Search Results (2,828)

This work examines the nonlinear dynamics of a generalized Korteweg–de Vries–Zakharov–Kuznetsov equation, a model that appears in plasma physics, shallow water flows, and nonlinear wave propagation. By applying a solitary-wave transformation, the governing partial differential equation is reduced to an autonomous dynamical system, enabling a direct study of its phase portraits and equilibrium behavior. Stability of the fixed points is assessed through Jacobian matrices and eigenvalue classification, revealing parameter regimes that admit saddle states, centers, and oscillatory structures. The system’s richer behavior is explored by varying key parameters, with phase-space trajectories exhibiting periodic, quasiperiodic, and irregular wave patterns. To probe the onset of complexity, we employ several diagnostic tools, including time-series evolution, Lyapunov exponents, bifurcation analysis, sensitivity tests, and Poincaré sections, which together indicate transitions to chaotic motion. The resulting dynamics are further captured using a nonlinear autoregressive neural network, which accurately reproduces the observed trajectories. The combination of analytical and computational perspectives provides a clear framework for understanding this generalized equation and offers a practical approach for investigating other nonlinear systems with a similar structure. Full article

This study introduces a novel empirical model to estimate the total pressure drag generated by trapped lee waves (TLW) and upward-propagating internal waves in moderate-to-strong non-hydrostatic, stratified flow over a mountain ridge, as a function of flow non-linearity. The core framework is based on a two-layer atmosphere characterized by a piecewise-constant Scorer parameter, l, where a lower layer of constant $l_1$ underlies an upper layer with $l_2<l_1$. This framework incorporates key features to extend beyond idealized assumptions, providing a reliable tool for predicting non-linear flow regimes over mountainous terrain, particularly those featuring realistic vertical profiles of the Scorer parameter. To develop the empirical formulation, a micro- to mesoscale numerical model is employed to simulate realistic, non-linear flows over steep topography. The proposed empirical model yields results that compare favorably with numerical simulations across a range of moderate-to-strong non-hydrostatic regimes, including complex cases derived from observational data and realistic vertical profiles of the Scorer parameter. The model demonstrates robust performance ranging from strongly to moderately non-hydrostatic regimes (the latter corresponding to dimensionless half-widths of approximately 5), and provides accurate drag estimates for non-linearities up to a dimensionless mountain height of approximately unity. Therefore, this empirical approach serves as a valuable foundation for improving drag parameterizations in weather prediction models, offering a computationally efficient alternative to high-resolution numerical downscaling over steep terrain. Full article

Fixed-bottom or floating offshore structures are the foundations, platforms, and associated infrastructure that allow for oil and gas production systems, offshore wind turbines, and cabling. The remote nature of these structures and the harsh environment with high variability in wind, waves, currents, and weather make construction activity very difficult and unpredictable; the cost of variation in the schedule can lead to high construction vessel and personnel costs. The adoption of artificial intelligence using trends observed in historical data can help achieve more accurate construction costs and schedule predictions, reducing the capital expenditure cost of installation. A resource-significant activity, sometimes called a resource-critical activity or high-resource-demand activity, is an activity on a construction or project schedule that consumes a disproportionately large share of one or more resources compared with others. Plant Design Modelling (PDM) is a digital process that creates and manages a detailed 3D model of a building’s physical and functional characteristics and semantic information, such as cost and schedule. PDM serves as a single source of truth for multidisciplinary activities and, therefore, serves as a rich data source for various construction applications, including project scheduling and cost estimation. Neural networks (NNs), a subset of machine learning algorithms inspired by the human brain, excel at identifying patterns in complex datasets and making predictions, such as forecasting costs based on non-linear relationships and historical trends. Data from an offshore structure modification project were extracted from Aveva’s Everything PDM, focusing on installation activities to create a dataset for machine learning model training. The structured data extracted exhibit non-linear patterns; therefore, linear, regularised linear, robust linear, and the ensemble (tree-based) models and supervised neural network models with varied architecture and hyperparameter values were evaluated and compared. The best performance was obtained using the deep-optimised ANN model. The result obtained is consistent with previous studies. The neural network models show a superior ability to predict the non-linear nature of offshore construction activities’ time. Full article

