Complex Wave Research Articles

A semi-analytical framework for predicting far-field responses of complex elastic waves emitters

Applications of guided waves in various fields of engineering and science rely on elastic wave emitters for wave generation. Accurate prediction and understanding of the far-field responses of these wave emitters are crucial for the reliable and efficient application of guided waves-based technologies. In this paper, we propose a novel semi-analytical framework capable of predicting the far-field response of complex wave emitters of arbitrary shape and internal structure in any type of substrate. This framework is general, and is not confined to specific methods, enhancing its versatility. We applied the proposed semi-analytical framework to predict the directivity patterns of two different macro-fiber composite transducers, accurately modeled using their exact topologies. The framework’s validity was experimentally confirmed by comparing the predicted directivity patterns with the results obtained from experimental measurements.

Numerical study of vehicle motion during water exit under combined lifting force and wave action

During the retrieval process of the deep-sea mining vehicle (DSMV), the stability of the retrieval system is strongly influenced by the interaction between the vehicle body and the surrounding seawater due to the vehicle's complex shape and wave motion. Naturally, the negative side effects of significant changes in the vehicle's attitude and the water exit position can only increase retrieval's challenge. To investigate the characteristic of the flow field of the DSMV, this study employs the computational fluid dynamics method based on the Reynolds-averaged Navier–Stokes equations integrating the volume-of-fluid multiphase flow model with a fifth-order Stokes-wave model to explore the attitude and displacement changes of the vehicle during the water exit process in the ocean wave environment. The results indicate that the wave phase and lifting force are the major effect factors in the DSMV's water exit process. An appropriate lifting force under a specific wave phase can effectively reduce attitude changes and positional drift of the DSMV during water exit, thereby enhancing recovery efficiency and stability.

Phase trajectories, chaotic behavior, and solitary wave solutions for (3+1)-dimensional integrable Kadomtsev–Petviashvili equation in fluid dynamics

This paper focuses on finding exact soliton solutions and further examining the qualitative characteristics of these solutions for a nonlinear partial differential equation known as the (3+1)-dimensional integrable Kadomtsev–Petviashvili equation that portrays a unique dispersion effect. The (3+1)-dimensional integrable Kadomtsev–Petviashvili equation models the evolution of weakly nonlinear dispersive waves in three spatial dimensions “x,y,z” and time “t”. It balances nonlinearity and dispersion, leading to solitary wave solutions that are stable and localized. This equation is crucial in understanding complex wave phenomena in fields like fluid dynamics, plasma physics, and optics. Initially, the traveling wave transformation is employed to convert the nonlinear partial differential equations into the non-linear ordinary differential equations. Then, we use the Riccati equation approach to find solitary wave solutions for the resulting ordinary differential equation. To better comprehend the physical significance of these derived solutions, we illustrate them using various visual representations. Diverse novel collections of solitary wave solutions are obtained such as bright solitons, dark solitons, and dark singular solitons. Second, we convert the nonlinear ordinary differential equation into a linear dynamical system using the planar dynamical transformation. Then, we undertake a qualitative analysis of the dynamical system to study its chaotic characteristics and bifurcation phenomena. Phase portraits of bifurcation are observed at the equilibrium points of the planner dynamical system. We discuss various tools to identify the chaos (random and unpredictable behavior) in dynamical systems. Graphical visualization of qualitative analysis of the system is also depicted in 3-D phase portraits, 2-D phase portraits, Poincaré mapping, and time series. Additionally, the Runge–Kutta technique is used to do a thorough sensitivity analysis of the dynamical system. Using this analytical procedure, it is verified that the stability of the solution has negligible impact while there is little change in the beginning circumstances. This paper aims to provide vital views to scientists and researchers seeking to advance their experimental operations. Furthermore, this research might be expanded by incorporating solitons and situations and investigating wave dynamics. The methods employed provide a direct and uncomplicated approximation of all solutions when compared to the previously established techniques. Various combinations and values of the physical parameters are utilized to explore the optical soliton solutions of the resultant system.

