Complex Wave Research Articles

Analytical and numerical solutions to the generalized Schrödinger equation with fourth-order dispersion and nonlinearity

This study aims to solve the generalized Schrödinger equation with fourth-order dispersion and cubic-quintic nonlinearity (4-Order-GNLSE) using advanced analytical and numerical methods. The 4-Order-GNLSE is critical in understanding complex wave propagation phenomena in various physical contexts, including optical fibers and fluid dynamics, where higher-order dispersion and nonlinear effects are significant. We employ the Khater II (Khat II) and modified Rational (MRat) methods to construct analytical solutions. To validate these solutions, we utilize the trigonometric-quantic-B-spline (TQBS) method as a numerical scheme, demonstrating a close match between analytical and numerical results. Our findings indicate that the proposed methods effectively capture the intricate dynamics governed by the 4-Order-GNLSE. The results highlight the relevance of these solutions in practical applications, offering new insights into the wave propagation behaviors influenced by higher-order dispersion and nonlinearities. This research provides a significant contribution to the field of nonlinear wave equations, presenting novel solutions and validating methodologies that enhance our understanding and potential applications of these complex systems.

Identifying Topological Defects in Lamellar Phases through Contour Analysis of Complex Wave Fields

Identifying Topological Defects in Lamellar Phases through Contour Analysis of Complex Wave Fields

Soliton solutions and sensitive analysis to nonlinear wave model arising in optics

In this study, we use analytical algorithms, specifically the auxiliary equation (AE) approach, the improved F-expansion method, and the modified Sardar sub-equation (MSSE) method to investigate complex wave structures for plentiful solutions associated with the fractional perturbed Gerdjikov-Ivanov (PGI) model with the M-fractional operator. The investigated model is a well-established mathematical model used to represent a variety of physical events in nonlinear dynamics and mathematical physics. By using the aforementioned techniques, we scrutinize some new optical wave solutions in the framework of dark, bright, periodic, combo, W-shaped, M-shape, V-shape, kink type, singular rational, exponential, trigonometric, and hyperbolic solutions. The acquired solutions address a wide range of optical solutions in the form of 3D plots, contour plots, and 2D plots, declaring the free parameters of such optical soliton solutions and comprehending their dynamic behavior. Also, the sensitive analysis of the selected model is analyzed. The main contribution of this study is to extract diverse solitary wave solutions of the adopted model. Some of the solutions are similar and some diverge from the previous solutions which justifies the novelty of the study. Finally, we discovered that the current technique provides a reliable instrument for investigating the analytic solutions of fractional differential equations. The proposed PGI model can be used to transmit ultra-fast pulses across optical fibers. This research goes beyond to the advancement of mathematical techniques for solving fractional differential equations and broadens their application to a wide range of real-world scientific and engineering problems.

Controllable manipulation of surface waves via a ferromagnetic elastic metasurface

In this paper, we study the propagation of surface waves on an A-shape metasurface, whose structure of the unit-cell is composed regularly of an A-shape surface column (made of steel), a thin magnetorheological plate and a soft thick rubber base. On the basis of the commercial program COMSOL Multiphysics, finite element method (FEM) analyses are carried out. The localization of elastic waves surrounding the surface allows surface waves to be distinguished among various complex wave modes. By adjusting the geometry, the A-shape surface column can be transformed from snowflake to A-shape. Owing to the C3v symmetry system, a Dirac cone of surface wave is observed in a snowflake metasurface. When the surface column changes to A-shape, the C3v symmetry is broken, making the Dirac cone vanish and a new band gap of surface waves arise. The band gap can be opened or closed by changing a geometric parameter, which determines the shape of the surface column changing from gadarene A-shape to snowflake or even upturned A-shape. Furthermore, we discover that although the topological phases of the gadarene A-shape and upturned A-shape metasurfaces are opposite, they share overlapped band gaps. Based on this phenomenon, we design a topological insulator for surface waves, whose super-cell is composed of gadarene A-shape units and upturned A-shape units. Through the calculation of the super-cell band structure, we observe the topologically protected interface states (TPISs). Subsequently, we design several waveguides whose paths are controllable. Up to now, most of the existing metasurfaces are made of passive materials, whose properties cannot be adjusted in real time, making them inconvenient for engineering applications when external conditions are changed. Therefore, we use tunable magnetorheological elastomer (MRE) to control the properties of the topological insulators. The stiffness of the surface layer can be converted by applying a magnetic field, which makes the topological metasurface controllable. These intelligent topological insulators may find important applications in the design of surface acoustic wave (SAW) devices.

