Solitary Waves Research Articles

Slow Electron Holes in the Earth's Magnetosheath

AbstractWe present a statistical analysis of electrostatic solitary waves observed aboard Magnetospheric Multiscale spacecraft in the Earth's magnetosheath. Applying single‐spacecraft interferometry to several hundred solitary waves collected in about 2‐minute interval, we show that almost all of them have the electrostatic potential of positive polarity and propagate quasi‐parallel to the local magnetic field with plasma frame velocities of the order of 100 km/s. The solitary waves have typical parallel half‐widths from 10 to 100 m that is between 1 and 10 Debye lengths and typical amplitudes of the electrostatic potential from 10 to 200 mV that is between 0.01% and 1% of local electron temperature. The solitary waves are associated with quasi‐Maxwellian ion velocity distribution functions, and their plasma frame velocities are comparable with ion thermal speed and well below electron thermal speed. We argue that the solitary waves of positive polarity are slow electron holes and estimate the time scale of their acceleration, which occurs due to interaction with ions, to be of the order of one second. The observation of slow electron holes indicates that their lifetime was shorter than the acceleration time scale. We argue that multi‐spacecraft interferometry applied previously to these solitary waves is not applicable because of their too‐short spatial scales. The source of the slow electron holes and the role in electron‐ion energy exchange remain to be established.

Novel solitonic structure, Hamiltonian dynamics and lie symmetry algebra of biofilm

In this study, the Lie point symmetries and optimal system have been established. We discuss the biofilm model’s soliton solutions. To examine a nonlinear dynamical biofilm system, which is simply a bistable Allen–Cahn equation with quartic potential, to determine solitary wave profiles using the considered equation, a new auxiliary equation technique is used. A suitable variable transformation is used to convert the governing equation into a nonlinear ordinary differential equation. The unified approach is utilized to evaluate periodic solutions, solitary and soliton solutions as well as several newly discovered exact solitary wave solutions, it can be accomplished via Mathematica (https://www.wolfram.com/mathematica/online/). The new auxiliary equation approach is an efficient method for creating unique wave profiles based on a variety of soliton families. Also, the results are graphically visualized, by using the appropriate parametric settings. The outcomes are shown graphically in two dimensions, three dimensions, and contour form. The Hamiltonian conditions are satisfied by the planer dynamical framework of equations to ensure as the system that was generated is a conservative Hamiltonian dynamical system which includes all traveling wave structures. A sensitivity evaluation is used to explore the governing model’s thoroughly dynamical properties. It is demonstrated that the model becomes more dependent on the beginning conditions than the variables. The strategy could be used to look for exact solutions to various nonlinear evolution equations. We believe that this study will have important applications in different areas of science.

Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional topological Maxwell lattice by exploring its large deformation quasi-static response using geometric numerical simulations and experiments. We observe spatial nonlinear wave-like phenomena such as harmonic generation, localized domain switching, amplification-enhanced frequency conversion, and solitary waves. We further map our linearized, homogenized system to a non-Hermitian, nonreciprocal, one-dimensional wave equation, revealing an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. Our study opens a regime for topological mechanical metamaterials and expands their application potential in areas including adaptive and smart materials and mechanical logic, wherein concepts from nonlinear dynamics may be used to create intricate, tailored spatial deformation and stress fields greatly transcending conventional elasticity.

On the dynamics of large-amplitude ion-acoustic waves in a non-Maxwellian plasma with nonthermal electrons and an electron beam

This work investigates the characteristics of nonlinear large-amplitude ion-acoustic waves that occur and propagate in a non-Maxwellian plasma consisting of inertial ions and electrons beam as well as inertialess Cairns-distributed electrons. For this purpose, this inquiry utilizes a two-fluid model with the Sagdeev pseudopotential technique. By utilizing the Sagdeev pseudopotential, a mathematical equation similar to an energy balance equation is derived. The effects of the related physical parameters, including the inertialess electron concentration, the electron beam concentration, and the electron beam velocity, on the existence region of the solitary waves (SWs), and accordingly, the properties of ion-acoustic SWs (IASWs) are examined. Also, the Cairns distribution of electrons can significantly affect the features of large-amplitude IASWs, depending on the parameter that controls the distribution (the inertialess electron nonthermality). Additionally, the distinctive features of the solitary waves and their existence domain in connection with the relevant plasma parameters are also addressed.

