Second-order Wave Research Articles

Vector bosons in the rotating frame of negative curvature wormholes

In this study, we investigate the relativistic dynamics of vector bosons within the context of rotating frames of negative curvature wormholes. We seek exact solutions for the fully-covariant vector boson equation, derived as an excited state of zitterbewegung. This equation encompasses a symmetric rank-two spinor, enabling the derivation of a non-perturbative second-order wave equation for the system under consideration. Our findings present exact results in two distinct scenarios. Notably, we demonstrate the adaptability of our results to massless vector bosons without compromising generality. The evolution of this system is shown to correlate with the angular frequency of the uniformly rotating reference frame and the curvature radius of the wormholes. Moreover, our results highlight that the interplay between the spin of the vector boson and the angular frequency of the rotating frame can give rise to real oscillation modes, particularly evident in excited states for massless vector bosons. Intriguingly, we note that the energy spectra obtained remain the same whether the wormhole is of hyperbolic or elliptic nature.

Bragg Resonance of Surface Gravity Waves by Surface-Piercing Vertical Multi-Plate Breakwaters

Abstract The interaction between surface gravity waves and surface-piercing vertical multi-plate breakwaters in finite water depth is investigated under the assumption of potential flow theory. The time-domain desingularized boundary integral equation method (DBIEM) is adopted to solve the boundary value problem. A decomposition method based on the superposition principle is used to obtain reflected waves. The effect of the vertical plates as a floating breakwater by making full use of Bragg resonance is analyzed. Initially, the waveforms calculated without breakwaters are compared with second-order Stokes regular wave to obtain the appropriate desingularization distance. Then, the interaction of surface gravity waves with the breakwaters with the single plate, double, and triple plates are analyzed. The transmission and reflection coefficients of the breakwater with the single plate are verified with the analytical solutions of previous literature. The transmission and reflection coefficients of the breakwaters with double and triple plates are verified with experimental results. Finally, the transmission and reflection coefficients of surface-piercing vertical multi-plate breakwaters with different plate numbers and drafts are also calculated. The occurring condition of Bragg resonance and its values affected by the plate number and the draft are analyzed. The present results are reference values for the optimal design of vertical plates as a floating breakwater for offshore and coastal engineering applications by fully using Bragg resonance.

Volumes of second-order rogue waves of the infinite NLS hierarchy

Volumes of second-order rogue waves of the infinite NLS hierarchy

A unified higher-order unsplit CFS-PML technique for solving second-order seismic equations using discontinuous Galerkin method

The absorbing boundary conditions play a key role in numerical simulations. The complex frequency-shifted perfectly matched layer (CFS-PML), one of the absorbing boundary conditions, has attracted widespread attention because it can efficiently attenuate near-grazing incident waves and evanescent waves. In practical application, the distinct boundary reflections still exist using the CFS-PML in a thin PML region. To further enhance the absorbing performance, we have developed a novel unified high-order unsplit CFS-PML technique. The high-order CFS-PML combined with the discontinuous Galerkin (DG) method is applied to solve the second-order seismic wave equation on an unstructured mesh. In this work, we establish a unified framework for high-order unsplit CFS-PML formulations. The classical CFS-PML is the first-order form of our proposed unsplit high-order approach. By using auxiliary variables and auxiliary ordinary differential equations (AODEs), a higher-order CFS-PML formulation can be reduced to a first-order CFS-PML formula. For an Nth-order AODE CFS-PML, it will lead to (2N-1) additional variables and (2N-1) auxiliary differential equations. Taking second- and third-order as examples, we have derived the high-order unsplit AODE CFS-PML expressions in detail. The DG method can effectively deal with complex geological structures, such as caves, cracks, faults, etc., which yields more accurate numerical solutions. We incorporate the high-order unsplit AODE CFS-PML technique into the DG method to approximate seismic wave equations. Their strengths are combined to calculate the propagating wavefield in more complex finite models and obtain better results. In addition, the stability conditions of the second- and third-order CFS-PMLs are provided. We perform the high-order unsplit CFS-PML implementation for seismic wave modeling in several models. The isotropic and anisotropic examples prove that the high-order unsplit CFS-PML enjoys better absorbing performance than the classical CFS-PML. The numerical result for the graben model certifies the feasibility and flexibility of our proposed high-order CFS-PML combined with the DG method.

