Complex Wave Research Articles

Sensors Layout Optimization Design of Rocket Sled Test System.

The rocket sled, as a ground dynamic test system, combines the characteristics of the wind tunnel test and the flight test. However, some practical factors, such as shock wave interference, ground effect, and high-intensity aerodynamic noise will cause serious interference and even failure of the uniformly distributed sensors during horizontal sliding in a wide speed range. The AGARD HB-2 standard model is employed as the payload to simulate the aerodynamic and aeroacoustic characteristics during the variable acceleration period, aiming to optimize the test sensors layout. It is observed that in the high Mach number flow fields, strong coupling behaviors among complex waves will occur. The peak of wake vortex strength will appear at 1.5 s and gradually diminish over time. In addition, when the vortex between the load and the booster is monitored, its position shifts forward in the subsonic stage, then gradually moves backward and expands in the supersonic stage. Acoustic directivity is pronounced at subsonic and transonic speeds, pointing towards 75° and 135° relative to the sliding speed, respectively. These results can provide technical support for sensor layout and high-precision testing in rocket sled tests.

A complex boundary wave superposition method for solving external acoustic problems

This paper proposes a complex boundary wave superposition method with a unique solution of full wavenumber based on the similarity between the acoustic wave superposition method (WSM) and the external excitation response of dynamic systems and combined with the idea that a damping system has a unique solution in dynamic theory. By placing the virtual equivalent source on the virtual boundary of complex space, the conventional WSM acquires damping properties comparable to those of the dynamical system. This approach successfully addresses the non-uniqueness of the solution at the eigenfrequency and is more efficient than the conventional combined layer potential method. The paper presents a comprehensive description of the proposed method, with a focus on theory, modeling, and parameter selection. The effectiveness of this method is evaluated by applying it to two types of acoustic problems, namely, radiation and scattering. The numerical results indicate that this method effectively addresses the non-unique problems encountered in conventional WSM. Furthermore, the proposed method is as accurate and efficient as the conventional WSM.

Unfolding of shocked hydrodynamic instability at SF[formula omitted] elliptical interface: Physical insights from numerical simulations

The Richtmyer–Meshkov (RM) instability widely exists in variety of industrial and scientific applications, such as in inertial confinement fusion, astrophysics explosions, supersonic combustion, bubble dynamics and cavitation. This study investigates the unfolding physical phenomena of RM instability at SF6 elliptical bubbles using numerical simulations. In contrast to cylindrical bubble, both shocked horizontal/vertical-aligned elliptical bubbles with different aspect ratios are considered, emphasizing the aspect ratio effects on flow morphology, complex wave patterns, interface deformation, vorticity generation, and interface features. For this purpose, a two-dimensional system of compressible Navier–Stokes-Fourier equations for multicomponent flows are solved using by a mixed modal discontinuous Galerkin method. Numerical simulations illustrate that the aspect ratio of elliptical bubbles have a significant influence on the vortex dynamics and the associated RM instability flows in contrast to the cylindrical bubble. In horizontal-aligned elliptical bubbles, some additional complex waves pattern, including inward jet and secondary vortex rings are observed. While, in vertical-aligned elliptical bubbles, the interface between two primary vortex rings is always vertical and has a “hippocampus” appearance due to the enhancement of downstream velocity. The baroclinic vorticity due to misalignment of density and pressure gradients at interface affects the bubble deformation and induces the Kelvin–Helmholtz instability, which leads to turbulent mixing. It is observed that the complexity of the vorticity fields is enhanced with increasing aspect ratios. Further, these aspect ratio effects result in integral diagnostic of important spatially integrated fields, and various interface features.

Local plasticity-induced nonlinear surface wave scattering in thick-walled structures

Thick-walled structures (TWSs) are frequently utilized as primary load-bearing structures. The early detection of damage is crucial to ensure the operational safety and integrity of these structures. Nonlinear elastic-wave-based techniques provide a potential solution to the problem, which heavily relies on the good understanding of nonlinear wave generation and propagation characteristics. The task, however, is technically challenging due to the complex wave modes existing in a TWS. Targeting a meticulously manufactured local plasticized damage region on the surface of a TWS, which can be regarded as the precursor of incipient damage, this study investigates the scattering features of nonlinear elastic waves resulting from the interaction between the fundamental quasi-surface wave and the local plasticity. Finite element simulations and experiments show that, upon interacting with the nonlinear material zone, both nonlinear quasi-surface waves and shear bulk waves can be generated, with the latter scattered towards the opposite surface of the TWS. The scattered nonlinear shear waves exhibit a strong and predictable directivity with high nonlinear energy content, which is conducive to the detection and localization of the incipient surface damage of the TWS.