Asymmetric scattering effect of solitary wave in a two-section composite granular chain

Asymmetric scattering effect of solitary wave in a two-section composite granular chain

Numerical research on internal solitary waves in stratified fluid

Internal solitary waves are a common nonlinear large amplitude internal wave in nature, which can cause strong divergence and sudden strong currents in seawater during propagation, thus having great destructive effects on marine structures. The paper focuses on numerical wave generation based on three types of internal solitary wave theories. The waves are numerical simulated by RANS method in the paper. The numerical results of internal solitary wave theories are compared and analyzed. It shows that under the same numerical water tank scale and calculation conditions, the mKdV theory can obtain the largest wave amplitude, followed by the eKdV theory and the KdV theory. In addition, background currents will accelerate the propagation speed of internal solitary waves and increase their amplitude slightly.

Sound intensity fluctuations caused by internal solitary wave train in the South China Sea

Dynamic internal solitary wave (ISW) can cause significant underwater sound fluctuations. In this paper, the periodic characteristics of sound intensity fluctuations and related physical mechanisms are investigated in the scenario that an ISW train passing through the acoustic path from source to receivers. From simulation results and experimental data, it is shown that the sound intensity fluctuates quasi-periodically, and the predominant fluctuation frequency is associated with modal interference and modal intensity. The initial mode coefficients at the source and the mode coupling are responsible for the fluctuations of modal intensities, and one of the predominant fluctuation periods is the same as that of the ISWs.

Excitation and stability of nonlinear waves by a pair of steady waves in incompressible boundary layers

The research explores the generation and stability of nonlinear waves in incompressible boundary layers, spotlighting the effects of dual steady waves. Using the Benjamin-Ono equation, modified for the incorporation of steady waves, we provide insights into the solitary wave generation process. A perturbed wave oscillator system is used for analyzing the stability of these nonlinear waves, uncovering that the loss of stability in low-order oscillators primarily governs wave transition and energy. Further, the study highlights the enlightening significance of complex terrain on the generation of nonlinear waves. Since the influence of terrain on the fluid passing over it usually appears as the external excitation of stationary waves, our study has important implications for terrain-fluid interactions.

On the transition from single- to multi-humped internal solitary waves

We provide numerical evidence of the transition from rank-ordered trains of internal solitary waves (ISWs) to multi-humped packets. We ascribe such peculiar and unexplored dynamics to the emergence of a long-range influence among waves, mediated by the hydrodynamic conditions developing in the wake of each ISW and promoting acceleration of the trailing waves. Both the train during the transition and its final multi-humped configuration share hydrodynamic features which are consistent with the recently proposed theory of ISWs propagating through moving stratified environments.

Laboratory Investigation of Energy Dissipation and Turbulent Mixing During Internal Solitary Wave Breaking on the Rough Shelf Slope

AbstractWhen internal solitary waves (ISW) propagate to the continental shelf, they typically runup and break on the forereef. This process might lead to periodic temperature drops at the reef slope, which has potential to protect coral reefs from bleaching threats. A series of laboratory experiments were conducted to investigate turbulence characteristics and energy dissipation during the ISW breaking events on the shelf slope with different bottom roughness to mimic the forereef environment. Particle image velocimetry (PIV) and planar laser‐induced fluorescence (PLIF) were coupled to obtain simultaneous high‐resolution velocity and density fields, based on which we then calculate the energy budget and turbulent dissipation rate. We found that the ISW breaking can be divided into two turbulent processes, the production of shear instability and coherent structures. Ratio of energy loss is weakened with the increase of bottom roughness and the collapse height, while the rough structure substantially enhanced the turbulent dissipation rate. The mixing efficiency is between 0.1 and 0.3, close to its maximal rate at 0.25. Our results reveal that the bottom roughness has impact on the mixing efficiency and turbulent process during the ISW breaking events. We found that rough structures at the shelf slope inhibit the mixing efficiency, especially in cases with small amplitude incline ISW. This finding may help us to better understand the reef damage and coral reef decline and support the management of coral protection strategy.

