Behavior Of Waves Research Articles

Rogue-wave structures for a generalized (3+1)-dimensional nonlinear wave equation in liquid with gas bubbles

This study explores the behavior of higher-order rogue waves within a (3+1)-dimensional generalized nonlinear wave equation in liquid-containing gas bubbles. It creates the investigated equation’s Hirota D-operator bilinear form. We employ a generalized formula with real parameters to obtain the rogue waves up to the third order using the direct symbolic technique. The analysis reveals that the second and third-order rogue solutions produce two and three-waves, respectively. To gain deeper insights, we use the Cole-Hopf transformation on the transformed variables ξ and η to produce a bilinear equation. Using the system software Mathematica, the dynamic analysis presents the graphics for the obtained solutions in transformed ξ, η, and original spatial-temporal coordinates x, y, z, t. These visualizations reveal rogue waves’ intricate structure and evolution, capturing their localized interactions and significant presence within nonlinear systems. We demonstrate that rogue waves, characterized by their substantial height and sudden appearance, are prevalent in various nonlinear events. The equation examined in this study offers valuable insights into the evolution of longer waves with smaller amplitudes, which is particularly relevant in fields such as fluid dynamics, dispersive media, and plasmas. The implications of this research extend across multiple scientific domains, including fiber optics, oceanography, dusty plasma, and nonlinear systems, where understanding the behavior of rogue waves is crucial for both theoretical and practical applications.

Traveling waves reflecting various processes represented by reaction–diffusion equations

The aim of this paper is to discover analytically the interactional responses of populations in a dynamic region where the reaction–diffusion process with forcing effects takes place through traveling wave solutions. An expansion method is considered here to properly capture the responses for the first time. In order to profoundly analyze the physical and mathematical discussions, some illustrative behavioral results are exhibited for various values of physical parameters. Especially for the different values of diffusion coefficients in the model under consideration, their effects on the behavior of the solitary wave are discussed and observationally supported by considering various illustrations. It is also seen that the solutions representing the diffusion seen to be in the form of the behavior of hexagonal Turing patterns in different time periods. The application of this study in mathematical biology is to analyze the relationship between the population density of certain species in any local region and the specific population density with invasion characteristics. In addition, the formation of the extinction vortex of the invading population, depending on the characteristics of the solutions presented, is also descriptively discussed.

Analytic solutions for effective elastic moduli of isotropic solids containing oblate spheroid pores with critical porosity

AbstractAccurate characterization for effective elastic moduli of porous solids is crucial for better understanding their mechanical behaviour and wave propagation, which has found many applications in the fields of engineering, rock physics and exploration geophysics. We choose the spheroids with different aspect ratios to describe the various pore geometries in porous solids. The approximate equations for compressibility and shear compliance of spheroid pores and differential effective medium theory constrained by critical porosity are used to derive the asymptotic solutions for effective elastic moduli of the solids containing randomly oriented spheroids. The critical porosity in the new asymptotic solutions can be flexibly adjusted according to the elastic moduli – porosity relation of a real solid, thus extending the application of classic David‐Zimmerman model because it simply assumes the critical porosity is one. The asymptotic solutions are valid for the solids containing crack‐like oblate spheroids with aspect ratio < 0.3, nearly spherical pores (0.7 < < 1.3) and needle‐like prolate pores with > 3, instead of just valid in the limiting cases, for example perfectly spherical pores (= 1) and infinite thin cracks (0). The modelling results also show that the accuracies of asymptotic solutions are weakly affected by the critical porosity and grain Poisson's ratio , although the elastic moduli have appreciable dependency of and . We then use the approximate equations for pore compressibility and shear compliance as inputs into the Mori–Tanaka and Kuster–Toksoz theories and compare their calculations to our results from differential effective medium theory. By comparing the published laboratory measurements with modelled results, we validate our asymptotic solutions for effective elastic moduli.

Analysis of Rayleigh wave dynamic response and propagation characteristics in layered site

Rayleigh waves are crucial in earthquake engineering due to their significant contribution to structural damage. This study aims to accurately synthesize Rayleigh wave fields in both uniform elastic half-spaces and horizontally layered elastic half-spaces. To achieve this, we developed a self-programmed FORTRAN program utilizing the thin layer stiffness matrix method. The accuracy of the synthesized wave fields was validated through numerical examples, demonstrating the program’s reliability for both homogeneous and layered half-space scenarios. A comprehensive analysis of Rayleigh wave propagation characteristics was conducted, including elliptical particle motion, depth-dependent decay, and energy concentration near the surface. The computational efficiency of the self-programmed FORTRAN program was also verified. This research contributes to a deeper understanding of Rayleigh wave behavior and lays the foundation for further studies on soil-structure interaction under Rayleigh wave excitation, ultimately improving the safety and resilience of structures in seismic-prone regions.