A p-adaptive discontinuous Galerkin method for solving second-order seismic wave equations

A <i>p</i>-adaptive discontinuous Galerkin method for solving second-order seismic wave equations

Enhancement of gravitational waves at Q-ball decay including non-linear density perturbations

The existence of a stochastic gravitational wave background is indicated by the recent pulsar timing array (PTA) experiments. We study the enhanced production of second-order gravitational waves from the scalar perturbations when the universe experiences a transition from the early matter-dominated era to the radiation-dominated era due to Q-ball decay. We extend the analysis in previous work by including the frequency range where density perturbations go non-linear and find that the resultant gravitational wave spectrum can be consistent with that favored by the recent PTA experiment results.

Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media

We introduce a generalized fractional nonlinear Schrödinger (FNLS) equation for the propagation of optical pulses in laser systems with two fractional-dispersion/diffraction terms, quantified by their Lévy indices, α 1 α 2 ∈ ( 1 , 2 ] , and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison with numerical results. We find that the soliton collapse, exhibited by the one-dimensional cubic FNLS equation with only one Lévy index (LI) α = 1 , can be suppressed in the two-LI FNLS system. Stability of the solitons is also explored against collisions with Gaussian pulses and adiabatic variation of the system parameters. Modulation instability (MI) of continuous waves is investigated in the two-LI system too. In particular, the MI may occur in the case of the defocusing nonlinearity when two diffraction coefficients have opposite signs. Using results for the MI, we produce first- and second-order rogue waves on top of continuous waves, for both signs of the Kerr nonlinearity.

Incident component extraction from disturbed waves around large fixed cylindrical structures

The parameters of incident waves are critical for real-time wave load estimation of structures in service. Nonetheless, it is challenging to characterize incident waves accurately using the measured wave surface elevation around large fixed cylindrical structures due to the interaction with the structure in the wave field. To provide a better understanding of incident waves, which are usually buried in directly measured waves, a new time-domain method for the extraction of first-order and second-order incident waves around large fixed cylindrical structures is proposed. In contrast to most existing separation methods that are suitable for structures with equal reflection coefficients, the amplitude and phase changes of near-field waves around cylindrical structures can be determined by considering the significant diffraction effect, and then the time-frequency characteristic of the wavelet transform is employed, which enables the extraction of incident waves in the time domain. The accuracy of the proposed method is studied using several examples with known incident waves which are generated with the OpenFOAM. The numerical results show that the deviations between the exact and extracted incident waves change from 6.16% to 16.77% for different wave conditions. To further investigate the performance of the proposed method, an experimental study on waves around a mono-pile offshore wind turbine (OWT) is conducted in the laboratory of the Ocean University of China. The predicted results basically agree well with the target waves in terms of amplitude and phase. The deviations between predicted waves using the proposed method and target waves are 110% smaller than those between directly experimental measured waves and target waves for all tested conditions. Finally, 48 h of measured wave data were obtained during calm and typhoon periods around a mono-pile OWT located near Rudong County, Jiangsu Province, in the Yellow Sea of China. There are almost 150% and 30% differences between the extraction results and measured data in the time series and statistical wave heights, respectively, which means that employing disturbed wave data as the input for calculating real-time wave loads leads to deviations that cannot be ignored.

Efficient Implementation of CFS-CPML in FDTD Solutions of Second-Order Seismic Wave Equations

Efficient Implementation of CFS-CPML in FDTD Solutions of Second-Order Seismic Wave Equations

Second-order wave loads on a floating bridge of T-type cross section

An analytical model for the complete second-order wave loads on a floating bridge of T-type cross section is established within the framework of potential flow theory. The first-order problem is solved using the matched eigenfunction expansion method (MEEM). Meanwhile, the second-order wave loads are divided into two distinct parts which are computed separately. The first part is dependent on the quadratic products of the first-order velocity potential and its derivative. It has been evaluated through two different ways. One is based on a direct pressure integration, i.e., a near-field method. To ensure a high accuracy of the computation, a local expansion is applied to determine the spatial derivative of the first-order velocity potential at a sharp corner. The other is based on the momentum conservation over a control volume. The effect of the control surface location on the computation has been discussed. In addition, the two proposed methods have been applied to both the time-independent wave-load component as well as the second-harmonic component, respectively. The second part of the complete second-order wave loads is due to the second-order velocity potential. It is evaluated based on an indirect method by introducing an auxiliary potential. Detailed numerical investigation is then conducted. The influence law of the sectional geometric parameters on the second-order wave loads is investigated. The numerical results reveal that the cantilever plate imposes an apparent protection effect on the inner web beam. Such effect gets obviously enhanced as the section net width or section height decreases or as the plate width or draft increases.

