Real Wave Research Articles

Frequency perturbation theory of bound states in the continuum in a periodic waveguide

In a lossless periodic structure, a bound state in the continuum (BIC) is characterized by a real frequency and a real Bloch wave vector for which there exist waves propagating to or from infinity in the surrounding media. For applications, it is important to analyze the high-$Q$ resonances that either exist naturally for wave vectors near that of the BIC or appear when the structure is perturbed. Existing theories provide quantitative results for the complex frequency (and the $Q$ factor) of resonant modes that appear or exist due to structural perturbations or wave vector variations. When a periodic structure is regarded as a periodic waveguide, eigenmodes are often analyzed for a given real frequency. In this paper, we consider periodic waveguides with a BIC and study the eigenmodes for a given real frequency near the frequency of the BIC. It turns out that such eigenmodes near the BIC always have a complex Bloch wave number, but they may or may not be leaky modes that radiate out power laterally to infinity. These eigenmodes can also be the so-called complex modes that decay exponentially in the lateral direction. Our study is relevant for applications of BICs in periodic optical waveguides, and it is also helpful for analyzing photonic devices operating near the frequency of a BIC.

Propagation of interfacial (Stoneley-type) waves at the joint boundary of two initially-stressed incompressible half-spaces

The presence of initial stress in solids changes the material’s response to finite and infinitesimal deformations. This paper presents a study on the effects of initial stress, finite deformation, and material properties on the speed of interfacial waves which are assumed to travel at the joint boundary of two incompressible half-spaces. The theory of infinitesimal deformations superimposed on finite deformations is used along with the theory of invariants. Boundary conditions at the interface result in an explicit secular equation, which is analyzed generally. For each half-space, a prototype strain–energy function is assumed, which is a function of the deformation gradient and initial stress tensors. The effect of different governing parameters is observed on the wave speed and is analyzed theoretically. Graphical illustrations are also presented to elaborate on the theoretical results. It is observed that for admissible values of parameters, a real wave speed exists and is bounded by values depending on the governing parameters. A comparison between Rayleigh and interfacial wave speeds is also made and supported with graphs of dimensionless wave speeds with respect to initial stresses.

One-Way Vibration Absorber

A vibration absorber consisting of a one-dimensional waveguide with a reflectionless termination extracts vibrational energy from a structure that is to be damped. An optimum energy dissipation occurs for the so-called power adjustment, i.e, the same level of resistance and the opposite reactance of structure and absorber. The dimensioning of these impedance parameters on the base of the classic second order “two-way” wave equation provides analytical solutions for a few simple waveguide shapes; solutions for all other waveguides are only accessible via numerical finite-element computation. However, the competing first order “one-way” wave equation allows for an analytical conception of both the known broadband vibration absorber and the “Acoustic Black Hole” absorber. For example, for an exponential waveguide, the two-way calculation shows no resistance (and hence no real wave propagation) below a cut-off frequency, while the one-way wave equation predicts absorption in the whole frequency range.

Dynamic roll instability of liquid natural gas carrier during offloading operations and prediction of downtime cost in Malaysian waters

The loss of revenue or global loss in term of cost due to downtime conditions is always a concern for field operators. Prevailing wave conditions may suddenly appear during offloading operations, which will influence the overall process and may lead to downtime of operations. Severe weather can significantly impact downtime costs of offloading operations and cause a huge loss of revenue. This research work integrates the dynamic stability with downtime cost for LNG carrier in different location of Malaysian waters using real time metocean data. This study on downtime cost utilizes the real time and location-specific wave scatters, as well as limiting criteria of offloading in Malaysian waters. The dynamic roll stability of LNG carrier was investigated for ABS criteria in two depths of water at three real-time locations. Susceptible wave conditions had been identified along with downtime cost analysis. This domain of downtime cost study was further rendered into mathematical package in the form of graphical interfaces for field operators. This mathematical based graphical interface facilitates in predicting location-specific downtime cost charts and allows operator companies to determine the fiscal losses for different range of downtime days and various capacities of LNG carrier. Overall, this research contributes by linking dynamic stability with operating costs through real time metocean data in Malaysian waters.

