Nonlinear Propagation Research Articles

Effect of Magnetic Diffusion in the Chromosphere on the Solar Wind

We investigate nonideal magnetohydrodynamical (MHD) effects in the chromosphere on the solar wind by performing MHD simulations for Alfvén-wave-driven winds, explicitly including ohmic and ambipolar diffusion. We find that MHD waves are significantly damped in the chromosphere by ambipolar diffusion so that the Alfvénic Poynting flux that reaches the corona is substantially reduced. As a result, the coronal temperature and the mass-loss rate of the solar wind are considerably reduced, compared with those obtained from an ideal MHD case, which is indicative of the great importance of the nonideal MHD effects in the solar atmosphere. However, the temperature and the mass-loss rate are recovered by a small increase in the convection-originated velocity perturbation at the photosphere because of the sensitive dependence of the ambipolar diffusion and reflection of Alfvén waves on the physical properties of the chromosphere. We also find that density perturbations in the corona are reduced by the ambipolar diffusion of Alfvén waves in the chromosphere because the nonlinear generation of compressible perturbations is suppressed.

Analytical solutions and soliton behaviors in the space fractional Heisenberg ferromagnetic spin chain equation

This study investigates soliton solutions to the (2 + 1)-dimensional space fractional Heisenberg ferromagnetic spin chain equation incorporating beta fractional derivatives that explain the nonlinear propagation of spin wave in the ferromagnetic material with magnetic interactions including the both classical and semi-classical frameworks. This model has applications in spintronics, plasma physics, magnet theory, and condensed matter physics. Employing the two-potential extended Kudryashov and (G′/G, 1/G)-expansion methods, we derive some original and generic solutions composed of trigonometric functions, hyperbolic functions, and their rational forms. For particular values of the parameters, these solutions offer V-shaped, bell-shaped, kink, periodic, flat kink, and singular periodic solitons. The physical behavior of these solitons is demonstrated through three-dimensional, contour, and two-dimensional plots. The results are important in the study of phase transitions in ferromagnetic materials, lattice vibrations in condensed matter, and the propagation of shock waves in plasma. This study also demonstrates the potential and reliability of the employed strategies.

Nonlinear poro-thermo-forced vibration in curved sandwich magneto-electro-elastic shells under hygrothermal environment

This research employs a multiple scales perturbation approach to evaluate the nonlinear wave propagation behaviors of a doubly curved sandwich composite piezoelectric shell with a flexible core in a hygrothermal environment. Stress and strain calculations for the flexible core and face sheets are carried out using Reddy's third-order shear deformation theory (TSDT) and third-order polynomial theory, respectively. The study explores the synergistic effects of a multilayered shell, flexible core, and magneto-rheological layer (MR) in revealing the nonlinearity of both in-plane and vertical moment within the core. The Halpin–Tsai model is employed to derive the properties of polymer/carbon nanotube/fiber (PCF) and polymer/graphene platelet/fiber (PGF) three-phase composite shells. The governing equations for the multiscale shell are derived using Hamilton's formulation. The research investigates temperature variations, diverse distribution patterns, curvature ratios, and magnetic fields through numerical analysis, presenting the results graphically and prior research has demonstrated the accuracy of these methods. Notably, these factors exert significant influence on the frequency-amplitude curves of the smart structure.

An optical fiber integrated device for nonlinear generation of femtosecond mid-infrared pulses

Compact and broadband mid-infrared (MIR) sources are in high demand because of a wide range of potential applications such as molecular sensing in the fingerprint region. The generation of coherent MIR radiation at arbitrary frequencies typically requires nonlinear mixing between at least two input waves, which is often cumbersome to implement. We present an integrated and, therefore, adjustment-free solution combining few-femtosecond pulse compression in a germanosilicate optical fiber and optical rectification. To this end, a 16-μm-thin GaSe crystal is directly mounted on the end facet of a highly nonlinear fiber assembly exploiting a focused ion beam. With input pulses of a minute energy of 5 nJ and a duration of 120 fs at the telecom wavelength of 1.55 μm, we directly obtain ultrabroadband and phase-stable output transients. Electro-optic sampling in free space reveals single-cycle pulses with spectral components covering the entire MIR from 10 to 120 THz.