Electrostatic Waves and Electron Holes in Simulations of Low-Mach Quasi-perpendicular Shocks

Collisionless low-Mach-number shocks are abundant in astrophysical and space plasma environments, exhibiting complex wave activity and wave–particle interactions. In this paper, we present 2D Particle-in-Cell (PIC) simulations of quasi-perpendicular nonrelativistic (v sh ≈ (5500–22000) km s−1) low-Mach-number shocks, with a specific focus on studying electrostatic waves in the shock ramp and precursor regions. In these shocks, an ion-scale oblique whistler wave creates a configuration with two hot counterstreaming electron beams, which drive unstable electron acoustic waves (EAWs) that can turn into electrostatic solitary waves (ESWs) at the late stage of their evolution. By conducting simulations with periodic boundaries, we show that the EAW properties agree with linear dispersion analysis. The characteristics of ESWs in shock simulations, including their wavelength and amplitude, depend on the shock velocity. When extrapolated to shocks with realistic velocities (v sh ≈ 300 km s−1), the ESW wavelength is reduced to one-tenth of the electron skin depth and the ESW amplitude is anticipated to surpass that of the quasi-static electric field by more than a factor of 100. These theoretical predictions may explain a discrepancy, between PIC and satellite measurements, in the relative amplitude of high- and low-frequency electric field fluctuations.

Unveiling the Dynamics of Nonlinear Landau-Ginzburg-Higgs (LGH) Equation: Wave Structures through Multiple Auxiliary Equation Methods

This comprehensive investigation delves deeply into the intricate dynamics governed by the nonlinear Landau-Ginzburg-Higgs equation. It uncovers a diversity of semi-analytical solutions by leveraging three auxiliary equation methods within the traveling wave framework. This article effectively utilizes the improved Kudryashov, Kudryashov's R, and Sardar's subequation methods. The methods discussed are advantageous because they are easy to implement and suitable for use with the Mathematica package program. Each method yields a distinct set of solutions, scrutinized across all cases. We elucidate the complex wave structures through 3D, 2D, and contour graphical representations, providing profound insights into their underlying characteristics. Furthermore, we scrutinize the influence of parameter variations on these wave structures, thereby offering a comprehensive understanding of their dynamic behavior.

Novel soliton solutions and phase plane analysis in nonlinear Schrödinger equations with logarithmic nonlinearities

This paper investigates a generalized form of the nonlinear Schrödinger equation characterized by a logarithmic nonlinearity. The nonlinear Schrödinger equation, a fundamental equation in nonlinear wave theory, is applied across various physical systems including nonlinear optics, Bose–Einstein condensates, and fluid dynamics. We specifically explore a logarithmic variant of the nonlinear Schrödinger equation to model complex wave phenomena that conventional polynomial nonlinearities fail to capture. We derive four distinct forms of the nonlinear Schrödinger equation with logarithmic nonlinearity and provide exact solutions for each, encompassing bright, dark, and kink-type solitons, as well as a range of periodic solitary waves. Analytical techniques are employed to construct bounded and unbounded traveling wave solutions, and the dynamics of these solutions are analyzed through phase portraits of the associated dynamical systems. These findings extend the scope of the nonlinear Schrödinger equation to more accurately describe wave behaviors in complex media and open avenues for future research into non-standard nonlinear wave equations.

Characterization of Laboratory-Confirmed Creutzfeldt-Jakob Disease From 3 Ontario Tertiary Care Centers Between 2012 and 2022: A Retrospective Cohort Study.

Globally, Creutzfeldt-Jakob disease (CJD) affects one in one million people annually, but there is a paucity of recent Canadian data. This study summarizes epidemiology trends and diagnostic timelines of laboratory-confirmed CJD cases in three tertiary Ontario hospitals. Using laboratory information systems, we identified 30 patients with a laboratory-confirmed CJD diagnosis between 2012 and 2022 at three major tertiary hospitals in Ontario. Retrospective chart reviews were then completed. Patients had a mean of 2.2 hospital visits (SD, 1.2) prior to being admitted for testing. The most common symptom presentations included loss of coordination (63.3%), behavioral changes (60%), progressive mobility loss (53.4%), memory loss (50.0%), and involuntary movements (50.0%). Magnetic resonance imaging findings showed potential CJD in 76.7% of cases, and 56.7% exhibited periodic sharp wave complexes characteristic of CJD on electroencephalogram. The mean duration from symptom onset to microbiologic testing was 91 days (SD, 90.7). End-point quaking-induced conversion (EP-QuIC) testing of cerebrospinal fluid was positive in 90.0% of patients, while 83.3% tested positive for 14-3-3 on enzyme-linked immunosorbent assay. Elevated cerebrospinal fluid 14-3-3 levels significantly correlated with shorter duration from symptom onset to death (R 2 = 0.71, F = 19.55, P = .0022). Post-diagnosis, 46.7% of patients were discharged home, 16.6% were transferred to external palliative care or hospice facilities, and 36.7% died during admission. The mean time from symptom onset to death was 121 days (SD, 120.7), and from diagnosis to death 35 days (SD, 83.9). This study highlights the importance of early CJD consideration and laboratory testing when appropriate neurologic symptoms are present.

