Wave Dynamics Research Articles

Dynamics of stress propagation in anharmonic crystals: MD simulations

Anharmonic inter-atomic potential ∼|x|n , n > 1, has been used in molecular dynamics (MD) simulations of stress dynamics of FCC oriented crystal. The model of the chain of masses and springs is found as a convenient and accurate description of simulation results, with masses representing the crystallographic planes. The dynamics of oscillations of two planes is found analytically to be given by Euler’s beta functions, and its scaling with non-linearity parameter and amplitude of oscillations, or applied shear pressure is discussed on examples of time dependencies of displacements, velocities, and forces acting on masses (planes). The dynamics of stress penetration from the surface of the sample with multiply-planes (an anharmonic crystal) towards its interior is confirmed to be given exactly as a series of Bessel functions, when n = 2 (Schrödinger and Pater solutions). When n ≠ 2 the stress dynamics (wave propagation) in bulk material remains qualitatively of the same nature as in the harmonic case. In particular, results suggest that the quasi-linear relationship between frequency and the wave number is preserved. The speed of the transverse sound component, dependent on sound wave amplitude, is found to be a strongly decreasing function of n. The results are useful in the analysis of any MD simulations under pressure, as they help to understand the dynamics of pressure retarded effects, as well as help design the proper methodology of performing MD simulations in cases such as, for instance, studies of the dynamics of dislocations.

Exploring the physical characteristics and nonlinear wave dynamics of a (3+1)-dimensional integrable evolution system

This study comprehensively explores the [Formula: see text]-dimensional Mikhailov–Novikov–Wang [Formula: see text] integrable equation, with the primary objective of elucidating its physical manifestations and establishing connections with analogous nonlinear evolution equations. The investigated model holds significant physical meaning across various disciplines within mathematical physics. Primarily, it serves as a fundamental model for understanding nonlinear wave propagation phenomena, offering insights into wave behaviors in complex media. Moreover, its relevance extends to nonlinear optics, where it governs the dynamics of optical pulses and solitons crucial for optical communication and signal processing technologies. Employing analytical methodologies, namely the unified [Formula: see text], Khater II ([Formula: see text]hat.II) method, and He’s variational iteration [Formula: see text] method, both numerical and analytical solutions are meticulously examined. Through this investigation, the intricate behaviors of the equation are systematically unveiled, shedding illuminating insights on various physical phenomena, notably including wave propagation in complex media and nonlinear optics. The outcomes not only underscore the efficacy of the analytical techniques deployed but also accentuate the equation’s pivotal role in modeling a broad spectrum of nonlinear wave dynamics. Consequently, this research significantly advances our comprehension of complex physical systems governed by nonlinear dynamics, thereby contributing notably to interdisciplinary pursuits in mathematical physics.

Optical solitons for the Hirota–Ramani equation via improved G′G-expansion method

In this work, first it is shown that the Hirota–Ramani equation, which governs the nonlinear propagation of coupled Langmuir and dust-acoustec wave in a multicomponent dusty plasma, possesses kinds of wave profile such as singular periodic profile, periodic profile, singular soliton profile, M-shape rational profile, bright soliton profile, kink profile in the form of the trigonometric, hyperbolic, and rational solutions. With the aid of symbolic computation, we select the Hirota–Ramani equation with a source to investigate the validity and advantage of the improved [Formula: see text]-expansion method and construct some frames of the 3D profiles and the contour profiles to the equation along with the 2D profiles of some solutions to understand the traveling wave dynamics. Following the selection of appropriate values for the associated parameters, more generalized solutions are provided, along with certain patterns in the solutions that are examined. This improved method is effective, concise, reliable, and can be applied for further futuristic applications.