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.

Surface treatment of metal by combined particle beam

This work is related to modeling of metal surface modification process by combined particles beam. On the basis of thermodynamics of irreversible processes, including equations of state in differential form, a nonlinear model is formulated. The model takes into account the interaction of thermal, diffusion and mechanical waves and finiteness of relaxation times of thermal and diffusion processes. For the combined particle flow such model is proposed for the first time. The numerical algorithm is based on implicit difference schemes. The study of the interaction of waves of different nature is carried out on the example of a copper target treated with nickel and gold particles. It is shown that deformations take the maximal value at the left boundary, which is directly related to the presence of impurity concentration gradients. Depending on the pulse duration, the difference between the extrema on the elastic wave becomes less significant. With increasing temperature, obviously, the diffusion process accelerates. The propagation velocities of the interacting waves are different. The character of distributions of concentrations of introduced particles directly depends on the value of parameters proportional to relaxation times.

Dynamics of Love-type wave propagation in composite transversely isotropic porous structures

The present study aims to analyze the propagation behavior of Love-type wave in a composite transversely isotropic porous structure. The structure comprises an inhomogeneous sandy porous layer lying between a non-homogeneous magneto-poroelastic layer and a heterogeneous fractured porous half-space. Analytic solutions of the field equations of the respective media involve the application of the variable separable method and Wentzel-Kramers-Brillouin (WKB) asymptotic approach for the conversion of partial differential equations into ordinary differential equations. Through careful imposition of boundary conditions and subsequent elimination of arbitrary constants, we derive a complex dispersion relation governing the propagation of Love-type waves. This dispersion equation yields both the phase velocity curve, corresponding to the real expression, and the damping velocity curve, derived from the imaginary expression. To represent our findings, we conduct extensive calculations and graphical simulations illustrating the influence of various material parameters such as heterogeneity, porosity, volume fraction of fractures, sandiness, magnet-oelastic coupling, angle at which wave crosses the magnetic field, and layer thickness on the dispersive nature of Love-type waves using MATHEMATICA software. Furthermore, we conduct case-specific analyses, revealing instances where the dispersion equation simplifies to the standard Love wave equation, thereby validating our mathematical framework. Our findings underscore the significant influence of the aforementioned material parameters on the phase and damping velocities of Love-type wave. This interdisciplinary investigation into different porous media opens new avenues for future research and has significant implications in various disciplines, ranging from engineering and geophysics to environmental science and beyond.

On examining the predictive capabilities of two variants of the PINN in validating localized wave solutions in the generalized nonlinear Schrödinger equation

We introduce a novel neural network structure called strongly constrained theory-guided neural network (SCTgNN), to investigate the behaviour of the localized solutions of the generalized nonlinear Schrödinger (NLS) equation. This equation comprises four physically significant nonlinear evolution equations, namely, the NLS, Hirota, Lakshmanan–Porsezian–Daniel and fifth-order NLS equations. The generalized NLS equation demonstrates nonlinear effects up to quintic order, indicating rich and complex dynamics in various fields of physics. By combining concepts from the physics-informed neural network and theory-guided neural network (TgNN) models, the SCTgNN aims to enhance our understanding of complex phenomena, particularly within nonlinear systems that defy conventional patterns. To begin, we employ the TgNN method to predict the behaviour of localized waves, including solitons, rogue waves and breathers, within the generalized NLS equation. We then use the SCTgNN to predict the aforementioned localized solutions and calculate the mean square errors in both the SCTgNN and TgNN in predicting these three localized solutions. Our findings reveal that both models excel in understanding complex behaviour and provide predictions across a wide variety of situations.