Linear and nonlinear spin-current generation in polar collinear antiferromagnets without relativistic spin-orbit coupling

Linear and nonlinear spin-current generation in polar collinear antiferromagnets without relativistic spin-orbit coupling

Observation of topological frequency combs.

On-chip generation of optical frequency combs using nonlinear ring resonators has enabled numerous applications of combs that were otherwise limited to mode-locked lasers. Nevertheless, on-chip frequency combs have relied predominantly on single-ring resonators. In this study, we experimentally demonstrate the generation of a novel class of frequency combs, the topological frequency combs, in a two-dimensional lattice of hundreds of ring resonators that hosts fabrication-robust topological edge states with linear dispersion. By pumping these edge states, we demonstrate the generation of a nested frequency comb that shows oscillation of multiple edge state resonances across ≈40 longitudinal modes and is spatially confined at the lattice edge. Our results provide an opportunity to explore the interplay between topological physics and nonlinear frequency comb generation in a commercially available nanophotonic platform.

Programming the scalable optical learning operator with spatial-spectral optimization

Electronic computers have evolved drastically over the past years with an ever-growing demand for improved performance. However, the transfer of information from memory and high energy consumption have emerged as issues that require solutions. Optical techniques are considered promising solutions to these problems with higher speed than their electronic counterparts and with reduced energy consumption. Here, we use the optical reservoir computing framework we have previously described (Scalable Optical Learning Operator or SOLO [1]) to program the spatial-spectral output of the light after nonlinear propagation in a multimode fiber. The novelty in the current paper is that the system is programmed through an output sampling scheme, similar to that used in hyperspectral imaging in astronomy. Linear and nonlinear computations are performed by light in the multimode fiber and the high dimensional spatial-spectral information at the fiber output is optically programmed before it reaches the camera. We then used a digital computer to classify the programmed output of the multi-mode fiber using a simple, single layer network. When combining front-end programming and the proposed spatial-spectral programming, we were able to achieve 89.9 % classification accuracy on the dataset consisting of chest X-ray images from COVID-19 patients. At the same time, we obtained a decrease of 99 % in the number of tunable parameters compared to an equivalently performing digital neural network. These results show that the performance of programmed SOLO is comparable with cutting-edge electronic computing platforms, albeit with a much-reduced number of electronic operations.

Improving small sample prediction performance via novel nonlinear interpolation virtual sample generation with self-supervised learning

In the early stages of production processes, due to expensive experimental costs and demanding experimental conditions, the amounts of collected samples are relatively limited. Information and knowledge extracted from minimal experimental data may be distorted and unreliable. Tackling this task, some researchers have recommended virtual sample generation (VSG), aiming at improving prediction accuracy of forecasting models for small sample sets by creating informative artificial samples. To more effectively capture nonlinear feature representations in small data, in this paper, we propose a promising VSG method based on self-supervised learning architecture to generate optimal, feasible virtual samples. The suggested technology considers distilling nonlinear feature representations using a manifold algorithm. Based on these representations, we integrated Newton’s divided difference and Chebyshev interpolation to create nonlinear interpolation points. We feed those interpolation points into a U-net model and an encoder-decoder net model to produce virtual sample inputs and output, respectively. Additionally, in this paper, we developed a Siamese network model to select virtual samples resembling original data. In the experiments, two industrial datasets were utilized to demonstrate efficacy of the proposed method. These experimental results show that the proposed method can more successfully boost prediction accuracy compared to the other three cutting-edge VSG methods.