An overview of ion-acoustic solitary and shock waves in a magnetized nonthermal plasma: influence of trapped positrons and electrons

A magnetized nonthermal electron–positron-ion (e-p-i) plasma is considered to study the propagation properties of ion-acoustic solitary and shock waves in the presence of trapped positrons and electrons for the first time. The Schamel-κ (kappa) distribution function that describes plasma nonthermality and particle trapping is assumed to consider electrons and positrons. The diffusive effect of ion plasma fluid, which is responsible for shock dynamics, is taken into account. A nonlinear Schamel-Korteweg–de Vries-Burgers’ (SKdVB) equation is derived by employing the reductive perturbation approach, and the solitary and shock wave solutions of the SKdVB equation have also been derived for different limiting cases. It is found that only positive potential nonlinear structures (for both solitary and shock waves) are formed in the proposed plasma system. The condition for stable solitons in the absence of dissipation is analyzed, and the nature of arbitrary amplitude solitary waves (obtained via the Sagdeev potential approach) is discussed. It is found through theoretical and numerical investigation that different plasma compositional parameters (such as the trapping effect of electrons (β e ) and positrons (β p ), the obliquity effect (θ), electron-to-ion number density ratio (µ e ), the magnetic field effect (via Ω) and the viscous effect (via η)) have a significant influence on the dynamics of ion-acoustic solitary and shock waves. The theoretical and numerical investigations in this study may be helpful in describing the nature of localized structures in different plasma contexts, e.g. space and astrophysical plasmas and experimental plasmas where electron–positron-ion plasmas exist.

Coupled Short-Ig Wave Dunamics Over A Shallow Barrier Reef

Reef barriers play a major role many coral islands, by sheltering the lagoon from the ocean wave energy and then creating a unique habitat for many species. This filtering action becomes increasingly crucial for ecosystems health and shoreline protection in the context of climate change and related sea level rise, degradation of coral systems and modification of wave conditions. A strong research effort has therefore been engaged by the coastal oceanographers community for the last two decades to improve our knowledge and prediction skills of wave dynamics over coral reef systems. A widely reported observation is the importance of infragravity waves (IG) over wave-driven reef systems, whether fringing or barrier reefs. IG are primarily forced by groups in the incoming short-wave (SW) field, either by the release of bound waves or the breakpoint oscillations (Bertin et al. 2018). IG period typically ranges between 30 and 200s, which makes them prone to excite or interact with natural seiching modes in reef-lagoon systems often ranging in the Very Low Frequency (VLF) band. Further research efforts are now necessary to better understand the interaction between long IG/VLF oscillations and SW field. In particular, long waves are expected to play a dynamic depth-filtering role on SW energy, acting as long carrier wave able to promote the propagation of larger SW groups by IG/VLF crests. More generally, the spectral energy transfers over the reef crest-flat system and their relative importance w.r.t. frictional and breaking dissipation are not fully understood over the complete range of surface waves. The aim of the present study is to analyse and to discuss a series of field observations performed on the barrier reef of Maupiti Island, French Polynesia. A particular focus is placed on the interaction between SW and IG wave fields across the reef crest-flat system.

Four-wave mixing induced general localized waves for a coupled generalized nonlinear Schrödinger system

In this paper, we investigate the general localized waves on the nonvanishing background for a coupled generalized nonlinear Schrödinger system with four wave mixing (FWM) effect. Using a uniform Darboux transformation, we construct a unified analytical solution formula which can be used not only to generate some reported localized waves, but also to yield some new results. Based on whether the relative wave vector of the two seed continuous-waves is zero, we respectively obtained various localized waves on the plane wave and periodic backgrounds, including bright/dark solitons, breathers, and rogue waves. Especially, we assort these localized waves and provide detailed parameter conditions for generating them, and find that the FWM term b plays a decisive role in generating the periodic background for those localized waves. In addition, interaction dynamics of the hybrid localized waves on both the plane wave and periodic backgrounds composed of the bright/dark soliton, breather and rogue wave are analyzed. We expect that these results will shed light on the understanding of localized waves on the periodic background owing to the interference of multiple continuous-wave fields.