Influences of damping, perturbation and variable coefficient on an extended nonlinear Gardner model

Describing the nonlinear wave propagation in fluids has posed a challenging task. The nonlinear Gardner equation stands as a crucial model in fluid dynamics. An extended Gardner model incorporates variable coefficients, damping, and perturbation terms, offering a more comprehensive approach to understanding complex wave dynamics in fluids. In our study, we employ the symbolic computation tool, specifically the Darboux transformation, to derive new analytic solutions up to the Nth order for this extended Gardner equation. By assigning the spectrum parameters in these solutions into real values, we are able to obtain line-like solitons. Moreover, when N⩾2 and pairs of complex conjugate values are assigned to two of the spectrum parameters, breathers emerge. This enables a comprehensive analysis of the dynamics involving solitons, breathers, and their hybrid forms, shedding light on their interactions. Furthermore, our work introduces several noteworthy insights by investigating the influences of three key factors: the damping, perturbation, and variable coefficient. Through a few of specific examples, we can confirm the following facts: (i) The damping factor plays a crucial role in rendering solitons and breathers unstable, causing them to undergo exponential changes in both amplitudes and directions during propagation. (ii) The perturbation function creates non-zero background waves along the time axis, which interact with solitons and breathers. (iii) The variable coefficient can introduce disturbances to solitons and breathers. Our findings disclose that this equation exhibits a wealth of intricate propagation patterns. Various factors can exert varying degrees of influence on solitons and their dynamics. This observation just underscores the complexity inherent in the real world and should be useful in applications.

Wave optics in silver and silver nihility structure

This research article thoroughly explores the electromagnetic behavior in silver metal at optical regime. Along the way, it uncovers some intriguing wave behaviors in terms of novel phenomenon – counterposition, negative phase velocity (NPV), orthogonal phase velocity (OPV) and/or negative refraction (NR), versus wavelength are investigated which is not previously deeply discussed in a silver configuration. Additionally, Minkowski momentum densities, revealing complex wave dynamics versus optical wavelength are studied first time for silver metal. Moreover, the influence on wave in silver metal due to L-nihility is notified fruitfully. These findings provide deeper insights platform for potential applications in diverse scientific and technological domains in condense matter physics, engineering and optics.

The nondegenerate solitons solutions for the generalized coupled higher-order nonlinear Schrödinger equations with variable coefficients via the Hirota bilinear method

In this paper, the generalized coupled higher-order nonlinear Schrödinger equations (GCHNLSEs) with variable coefficients, describing the propagation of femtosecond pulse with high peak power in birefringence fibers and inhomogeneous media, are researched by the Hirota bilinear method. The nondegenerate two-solitons and nondegenerate N-solitons solutions for these equations are obtained successfully for the first time. Then, we attain the v-shape, u-shape and wave-type double-hump solitons by adjusting the group velocity dispersion, cross-phase modulation and group velocity effect. Finally, through selecting the appropriate complex wave parameters, we change the distances between solitons and analyze the dynamic behaviors of the collisions.

Vibration control and stroke evaluation of bi-directional bistable nonlinear energy sinks applied in monopile offshore wind turbines during emergency shutdown

Monopile offshore wind turbines (OWTs) in complex wind and wave environments can generate more excessive vibrations in the fore-aft (FA) and side-to-side (SS) directions when emergency shutdowns occur, and therefore damping techniques to alleviate such vibrations are essential. Due to the potential frequency detuning (reduced damping effectiveness) of traditional tuned mass dampers (TMDs) and stroke issues (such as large strokes of TMDs and limited maximum strokes of unidirectional nonlinear energy sinks (NESs)) in existing absorbers, this paper proposes a bi-directional bistable nonlinear energy sink (BBNES) to mitigate the vibration of the OWT in the FA and SS directions during the emergency shutdown. First, the proposed device and its operation mechanism are elaborated, and an optimization method for the device is introduced. Then, the dynamic analysis model of the BBNES is developed for vibration control of the OWT and incorporated into a fully coupled numerical simulation tool with high fidelity, FAST v8. Subsequently, the responses of the OWT without and with the proposed BBNES and the bi-directional tuned mass damper (BTMD) are exhaustively investigated under diverse conditions (including mass ratios, wind-wave loadings, emergency shutdown times, wind-wave misalignments, and 1st mode natural frequencies of the OWT) to reveal their performances and compare them. The research results show that under most conditions, the BBNES and BTMD have a similar damping performance in the FA direction, whereas the BBNES has a slightly lower damping performance in the SS direction than the BTMD. In addition, except for the wind velocity of 8 m/s at the hub and the wind-wave misalignment of 90°, the FA stroke of the BBNES with a small mass ratio (i.e., 0.01∼0.035) is significantly smaller than that of the BTMD with the same mass ratio by more than 1.1 m, and even up to about 4 m. The SS stroke of the BBNES is slightly greater than that of the BTMD, and in most cases, the difference between both is less than 0.52 m. Therefore, the BBNES is superior to the BTMD in this regard. When the 1st mode natural frequency of the OWT decreases, the BTMD can lose its tuning efficacy and makes the tower more susceptible to resonance caused by 1p and wave loadings, while the BBNES is not affected by the 1st mode natural frequency variation of the OWT, demonstrating its stronger robustness.