Large Scale Experimental Study on Waves and Submerged Horizontal Cylinders

A large-scale physical model experiment was conducted to study the interaction between regular waves and submerged horizontal cylinders, breaking through the bottleneck of a low Reynolds number in a traditional small water tank. The surface pressure distribution and overall force of submerged horizontal cylinders at different submerged depths in waves with different heights and periods under a high Reynolds number were analyzed, and the variation in first- and second-order wave forces with wave height periods was analyzed. Subsequently, the influence of the cylinder on the wave field was analyzed, and the reflection coefficient was obtained through the three-point separation method. According to the analysis of the experimental results, the horizontal and vertical forces acting on the submerged cylinder per linear meter are similar, with the horizontal force slightly greater than the vertical force; at the same time, the submerged cylinder has a certain reflection effect on long-period waves. The summary, analysis, and display of relevant experimental results provide validation support for the current high-precision mathematical model as much as possible.

Computation of unsteady electromagnetic scattering about 3D complex bodies in free space with high-order difference potentials

We extend the previously developed high-order accurate method for acoustic scattering to electromagnetic scattering, i.e., from the scalar setting to a vector setting. First, the governing Maxwell's equations are reduced from their original first-order form to a system of second-order wave equations for the individual Cartesian components of electromagnetic field. In free space, these wave equations are uncoupled. Yet at the boundary of the scatterer, the variables that they govern (i.e., Cartesian field components) remain fully coupled via the boundary conditions that account for the specific scattering mechanism. Next, the wave equations are equivalently replaced with Calderon's boundary equations with projections obtained using the method of difference potentials and a compact high-order accurate scheme. The Calderon's boundary equations are combined with the boundary conditions and the overall system is solved by least squares. The resulting vector methodology (electromagnetic) inherits many useful properties of the scalar one (acoustic). In particular, it offers sub-linear computational complexity, does not require any special treatment of the artificial outer boundary, and has the capacity to solve multiple similar problems at a low individual cost per problem. We demonstrate the performance of the new method by computing the scattering of a given impinging wave about a double-cone hypersonic shape.

A novel analysis of Cole–Hopf transformations in different dimensions, solitons, and rogue waves for a (2 + 1)-dimensional shallow water wave equation of ion-acoustic waves in plasmas

This work investigates a (2 + 1)-dimensional shallow water wave equation of ion-acoustic waves in plasma physics. It comprehensively analyzes Cole–Hopf transformations concerning dimensions x, y, and t and obtains the dispersion for a phase variable of this equation. We show that the soliton solutions are independent of the different logarithmic transformations for the investigated equation. We also explore the linear equations in the auxiliary function f present in Cole–Hopf transformations. We study this equation's first- and second-order rogue waves using a generalized N-rogue wave expression from the N-soliton Hirota technique. We generate the rogue waves by applying a symbolic technique with β and γ as center parameters. We create rogue wave solutions for first- and second-order using direct computation for appropriate choices of several constants in the equation and center parameters. We obtain a trilinear equation by transforming variables ξ and y via logarithmic transformation for u in the function F. We harness the computational power of the symbolic tool Mathematica to demonstrate the graphics of the soliton and center-controlled rogue wave solutions with suitable choices of parameters. The outcomes of this study transcend the confines of plasma physics, shedding light on the interaction dynamics of ion-acoustic solitons in three-dimensional space. The equation's implications resonate across diverse scientific domains, encompassing classical shallow water theory, fluid dynamics, optical fibers, nonlinear dynamics, and many other nonlinear fields.