Impact of diffraction on screening of dynamic compaction waves with barriers

Impact of diffraction on screening of dynamic compaction waves with barriers

Spiral wave dynamics in a neuronal network model

Spiral waves are spatial-temporal patterns that can emerge in different systems as heart tissues, chemical oscillators, ecological networks and the brain. These waves have been identified in the neocortex of turtles, rats, and humans, particularly during sleep-like states. Although their functions in cognitive activities remain until now poorly understood, these patterns are related to cortical activity modulation and contribute to cortical processing. In this work, ,we construct a neuronal network layer based on the spatial distribution of pyramidal neurons. Our main goal is to investigate how local connectivity and coupling strength are associated with the emergence of spiral waves. Therefore, we propose a trustworthy method capable of detecting different wave patterns, based on local and global phase order parameters. As a result, we find that the range of connection radius (R) plays a crucial role in the appearance of spiral waves. For R < 20 µm, only asynchronous activity is observed due to small number of connections. The coupling strength ( gsyn ) greatly influences the pattern transitions for higher R, where spikes and bursts firing patterns can be observed in spiral and non-spiral waves. Finally, we show that for some values of R and gsyn bistable states of wave patterns are obtained.

Exploring Wave-Vegetation Interaction At Blade Scale: A Comprehensive Analysis Of A Flexible Cylinder Through Experimental Data And A Direct Numerical Simulation

Aquatic vegetation in the littoral zone, particularly seagrass, is gaining increasing recognition for its net positive impact on the hosting environment. This recognition is rooted in its capacity to absorb wave energy, regulate water flow, and manage nutrient levels, sedimentation and accretion. Thus, there is a growing interest in integrating seagrass as a key component of a comprehensive climate-conscious strategy (Ondiviela et al., 2014). An effective approach to quantify the positive potential of seagrasses in altering coastal wave dynamics is by using numerical models. These numerical models operate at various spatio- temporal scales, ranging from large domains and multiple years to just a few regular waves in high resolution CFD numerical simulations. Zeller et al. (2014) classified these models, operating at different scales into three categories, each addressing the wave-vegetation interaction at a distinct scale: (1) blade scale, (2) meadow scale, and (3) ecosystem scale. The aim of the present study is to investigate the interaction between waves and vegetation at the blade scale. The primary objectives are two: first, to introduce a direct numerical technique that involves a two-way coupling between a fluid solver and a structural solver, and second, to present novel experimental data for a single flexible cylinder (Reis, 2022) serving as validation for the present (and future) numerical model(s).

120 kHz mid-infrared TDLAS sensor for H2O concentration and temperature measurement in rotating detonation engine exhaust flows

Rotating detonation engines (RDEs) require advanced rapid combustion diagnostic techniques to better understand their complex detonation processes. A fast mid-infrared TDLAS sensor was proposed to simultaneously monitor H2O concentration and temperature at the outlet of an H2/air-fueled RDE annular combustor. An iterative parameter extraction method from transmitted laser intensity was proposed to extract the H2O concentration and temperature of the detonation waves. A measurement rate of 120 kHz enables high-speed and simultaneous quantification of detonation wave combustions. The results show that when RDE operates stably, the detonation frequency, average temperature, and average molar percentage of H2O concentration of the detonation waves are 4.631 kHz, 1572.8 K, and 0.335, respectively. The detonation frequency extracted from H2O concentration and temperature is highly consistent with that extracted from thermal radiation, and the relative frequency error is only 0.022 %. The time-resolved H2O concentration and temperature data measured by the sensor accurately capture the thermal dynamics of the transient detonation waves.