Scar/WAVE drives actin protrusions independently of its VCA domain using proline-rich domains

Cell migration requires the constant modification of cellular shape by reorganization of the actin cytoskeleton. Fine-tuning of this process is critical to ensure new actin filaments are formed only at specific times and in defined regions of the cell. The Scar/WAVE complex is the main catalyst of pseudopod and lamellipodium formation during cell migration. It is a pentameric complex highly conserved through eukaryotic evolution and composed of Scar/WAVE, Abi, Nap1/NCKAP1, Pir121/CYFIP, and HSPC300/Brk1. Its function is usually attributed to activation of the Arp2/3 complex through Scar/WAVE's VCA domain, while other parts of the complex are expected to mediate spatial-temporal regulation and have no direct role in actin polymerization. Here, we show in both B16-F1 mouse melanoma and Dictyostelium discoideum cells that Scar/WAVE without its VCA domain still induces the formation of morphologically normal, actin-rich protrusions, extending at comparable speeds despite a drastic reduction of Arp2/3 recruitment. However, the proline-rich regions in Scar/WAVE and Abi subunits are essential, though either is sufficient for the generation of actin protrusions in B16-F1 cells. We further demonstrate that N-WASP can compensate for the absence of Scar/WAVE's VCA domain and induce lamellipodia formation, but it still requires an intact WAVE complex, even if without its VCA domain. We conclude that the Scar/WAVE complex does more than directly activating Arp2/3, with proline-rich domains playing a central role in promoting actin protrusions. This implies a broader function for the Scar/WAVE complex, concentrating and simultaneously activating many actin-regulating proteins as a lamellipodium-producing core.

Diverse soliton wave profile analysis in ion-acoustic wave through an improved analytical approach

In engineering and applied sciences, several physical phenomena can be more precisely characterized by employing nonlinear fractional partial differential equations. The primary goal of this research is to examine the traveling wave solution in closed form for the nonlinear acoustic wave propagation model known as the time fractional simplified modified Camassa–Holm equation, which is used to explain the unidirectional propagation of shallow-water waves with non-hydrostatic pressure and explains the dispersion properties of numerous phenomena like fluid flow, control theory, liquid drop patterning in plasma, acoustics, fusion, and fission processes, etc. The utmost potential approach, namely the new auxiliary equation technique, is applied for analyzing the time nonlinear fractional simplified modified Camassa-Holm equation in the logic of the newest established truncated M-fractional derivative. The fractional partial differential equations have been transformed to the ordinary differential equation using the complex wave transformation in the sense of truncated M-fractional derivative. A variety of soliton solutions, including anti-kink, single soliton, anti-bell, bell, kink, multiple soliton, double soliton, singular-kink, compacton shape, periodic shape, and so many, are displayed in the diagram of 3D and contour plots by taking into account a number of various parameters. It is essential to point out that all derived outcomes are directly compared to the original solutions to certify their exactness. Results show that the used scheme is capable, simple, and straightforward and can be useful to a variety of complex phenomena. The acquired results are unique for the model equation and could be applied to the analysis of several nonlinear study fields.