Convergence and divergence of storm waves induced by multi-scale currents: Observations and coupled wave-current modeling

Current effects on waves (CEW) are among the most intricate physical processes in wave evolution. In this study, we used a coupled wave-tide-circulation model for the Northwest Atlantic to investigate current effects on storm waves during Hurricane Igor in 2010. Validated with extensive buoy and altimeter data, the inclusion of CEW in the model significantly improves the accuracy in simulating significant wave heights (Hs) by up to 21.3% for a wave buoy. Storm waves experience significant temporal and spatial modulation by multi-scale currents. Storm-driven currents have the most pronounced impact to the right of the storm track, which typically align with wave propagation and reduce Hs by up to 12.1%. The subsequent near-inertial oscillations induce temporal fluctuations of wave convergence and divergence at near-inertial frequencies, which also occurs in regions with strong tidal currents but at tidal frequencies. Furthermore, storm waves are modulated by the Gulf Stream, Labrador Current and associated mesoscale eddies. Overall, these multi-scales yield strong effects on storm waves (Hs > 3.0 m), significantly modulating Hs (−25.2%–+55.4%) and mean wave periods (−14.9%–+15.7%). The mean wave energy power shows more significant modulation by multi-scale currents, reflecting the combined effects of changing wave states and current-induced transport of wave energy. CEW are governed by the interactive dynamic and kinematic effects. The relative wind effect is the primary mechanism for lower storm waves by reducing energy input to waves and influences downstream wave states. Among kinematic effects, current-induced wave refraction typically plays a dominant role in redistributing wave energy. This study systematically quantified the modulation of storm waves by multi-scale currents and revealed the underlying mechanisms, providing a comprehensive understanding of extreme wave states under coupled ocean dynamics.

Optical soliton solutions for the nonlinear Schrödinger equation with higher-order dispersion arise in nonlinear optics

Optical solitons and traveling wave solutions for the higher-order dispersive extended nonlinear Schrödinger equation are studied. Ultrashort pulse propagation in optical communication networks is described by this equation. To find exact solutions to the model, the unified Riccati equation expansion method and the Jacobi elliptic function expansion method are successfully applied. The optical solutions includes various solitary wave solutions, such as dark, bright, combined dark-bright, singular, combined periodic, periodic, Jacobian elliptic, and rational functions. Three-dimensional and two-dimensional graphs of solutions are presented. Also, the dynamical behavior of waves and the impact of time on solutions by selecting appropriate parameters are illustrated.

Simple waves for anti-van der Waals modified Chaplygin gas in 2-D magnetohydrodynamics

Abstract This paper presents essential findings on the reducible equations introduced by Courant and Friedrichs in their seminal work, Supersonic Flow and Shock Waves. In this paper, we discuss the presence of simple waves in a 2-D magnetohydrodynamic system with an anti-van der Waals-modified Chaplygin gas. Following the approach of Hu and Sheng (characteristic decomposition of the 2 × 2 quasilinear strictly hyperbolic systems). Appl. Math. Lett. 25(3), 262–267 (2012), and (simple waves and characteristic decompositions of quasilinear hyperbolic systems in two independent variables). Math. Methods Appl. Sci. 38(8), 1494–1505 (2015) for the characteristic decomposition of a strictly hyperbolic system, we establish the existence of simple waves for a non-reducible system. This extends Courant and Friedrichs’s fundamental finding, which was initially proposed for reducible system (R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, New York, Interscience Publishers, Inc, 1948, p. 464). These results enhance our understanding of simple wave behaviour in magnetohydrodynamic systems with modified Chaplygin gas, expanding the applicability of Courant and Friedrichs’s theoretical framework.

Wave Mechanics of Microwave Absorption in Films: Multilayered Films

Wave Mechanics of Microwave Absorption in Films: Multilayered Films

Response of Upper Ocean to Parameterized Schemes of Wave Breaking under Typhoon Condition

The study of upper ocean mixing processes, including their dynamics and thermodynamics, has been a primary focus for oceanographers and meteorologists. Wave breaking in deep water is believed to play a significant role in these processes, affecting air–sea interactions and contributing to the energy dissipation of surface waves. This, in turn, enhances the transfer of gas, heat, and mass at the ocean surface. In this paper, we use the FVCOM-SWAVE coupled wave and current model, which is based on the MY-2.5 turbulent closure model, to examine the response of upper ocean turbulent kinetic energy (TKE) and temperature to various wave breaking parametric schemes. We propose a new parametric scheme for wave breaking energy at the sea surface, which is based on the correlation between breaking wave parameter RB and whitecap coverage. The impact of this new wave breaking parametric scheme on the upper ocean under typhoon conditions is analyzed by comparing it with the original parametric scheme that is primarily influenced by wave age. The wave field simulated by SWAVE was verified using Jason-3 satellite altimeter data, confirming the effectiveness of the simulation. The simulation results for upper ocean temperature were also validated using OISST data and Argo float observational data. Our findings indicate that, under the influence of Typhoon Nanmadol, both parametric schemes can transfer the energy of sea surface wave breaking into the seawater. The new wave breaking parameter RB scheme effectively enhances turbulent mixing at the ocean surface, leading to a decrease in sea surface temperature (SST) and an increase in mixed layer depth (MLD). This further improves upon the issue of uneven mixing of seawater at the air–sea interface in the MY-2.5 turbulent closure model. However, it is important to note that wave breaking under typhoon conditions is only one aspect of wave impact on ocean disturbances. Therefore, further research is needed to fully understand the impact of waves on upper ocean mixing, including the consideration of other wave mechanisms.