Propagation of solitary wave in micro-crystalline materials

In this article, the propagation of waves in micro-crystalline materials is governed by the structure of the strain wave equation and takes into consideration various dimensions of micro-crystalline. Micro-crystalline materials that are deserving of special attention in material physics. The strain wave equation represents the dynamic behavior associated with multiple phenomena of a physical nature. The new extended direct algebraic methodology is applied to acquire the different types of exact solitonic solutions. This technique stands out as one of the most effective approaches for producing a diverse set of exact solutions to nonlinear partial differential equations. By applying a new extended direct algebraic approach, we get solutions in the form of smooth periodic, anti-dark, anti-bell-shape, periodic bright, Combined bright-dark soliton, mixed-periodic solution, anti-kink formations, Stumpons, mixed periodic solitons, and decaying cusped solitons. Furthermore, two-dimensional, three-dimensional, and contour plots are created for different solutions, helping us make sense of their physical significance more clearly. The importance of the obtained results lies in their ability to represent diverse and complex phenomena in mathematical and physical systems.

Predicting shear stress distribution on structural surfaces under internal solitary wave loading: A deep learning perspective

The density of the ocean varies unevenly along the vertical axis. In the presence of external disturbances, internal solitary waves (ISWs) are generated. The strong shear flow field induced by ISW seriously threatens the operational safety of marine structures. Therefore, it has become a hot spot to study the force law of marine structures in ISW. The existing studies are conducted when the ISW parameters are known. However, ISW is not visible in real situations, which leads to difficulties in obtaining ISW parameters. Therefore, it is of great engineering value to accomplish real-time force prediction of marine structures without knowing the ISW parameters in advance. To fill the gap, this study proposes a novel hydrodynamic prediction model with a sensor array as the sensing system and a deep learning algorithm as the decision-making system. The model successfully achieves accurate prediction of the shear stress on the cylinder in the ISW. In addition, a technique for optimizing sensor placement is proposed. This will help identify critical regions in the graphical representations to enhance exploration of flow field information. The results demonstrate that the prediction accuracy of the optimized sensor layout scheme surpasses that of randomly deployed sensors. As a result, this study will provide an important assurance for the safe operation of marine structures.

Experimental investigation of propagation evolution characteristics of internal solitary waves passing through downslope topography

In contrast to the extensive research on the propagation evolution of internal solitary waves (ISWs) over continental shelf topography, few investigations have been conducted on the propagation evolution of ISWs over downslope topography. In this experiment, the characteristics of the ISWs passing over a downslope topography were investigated in an immiscible two-layer fluid system to clearly capture the waveform information. The main objective of this study was to analyze the propagation evolution of ISWs with different incident amplitudes passing through a downslope topography. Using the particle image velocimetry technique, the evolutionary characteristics of ISWs (such as waveform, wave height, energy budget, and flow field) are investigated. According to the flow field analysis results, the phase velocity near the downslope topography changes with the propagation of ISWs. Moreover, the gradient distribution of velocity progressively becomes perpendicular to the right surface of the topography. Furthermore, a counterclockwise vortex gradually forms at the right upper vertex of the topography. The propagation of ISWs is influenced by varying water depth and topography. The front waveform of ISWs is significantly flat, and the back is steeper than the original back waveform. Around the tail wave, an upward convex wave packet is generated. The trends of wave energy and wave height losses are broadly consistent. Furthermore, the energy loss is related to the incident wave height with a 20% higher loss rate for large-amplitude ISWs than small-amplitude ISWs at the inflection point of the topography.

Dust Ion Acoustic Solitary Waves in Plasma with Cairns Distributed Electrons and New Classical Distribution of Ions

Dust Ion Acoustic Solitary Waves in Plasma with Cairns Distributed Electrons and New Classical Distribution of Ions

Qualitative analysis, exact solutions and symmetry reduction for a generalized (2＋1)-dimensional KP–MEW-Burgers equation

The objective of this manuscript is to examine the non-linear characteristics of the modified equal width-Burgers equation, known as the generalized Kadomtsive–Petviashvili equation, and its ability to generate a long-wave with dispersion and dissipation in a nonlinear medium. We employ the Lie symmetry approach to reduce the dimension of the equation, resulting in an ordinary differential equation. Utilizing the newly developed generalized logistic equation method, we are able to derive solitary wave solutions for the aforementioned ordinary differential equation. In order to gain a deeper understanding of the physical implications of these solutions, we present them using various visual representations, such as 3D, 2D, density, and polar plots. Following this, we conduct a qualitative analysis of the dynamical systems and explore their chaotic behavior using bifurcation and chaos theory. To identify chaos within the systems, we utilize various chaos detection tools available in the existing literature. The results obtained from this study are novel and valuable for further investigation of the equation, providing guidance for future researchers.