Strain rate sensitivity of rotating-square auxetic metamaterials

This study provides an in-depth analysis of the mechanical behavior of rotating-square auxetic structures under various strain rates. The structures are fabricated using stereolithography additive manufacturing with a flexible resin. Mechanical tests performed on structures include quasi-static, intermediate, and high strain rate compression tests, supplemented by high-speed optical imaging and two-dimensional digital image correlation analyses. In quasi-static conditions (5 × 10–3 s-1), multiscale measurements reveal the correlation between local and global strains. It is shown that cell hinges play a significant role in structural deformation and load-bearing capacity. In drop tower impact conditions (intermediate strain rate of ca. 200 s-1), the auxetic structures display significant strain rate hardening compared to loading at quasi-static rates. The thin-hinge structures maintain a Poisson's ratio of approximately -0.8, showing higher auxeticity than slow-rate compression tests. High strain rate conditions (ca. 2000s-1) activate additional deformation mechanisms, including a delayed state of equilibrium exemplified by a heterogeneous distribution of lateral strains, possibly due to stress wave interactions and inertial stresses. The study further reveals nonlinear correlations between Poisson's ratio, strain, and strain rate, indicating reduced auxeticity at higher strain rates. These observations are discussed in terms of complex wave interactions and the strain rate hardening characteristics of the base polymer.

The Ithildin library for efficient numerical solution of anisotropic reaction-diffusion problems in excitable media

Ithildin is an open-source library and framework for efficient parallelized simulations of excitable media, written in the C++ programming language. It uses parallelization on multiple CPU processors via the message passing interface (MPI). We demonstrate the library’s versatility through a series of simulations in the context of the monodomain description of cardiac electrophysiology, including the S1S2 protocol, spiral break-up, and spiral waves in ventricular geometry. Our work demonstrates the power of Ithildin as a tool for studying complex wave patterns in cardiac tissue and its potential to inform future experimental and theoretical studies. We publish our full code with this paper in the name of open science.

The effect of ship-induced wave trains on periphytic algal communities in the littoral zone of a large regulated river (River Danube, Austria)

Riverine ecosystems are profoundly influenced by hydrological dynamics and natural flow regimes, which dictate the temporal variability of water levels and the amplitude of fluctuations. Human activities, particularly navigation and hydropower generation, have significantly altered these natural patterns, leading to detrimental impacts on the physical, chemical, and biological integrity of river ecosystems. The littoral zone, in particular, is highly susceptible to anthropogenic disturbances, experiencing disruptions in biological activity and biogeochemical processes. This study evaluates the effects of ship-induced wave trains on the structural and functional properties of periphytic algal communities in a regulated river environment. Using data from the Austrian Danube River, periphytic algae's immediate and long-term responses to wave events generated by different types of ships were investigated. Immediate reactions of periphytic algae to wave trains were characterized by reductions in the effective quantum yield of PS II, indicating stress-induced down-regulation of photosystem II photochemistry. Abrasion and remobilization of periphytic algae due to wave action led to increased resuspension of chlorophyll-a into the water column. Furthermore, ship-induced wave trains influenced the pigment composition of periphyton, with photoprotective mechanisms being activated in response to fluctuating light conditions. Long-term effects of wave impact on periphytic algae biomass varied depending on water depth and exposure to aerial stress. While wave action mitigated desiccation stress in shallow areas, it resulted in biomass reduction and alterations in community composition in deeper zones. Notably, the occurrence of diatoms decreased in wave-impacted areas, potentially shifting the community towards Chlorophyceae dominance. Overall, this study underscores the complexity of ship-induced wave impacts on riverine ecosystems and highlights the importance of considering both immediate and long-term responses of periphytic algal communities. Understanding these dynamics is crucial for informing sustainable management strategies aimed at mitigating the adverse effects of navigation activities on riverine biodiversity and ecosystem functioning.

Relative Moment Tensor Inversion for Microseismicity: Application to Clustered Earthquakes in the Cascadia Forearc

The relative abundance of small earthquakes affords significant opportunities for improved understanding of regional seismotectonics; however, determining moment tensors for such events recorded on regional networks is complicated by low signal-to-noise ratios, sparse station sampling and complex wave propagation at short periods. We build upon previous work in designing a multiple-event, simultaneous moment tensor inversion scheme for small earthquakes that employs constraints from P-wave polarities, relative amplitudes of P- and S-waves recorded at common stations, and local magnitude estimates. Our method does not require a priori knowledge of a reference moment tensor. High-fidelity polarity and relative amplitude data are recovered using principal component decomposition of clustered-event waveforms. These data are employed within a multi-stage iterative framework to invert for moment tensors and incorporate local magnitude information. Synthetic examples employing as few as four high-quality and spatially-distributed stations yield accurate moment tensor estimates. We demonstrate our approach on a cluster of seismicity near San Juan Island, Washington, USA, within the Cascadia forearc. Our results are consistent with previous characterization of the local stress regime, and support an interpretation of swarm behaviour resulting from migration of fluids originating from dehydration of the subducting Juan de Fuca plate.