Nonlinear wave propagation in a bistable optical chain with nonreciprocal coupling

The propagation of nonlinear waves, such as fires, weather fronts, and disease spread, has drawn attention since the dawn of time. A well-known example of nonlinear wave–fronts–in our daily lives is the domino waves, which propagate equally toward the left or right flank due to their reciprocal coupling. However, there are other situations where front propagation is not fully understood, such as bistable fronts with nonreciprocal coupling. These couplings are characterised by the fact that the energy emitter and receiver are not interchangeable. Here, we study the propagation of nonlinear waves in a bistable optical chain forced by nonreciprocal optical feedback. The spatiotemporal evolution and the front speeds are characterised as a function of the nonreciprocal coupling. We derive an equation to describe the interacting optical elements in a liquid crystal light valve with nonreciprocal optical feedback and compare the experimental results with numerical simulations of the coupled bistable systems.

Inversion Symmetry-Broken Tetralayer Graphene Probed by Second-Harmonic Generation.

Stacking orders provide a unique way to tune the properties of two-dimensional materials. Recently, ABCB-stacked tetralayer graphene has been predicted to possess atypical elemental ferroelectricity arising from its symmetry breaking but has been experimentally explored very little. Here, we observe pronounced nonlinear optical second-harmonic generation (SHG) in ABCB-stacked tetralayer graphene while absent in both ABAB- and ABCA-stacked allotropes. Our results provide direct evidence of symmetry breaking in ABCB-stacked tetralayer graphene. The remarkable contrast in the SHG spectra of tetralayer graphene allows straightforward identification of ABCB domains from the other two kinds of stacking order and facilitates the characterization of their crystalline orientation. The employed SHG technique serves as a convenient tool for exploring the intriguing physics and novel nonlinear optics in ABCB-stacked graphene, where spontaneous polarization and intrinsically gapped flat bands coexist. Our results establish ABCB-stacked graphene as a unique platform for studying the rare ferroelectricity in noncentrosymmetric elemental structures.

Exploring the dynamics of shallow water waves and nonlinear wave propagation in hyperelastic rods: Analytical insights into the Camassa–Holm equation

The objective of this paper is to examine the analytical properties of the nonlinear [Formula: see text]-dimensional Camassa–Holm equation ([Formula: see text]), a fundamental model within the domain of nonlinear evolution equations. The aforementioned equation serves as a valuable tool in elucidating the unidirectional propagation of shallow water waves over a level terrain, as well as in representing certain nonlinear wave phenomena seen in cylindrical hyperelastic rods. We use the Khater III ([Formula: see text]hat.III) and improved Kudryashov ([Formula: see text]ud) technique to provide accurate solutions, drawing inspiration from the intricate mathematical framework of the [Formula: see text] issue. He’s variational iteration ([Formula: see text]) technique is used as a numerical methodology to assess the correctness of the generated answers. This strategy reveals a notable concurrence between the analytical and numerical outcomes. This alignment guarantees the suitability of the acquired solutions within the framework of the studied model. The importance of this investigation lies in its ability to improve our comprehension of the intricate dynamics regulated by the [Formula: see text] equation and its connections with other nonlinear evolution equations that describe shallow water wave behaviors and nonlinear wave propagation in cylindrical hyperelastic rods. The results of the study demonstrate novel analytical approaches, expanding the range of potential solutions and offering valuable insights into the physical characteristics of the interconnected wave phenomena. This research offers valuable insights and methodologies for addressing intricate mathematical models in shallow water wave theory and studying nonlinear waves in hyperelastic materials, therefore making substantial advances to the subject of nonlinear partial differential equations.