Symmetry-based closed-form solutions and conserved quantities of the new (2+1)-dimensional Bogoyavlensky-Konopelchenko equation in fluid mechanics

In this investigation, we explore the mathematical intricacies of the novel (2+1)-dimensional Bogoyavlensky-Konopelchenko equation, a model with practical applications in elucidating the dynamics of internal waves within deep water. The equation’s significance spans various scientific domains, including plasma physics, nonlinear optics, and fluid dynamics. Employing a comprehensive analytical approach, specifically Lie symmetry analysis, we aim to unravel the underlying complexities of this equation and obtain new analytical solutions. To further scrutinize the equation, we apply various methods, namely Kudryashov’s method, the (G′/G)-expansion method, the simplest equation technique, and the power series method, all of which have not been applied to the equation before. Through these techniques, we successfully derive solutions in diverse functional forms, encompassing rational, trigonometric, exponential, hyperbolic, and Jacobi elliptic functions. To enhance comprehension, we present our findings visually using three-dimensional and two-dimensional plots density plots via the Mathematica tool. These graphical representations effectively communicate the intricate characteristics and nuances inherent in the solutions. Our visual representations reveal a spectrum of patterns, including periodic, singular periodic, kink-shaped structures. Additionally, our investigation extends to the determination of conserved quantities associated with the new (2+1)-dimensional Bogoyavlensky-Konopelchenko equation. This involves the application of the multiplier method and Ibragimov’s theorem, two potent techniques for identifying and understanding the conservation laws governing the model.

Exact solutions for travelling waves using Tanh method for two dimensional stochastic Allen–Cahn equation with multiplicative noise

AbstractThe research outlined here focuses on the hyperbolic tangent (tanh) method for deriving analytical solutions for travelling wave to the two-dimensional stochastic Allen–Cahn equation with multiplicative noise. The novelty of our work is to derive these exact solutions since the previous studies focused on the solutions of numerical nature. The tanh approach, which employs a finite tanh power series, is particularly adept at modeling travelling wave profiles. A key area of interest in this study is the effect of multiplicative noise on these travelling waves dynamics, especially how high levels of noise can lead to propagation failure of waves. The results demonstrate that for weak noise, the propagation of the travelling wave is basically unaffected, while the wave fails to propagate in the strong noise regime.

Nonlinear tunneling of chirped similaritons in non-centrosymmetric waveguides with quadratic-cubic nonlinearity

The nonlinear tunneling of the optical similaritons through both dispersion and nonlinear barriers in a non-centrosymmetric waveguide exhibiting second- and third-order nonlinearity is studied. Within the framework of an inhomogeneous quadratic-cubic nonlinear Schrödinger equation with distributed group velocity dispersion, reciprocal of the group velocity, quadratic-cubic nonlinearity, and gain or loss, we demonstrate the existence of a rich variety of exact similariton solutions in the shape of bright, kink, anti-kink, W-shaped, and gray solutions. The results show that these self-similar waves involve certain control parameters in their amplitude, phase, width, and shift of the inverse group velocity, which enables us to control their evolution dynamics in the waveguide system through a suitable choice of these parameters. It is found that the parameter of reciprocal of the group velocity decides the phase shift and group velocity of these self-similar waves. Also, the stability of the solutions is discussed numerically. Results of this paper are helpful for enriching the similariton theory and inderstanding the dynamics of self-similar waves in systems with quadratic–cubic nonlinearities.

The Hybrid Recharge Delayed Oscillator: A More Realistic El Niño Conceptual Model