Nonlinear Complex Wave Excitations in (2+1)-Dimensional Klein–Gordon Equation Investigated by New Wave Transformation

The Klein–Gordon equation plays an important role in mathematical physics, such as plasma and, condensed matter physics. Exploring its exact solution helps us understand its complex nonlinear wave phenomena. In this paper, we first propose a new extended Jacobian elliptic function expansion method for constructing rich exact periodic wave solutions of the (2+1)-dimensional Klein–Gordon equation. Then, we introduce a novel wave transformation for constructing nonlinear complex waves. To demonstrate the effectiveness of this method, we numerically simulated several sets of complex wave structures, which indicate new types of complex wave phenomena. The results show that this method is simple and effective for constructing rich exact solutions and complex nonlinear wave phenomena to nonlinear equations.

Classical and nonclassical Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to a 3D-modified nonlinear wave equation in liquid involving gas bubbles

The current paper undertakes an in-depth exploration of the dynamics of nonlinear waves governed by a 3D-modified nonlinear wave equation, a significant model in the study of complex wave phenomena. To this end, the study employs both classical and nonclassical Lie symmetries for rigorously deriving invariant solutions of the governing equation. These symmetries enable the formal construction of exact solutions, which are crucial for understanding the complex behavior of the model. Furthermore, the research extends into the realm of bifurcation analysis through the application of planar dynamical system theory. Such an analysis reveals the conditions under which the 3D-modified nonlinear wave equation admits Jacobi elliptic function solutions. The study also delves into the impact of the nonlinear parameter on the physical characteristics of bright and kink solitary waves as well as continuous periodic waves using Maple. Overall, the comprehensive analysis presented not only enhances the understanding of complex nonlinear wave dynamics but also sets the stage for future advancements in vast areas of fluid dynamics and plasma physics.

Review of Atrioventricular Node Ablation Combined with Permanent His-Purkinje Conduction System Pacing in Patients with Atrial Fibrillation with Heart Failure.

With the advancement of pacing technologies, His-Purkinje conduction system pacing (HPCSP) has been increasingly recognized as superior to conventional right ventricular pacing (RVP) and biventricular pacing (BVP). This method is characterized by a series of strategies that either strengthen the native cardiac conduction system or fully preserve physical atrioventricular activation, ensuring optimal clinical outcomes. Treatment with HPCSP is divided into two pacing categories, His bundle pacing (HBP) and left bundle branch pacing (LBBP), and when combined with atrioventricular node ablation (AVNA), can significantly improve left ventricular (LV) function. It effectively prevents tachycardia and regulates ventricular rates, demonstrating its efficacy and safety across different QRS wave complex durations. Therefore, HPCSP combined with AVNA can alleviate symptoms and improve the quality of life in patients with persistent atrial fibrillation (AF) who are unresponsive to multiple radiofrequency ablation, particularly those with concomitant heart failure (HF) who are at risk of further deterioration. As a result, this "pace and ablate" strategy could become a first-line treatment for refractory AF. As a pacing modality, HBP faces challenges in achieving precise localization and tends to increase the pacing threshold. Thus, LBBP has emerged as a novel approach within HPCSP, offering lower thresholds, higher sensing amplitudes, and improved success rates, potentially making it a preferable alternative to HBP. Future large-scale, prospective, and randomized controlled studies are needed to evaluate patient selection and implantation technology, aiming to clarify the differential clinical outcomes between pacing modalities.

Full transmission of vectorial waves through 3D multiple-scattering media.