Modelling collective invasion with reaction–diffusion equations: When does domain curvature matter?

Real-world cellular invasion processes often take place in curved geometries. Such problems are frequently simplified in models to neglect the curved geometry in favour of computational simplicity, yet doing so risks inaccuracies in any model-based predictions. To quantify the conditions under which neglecting a curved geometry is justifiable, we explore the dynamics of a system of reaction–diffusion equations (RDEs) on a two-dimensional annular geometry analytically. Defining ϵ as the ratio of the annulus thickness δ and radius r0 we derive, through an asymptotic expansion, the conditions under which it is appropriate to ignore the domain curvature for a general system of reaction–diffusion equations. To highlight the consequences of these results, we simulate solutions to the Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher–KPP) model, a paradigm nonlinear RDE typically used to model spatial invasion, on an annular geometry. Thus, we quantify the size of the deviation from an analogous simulation on the rectangle, and how this deviation changes across the width of the annulus. We further characterise the nature of the solutions through numerical simulations for different values of r0 and δ. Our results provide insight into when it is appropriate to neglect the domain curvature in studying travelling wave behaviour in RDEs.

The mBBM equation: a mathematical key to unlocking wave behavior in fluids

The mBBM equation: a mathematical key to unlocking wave behavior in fluids

Numerical investigation on the VIV response of the flexible cylindrical structures subjected to non-linearly varying shear flow

Vortex-induced vibration (VIV) of flexible cylinders is an important phenomenon in ocean structures, which may cause fatigue damage and structural failure of offshore structures. Much literature has extensively explored VIV of flexible cylinders under various flow conditions, such as uniform and linearly varying shear flow. However, real scenarios in most cases involve non-uniform, non-linearly varying shear flow profiles. Hence, it is important to investigate the VIV response of the flexible cylindrical structures subjected to non-linearly varying shear flow profiles. This study employs a wake oscillator model (WOM) that simulates the VIV response of the flexible cylinder under the action of non-linearly varying shear flow velocity profiles. The flexible cylinder subjected to linearly varying sheared flow velocity profiles not only overpredicts but also underpredicts the VIV responses compared to the non-linearly varying sheared flow profile, which represents the real scenario. The VIV mode number for the flexible cylinder subjected to non-linear shear flow was found to have a non-linear relationship with that of linear shear flow. The VIV response of the flexible cylinder subjected to a linearly varying shear flow profile exhibits more travelling wave behaviour compared to non-linear shear flow. The location of the maximum VIV response of the structure having the same aspect ratio (L/D) and shear parameter (β), was different for linear and non-linear flow profiles across the span. The time and frequency domain responses showed a shift in the frequency band. The results obtained from the numerical simulations give better insights into the vibrational behaviour of flexible cylinders in realistic flow environments.

Unveiling the charge density wave mechanism in vanadium-based Bi-layered kagome metals

The charge density wave (CDW), as a hallmark of vanadium-based kagome superconductor AV3Sb5 (A = K, Rb, Cs), has attracted intensive attention. However, the fundamental controversy regarding the underlying mechanism of CDW therein persists. Recently, the vanadium-based bi-layered kagome metal ScV6Sn6, reported to exhibit a long-range charge order below 94 K, has emerged as a promising candidate to further clarify this core issue. Here, employing micro-focusing angle-resolved photoemission spectroscopy (μ-ARPES) and first-principles calculations, we systematically studied the unique CDW order in vanadium-based bi-layered kagome metals by comparing ScV6Sn6 with its isostructural counterpart YV6Sn6, which lacks a CDW ground state. Combining ARPES data and the corresponding joint density of states (DOS), we suggest that the VHS nesting mechanism might be invalid in these materials. Besides, in ScV6Sn6, we identified multiple hybridization energy gaps resulting from CDW-induced band folding, along with an anomalous band dispersion, implying a potential electron-phonon coupling-driven mechanism underlying the formation of the CDW order. Our finding not only comprehensively maps the electronic structure of V-based bi-layer kagome metals but also provides constructive experimental evidence for the unique origin of CDW in this system.