MpNet: Variable Depth Unfolded Neural Network for Massive MIMO Channel Estimation

Massive multiple-input multiple-output (MIMO) communication systems have a huge potential both in terms of data rate and energy efficiency, although channel estimation becomes challenging for a large number of antennas. Using a physical model allows to ease the problem by injecting a priori information based on the physics of propagation. However, such a model rests on simplifying assumptions and requires to know precisely the configuration of the system, which is unrealistic in practice. In this paper we present mpNet, an unfolded neural network specifically designed for massive MIMO channel estimation. It is trained online in an unsupervised way. Moreover, mpNet is computationally efficient and automatically adapts its depth to the signal-to-noise ratio (SNR). The method we propose adds flexibility to physical channel models by allowing a base station (BS) to automatically correct its channel estimation algorithm based on incoming data, without the need for a separate offline training phase. It is applied to realistic millimeter wave channels and shows great performance, achieving a channel estimation error almost as low as one would get with a perfectly calibrated system. It also allows incident detection and automatic correction, making the BS resilient and able to automatically adapt to changes in its environment.

A MODIFICATION TO THE SCHRÖDINGER EQUATION FOR BROADER BANDWIDTH GRAVITY-CAPILLARY WAVES ON DEEP WATER WITH DEPTH-UNIFORM CURRENT

AbstractWe derive a nonlinear Schrödinger equation for the propagation of the three-dimensional broader bandwidth gravity-capillary waves including the effect of depth-uniform current. In this derivation, the restriction of narrow bandwidth constraint is extended, so that this equation will be more appropriate for application to a realistic sea wave spectrum. From this equation, an instability condition is obtained and then instability regions in the perturbed wavenumber space for a uniform wave train are drawn, which are in good agreement with the exact numerical results. As it turns out, the corrections to the stability properties that occur at the fourth-order term arise from an interaction between the mean flow and the frequency-dispersion term. Since the frequency-dispersion term, in the absence of depth-uniform current, for pure capillary waves is of opposite sign for pure gravity waves, so too are the corrections to the instability properties.

Fault Diagnosis and Fault-Tolerant Control of Energy Maximization for Wave Energy Converters

This paper investigates a new wave energy converter (WEC) control problem, which is the energy maximization subject to sensor and actuator faults. Unexpected deviation of system variables from standard conditions, defined as a fault, degrades the control performance and even introduces damages breaking down the whole system. Fault detection for wave energy converters is therefore of great importance in maintaining the high reliability of the system. This paper presents a robust fault diagnosis approach effectively detecting sensor and actuator faults in real-time. A compensator is then designed to minimize the influence from faults and maintain the control performance. A non-causal linear optimal control is applied to maximize the energy output, in which the future excitation force is incorporated to determine the current control action. This approach can also be straightforwardly applied to other control methods. The parameters of the proposed fault detection method and fault-tolerant control method can be calculated off-line, which enhances the real-time implementation with a low computational burden. A realistic sea wave collected from the coast of Cornwall, U.K. is used to demonstrate the efficacy of the proposed approach.

Wave power forecasting using an effective decomposition-based convolutional Bi-directional model with equilibrium Nelder-Mead optimiser

Energy industries and governments consider ocean wave power a promising renewable energy source for reaching the net-zero plan by 2050 and restricting the rise in global temperatures. It expects the potential global ocean wave power production to be around 337 GW annually. Although wave energy forecasting critically enables economic dispatch, optimal power system management, and the integration of wave energy into power grids, the forecasting process is complicated by the stochastic, intermittent, and non-stationary nature of waves. Thus, this paper proposes a novel hybrid forecasting model comprising an adaptive decomposition-based method (Nelder-Mead variational mode decomposition) and a convolutional neural network featuring bi-directional long short-term memory. Furthermore, we propose a fast and effective optimiser to adjust the hybrid model's hyper-parameters and evaluate the decomposition technique's role in increasing the accuracy of wave energy flux predictions considering a forecasting period of 6 h. With regard to assessing the proposed model's effectiveness, we use a real wave dataset from a buoy positioned off Favignana Island in the Mediterranean Sea and compare the proposed model with six well-known forecasting methods and five hybrid deep-learning models. According to our findings, the proposed model significantly outperforms existing approaches over extended time periods and compared with the bi-directional long short-term memory, the developed adaptive decomposition method, and new hyper-parameters tuner improve the prediction accuracy at 45% and 13.6%, respectively.