This study presents a fourth-order implicit compact finite difference scheme for the Benjamin–Bona–Mahony–Burgers (BBMB) equation, a nonlinear long-wave equation describing the dynamics of various wave phenomena. By employing an order-reduction framework via an auxiliary variable, we construct a compact difference scheme that yields a nonlinear algebraic system with a narrowly banded structure. Because the continuous BBMB model is governed by an underlying conservation law, the proposed numerical method is designed to preserve this structural property in the discrete sense. The discrete conservation, boundedness, and unique solvability of the scheme are firmly established, and an optimal discrete maximum norm error estimate is derived. Finally, comprehensive numerical experiments are conducted to validate both the conservative properties and the theoretical order of accuracy of the proposed scheme. Full article

We consider a generalization of the modified Korteweg–de Vries–Burgers equation with a nonlinear source. Using the Painlevé test for partial differential equation with the Kruskal variable, we show that the corresponding Cauchy problem cannot be solved by the inverse scattering transform. However, the equation admits a two-wave solution, which is obtained by means of the Cole–Hopf transformation. Taking into account the traveling wave reduction, we derive the resulting nonlinear ordinary differential equation and determine the parameter conditions under which it passes the Painlevé test. This finding suggests the possible existence of the general solution for the ordinary differential equation, which can be reduced to the linear third-order equation. The general solution of the resulting linear equation is expressed in terms of the hypergeometric function. Full article

Accurate fault location is essential for improving the reliability and service restoration capability of distribution networks. With the increasing penetration of distributed generation, power electronic devices, and flexible loads, fault transient signals become increasingly nonlinear and nonstationary, posing challenges to conventional impedance-based, traveling-wave-based, and feature-engineering-based methods. To improve transient fault feature representation, this paper proposes a wavelet-embedded residual attention convolutional neural network (CNN) for distribution network fault location. The task is formulated as a multi-class classification problem, in which each predefined line section is treated as a candidate fault location class. The proposed method embeds discrete wavelet decomposition into the convolutional feature extraction process, enabling low-frequency trend components and high-frequency transient components to be jointly represented and fused by subsequent trainable network modules. Residual connections improve deep feature propagation, and an attention mechanism enhances fault-sensitive representations. Simulation studies on the IEEE 33-bus distribution system show that the proposed method outperforms multi-layer perceptron (MLP), support vector machine (SVM), standard CNN, ResNet, and Attention-CNN, achieving 98.27% accuracy and a 98.33% F1-score. The class-wise results and robustness tests under different transition resistances, noise levels, and fault types further verify the effectiveness and adaptability of the proposed method. Full article

Space gravitational wave detection missions demand ultra-stable calibration of inertial sensor capacitive sensing. Conventional dynamic methods suffer from mechanical vibration noise and bias separation difficulties, while large-displacement operation introduces pronounced nonlinearity. This work proposes a static calibration method using an image-based displacement measurement system to establish a vibration-free benchmark. A subpixel edge detection algorithm locates the Test Mass and Electrode Housing edges with a repeatability of approximately 0.05 pixels, and the Test Mass geometry is independently calibrated by a Coordinate Measuring Machine (CMM, ±2 µm, $k=2$) to provide SI traceability. A nonlinear calibration model incorporating higher-order Taylor terms is developed, combined with a forward/reverse connection technique for composite bias modeling. Experimental validation at $x_0=665$ µm ($x_0/d_0\approx 0.665$) demonstrated a gain coefficient repeatability of 0.01658% RMSPER and a combined expanded uncertainty of $U\approx 2.18\times {10}^{-5}$$1/\text{µ}\mathrm{m}$ ($k=2$). Intended as a complementary ground-based technique to dynamic calibration, this method avoids dynamic excitation-induced noise while establishing complete SI traceability, offering a reliable solution for ground validation and long-term monitoring of space inertial sensors. Full article

Artificial intelligence (AI), particularly deep learning (DL), is revolutionizing optical metamaterial design by overcoming the fundamental challenges of multidimensional parameter spaces, nonlinear structure–property relationships, and the intrinsic non-uniqueness of inverse problems. By learning complex mappings between geometric structures and electromagnetic responses, DL enables rapid forward prediction and on-demand inverse design without computationally intensive full-wave simulations. This review provides a comprehensive survey of AI-driven design methodologies across four key metamaterial platforms: localized resonant nanostructures, metasurfaces, periodic and guided-wave photonic structures, and complex scattering systems. For each platform, we systematically examine the neural network architectures employed, the specific design challenges addressed, and the representative achievements attained. These data-driven approaches not only significantly accelerate the discovery of high-performance structures but also offer new opportunities for extracting physical insights into light–matter interactions. We assess the critical challenges of data efficiency, model interpretability, and experimental feasibility, and outline emerging research directions that may address these barriers. This review aims to provide both a comprehensive summary of the current state of the art and forward-looking perspectives for this rapidly evolving interdisciplinary field. Full article