Abstract El Niño–Southern Oscillation (ENSO) is the leading mode of climate interannual variability, with large socioeconomical and environmental impacts, potentially increasing with climate change. Improving its understanding may shed further light on its predictability. Here we revisit the two main conceptual models for explaining ENSO cyclic nature, namely, the recharge oscillator (RO) and the advective–reflective delayed oscillator (DO). Some previous studies have argued that these two models capture similar physical processes. Yet, we show here that they actually capture two distinct roles of ocean wave dynamics in ENSO’s temperature tendency equation, using observations, reanalyses, and Climate Model Intercomparison Project (CMIP) models. The slow recharge/discharge process mostly influences central-eastern Pacific by favoring warmer equatorial undercurrent and equatorial upwelling, while the 6-month delayed advective–reflective feedback process dominates in the western-central Pacific. We thus propose a hybrid recharge delayed oscillator (RDO) that combines these two distinct processes into one conceptual model, more realistic than the RO or DO alone. The RDO eigenvalues (frequency and growth rate) are highly sensitive to the relative strengths of the recharge/discharge and delayed negative feedbacks, which have distinct dependencies to mean state. Combining these two feedbacks explains most of ENSO frequency diversity among models. Thanks to the two different spatial patterns involved, the RDO can even capture ENSO spatiotemporal diversity and complexity. We also develop a fully nonlinear and seasonal RDO, even more robust and realistic, investigating each nonlinear term. The great RDO sensitivity may explain the observed and simulated richness in ENSO’s characteristics and predictability. Significance Statement El Niño and La Niña events, and the related Southern Oscillation, cause the largest year-to-year variations of Earth’s climate. Yet the theories behind them are still debated, with two main conceptual models being the recharge oscillator and the delayed oscillator. Our purpose here is to address this debate by developing a more realistic theory, a hybrid recharge delayed oscillator. We show how simple yet realistic it is, with equivalent contributions from the slow recharge process and from the faster delayed feedback. It even captures the observed El Niño and La Niña diversity in space and in frequency. Future studies could use the simple theoretical framework provided here to investigate El Niño–Southern Oscillation (ENSO) in observations, theories, climate models diagnostics and forecasts, and global warming projections.

Gravitational probe of uantum spacetime

A quest for phenomenological footprints of quantum gravity is among the central scientific tasks in the rising era of gravitational wave astronomy. We study gravitational wave dynamics within the noncommutative geometry framework, based on a Drinfeld twist and newly proposed noncommutative Einstein equation, and obtain the leading quantum correction to Regge-Wheeler potential up to first order in the noncommutativity parameter. By calculating the quasinormal mode frequencies we show that the noncommutative Schwarzschild black hole remains stable under axial gravitational perturbations.

High flow prediction model integrating physically and deep learning based approaches with quasi real-time watershed data assimilation

When operating a flood forecasting system, it is crucial to prioritize both promptness and accuracy, along with reflecting the latest watershed conditions. This study proposes a hybrid model for rainfall-induced high flow prediction that combines an instantaneous physically-based model and a deep learning-based rainfall loss model assimilating with quasi real-time watershed conditions. Its primary objective is to present immediate and reliable high flow predictions, ensuring stability in prediction procedures. The surface runoff component of the model is based on nonlinear instantaneous unit hydrograph (IUH) derived using a dynamic wave model, which considers the nonlinearity between the rainfall excess intensity and the time to peak and peak flow of the IUH. To account for rainfall loss, which can significantly influence rainfall-runoff quantity, Long Short-Term Memory (LSTM) model is employed to establish link between key rainfall loss parameters and the latest watershed conditions obtained from the Global Land Data Assimilation System (GLDAS). The application of the proposed model to 28 high flow events reveals several noteworthy outcomes. Firstly, unlike conventional models that depend on fixed parameter values specific to each event, the proposed model offers immediate, stable, and highly accurate high flow predictions without the need for manual calibration. Secondly, the prioritization of parameters reflecting watershed conditions varies between different watersheds and depends on the rainfall events. These findings indicate the necessity to estimate rainfall loss parameters individually for each rainfall-runoff event in each watershed, as no universal value exists for these parameters. Lastly, despite the limited number of test cases conducted in this study, the LSTM model achieved sufficiently accurate rainfall loss estimation for high flow prediction using only 50 datasets.

The influence of fractionality and unconstrained parameters on mathematical and graphical analysis of the time fractional phi-four model

In the framework of several nonlinear physical phenomena arising from water wave mechanics, this work recovers some new precise solutions to the time-fractional phi-four equation. For this, the phi-four equation's space and time fractional transformation is converted into an ordinary differential equation (ODE). The improved modified extended tanh function (imETF) approach is then employed by the ODE as a powerful method based on the conformable derivative. Thus, lump solutions, periodic solutions, solitary and multiple soliton solutions, dark-bright soliton solutions, and Jacobi elliptic doubly periodic type solutions are studied. The imETF appro solitons applications in many scientific and engineering fields develops mathematical methodologies, helps research solitons, and advances our knowledge of nonlinear processes. The differences between the results of this investigation and those obtained earlier using alternative methods are analyzed. In terms of fractionality, unconstrained parameters, and applied method sense, all generated wave solutions are found to be new. Physical explanations and a visual representation of the effects of unconstrained parameters and fractionality on the derived solutions are provided. We find that the wave portents change as the number of unconstrained parameters and fractionality increases. In conclusion, we dynamically show that the proper transformation and the applicable imETF method are more effective in analyzing water wave dynamics and might be employed in subsequent studies to shed light on various physical phenomena.