Extraordinary mode conversion of elastic waves through asymmetric metaplates

Recently, the mode conversion of elastic waves has attracted much attention, due to its scientific significance and potential applications. The applications based on the high mode conversion efficiency were also explored in many fields. However, because of the complexity of elastic waves, the existing structures for the high efficient conversion of elastic waves are relatively complicated, and there are also some limitations in the practical design. Here, we report the extraordinary mode conversion of elastic waves through asymmetric brass plates partitioned by subwavelength cuts. It is demonstrated that high efficiencies (90%) and one-way conversions between transversal waves and longitudinal waves are achieved by the structured solid plate at the resonant frequency, which leads to the striking unidirectional transmission of elastic waves. Analyzing the resonant fields demonstrates that the intrinsic modes within the individual pieces derived by the cuts are responsible for this abnormal wave conversion. The simple scheme for wave conversion presented here may have potential applications, such as non-invasive flow sensing.

Recovery of a general nonlinearity in the semilinear wave equation

We study the inverse problem of recovery a nonlinearity f ( t , x , u ), which is compactly supported in x, in the semilinear wave equation u tt − Δ u + f ( t , x , u ) = 0. We probe the medium with either complex or real-valued harmonic waves of wavelength ∼ h and amplitude ∼ 1. They propagate in a regime where the nonlinearity affects the subprincipal but not the principal term, except for the zeroth harmonics. We measure the transmitted wave when it exits supp x f. We show that one can recover f ( t , x , u ) when it is an odd function of u, and we can recover α ( x ) when f ( t , x , u ) = α ( x ) u 2 m . This is done in an explicit way as h → 0.

Research On Numerical Wave Tank Based on SPH Method

Numerical wave-current flume is one of the effective methods to study waves and their effects on structures. In this paper, the Smoothed Particle Hydrodynamics (SPH) method is used to simulate and analyze the numerical wave flume. Based on the SPH method, an efficient and flexible numerical wave tank model is constructed to simulate complex water wave dynamics. Firstly, the basic principle of SPH method is summarized, and then the establishment process of numerical wave tank model is described in detail, including particle initialization, boundary condition setting and so on. Through the flume simulation under different wave conditions, the accuracy and stability of the model are verified. Finally, the interaction between wave and structure is studied. It provides a new and effective tool for the numerical simulation of wave flume, and also provides a useful reference for the related research in the fields of marine engineering and coastal protection.

New Perceptions for the Soliton Solutions to the Complex Wave Patterns Model Against its Numerical Solutions

New Perceptions for the Soliton Solutions to the Complex Wave Patterns Model Against its Numerical Solutions

On the Existence of Superposed and Superposed-type Real and Complex Elliptic Periodic Waves of KdV Equation

On the Existence of Superposed and Superposed-type Real and Complex Elliptic Periodic Waves of KdV Equation

A mathematical model for flow field with condensation discontinuity: One‐dimensional Euler equations with singular sources