Investigation of wave effects on motion of an unmanned surface vehicle at various scales

Motion characteristics of unmanned surface vehicle are mainly affected by sea wave during its operation. This paper shows the numerical results of the unmanned surface ship at various scales in irregular waves based on the boundary element method. The effects of different sea states on each scaled model in a head sea, bow quartering sea, and beam sea are analyzed to predict the safety region of the ship motion. The significant amplitudes of ship motion are obtained from the ship motion responses in regular waves. Steady wave drift forces in the cases of bow oblique sea are calculated to find the impact of second-order waves on the models. It is proved that the motion of model C is remarkable in the narrow frequency domain from 0.2 to 1.4 rad/s but the ship responses of model A are considerable in the range of frequency of 0.2 to 2.5 rad/s. The significant amplitude of surge and pitch motion reaches the peak values in head sea conditions while the peak values of yaw motion are in the oblique sea of 120 degrees. The left motion is maximum in head sea condition.

Exploiting second-order advantage for simultaneous biosensing of romidepsin and vorinostat in the presence of belinostat as uncalibrated interference in human serum samples

In this work, a novel, ultra-sensitive, selective, and multi-electrochemical techniques biosensor was fabricated for simultaneous determination of romidepsin (RD) and vorinostat (VN) in the presence of belinostat (BS) as uncalibrated interference in human serum samples. A glassy carbon electrode (GCE) was modified with chitosan-ionic liquid (CS-IL) which was used as a platform to immobilize histone deacetylase (HDAC) by the use of glutaraldehyde. The RD and VN as inhibitors of the HDAC were trapped by the HDAC onto the biosensor surface which didn’t show any response at the surface of the CS-IL/GCE. In order to simultaneous biosensing of RD and VN, the biosensor was immersed into a probe solution to get a response from the biosensor. By individual immersion of the biosensor into RD and VN solutions different steric hindrances were occurred at the biosensor surface which caused generation of two different responses from the biosensor. The biosensor responses were individually calibrated and used to develop second-order calibration models to support the biosensor for simultaneous determination of RD and VN. Second-order hydrodynamic square wave voltammetric (HSWV) data were generated and modeled by PARAFAC2, MCR-ALS, PARASIAS, and U-PCA/RBL to find the best method to couple with outputs of the biosensor. The results confirmed the best performance for the biosensor- U-PCA/RBL for simultaneous determination of RD and VN in the presence of BS in artificial human serum samples. The biosensor-U-PCA/RBL combinatorial method was also successful in simultaneous determination of RD and VN in the presence of BS in real human serum samples with a comparable performance with HPLC as the reference method.

Wave behavior in a numerical wave tank at intermediate depth of water using stokes wave theory

The paper analyzes a second-order Stokes wave theory by CFD code and uses the volume of fluid (VOF) method in a 2D numerical wave tank (NWT) in the intermediate depth of water under different wave steepness conditions. The CFD simulation in an NWT generates a wave, validated with the already published experimental and numerical data to check the accuracy. It shows that current results are in good agreement with the published result and the difference in the results is within 2.1027%. Six tests under different wave heights for the time period [Formula: see text][Formula: see text]s have been conducted in an NWT to verify the analysis of the wave theory. Horizontal and vertical velocity, surface elevation, and the velocity vector of the particle motion are the important objectives in this analysis. The study shows that the free surface of the water is a high energy density zone. The time discretization has been achieved with the first-order implicit scheme and the second-order upwind scheme. This analysis shows that the ocean characteristic of second-order Stokes wave theory on the free surface is important to the engineering sciences and further investigation.

A Novel Method for Fatigue Damage Assessment in Bimodal Processes Considering High- and Low-Frequency Reduction Effects

Due to inherent nonlinearities within floating systems and the second-order wave forces affecting them, the dynamic responses of floating systems manifest as bimodal Gaussian processes. Consequently, the classical spectral fatigue assessment method grounded in the Rayleigh distribution cannot be applied. This paper introduces the double frequency coupled (DFC) method as a spectral fatigue assessment approach, providing an accurate estimation of fatigue damage originating from bimodal Gaussian processes. Within the DFC method, the bimodal Gaussian process is partitioned into two components: low-frequency (LF) and high-frequency (HF) processes. A Gaussian distribution is employed to describe the probability distribution function (PDF) of the amplitude reduction induced by the interaction between LF and HF processes. The PDF of small-cycle fatigue can be computed by convoluting the PDF of HF amplitudes and the reduction amplitude between LF and HF. Similarly, the PDF of large-cycle fatigue can be determined through convolution, which involves the PDF of LF amplitudes and small-cycle fatigue. The overall fatigue damage arising from the bimodal Gaussian process is obtained by directly summing the contributions of small-cycle and large-cycle fatigue. Numerical investigations of the DFC method’s effectiveness are presented through a series of parametric studies, demonstrating its robustness, efficiency, and accuracy within engineering expectations. Furthermore, the DFC method is found to be applicable to both single-slope and two-slope S-N curves.

