity profiles under the flexible structure but underestimates the velocities under the rigid one which further lacks the typical exponential decay with water depth. The presence of a wave boundary layer is showcased and compared to an adaptation of the Stokes 2nd problem.

An analytical method for effective dynamic properties of SH wave in piezoelectric nanocomposites with coated nano-fibers

In this paper, a generalized self-consistent model of nanocoated fiber composite material considering interface effect is established by using the Gurtin-Murdoch surface/interface elasticity theory, elastic wave theory and micromechanics methods, and the propagation of anti-plane shear electroelastic wave in infinite nano-piezoelectric material is analyzed. Based on the wave function expansion method, the displacement potential and electric potential functions of each phase medium in composite materials are described, and the function expressions of displacement, electric potential, stress and electric displacement are obtained. The dynamic effective shear modulus of piezoelectric reinforced composites is obtained by satisfying the boundary conditions of the electroelastic coupling surface/interface theory and the multiple scattering formulas. The effects of coating thickness, coating material parameters, interfacial shear modulus and piezoelectric properties on dynamic effective shear modulus at different incident frequencies are discussed. The results show that the effective shear modulus fluctuates obviously with the increase of frequency. The effective shear modulus increases with the increase of interfacial shear modulus and piezoelectric constant, and is more sensitive to the change of interfacial shear modulus. The effective shear modulus is more affected by the interface effect on the outer surface of the coating than the inner interface, and the effect of interface mechanical properties decreases with the increase of coating stiffness. The larger the parameter of the coating material, the larger the dynamic effective shear modulus and the smaller the influence of the interface effect.

An integrated analytical–numerical framework for studying nonlinear PDEs: The GBF case study

In this study, we investigate the complex dynamics of the [Formula: see text]-dimensional generalized Burgers–Fisher (GBF) model, a nonlinear partial differential equation that encapsulates the interplay between wave propagation, diffusion, and reaction processes. Our work employs a combination of the modified Khater (MKhat) method, the unified (UF) method, and He’s variational iteration (HVI) scheme to derive and validate analytical and numerical solutions. We present a comprehensive analysis of solitary wave, shock wave, and diffusion-driven phenomena within the GBF framework. The novelty of our study lies in the integration of these methods to provide deeper insights into the model’s physical implications, specifically highlighting the interactions between nonlinear advection, diffusion, and reaction mechanisms. This approach not only enhances the accuracy and applicability of the derived solutions, but also contributes to the advancement of nonlinear wave theory and related interdisciplinary fields.

Investigating the Dynamics of a Unidirectional Wave Model: Soliton Solutions, Bifurcation, and Chaos Analysis

The current work investigates a recently introduced unidirectional wave model, applicable in science and engineering to understand complex systems and phenomena. This investigation has two primary aims. First, it employs a novel modified Sardar sub-equation method, not yet explored in the literature, to derive new solutions for the governing model. Second, it analyzes the complex dynamical structure of the governing model using bifurcation, chaos, and sensitivity analyses. To provide a more accurate depiction of the underlying dynamics, they use quantum mechanics to explain the intricate behavior of the system. To illustrate the physical behavior of the obtained solutions, 2D and 3D plots, along with a phase plane analysis, are presented using appropriate parameter values. These results validate the effectiveness of the employed method, providing thorough and consistent solutions with significant computational efficiency. The investigated soliton solutions will be valuable in understanding complex physical structures in various scientific fields, including ferromagnetic dynamics, nonlinear optics, soliton wave theory, and fiber optics. This approach proves highly effective in handling the complexities inherent in engineering and mathematical problems, especially those involving fractional-order systems.