Analysis of viscous wave generation at low Ursell number in an optimal numerical wave tank using inlet velocity method

The present study analyzes the viscous wave generation at a low Ursell number in an optimal numerical wave tank. Commercial computational fluid dynamics code ANSYS FLUENT software is used in a two-dimensional numerical wave tank in this model. The finite volume method is a discretization technique to solve the Reynolds-average Navier–Stokes equations. The inlet velocity method is used to generate the desired waves. The standard k–ε turbulent model is used for the verification. Viscous models were tested at a constant water depth ( d) under 12 cases to complete the analysis. Surface elevation, wave velocities, velocity contour, and streamlined motions are important studies in this problem. Simulating result shows that the wave velocities ( u, w) at the free surface ( z = 0) increase with the wave steepness ( H/L) at a particular time period ( T) and gradually decrease from the free surface ( z = 0) toward the bottom of the water ( z = − d). Many practical systems, such as wave energy converters, offshore marine constructions, and other ocean engineering challenges, may benefit significantly from this research's realistic wave creation. This analysis of different periods gives the knowledge of flow behavior which provides the previous test of the scale model.

Numerical Simulation of the Kelvin Wake Patterns

The ship wave is of great interest for wave drag and coastal erosion. This paper proposes a mechanism of ship wave transformation to explore the effects of ship speed and ship size on the waveform. Firstly, based on the theory of potential flow, the boundary integral equations for the Kelvin ship waves are obtained by deploying the different Kelvin sources or Rankine sources. Then, these integral equations are numerically discretized to a set of nonlinear equations. Finally, the Jacobian−free Newton–Krylov method with a preconditioner is adopted to solve the nonlinear equations. Though imitating plenty of different Kelvin wave patterns, the mechanism of ship wave transformation is proposed to conveniently generate the polymorphic Kelvin wake patterns. The above numerical simulation scheme is verified by comparing simulation results with real ship waves. After that, the wake angle is discussed with the effects of Froude number, source strength and source type by following the mechanism of ship wave transformation. The results show that the wake angle tends to decrease with ship speed but increase with ship size. In addition, for high ship speeds, the effect on the wake angle can be more dramatic.

Self-steepening, Raman scattering and self-phase modulation-interactions via the perturbed Chen–Lee–Liu equation with an extra dispersion. Modulation insability and spectral analysis

It is worth mentioning that the perturbed Chen–Lee–Liu equation (PCLLE) exhibits the effects of self-steepening (SS), Raman scattering (RS) and self-phase modulation (SPM). Our attention is focused, here, to inspect the challenge between these phenomena may lead to a dominant one among them. On the other hand, we investigate the dominant phenomena produced due to these interactions. Furthermore, the structure of the configuration of pulses propagation in optical fibers are depicted. These phenomena are illustrated, here, via studying the PCLLE with an extra dispersion. This equation is formulated and the exact solutions of this new equation are found by using the unified method (UM). The importance of the UM stems from the fact that, in the applications, we have found that the UM is of low time cost in symbolic computation. So, we think that it prevails the known methods in the literature. On the other hand, the solutions for the complex envelope field equations, found in the literature, are always considered with real wave amplitude. Here, a transformation based on using complex wave amplitude is introduced. Indeed, in this case, solutions describe the waves that result from soliton- periodic wave collision, which may reveal novel phenomena. The solutions obtained are evaluated numerically and represented in graphs. It is shown that pulses compression occurs which may be due to self-phase modulation. Also, dispersive shock wave can be produced which may be argued to the presence of the extra dispersion and self-sdteepening. It is worthy to mention that, self-steepening arises for a small value of the related coefficient. The results obtained, here, are novel. The modulation instability is analyzed and it is found that it triggers at a critical values of SS and RS coefficients. At this stage, shock wave may occur. It is observed that the spectrum shows soliton with periodic waves background.