Condensation induces both heat addition and mass consumption effects on the carrier flow field, leading to complex wave patterns. In this study, we aim to elucidate the structures of flow field under the influence of condensation. To achieve this, we present a mathematical model, which is formulated using Euler equations with a singular source term. Given the difficulties posed by both weak solution theory and the Dal Maso–LeFloch–Murat (DLM) theory (J. Math. Pures Appl. 483‐548 (1995)) in defining solutions to the Riemann problem, we propose a novel approach. This involves the coupling of weak solutions within two subregions, taking into consideration the discontinuity of source term. Firstly, we identify two stationary discontinuities originating from the singular source term—namely, stationary waves and composite waves. Admissibility criterions are developed for these discontinuities to facilitate the selection of physically meaningful solutions. Secondly, we employ a double classical Riemann problems (CRPs) framework to analyze the structures of Riemann solution. Our analysis reveals that the Riemann solution may exhibit seven structures with stationary wave and four structures with composite wave. Finally, the proposed model and its theoritical results are applied to validate the structure of the flow field with condensation discontinuities. For the pure heat addition problem, we successfully demonstrate all wave patterns of the flow field, perfectly matching the outcomes of numerical experiments.

Towards the systematic reconnaissance of seismic signals from glaciers and ice sheets – Part 2: Unsupervised learning for source process characterization

Abstract. Given the high number and diversity of events in a typical cryoseismic dataset, in particular those recorded on ice sheet margins, it is desirable to use a semi-automated method of grouping similar events for reconnaissance and ongoing analysis. We present a workflow for employing semi-unsupervised cluster analysis to inform investigations of the processes occurring in glaciers and ice sheets. In this demonstration study, we make use of a seismic event catalogue previously compiled for the Whillans Ice Stream, for the 2010–2011 austral summer (outlined in Part 1, Latto et al., 2024). We address the challenges of seismic event analysis for a complex wave field by clustering similar seismic events into groups using characteristic temporal, spectral, and polarization attributes of seismic time series with the k-means++ algorithm. This provides the basis for a reconnaissance analysis of a seismic wave field that contains local events (from the ice stream) set in an ambient wave field that itself contains a diversity of signals (mostly from the Ross Ice Shelf). As one result, we find that two clusters include stick-slip events that diverge in terms of length and initiation locality (i.e., central sticky spot and/or the grounding line). We also identify a swarm of high-frequency signals on 16–17 January 2011 that are potentially associated with a surface melt event from the Ross Ice Shelf. Used together with the event detection presented in Part 1, the semi-automated workflow could readily be generalized to other locations and, as a possible benchmark procedure, could enable the monitoring of remote glaciers over time and comparisons between locations.

Multibranch Elastic Bound States in the Continuum.

Constructing a highly localized wave field by means of bound states in the continuum (BICs) promotes enhanced wave-matter interaction and offers approaches to high-sensitivity devices. Elastic waves can carry complex polarizations and thus differ from electromagnetic waves and other scalar mechanical waves in the formation of BICs, which is yet to be fully explored and exploited. Here, we report the investigation of local resonance modes supported by a Lamb waveguide side-branched with two pairs of resonant pillars and show the emergence of two groups of elastic BICs with different polarizations or symmetries. Particularly, the two groups of BICs exhibit distinct responses to external perturbations, based on which a label-free sensing scheme with enhanced-sensitivity is proposed. Our study reveals the rich properties of BICs arising from the complex wave dynamics in elastic media and demonstrates their unique functionality for sensing and detection.

Stability analysis and conserved quantities of analytic nonlinear wave solutions in multi-dimensional fractional systems

The (3+1)-dimensional generalized nonlinear fractional Konopelchenko–Dubrovsky–Kaup–Kupershmidt [Formula: see text] model represents the propagation and interaction of nonlinear waves in complex multi-dimensional physical media characterized by anomalous dispersion and dissipation phenomena. By incorporating fractional derivatives, this model introduces non-locality and memory effects into the classical [Formula: see text] equations, commonly utilized in phenomena such as shallow water waves, nonlinear optics, and plasma physics. The fractional approach enhances mathematical representations, allowing for a more realistic depiction of the intricate behaviors observed in numerous modern physical systems. This study focuses on the development of accurate and efficient numerical techniques tailored for the computationally demanding [Formula: see text] model, leveraging the Khater II and generalized rational approximation methods. These methodologies facilitate stable time-integration, effectively addressing the model’s stiffness and multi-dimensional nature. Through numerical analysis, insights into the stability and convergence of the algorithms are gained. Simulations conducted validate the performance of these methods against established solutions while also uncovering novel capabilities for exploring complex wave dynamics in scenarios involving complete fractional formulations. The findings underscore the potential of integrating fractional calculus into higher-dimensional nonlinear partial differential equations, offering a promising avenue for advancing the modeling and computational analysis of complex wave phenomena across a spectrum of contemporary physical disciplines.