A striking prediction from the random matrix theory (RMT) in mesoscopic physics is the existence of "open channels": waves that use multipath interference to achieve perfect transmission across an opaque disordered medium even in the multiple-scattering regime. Realization of such open channels requires a coherent control of the complete incident wavefront and has only been achieved for scalar waves in two dimensions (2D) so far. Here, we utilize a recently proposed "augmented partial factorization" full-wave simulation method to compute the polarization-resolved scattering matrix from 3D vectorial Maxwell's equations and demonstrate the existence of open channels in 3D disordered media. We examine the spatial profile of such open channels, demonstrate the existence of a bimodal transmission eigenvalue distribution, and study the effects of incomplete polarization control and finite-area illumination. The simulations provide full access to all spatiotemporal properties of the complex wave transport in 3D disordered systems, filling the gap left by experimental capabilities.

Long-range-interacting topological photonic lattices breaking channel-bandwidth limit

The presence of long-range interactions is crucial in distinguishing between abstract complex networks and wave systems. In photonics, because electromagnetic interactions between optical elements generally decay rapidly with spatial distance, most wave phenomena are modeled with neighboring interactions, which account for only a small part of conceptually possible networks. Here, we explore the impact of substantial long-range interactions in topological photonics. We demonstrate that a crystalline structure, characterized by long-range interactions in the absence of neighboring ones, can be interpreted as an overlapped lattice. This overlap model facilitates the realization of higher values of topological invariants while maintaining bandgap width in photonic topological insulators. This breaking of topology-bandgap tradeoff enables topologically protected multichannel signal processing with broad bandwidths. Under practically accessible system parameters, the result paves the way to the extension of topological physics to network science.

Atypical second harmonic A0 mode Lamb waves in non-uniform plates for local incipient damage monitoring

Plates with non-uniform thickness, such as stiffened and notched plates, are commonly seen in engineering applications. Monitoring incipient damage in these structures is crucial to ensure their safety during service. Second harmonic Lamb waves hold great promise for structural health monitoring applications. However, the mechanisms underpinning the generation of the second harmonic Lamb waves in non-uniform plates are still not well understood due to the complex wave field. To tackle this issue, a theoretical analysis is first conducted to highlight the so-called atypical second harmonic A0 mode waves (2nd A0 waves) generated at the structural non-uniform section. Their existence, as well as their potential for local incipient damage monitoring applications, is then confirmed by finite element simulations. Experiments are carried out on a notched aluminum plate to monitor the incipient plastic damage induced by bending. Three mechanisms contributing to the generation of the atypical 2nd A0 waves in the non-uniform plate are identified: mode conversion from the second harmonic S0 mode waves, asymmetric nonlinear driving forces at the non-uniform section, and the mutual interaction between the mode-converted fundamental A0 and S0 waves. This study shows that the reported atypical 2nd A0 waves provide an effective means for monitoring local incipient damage in non-uniform structures.

Dynamic responses of steep bedding slope-tunnel system under coupled rainfall-seismicity: Shaking table test

The coupling effects of rainfall, earthquake, and complex topographic and geological conditions complicate the dynamic responses and disasters of slope-tunnel systems. For this, the large-scale shaking table tests were carried out to explore the dynamic responses of steep bedding slope-tunnel system under the coupling effect of rainfall and earthquake. Results show that the slope surface and elevation amplification effect exhibit pronounced nonlinear change caused by the tunnel and weak interlayers. When seismic wave propagates to tunnels, the weak interlayers and rock intersecting areas present complex wave field distribution characteristics. The dynamic responses of the slope are influenced by the frequency, amplitude, and direction of seismic waves. The acceleration amplification coefficient initially rises and then falls as increasing seismic frequency, peaking at 20 Hz. Additionally, the seismic damage process of slope is categorized into elastic (2-3 m/s2), elastoplastic (4-5 m/s2) and plastic damage stages (≥ 6.5m/s2). In elastic stage, ΔMPGA (ratio of acceleration amplification factor) increases with increasing seismic intensity, without obvious strain distribution change. In plastic stage, ΔMPGA begins to gradually plummet, and the strain is mainly distributed in the damaged area. The modes of seismic damage in the slope-tunnel system are mainly of tensile failure of the weak interlayer, cracking failure of tunnel lining, formation of persistent cracks on the slope crest and waist, development and outward shearing of the sliding mass, and buckling failure at the slope foot under extrusion of the upper rock body. This study can serve as a reference for predicting the failure modes of tunnel-slope system in strong seismic regions.