Multicomponent nonlinear fractional Schrödinger equation: On the study of optical wave propagation in the fiber optics

In this article, we investigate the soliton wave dynamics of the fractional three-component coupled nonlinear Schrödinger equation. This equation is considered as a fundamental tool for describing the behavior of optical pulses in optical fibers. There is increasing interest in studying these equations as they can be used to explain a wide range of complex physical phenomena in various scientific and engineering fields, including nonlinear fiber optics, electromagnetic field waves, and signal processing through optical fibers. In order to obtain the required solutions, the first step is to apply the complex wave transformations with β-fractional derivative to obtain the nonlinear ordinary differential equations of the governing model. Furthermore, by applying the novel integration methods known as generalized Arnous method and multivariate generalized exponential rational integral function approach, different type of soliton solutions are extracted. Different sets and values of the physical parameters are used to study the optical soliton solutions of the studied system. Based on a comparative analysis of our results with existing techniques, this study concludes that our proposed solutions are novel. The results described in this work are able to enhance the nonlinear dynamical behavior of a given system and confirm the effectiveness of the methods used. Furthermore, the different graphs are sketched to visualize the solutions behavior with various parametric values. It is anticipated that obtained solutions will be significant in the study of wave propagation and other related fields.

The WAVE complex forms linear arrays at negative membrane curvature to instruct lamellipodia formation.

Cells generate a wide range of actin-based membrane protrusions for various cell behaviors. These protrusions are organized by different actin nucleation promoting factors. For example, N-WASP controls finger-like filopodia, whereas the WAVE complex controls sheet-like lamellipodia. These different membrane morphologies likely reflect different patterns of nucleator self-organization. N-WASP phase separation has been successfully studied through biochemical reconstitutions, but how the WAVE complex self-organizes to instruct lamellipodia is unknown. Because WAVE complex self-organization has proven refractory to cell-free studies, we leverage in vivo biochemical approaches to investigate WAVE complex organization within its native cellular context. With single molecule tracking and molecular counting, we show that the WAVE complex forms highly regular multilayered linear arrays at the plasma membrane that are reminiscent of a microtubule-like organization. Similar to the organization of microtubule protofilaments in a curved array, membrane curvature is both necessary and sufficient for formation of these WAVE complex linear arrays, though actin polymerization is not. This dependency on negative membrane curvature could explain both the templating of lamellipodia and their emergent behaviors, including barrier avoidance. Our data uncover the key biophysical properties of mesoscale WAVE complex patterning and highlight an integral relationship between NPF self-organization and cell morphogenesis.

Wave Impedance Determination for PCB SIWs Considering Metal Roughness Loss Effects.

This paper presents an expression to determine the complex wave impedance of a substrate-integrated waveguide for the dominant TE10 propagation mode, notably enhancing the accuracy in modeling the corresponding imaginary part. This was accomplished by systematically identifying the need to consider additional conductor losses caused by the interaction of the propagating fields with the conductor material. In fact, by using the proposed expression, the complex impedance can straightforwardly be determined by combining propagation constant data, and the resistance that represents the loss associated with longitudinal currents occurring at the top and bottom walls, which are influenced by the conductor surface roughness. This allows for completely describing the characteristics of the waveguide when assuming uniform propagation along its length. Furthermore, since the voltage-current, the power-current, and the power-voltage impedances can easily be obtained from the wave impedance, the proposal enables representing the matching characteristics of the waveguide for circuit design purposes. An agreement between simulated and experimental insertion loss is achieved for substrate-integrated waveguides of two different widths when reconstructing the corresponding S-parameters using the determined wave impedance.

Exploring the Atwood number impact on shock-driven hydrodynamic instability at pentagonal interface using discontinuous Galerkin simulations

Investigation of Atwood number impact is crucial for comprehending the flow dynamics of the evolving hydrodynamic instability. In this paper, the Atwood number impacts on the shock-driven hydrodynamic instability at a backward-facing pentagonal interface in its early stages are explored numerically. The shock-driven pentagonal interface has a unique property in which the incident angle of the shock wave is constant along the interface edge. This property provides the ideal environment for the shock-refraction process. To examine the Atwood number impact, we consider five distinct gases, including sulfur hexafluoride, krypton, argon, neon, and helium, which are filled inside the pentagonal interface and surrounded by nitrogen gas. A mixed modal discontinuous Galerkin method is used to solve the two-dimensional Navier–Stokes–Fourier equations for two-component gas flows for numerical simulations. The simulation results illustrate that the Atwood number plays a crucial role in the flow fields of the shocked-pentagonal gas interface, which have not been reported in the literature. The flow fields are greatly impacted by the Atwood number, leading to complex wave patterns, shock focusing, jet formation, interface deformation, and vorticity generation. Further, the Atwood number effects on the flow fields are also thoroughly examined by a quantitative study based on the integral quantities and the interface features. Finally, a quantitative analysis is performed to examine the intrinsic differences between the evolution of the flow fields at the square and pentagonal interfaces.