Design and optimization of a wave energy converter for drifting sensor platforms in realistic ocean waves

One of the biggest challenges in converting wave energy is to enable the use of low frequency waves, since the highest waves in typical sea states have low frequencies, as can be seen from the corresponding wave spectra, such as the Pierson–Moskowitz or JONSWAP spectra. In this paper, we show that this challenge is indeed achievable for the operation of small autonomous drifting sensor platforms. We present the design and optimization of a compact wave energy converter that freely floats in random sea waves. An optimization of the dynamical behavior as well as the electromagnetic power take-off is conducted based on simulations and experiments. The platform has compact dimensions of 50 cm draft and 50 cm diameter, which leads to special requirements for size and appearance. To meet these requirements, a two-body self-reacting point absorber is designed and a flux switching permanent magnet linear machine is developed for the power take-off. The developed system is validated by experiments in a wave flume and the linear generator is analyzed on a test bench. A coupled model is used to simulate and optimize the corresponding mechanical system, which leads to an increased output power from below 10 mW for the simulated initial setup to a power output of more than 100 mW in the simulation. Simulations and experiments are performed for regular and random waves in order to provide realistic approximations of the total output power.

Spin accumulation and longitudinal spin diffusion of magnets

We extend to the longitudinal component of the magnetization the spintronics idea that a magnet near equilibrium can be described by two magnetic variables. One is the usual magnetization $\stackrel{P\vec}{M}$. The other is the nonequilibrium quantity $\stackrel{P\vec}{m}$, called the spin accumulation, by which the nonequilibrium spin current can be transported. $\stackrel{P\vec}{M}$ represents a correlated distribution of a very large number of degrees of freedom, as expressed in some equilibrium distribution function for the excitations; we therefore forbid $\stackrel{P\vec}{M}$ to diffuse, but we permit $\stackrel{P\vec}{M}$ to decay. On the other hand, we permit $\stackrel{P\vec}{m}$, due to spin excitations, to both diffuse and decay. For this physical picture, diffusion from a given region occurs by decay of $\stackrel{P\vec}{M}$ to $\stackrel{P\vec}{m}$, then by diffusion of $\stackrel{P\vec}{m}$, and finally by decay of $\stackrel{P\vec}{m}$ to $\stackrel{P\vec}{M}$ in another region. This somewhat slows down the diffusion process. Restricting ourselves to the longitudinal variables $M$ and $m$ with equilibrium properties ${M}_{eq}={M}_{0}+{\ensuremath{\chi}}_{M\ensuremath{\parallel}}H$ and ${m}_{eq}=0$, we argue that the effective energy density must include a new, thermodynamically required exchange constant ${\ensuremath{\lambda}}_{M}=\ensuremath{-}1/{\ensuremath{\chi}}_{M\ensuremath{\parallel}}$. We then develop the appropriate macroscopic equations by applying Onsager's irreversible thermodynamics and use the resulting equations to study the space and time response. At fixed real frequency $\ensuremath{\omega}$ there is, as usual, a single pair of complex wave vectors $\ifmmode\pm\else\textpm\fi{}k$ but with an unusual dependence on $\ensuremath{\omega}$. At fixed real wave vector, there are two decay constants, as opposed to one in the usual case. Extending the idea that nonequilibrium diffusion in other ordered systems involves a nonequilibrium quantity, this work suggests that, in a superconductor, the order parameter $\mathrm{\ensuremath{\Delta}}$ can decay but not diffuse, but a nonequilibrium gap-like $\ensuremath{\delta}$, due to pair excitations, can both decay and diffuse.