Probabilistic impact localization in composites using wavelet scattering transform and multi-output Gaussian process regression

Data-driven machine-learning models offer considerable promise for acoustic source localization. However, many existing models rely on training data that correlates time-of-flight (TOF) measurements with source locations, yet they struggle to handle the complexities arising from nonlinear wave propagation in materials with varying properties. Furthermore, these models overlook the noise and uncertainties inherent in real-world experiments when predicting outputs. This paper aims to bridge a gap in impact localization for such structures, particularly focusing on scenarios involving noisy field measurements. This study proposes a framework based on probabilistic machine learning to identify impact locations, utilizing wavelet scattering transform (WST) and Multi-Output Gaussian Process Regression (moGPR). WST extracts informative features from Lamb waves, capturing relevant signatures for training the probabilistic machine learning model, while moGPR estimates correlated impact location coordinates (x, y) while accounting for inherent uncertainties in the data. To assess the proposed method’s performance in handling measurement uncertainties, an experiment was conducted using a CFRP composite panel instrumented with a sparse array of piezoelectric transducers. The results demonstrate that the probabilistic framework effectively addresses measurement uncertainties, enabling reliable source location estimation with confidence intervals and providing valuable insights for decision-making.

DISSIPATION AND DISPERSION IN FRACTIONAL NONLINEAR WAVE DYNAMICS: ANALYTICAL AND NUMERICAL EXPLORATIONS

The fractional nonlinear generalized [Formula: see text]-dimensional Chaffee–Infante (FGCI) equation is a nonlinear evolution equation that governs the propagation of waves in dispersive media, exhibiting both dissipative and dispersive effects. It finds applications in various fields such as fluid mechanics, plasma physics, and nonlinear optics, where the interplay between nonlinearity, dispersion, and dissipation plays a crucial role in determining the dynamics of the system. This study aims to obtain analytical and numerical solutions for the FGCI equation, which is a generalization of the Chaffee–Infante equation. The analytical approach employed is the Khater II (Khat II) method, an efficient technique for constructing approximate analytical solutions to nonlinear fractional differential equations. Additionally, He’s variational iteration (HVI) method is implemented as a numerical scheme to validate the accuracy of the analytical solutions obtained from the Khat II method. The results obtained through these methods demonstrate the effectiveness of the proposed techniques in solving the FGCI equation and provide valuable insights into the dynamics of wave propagation phenomena governed by the equation. The significance of this study lies in its contribution to the understanding of nonlinear wave propagation phenomena and the development of analytical and numerical techniques for solving fractional differential equations. The novelty of the research lies in the application of the Khat II method to the FGCI equation, which has not been previously explored, and the validation of the analytical solutions through the HVI method. The study is conducted in the field of applied mathematics, with a focus on nonlinear fractional differential equations and their applications in various physical systems.

Dynamics of pulse propagation with solitary waves in monomode optical fibers with nonlinear Fokas system

In this study, a unified auxiliary equation method, which is one of the powerful methods for exploring nonlinear model solutions, is used in the Fokas system, with complex functions representing nonlinear pulse propagation in monomode optical fibers. As a result, we get some solutions, including dark–bright, singular, periodic, bright–dark, Jacobi elliptic functions, trigonometric, hyperbolic and exponential ones. In addition, we use a computer program to generate 3D, 2D and counterplot graphics from the obtained solutions by assigning specific values to the involved parameters. While discussing, the graphs for various values of an arbitrary constant are examined. These findings constitute an important step in understanding how solitary waves are generated in nonlinear media. Since the studied model is used in many domains, including Bose–Einstein condensates and plasma physics, these results improve our theoretical knowledge and open up new avenues for potential real-world applications and the development of cutting-edge technologies.

An iteration method to study nonlinear wave propagation for a non-Green elastic 1D bar

Abstract The problem of propagation of nonlinear waves in a 1D bar is studied, wherein the linearized strain tensor is considered as a function of the Cauchy stress tensor. Specifically, two constitutive equations for non-Green elastic solids are investigated, introducing a novel numerical iterative method capable of obtaining approximate solutions of one nonlinear constitutive equation for rock, and one constitutive equation that shows a strain-limiting behaviour. The numerical results are compared with exact solutions for the case of a linearized elastic solid.