Infrared Fourier transform spectrometers using interferometric spectroscopy are widely used in space remote sensing owing to their high spectral resolution and sensitivity. We investigated the distorted spectral characteristics introduced by nonlinear errors of different orders through simulation for infrared detectors with strong nonlinear effects. A high-order nonlinear correction scheme was proposed based on two iterative correction methods for in-band and out-of-band spectra. Further, the effects of second-order, third-order, in-band, and out-of-band correction methods were compared using prelaunch radiometric calibration experimental data from the DQ-2 satellite infrared hyperspectral atmospheric composition sounder. The results showed that the third-order in-band correction scheme performed the best, while various other correction schemes also effectively reduced nonlinear errors. The maximum average deviation was 0.18–0.25 K for the long-wave band and 0.11–0.19 K for the mid-wave band in the temperature range of 230–300 K. According to the correction evaluation and methods comparison, the proposed method is appropriate for nonlinearity detectors to improve radiometric calibration accuracy. Full article

In this paper, we consider a damped p-Laplacian-type wave equation with logarithmic nonlinearity driven by multiplicative noises. We first establish the local existence and uniqueness of a mild solution to the equation using the truncation technique and semigroup method and show that the local solution is global under certain conditions. Secondly, we show the blow-up properties of solutions using an appropriate energy inequality. Moreover, we also derive estimates of the upper bound of the blow-up time. Full article

Background/Objectives: Long COVID-19 (LC) has been associated with persistent inflammation and impaired vascular health. Dietary minerals are involved in oxidative stress, endothelial homeostasis, and arterial stiffness; however, their relationship with vascular health in LC remains poorly explored. This study aimed to examine the association between energy-adjusted dietary mineral intake and markers of vascular stiffness and vascular aging in adults with LC, while exploring potential sex-specific patterns. Methods: A total of 304 adults with LC from the BioICOPER study were included. Dietary mineral intake was assessed using a validated 7-day dietary record from the EVIDENT tool and expressed as mineral density per 1000 kcal for the regression analyses. Vascular assessment included carotid intima-media thickness (cIMT), carotid-femoral pulse wave velocity (cfPWV), brachial-ankle pulse wave velocity (baPWV), and the vascular aging index (VAI). Hierarchical multivariable linear regression models, false discovery rate (FDR) correction, restricted cubic spline analyses, sensitivity analyses excluding supplement users, and formal sex × mineral interaction tests were performed. Results: In descriptive adequacy analyses, adequate iron intake was associated with lower baPWV. In energy-adjusted linear regression models, no mineral-outcome association remained statistically significant after FDR correction. In the fully adjusted sensitivity model, zinc density showed a nominal positive association with cfPWV, but this association did not survive FDR correction. Restricted cubic spline analyses suggested possible non-linear associations of magnesium and potassium density with cfPWV and VAI. Formal interaction analyses did not provide robust evidence of sex-related effect modification. Conclusions: After energy adjustment and correction for multiple testing, the evidence for independent linear associations between dietary mineral density and vascular outcomes in adults with LC was limited. These exploratory findings suggest that mineral intake, dietary sources, and non-linear patterns deserve further evaluation in prospective studies and nutritional intervention trials. Full article

Existing single-ended protection schemes for flexible DC transmission lines are negatively affected by traveling wave (TW) refraction and reflection interference and nonlinear overfitting under low-resistance faults. To address this, in this study, line-mode voltage reverse TWs are mathematically analyzed, revealing that internal faults and forward external faults exhibit single- and double-exponential attenuation, respectively. An adaptive constant-value flattening method is proposed to suppress subsequent TW refraction and reflection. Additionally, a composite fitting strategy utilizing Levenberg–Marquardt (LM) and Moore–Penrose pseudoinverse (PINV) algorithms is proposed to fit the measured waveforms, solving the problem of low-resistance overfitting and amplifying residual differences between internal and external faults. Based on these principles, a novel single-ended protection scheme is proposed. Simulations verify that this scheme exhibits a high operating speed and strong robustness against different fault distances, different fault resistances, and noise. Full article