Integrated analysis of surface wave velocity and gravity data for the development of new density-velocity models of the crust and upper mantle in SE Iran

Inversion of Rayleigh wave dispersion curves is challenging due to its nonlinearity and multimodality. In this paper, a Simulated Annealing (SA) algorithm is applied to the nonlinear inversion of fundamental-mode Rayleigh wave group dispersion curves for shear and compressional wave velocities. In our approach, we invert thickness, velocities and densities and their vertical gradients of four layers, sediments, upper-crust, lower-crust and lithospheric mantle.At first, to determine the efficiency and stability of the method, noise-free and noisy synthetic data sets are inverted. Results from the synthetic data demonstrate that the SA applied to the nonlinear inversion of surface wave data is interesting not only in terms of accuracy but also in terms of the convergence speed. In fact, the SA method is suitable for large-scale optimization problems, especially for those in which a desired global minimum is hidden among many local minima. In a second step, real data in SE Iran are inverted to examine the usage and robustness of the proposed approach on real surface wave data. Then, we applied 3D gravity modeling based on surface wave analysis results to obtain the density structure of each layer. The reason for using both types of data sets is that the gravity anomaly does not have a good vertical resolution and surface wave group velocities are more appropriate for placing layer limits at depth, but they are not very sensitive to density variations. Therefore, the use of gravity data increases the overall resolution of density distribution. Compared with the Shuffle Complex Evolution (SCE) method that was implemented in a previous study, we found out that the SA method is more stable and has less variability of model parameter values in successive tests. In the final step, we reapplied the SA method to invert the fundamental-mode Rayleigh wave group velocities based on the results of gravity modeling. Gravity results, such as thicknesses and densities were used to limit the search space in the SA method.Our results show that the Moho depth across the Makran subduction zone is increasing from the Oman seafloor (24–30 km) and Makran forearc setting (34–42 km) to the Taftan-Bazman volcanic arc (47–49 km). Also, the results show high shear and compressional velocities under the Gulf of Oman, decreasing to the north of the Makran region. The density image shows an average crustal density with maximum values under the Gulf of Oman, decreasing northward to the Makran region.

Intuitive LTI energy-maximising control for multi-degree of freedom wave energy converters: The PeWEC case

Energy-maximising wave energy conversion control strategies are commonly based upon direct optimal control theory, where the control problem is discretised and transcribed into a nonlinear programme, and a solution is found via numerical routines. Though appealing from an optimality viewpoint, the real-time application of such strategies to realistic (complex) wave energy systems, such as the PeWEC device, can become potentially challenging, due to its intrinsic multiple degree-of-freedom (DoF) nature. Furthermore, this pendulum-based system is not only multi-DoF in its nature, but also underactuated, i.e. only one mode, associated to the pendulum mechanism installed inside the wave-excited floating body, can be effectively actuated. We propose, in this paper, a set of four simple and intuitive energy-maximising controllers for the PeWEC system based, upon linear time-invariant (LTI) systems. We achieve this by deriving the so-called impedance-matching conditions for the PeWEC, and extending well-established LTI controllers, originally designed for fully actuated single-DoF systems, to this multi-DoF underactuated case. In particular, we explore, design, and synthesise both feedback, and feedforward configurations, making explicit emphasis in their main characteristics. Furthermore, we provide a performance assessment for each of the proposed controllers, showing their energy-maximising capabilities for the wave resource characterising the Mediterranean Sea.

Computational investigation on a nonlinear dispersion model with the weak non-local nonlinearity in quantum mechanics

In the presence of nonlinear dispersion, we examine certain solitary wave solutions of a dimensionless nonlinear Schrödinger (DLNLS) equation with the parabolic law of nonlinearity. We use a unique computational (generalized rational (GRat)) approach to build a variety of solutions with varying shapes. These answers show how the nonlinear interaction between Langmuir waves and electrons causes the parabolic law nonlinearity. For a better visual description of the examined model, these interactions are shown using several graphs in three-, two-dimensional, and polar plots. These representations of the obtained solutions are considered as numerical simulaions to explain the investigated model’s characterizations, the pulse waves’ behaviour and the interaction between complex short wave and real long wave envelope.