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.

Langmuir wave dynamics and plasma instabilities: Insights from generalized coupled nonlinear Schrödinger equations

This study aims to tackle the generalized coupled nonlinear Schrödinger ([Formula: see text] – [Formula: see text]) equations, with a focus on understanding their physical significance and stability, especially in the realm of plasma physics. These equations are crucial for grasping the complex dynamics of wave interactions within plasma systems, which are fundamental for phenomena like wave-particle interactions, turbulence, and magnetic confinement. We employ analytical methods such as the generalized rational ([Formula: see text]at) and Khater II ([Formula: see text]hat.II) techniques, along with characterizing the system using Hamiltonian principles, to carefully examine the stability of solutions. The relevance of this model extends across various plasma phenomena, including electromagnetic wave propagation, Langmuir wave dynamics, and plasma instabilities. By applying these analytical techniques, we derive solutions and investigate their stability using Hamiltonian dynamics, providing valuable insights into the fundamental behavior of nonlinear plasma waves. Our findings reveal the existence of stable solutions under specific conditions, thus advancing our understanding of plasma dynamics significantly. This research carries significant implications for fields such as plasma physics, astrophysics, and fusion research, where a deep understanding of plasma wave stability and dynamics is crucial. Essentially, our study represents a scholarly effort to offer fresh perspectives on the behavior of [Formula: see text] – [Formula: see text] equations within plasma systems, contributing to the academic discourse on plasma wave phenomena.

Life cycle dynamics of Greenland blocking from a potential vorticity perspective

Abstract. Blocking over Greenland stands out in comparison to blocking in other regions, as it favors accelerated Greenland Ice Sheet melting and has substantial impacts on surface weather in adjacent regions, particularly in Europe and North America. Climate models notoriously underestimate the frequency of blocking over Greenland in historical periods, but the reasons for this are not entirely clear, as we are still lacking a full dynamical understanding of Greenland blocking from formation through maintenance to decay. This study investigates the dynamics of blocking life cycles over Greenland based on ERA5 reanalysis data from 1979–2021. A year-round weather regime definition allows us to identify Greenland blocking as consistent life cycles with an objective onset, maximum, and decay stage. By applying a new quasi-Lagrangian potential vorticity (PV) perspective, following the negative, upper-tropospheric PV anomalies (PVAs−) associated with the block, we examine and quantify the contribution from different physical processes, including dry and moist dynamics, to the evolution of the PVA− amplitude. We find that PVAs− linked to blocking do not form locally over Greenland but propagate into the region along two distinct pathways (termed “upstream” and “retrogression”) during the days before the onset. The development of PVAs− differs more between the pathways than between seasons. Moist processes play a key role in the amplification of PVAs− before the onset and are linked to midlatitude warm conveyor belts. Interestingly, we find moist processes supporting the westward propagation of retrograding PVAs− from Europe, too, previously thought to be a process dominated by dry-barotropic Rossby wave propagation. After onset, moist processes remain the main contribution to PVA− amplification and maintenance. However, moist processes weaken markedly after the maximum stage, and dry processes, i.e., barotropic, nonlinear wave dynamics, dominate the decay of the PVAs− accompanied by a general decrease in blocking area. Our results corroborate the importance of moist processes in the formation and maintenance of Greenland blocking and suggest that a correct representation of moist processes might help reduce forecast errors linked to blocking in numerical weather prediction models and blocking biases in climate models.