Optimization of the design of an oscillating water column for the Pacific Ocean conditions using the response surface methodology

Wave energy possesses a significant potential as a sustainable and renewable source of power due to its abundant presence in the Earth’s oceans. This research focused on the assessment of the hydrodynamic efficiency (ɛ) of a resonant chamber within an OWC (oscillating water column) system. Four geometric design parameters of the resonant chamber (h1/h, b2/h, d/b2 and α) were selected to optimize ɛ, being h the depth of the water; h1 and α correspond to the vertical length and angle of inclination of the front wall, respectively; b2 is the width of the resonant chamber, and d represents the diameter of the air outlet hole. To analyze the system, a combined approach utilizing CFD with the VoF (volume of fluid) method and the response surface methodology (RSM) was adopted. The RSM employed a FCCD (face-centered central composite design) to optimize the factors, while the VoF method enabled to simulate in a detailed way the fluid behavior. The ANSYS-Fluent software was employed to perform a transient simulation. A second-order regression model was constructed and validated based on the simulation results. The quadratic regression model exhibited a high Radj2 value (82.81%) and had a p-value associated ¡0.05 (4.66 × 10-8). Therefore, the model was highly significant in accurately representing the ɛ of the OWC resonant chamber. The highest ɛ value (67.01%) was obtained for h1/h, b2/h , d/b2 and α equal to 0.7786, 0.4455, 0.0863, and 89.38°, respectively. The numerical results were validated with the Stokes second-order wave theory and a good correlation was observed with the numerical findings. This study demonstrates that the designed and optimized OWC can be effectively utilized in the Colombian Pacific Ocean to generate electrical energy, promoting economic development in the area.

Time-dependent responses and mooring tensions of a moored floating structure in tsunami waves

This study evaluates the effects of tsunami waves on the global performance of a spread-moored Floating Storage Unit (FSU) through tsunami-floater-mooring coupled dynamics simulations. The time-domain equations of motions for the FSU used the Cummins equation with a body-nonlinear method, in which the nonlinear Froude-Krylov and hydrostatic restoring forces were evaluated at the instantaneous tsunami elevation and body position at each time step. As input tsunami waves, second-order solitary waves and Tohoku-tsunami-like waves constructed by the superposition of several solitary waves were used. The lumped-mass-line model was used for the coupled mooring-line dynamics. Then, the coupled interactions between the floater and mooring system were solved by applying various tsunamis of different shapes, durations, heights, and incident angles. The body-nonlinear results were systematically compared with the linear analyses to demonstrate the pertinent nonlinear effects. Following a significant initial drift of the vessel induced by tsunamis, the moored floating structure exhibits transient motions at natural periods. Larger tsunami heights with relatively short duration result in significantly higher FSU motions and mooring tensions.

Fourth-order moments analysis for partially coherent electromagnetic beams in random media

A theory for the characterization of the fourth-order moment of electromagnetic wave beams is presented in the case when the source is partially coherent. A Gaussian–Schell model is used for the partially coherent random source. The white-noise paraxial regime is considered, which holds when the wavelength is much smaller than the correlation radius of the source, the beam radius of the source, and the correlation length of the medium, which are themselves much smaller than the propagation distance. The complex wave amplitude field can then be described by the Itô-Schrödinger equation. This equation gives closed evolution equations for the wave field moments at all orders and here the fourth-order moment equations are considered. The general fourth-order moment equations are solved explicitly in the scintillation regime (when the correlation radius of the source is of the same order as the correlation radius of the medium, but the beam radius is much larger) and the result gives a characterization of the intensity covariance function. The form of the intensity covariance function derives from the solution of the transport equation for the Wigner distribution associated with the second-order wave moment. The fourth-order moment results for polarized waves are used in an application for imaging of partially coherent sources.