Solitary waves forming pulsating thermal plumes and their implications for multiple eruption events in large igneous provinces

Solitary waves forming pulsating thermal plumes and their implications for multiple eruption events in large igneous provinces

Experimental Investigation on a convex Mode-2 internal solitary wave and its induced flow field

The second mode internal solitary wave (Mode-2 ISW) and its wave-induced flow field structure are investigated by conducted physical experiments in a large stratified fluid flume. The Mode-2 ISW is generated by the method of the gravity collapse of fluid, and the measurements of its wave-flow structure are obtained by the combined method of conductivity probe array and particle image velocimetry (PIV). The flow field structure and its influencing factors were analysed quantitatively. The results reveal the characteristic of the Mode-2 ISW waveform and density field and the effect of the wave amplitude on the flow and shear characteristics of induced flow field.

3D cylindrical BGK model of electron phase-space holes with finite velocity and polarization drift

Nonlinear kinetic structures, called electron phase-space holes (EHs), are regularly observed in space and experimental magnetized plasmas. The existence of EHs is conditioned and varies according to the ambient magnetic field and the parameters of the electron beam(s) that may generate them. The objective of this paper is to extend the 3D Bernstein–Greene–Kruskal model with cylindrical geometry developed by L.-J. Chen et al. [“Bernstein–Greene–Kruskal solitary waves in three-dimensional magnetized plasma,” Phys. Rev. E 69, 055401 (2004)] and L.-J. Chen et al., [“On the width-amplitude inequality of electron phase space holes,” J. Geophys. Res. 110, A09211 (2005)] to include simultaneously finite effects due to (i) the strength of the ambient magnetic field B0, by modifying the Poisson equation with a term derived from the electron polarization current, and (ii) the drift velocity ue of the background plasma electrons with respect to the EH, by considering velocity-shifted Maxwellian distributions for the boundary conditions. This allows us to more realistically determine the distributions of trapped and passing particles forming the EHs, as well as the width-amplitude relationships for their existence.

A gradient reproducing kernel based stabilized collocation method for the 5th order Korteweg–de Vries equations

This paper presents a gradient reproducing kernel based stabilized collocation method (GRK-SCM) to solve the generalized nonlinear 5th order Korteweg–de Vries (KdV) equations. By introducing gradient reproducing kernel (GRK) approximations, one can circumvent the intricacy of high-order derivatives in RK approximations, while still satisfying high-order consistency requirements. This leads to the high accuracy and efficiency. GRKs are very good approximation candidates for addressing high order partial differential equations that require higher order derivatives formulated as strong form. The stabilized collocation method (SCM) effectively meets high-order integration constraints which can achieve accurate integration in the subdomains. This ensures both high precision and optimal convergence. Von Neumann analysis is utilized to establish the stability criteria for GRK-SCM when combined with forward difference temporal discretization. Numerical solutions for Sawada–Kotera (SK) equation and Kaup-Kupershmidt (KK) equation are studied where the solitary wave migration and collision, and periodic waves are represented. A fifth order forced KdV equation is also considered. The presented method's high accuracy and convergence are demonstrated through comparative studies with analytical solutions, and investigations of invariants and corresponding errors determine the good conservation properties of this algorithm.

Stripe Extraction of Oceanic Internal Waves Using PCGAN with Small-Data Training

Playing a crucial role in ocean activities, internal solitary waves (ISWs) are of significant importance. Currently, the use of deep learning for detecting ISWs in synthetic aperture radar (SAR) imagery is gaining growing attention. However, these approaches often demand a considerable number of labeled images, which can be challenging to acquire in practice. In this study, we propose an innovative method employing a pyramidal conditional generative adversarial network (PCGAN). At each scale, it employs the framework of a conditional generative adversarial network (CGAN), comprising a generator and a discriminator. The generator works to produce internal wave patterns as authentically as possible, while the discriminator is designed to differentiate between images generated by the generator and reference images. The architecture based on pyramids adeptly captures the encompassing as well as localized characteristics of internal waves. The incorporation of upsampling further bolsters the model’s ability to recognize fine-scale internal wave stripes. These attributes endow the PCGAN with the capacity to learn from a limited amount of internal wave observation data. Experimental results affirm that the PCGAN, trained with just four internal wave images, can accurately detect internal wave stripes in the test set. Through comparative experiments with other segmentation models, we demonstrate the effectiveness and robustness of PCGAN.