Internal Variability Dominated the Extreme Cold Wave Over North America in December 2022

AbstractIn December 2022, North America experienced an unprecedented extreme cold event. However, the underlying physical mechanisms of this cold wave, and the extent to which it is driven by internal variability or external forcing, are not fully understood. Using ERA5 reanalysis data and the HadGEM3‐A‐N216 attribution simulations, we identified internal variability as the main cause, contributing −5.14 K to surface air temperature (SAT) anomalies in North America. External forcing slightly mitigated the cold by 0.42 K. An internally generated wave train from the North Pacific, influenced in combination by Pacific‐North American (PNA) and North Pacific Oscillation (NPO) teleconnection patterns, initiated this intense cyclonic event, contributing −2.18 K and −2.12 K to SAT anomalies, respectively. La Niña‐like sea surface temperature anomalies amplified this wave train and resultant cold wave. Additionally, excessive snow cover in the previous November also intensified the December cold anomalies by enhancing surface albedo and reducing solar radiation.

Detection of natural pulse waves (PWs) in 3D using high frame rate imaging for anisotropy characterization

IntroductionNumerous studies have shown that natural mechanical waves have the potential to assess the elastic properties of the myocardium. When the Aortic and Mitral valves close, a shear wave is produced, which provides insights into tissue stiffness. In addition, the Atrial Kick (AK) generates a wave similar to Pulse Waves (PWs) in arteries, providing another way to assess tissue stiffness. However, tissue anisotropy can also impact PW propagation, which is currently underexplored. This study aims to address this gap by investigating the impact of anisotropy on PW propagation in a phantom.MethodsTube phantoms were created using Polyvinyl Alcohol (PVA). Anisotropy was induced between two sets of two freeze-thaw cycles by stretching and twisting the material. The study first tests and validates the procedure of making helical anisotropic vessel phantoms using the shear wave imaging technique (by estimating the shear wave speed at different probe angles). Using plane wave ultrasound tomography synchronized with a peristaltic pump, 3D high frame rate imaging is performed and used to detect the 3D propagation pattern of PW for each manufactured vessel phantom. Finally, the study attempts to extract the anisotropic coefficient of the vessel using pulse wave propagation angle.ResultsThe Shear wave imaging results obtained for the isotropic vessel show very similar values for each probe angle. On the contrary, the results obtained for the axial anisotropy vessel show a region with a higher shear wave speed at about 0°, corresponding to the long axis of the vessel. Finally, the results obtained for the helical anisotropy depicted increasing shear wave velocity value from −20° to 20°. For the axial phantom, the wavefront of the pulse wave is perpendicular to the long axis of the vessel, while oriented for the helical anisotropic vessels phantom. The pulse wave propagation angle increased with the number of twists made during the vessel manufacturing.DiscussionThe results show that anisotropy can be induced in PVA vessel phantoms by stretching and twisting the material in freeze-thaw cycles. The findings also suggest that vessel anisotropy affects pulse wave propagation angles. Estimating the pulse wave propagation angle may be interesting in characterizing tissue anisotropy in organs where such waves are naturally present.

Investigating Static and Dynamic Behaviors in 3D Chiral Mechanical Metamaterials by Disentangled Generative Models

AbstractChiral mechanical metamaterials with engineered asymmetric structures have garnered significant interest owing to their potential for manipulating mechanical waves and unconventional mechanical properties. Although several design methodologies have made significant strides in the design and discovery of chiral mechanical metamaterials, 3D designs that incorporate multiple mechanical characteristics remain largely unexplored and the static and dynamic properties of these structures have not received sufficient attention. Here, an innovative approach is introduced for the inverse design of 3D chiral mechanical metamaterials with desired static and dynamic properties, leveraging streamlined shapes to enable a versatile design. By employing conditional generative adversarial networks (c‐GANs), the desired mechanical properties are targeted by focusing on both wave attenuation and stress distribution under compression and shear loading. 3D chiral mechanical metamaterials with additive manufacturing are fabricated to demonstrate the performance of the proposed c‐GAN. Experimental investigations show that the generated structures exhibited a wide range of wave attenuation properties, low stress concentrations, and a variety of stress‐strain curve profiles including nonlinear stiffness, demonstrating their effectiveness in achieving the desired mechanical characteristics. This research offers significant advancements in the on‐demand design capabilities of metamaterials and their applications.