We study a special case of the extended Korteweg–de Vries (eKdV) equation, arising in the description of weakly nonlinear long waves with higher-order dispersive effects. The model incorporates both third- and fifth-order dispersion and quadratic nonlinearity and describes steeper and shorter waves than the classical KdV equation. First, we determine the Lie point symmetry algebra of the equation and show that it reduces to space–time translations, which in turn motivates a traveling-wave reduction. The reduced fifth-order ODE is then analyzed by means of a calibrated $(G^{\prime }/G)$-expansion ansatz. Although homogeneous balance suggests a degree $M=4$ for exact solutions, a degree-$M=2$ truncation already yields three coherent families of traveling waves—hyperbolic (solitary), trigonometric (periodic), and rational—distinguished by the discriminant of the auxiliary linear equation. Using the direct multiplier method, we construct four conservation laws, corresponding to mass, momentum, energy, and a higher-order dispersion invariant, with all ${\alpha }^2$ contributions retained. Direct substitution and numerical diagnostics demonstrate that, once the algebraic wave speed is imposed, the $M=2$ profiles satisfy the PDE with residuals of order ${10}^{-3}$ and preserve the conserved quantities to machine precision (below ${10}^{-13}\%$ relative variation) over extended integration domains. These results extend the known solution structure of the special eKdV equation and illustrate the effectiveness of the $(G^{\prime }/G)$ framework for higher-order dispersive models. Full article

The Korteweg–de Vries (KdV) equation is widely known as a canonical model for weakly nonlinear and weakly dispersive waves, notably and historically for water waves in shallow depths. Being integrable, it has a rich solution set of interacting solitary and periodic waves. Recently, we extended it with several forcing/friction terms to describe the evolution of wind-driven water wave packets in shallow water. The outcome is a modified KdV–Burgers equation, whose relevant solutions are principally solitary wave trains forming a soliton gas. In this article that is extended further by allowing the water depth to be slowly spatially varying, and introducing a basic horizontal current, also slowly spatially varying. The outcome is a modified KdV–Burgers equation with spatially slowly varying coefficients. We adapt the Whitham modulation theory for a slowly varying solitary wave train, allowing for the prediction of wave amplitude growth/decay due to a combination of the slowly varying background and the forcing/friction terms. Numerical simulations using a Fourier spectral method are performed to exhibit and validate the modulation theory. Full article

In traditional mechanical de-icing technologies, the time-frequency evolution and spatial propagation mechanisms of transient high-frequency impact signals in flexible transmission lines remain unclear. To address this issue, transient impact responses were experimentally investigated using a full-scale transmission line model. An active de-icing exciter, featuring controllable impact energy and the potential for sustained online operation, was independently developed. High-frequency transient acceleration signals were acquired at multiple measurement points on a 20 m single-span line. The spatial distribution and time-frequency attenuation characteristics of the impact energy were quantitatively evaluated by extracting high-order time-domain statistical features, including root mean square, kurtosis, and crest factor, together with frequency-domain analyses based on Fast Fourier Transform (FFT) and wavelet entropy. The results indicate that: (1) The exciter generated highly impulsive transient responses, with a kurtosis up to 795.3 and a crest factor approaching 40. This suggests a strong local concentration of impact energy at the excitation source, which provides a dynamic basis for analyzing potential localized stress concentration and dynamic responses of the conductor system. (2) The transmission line structure exhibited a significant low-pass filtering effect on transient high-frequency shock waves. As the shock wave propagated towards the distal end, its high-frequency components above 30 Hz were substantially attenuated, likely due to internal dry friction within the stranded conductor. Consequently, the dominant frequency decreased to a low-frequency macroscopic sway of approximately 12 Hz, indicating a reduced risk of transmitting high-frequency shock loads to distal fittings and towers. (3) Under geometric nonlinear coupling, the vertical impact energy was partially transferred to the longitudinal and lateral directions during propagation, leading to sustained out-of-plane swaying. This study reveals the signal evolution characteristics of transient impacts in overhead transmission lines and provides experimental evidence for optimizing excitation parameters and assessing the engineering safety of active impact de-icing technologies. Full article