Laser-accelerated MeV-scale collimated electron bunch from a near-critical plasma of a liquid jet target

Generation of a collimated electron bunch with energy of a few MeV is demonstrated experimentally during propagation of 1 TW 10 Hz femtosecond laser radiation through a near-critical plasma formed from a micrometer-scale liquid jet (ethanol) target by ablation and boring with an intense nanosecond pulse. Hydrodynamic and particle-in-cell simulations reveal the evolution of the plasma cloud and help to identify the acceleration mechanism, which is related to self-modulated laser Wakefield acceleration during nonlinear propagation of laser radiation through plasma. The measured bunch divergence is at the level of 0.04 rad with high shot-to-shot stability. The total charge of the particles with energy above 1.6 MeV was estimated at ∼15 pC. The simplicity and robustness of the target design allows for enhanced pulse repetition rate with suppressed debris formation.

A hybrid variational method for beam propagation and interaction in a graded-index nonlinear waveguide

The hybrid variational method can be used to simplify multidimensional numerical simulations. We examine the applicability of this method to study the nonlinear propagation of a single beam and the interference of two spatial soliton beams in a graded-index optical waveguide governed by a two-dimensional nonlinear Schrodinger equation. We classified three distinct regimes of the dynamics that emerge during single Gaussian beam propagation, corresponding to beam decay, breather formation, and self-focusing. When two spatial soliton beams were set up to interfere in the waveguide, we identified the boundary where the nonlinear interaction during the interference led to excitation or self-focusing. These quite involved dynamics were used to test the predictive power of our variational models by comparing them with direct numerical simulations, obtaining good agreement.

Improving PID Controller Performance in Nonlinear Oscillatory Automatic Generation Control Systems Using a Multi-objective Marine Predator Algorithm with Enhanced Diversity

Power systems are pivotal in providing sustainable energy across various sectors. However, optimizing their performance to meet modern demands remains a significant challenge. This paper introduces an innovative strategy to improve the optimization of PID controllers within nonlinear oscillatory Automatic Generation Control (AGC) systems, essential for the stability of power systems. Our approach aims to reduce the integrated time squared error, the integrated time absolute error, and the rate of change in deviation, facilitating faster convergence, diminished overshoot, and decreased oscillations. By incorporating the spiral model from the Whale Optimization Algorithm (WOA) into the Multi-Objective Marine Predator Algorithm (MOMPA), our method effectively broadens the diversity of solution sets and finely tunes the balance between exploration and exploitation strategies. Furthermore, the QQSMOMPA framework integrates quasi-oppositional learning and Q-learning to overcome local optima, thereby generating optimal Pareto solutions. When applied to nonlinear AGC systems featuring governor dead zones, the PID controllers optimized by QQSMOMPA not only achieve 14%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} reduction in the frequency settling time but also exhibit robustness against uncertainties in load disturbance inputs.

Traveling wave solution and qualitative behavior of fractional stochastic Kraenkel–Manna–Merle equation in ferromagnetic materials

The main purpose of this article is to investigate the qualitative behavior and traveling wave solutions of the fractional stochastic Kraenkel–Manna–Merle equations, which is commonly used to simulate the zero conductivity nonlinear propagation behavior of short waves in saturated ferromagnetic materials. Firstly, fractional stochastic Kraenkel–Manna–Merle equations are transformed into ordinary differential equations by using the traveling wave transformation. Secondly, the phase portraits, sensitivity analysis, and Poincaré sections of the two-dimensional dynamic system and its perturbation system of ordinary differential equations are drawn. Finally, the traveling wave solutions of fractional stochastic Kraenkel–Manna–Merle equations are obtained based on the analysis theory of planar dynamical system. Moreover, the obtained three-dimensional graphs of random solutions, two-dimensional graphs of random solutions, and three-dimensional graphs of deterministic solutions are drawn.

On the maximization of entropy in the process of thermalization of highly multimode nonlinear beams.

We present a direct experimental confirmation of the maximization of entropy which accompanies the thermalization of a highly multimode light beam, upon its nonlinear propagation in standard graded-index (GRIN) optical fibers.