Numerical modelling of ship-generated solitary waves

A ship sailing at the wave speed in shallow water produces a complex wave pattern including a downstream disturbance in addition to a periodically generated upstream disturbance. The upstream component consists of solitary waves which are generated at the ship bow and emitted forward as soon as the local water depth is sufficiently modified enabling them to bypass the shallow water wave speed limit. Reynolds Averaged Navier-Stokes numerical simulations are carried out to explore this phenomenon in a fully non-linear and viscous virtual towing tank in cases where a ship sails at the waterway centreline as well as off-centreline conditions. Results indicate that friction attains no more than approximately 25 % of the total resistance coefficient, justifying the use of inviscid methods by previous studies in the literature. Water depth may have a significant impact on the frequency and amplitude of ship-generated solitary waves, but the manner in which this occurs is highly sensitive to the width of the waterway.

Environmental Microvibration Analysis Method for Vibration Isolation Research in High-Precision Laboratories

Environmental microvibrations, often originating from unidentified sources, pose a significant challenge for predicting and controlling their complex wave fields, potentially leading to measurement errors of sensitive instruments in high-precision laboratories and impacting the accuracy of experimental outcomes. Therefore, investigating effective control measures for environmental microvibrations under passive conditions is key to addressing such engineering issues. This paper presents a finite element analysis method tailored to address environmental microvibrations in the absence of apparent sources. This method involves obtaining the vibration time history at specific ground surface points through field measurements and combining the Rayleigh wave velocity attenuation character with depth at the center frequencies of one-third octave bands within the 1–100 Hz frequency range; the vibration time history at any depth in the soil is calculated. These calculated vibrations are then applied as input loads to the corresponding nodes on one boundary of the foundation–soil model, serving as the source of environmental microvibrations. The predicted results are compared with measured data and the empirical point source input method, indicating that this approach is more precise and efficient, providing valuable reference for the prediction and analysis of environmental microvibrations. In addition, utilizing this method, the study examines the effects of pile foundation parameters such as the pile length, burial depth, and concrete baseplate thickness on the vibration isolation performance of environmental microvibrations, providing guidance for designing pile foundation isolation.

Antenna modeling based on meta-heuristic intelligent algorithms and neural networks

As wireless communication technology continues to advance, the antenna, as an essential front-end device in radio communication system, is surrounded by more and more complex electromagnetic wave environments with increasing variety, resulting in greater demand for antennas and higher design requirements. While the traditional antenna design methods suffered from the disadvantage of low design efficiency, a powerful tool for accelerating antenna design is the modelling of antennas with neural networks. Aiming to enhance the modeling accuracy of neural network, multiple novel meta-heuristic swarm intelligent algorithms are introduced and part of them are modified for the purpose of applying to optimizing network’s weights and biases so as to raise the antenna model`s prediction precision on the basis of neural network. Specifically, the intelligent algorithms and their improvement directions include the strategy of optimizing weights and biases for neural networks with seagull optimization algorithm, optimizing the weights and biases of neural network with the improved butterfly algorithm fused with reverse learning, and the artificial rabbit algorithm optimizing the neural network weights and biases. In addition, two intelligent optimization algorithms that are already more mature: the particle swarm algorithm and the genetic algorithm are added to compare with the above three algorithms. The accuracy of neural network prediction before and after the optimisation of neural network by seagull algorithm, the butterfly algorithm incorporating reverse learning, the artificial rabbit algorithm, the particle swarm algorithm, and the genetic algorithm are got through the results respectively. The results of the experiments displayed that the neural network optimized of the improved butterfly algorithm incorporating reverse learning has a prediction accuracy of 99.69 % with stable results, the optimised neural network prediction accuracy of the seagull algorithm reaches 99.51%, and the optimised neural network prediction accuracy of the artificial rabbit algorithm is 99.49 %. The remaining two traditional algorithms optimized neural network accuracy is 83.1 % and 99.43 % respectively. Therefore, the improved butterfly algorithm incorporating reverse learning is the most effective among these three new algorithms applied to the field of antenna prediction. Moreover, the running time of the network optimized by different algorithms is quite distinct, among which the neural network optimized by the improved butterfly algorithm incorporating reverse learning takes the shortest time, which increases the prediction efficiency of the network by more than 70%. In summary, the application of the fused reverse learning improved butterfly algorithm in optimizing neural network predictions yields the shortest processing time and highest accuracy. This not only enables faster and more precise antenna design but also holds greater significance for the field of antenna design and analysis.