New exact solitary waves for the Sasa-Satsuma model with variable coefficients

In this paper, we investigate the variable coefficients Sasa-Satsuma model, which can describe the propagation of a light pulse in a cylindrical fiber. We study this model and obtain rich solutions using two separate methods. We obtain analytical Weierstrass elliptic function solutions using the Weierstrass elliptic function expansion method. Some Jacobi elliptic function solutions are obtained using the modified Jacobi elliptic function expansion method. When the Jacobi elliptic function degenerates, we obtain the corresponding trigonometric, hyperbolic function solutions and periodic solutions. We also try to take the coefficients of the equation as some functions and obtain some more complicated exact solutions, which have not appeared in previous studies. Finally, we simulate some waveform diagrams of the solutions using the computer software Mathematica and obtain periodic waves, bright and dark soliton, double solitons and some complex periodic waves. With these waveform diagrams, we can observe the dynamical behavior of the solutions more clearly.

Secure hardware IP of GLRT cascade using color interval graph based embedded fingerprint for ECG detector

This paper presents a security aware design methodology to design secure generalized likelihood ratio test (GLRT) hardware intellectual property (IP) core for electrocardiogram (ECG) detector against IP piracy and fraudulent claim of IP ownership threats. Integrating authentic (secure version) GLRT hardware IP core in the system-on-chip (SoC) of ECG detectors is paramount for reliable operation and estimation of ECG parametric data, such as Q wave, R wave and S wave (QRS) complex detection. A pirated GLRT hardware IP integrated into an ECG detector may result in an unreliable/erratic estimation of ECG parametric data that can be hazardous and fatal for the end patient. The proposed methodology presents an integrated design flow to secure micro GLRT and GLRT cascade hardware IP cores for the ECG detector, using the colored interval graph (CIG) framework based fingerprint biometric, during high level synthesis (HLS). The proposed approach integrates a fingerprint biometric based security constraint generation process for securing the GLRT hardware IP core. This paper also presents a secure register transfer level (RTL) datapath design corresponding to micro GLRT and GLRT cascade hardware IP cores with embedded IP vendor's fingerprint. The proposed secure GLRT hardware IP core embedded with fingerprint biometric achieves superior results in terms of probability of coincidence and tamper tolerance than other security approaches. More explicitly, the proposed approach reports a significantly lower value of probability of coincidence and stronger value for tamper tolerance. Further, the proposed approach incurs zero design cost overhead.

Modulation instability analysis, and characterize time-dependent variable coefficient solutions in electromagnetic transmission and biological field

This study integrates the telegraph model with the traveling wave coefficient. This model characterizes planar random motion of particles in fluid flow, pressure waves from pulsatile blood flow in arteries, electrical impulses in nerve and muscle cell axons, and electromagnetic waves in superconducting media. Using the efficient and well-established Enhanced Modified Simple Equation (EMSE) method, we investigate solitary wave solution with the variable coefficient of the telegraph model. To investigate the variable coefficient solitary wave solution, we apply a transformation variable η = h(t)x + g(t), which is dependent on the time variable function. The diverse functions of h(t) and g(t) yield many novel and exclusive solutions. Numerical solutions are plotted in 3D, density, and 2D. instanton soliton, kinky periodic wave, lump wave, kink wave, anti-kink wave, double periodic wave, diverse types periodic wave, lump with bell wave periodic wave, periodic lump wave, etc. Solitary waves explain complex wave phenomena through nonlinear effects like self-interaction and dispersion. Due to the classical nonlinear telegraph model's wave dynamics, they are used in brain function and communication system design. We conclude by testing the governing model's modulation instability. Dispersive and nonlinear processes modulating the stable state cause instability in high-order nonlinear equations. Examining the wave movement role and modulation instability analysis to assess solution stability shows that all solutions are accurate and stable. The computational difficulties and results demonstrate the approaches' clarity, effectiveness, and simplicity, suggesting they can be applied to evolutionary dynamic and static nonlinear equations in computational physics, other real-world situations, and numerous academic disciplines.

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.