Assessment of Diagnostic Accuracy of Real Time Shear Wave Elastography in Detecting Liver Cirrhosis Keeping Histopathology as Reference Standard

Objective: To determine the diagnostic accuracy of real-time Shear Wave Elastography (SWE) in detecting liver cirrhosis among patients suffering from diseases predisposing to it, keeping histopathology as the reference standard.
 Study Design: Cross-sectional study.
 Place and Duration of Study: Armed Forces Institute of Radiology and Imaging, Rawalpindi, from Jan 2018 to Jul 2018.
 Methodology: A total of 114 patients were recruited, and relevant history taken from patientsreal-time shear wave elastography (SWE) of the liver was performed, followed by USG guided liver biopsy. Patients having clinically suspected diseases predisposing to hepatic fibrosis were sent to the Radiology department for ultrasound or ultrasound-guided liver biopsy. Elasticity values using sheer waves of 14.9 kPa (2.23m/s) or more was taken as suggestive of cirrhosis. Elastography findings were compared with histopathology findings.Results: Real-time SWE showed high diagnostic accuracy for detecting liver cirrhosis with sensitivity, specificity, positive predictive value, negative predictive value and diagnostic accuracy of 92.86%, 89.66%, 89.66%, 92.86% and 91.23%, respectively.
 Conclusion: This study concluded that the diagnostic accuracy of RTSW elastography in detecting liver cirrhosis is relatively high.

Impedance Cardiography Signal Improvement Through Sign Related Adaptive Removers for Remote Health Care

The impedance cardiography (ICG) shows the impedance caused in the heart. The ICG gives a clear and accurate results and the applied techniques reduce artifacts and also mathematical calculations. The ICG signal shows various physiological and non-physiological situations, and can calculate the heart volume. The computational complexity is also a main part for remote health care. The adaptive techniques used in this project reduces or removes the noise in the signal, Improve the signal. Mainly to take over the applied signal, convergence rate, and to reduce computations of the proposed theory, we added the sign and normalized adaptive algorithms to take out the realistic wave. In final, the results are taken out from the outcomes by additionally relating it with the adaptive filter to situate it in the proper format.

Noniterative method for frequency estimation based on interpolated DFT with low-order harmonics elimination

The paper describes a new interpolated discrete Fourier transform (IpDFT) method for the frequency estimation of the real sine wave distorted by harmonics. The method complements recent work on the direct-formula IpDFT methods by expanding the model of the signal included in the interpolation. Spectral superposition for a total of four frequency components is accounted for in a one-step formula. Alongside the positive and negative components of the fundamental frequency, the influence from the closest low-order real harmonic is eliminated. By using the generalized maximum sidelobe decay (GMSD) window family, the interference from more distant harmonics and interharmonics is suppressed. This approach allows us to perform the measurement with a shortened data record compared to previous methods and improves accuracy in the case that a second-order harmonic is present in the signal. The study provides a five-point analytical, one-step formula that is verified by simulations and experiments in terms of accuracy and complexity. The experimental results are presented featuring straightforward C implementation on the system with an affordable microcontroller.

Data-driven soliton solutions and model parameters of nonlinear wave models via the conservation-law constrained neural network method

In the process of the deep learning, we integrate more integrable information of nonlinear wave models, such as the conservation law obtained from the integrable theory, into the neural network structure, and propose a conservation-law constrained neural network method with the flexible learning rate to predict solutions and parameters of nonlinear wave models. As some examples, we study real and complex typical nonlinear wave models, including nonlinear Schrödinger equation, Korteweg-de Vries and modified Korteweg-de Vries equations. Compared with the traditional physics-informed neural network method, this new method can more accurately predict solutions and parameters of some specific nonlinear wave models even when less information is needed, for example, in the absence of the boundary conditions. This provides a reference to further study solutions of nonlinear wave models by combining the deep learning and the integrable theory.