Search Results (27)

Fluid flow and mass transfer processes in some fractured aquifers are negligible in the low-permeability rock matrix and occur mainly in the fracture network. In this work, we consider coupled variable-density flow (VDF) and mass transport with dissolution in discrete fracture networks (DFNs). These three processes are ruled by nonlinear and strongly coupled partial differential equations (PDEs) due to the (i) density variation induced by concentration and (ii) fracture aperture evolution induced by dissolution. In this study, we develop an efficient model to solve the resulting system of nonlinear PDEs. The new model leverages the method of lines (MOL) to combine the robust finite volume (FV) method for spatial discretization with a high-order method for temporal discretization. A suitable upwind scheme is used on the fracture network to eliminate spurious oscillations in the advection-dominated case. The time step size and the order of the time integration are adapted during simulations to reduce the computational burden while preserving accuracy. The developed VDF-DFN model is validated by simulating saltwater intrusion and dissolution in a coastal fractured aquifer. The results of the VDF-DFN model, in the case of a dense fracture network, show excellent agreement with the Henry semi-analytical solution for saltwater intrusion and dissolution in a coastal aquifer. The VDF-DFN model is then employed to investigate coupled flow, mass transfer and dissolution for an injection/extraction well pair problem. This test problem enables an exploration of how dissolution influences the evolution of the fracture aperture, considering both constant and variable dissolution rates. Full article

Background: Sensorimotor beta oscillations are critical for motor control and become synchronized with muscle activity during sustained contractions, forming corticomuscular coherence (CMC). Although beta activity manifests in transient bursts, suggesting nonlinear behavior, most studies rely on linear analyses, leaving the underlying dynamic structure of brain–muscle interactions underexplored. Objectives: To investigate the nonlinear dynamics underlying beta oscillations during isometric contraction. Methods: MEG and EMG were recorded from 17 right-handed healthy adults performing a 10 min isometric pinch task. Lyapunov exponent (LE), fractal dimension (FD), and correlation dimension (CD) were computed in 10 s windows to assess temporal stability. Signal similarity was assessed using Pearson correlation of amplitude envelopes and the nonlinear features. Burstiness was estimated using the coefficient of variation (CV) of the beta envelope to examine how transient fluctuations in signal amplitude relate to underlying nonlinear dynamics. Phase-randomized surrogate signals were used to validate the nonlinearity of the original data. Results: In contrast to FD, LE and CD revealed consistent, structured dynamics over time and significantly differed from surrogate signals, indicating sensitivity to non-random patterns. Both MEG and EMG signals demonstrated temporal stability in nonlinear features. However, MEG–EMG similarity was captured only by linear envelope correlation, not by nonlinear features. CD was strongly associated with beta burstiness in MEG, suggesting it reflects information similar to that captured by the amplitude envelope. In contrast, LE showed a weaker, inverse relationship, and FD was not significantly associated with burstiness. Conclusions: Nonlinear features capture intrinsic, stable dynamics in cortical and muscular beta activity, but do not reflect cross-modal similarity, highlighting a distinction from conventional linear analyses. Full article

To investigate the mechanisms of unexpected failures in a multi-stage gear transmission system under a relatively low load, a rigid–flexible coupled multi-body dynamics model with 10 spur gears and 12 helical gears is established. The dynamic condensation theory is applied to improve computational efficiency. The construction of this model incorporates critical nonlinear factors, ensuring high precision and reliability. Based on the proposed model, four critical dynamic parameters, including acceleration, mesh stiffness, dynamic transmission error, and vibration displacement, are analyzed. This research systematically reveals the nonlinear dynamic mechanism under the multi-gear coupling effect. The spectrum of the gears exhibits prominent low-frequency peaks at 320 Hz and 750 Hz. Notably, alternate load-dominated gears show a shift in prominent low-frequency peaks. The phenomenon of marked oscillations in mesh stiffness suggests a potential risk of localized weakening in the system’s load-carrying capacity. Critically, alternating torques induce periodic double-tooth contact regions in the gear at specific time points (0.115 s and 0.137 s), which are identified as critical factors leading to gear transmission system failures. The variation characteristics of the dynamic transmission error (DTE) demonstrate that the DTE is strongly correlated with the meshing state. The analysis of vibration displacement further indicates that the alternating external loads are the dominant excitation source of vibrations, noise, and failures in the gear transmission system. Full article

The study offers a comprehensive investigation of periodic solutions in highly nonlinear oscillator systems, employing advanced analytical and numerical techniques. The motivation stems from the urgent need to understand complex dynamical behaviors in physics and engineering, where traditional linear approximations fall short. This work precisely applies He’s Frequency Formula (HFF) to provide theoretical insights into certain classes of strongly nonlinear oscillators, as illustrated through five broad examples drawn from various scientific and engineering disciplines. Additionally, the novelty of the present work lies in reducing the required time compared to the classical perturbation techniques that are widely employed in this field. The proposed non-perturbative approach (NPA) effectively converts nonlinear ordinary differential equations (ODEs) into linear ones, equivalent to simple harmonic motion. This method yields a new frequency approximation that aligns closely with the numerical results, often outperforming existing approximation techniques in terms of accuracy. To aid readers, the NPA is thoroughly explained, and its theoretical predictions are validated through numerical simulations using Mathematica Software (MS). An excellent agreement between the theoretical and numerical responses highlights the robustness of this method. Furthermore, the NPA enables a detailed stability analysis, an area where traditional methods frequently underperform. Due to its flexibility and effectiveness, the NPA presents a powerful and efficient tool for analyzing highly nonlinear oscillators across various fields of engineering and applied science. Full article

To solve the nonlinear vibration problems of second- and third-order nonlinear oscillators, a modified harmonic balance method (HBM) is developed in this paper. In the linearized technique, we decompose the nonlinear terms of the governing equation on two sides via a constant weight factor; then, they are linearized with respect to a fundamental periodic function satisfying the specified initial conditions. The periodicity of nonlinear oscillation is reflected in the Mathieu-type ordinary differential equation (ODE) with periodic forcing terms appeared on the right-hand side. In each iteration of the linearized harmonic balance method (LHBM), we simply solve a small-size linear system to determine the Fourier coefficients and the vibration frequency. Because the algebraic manipulations required for the LHBM are quite saving, it converges fast with a few iterations. For the Duffing oscillator, a frequency–amplitude formula is derived in closed form, which improves the accuracy of frequency by about three orders compared to that obtained by the Hamiltonian-based frequency–amplitude formula. To reduce the computational cost of analytically solving the third-order nonlinear jerk equations, the LHBM invoking a linearization technique results in the Mathieu-type ODE again, of which the harmonic balance equations are easily deduced and solved. The LHBM can achieve quite accurate periodic solutions, whose accuracy is assessed by using the fourth-order Runge–Kutta numerical integration method. The optimal value of weight factor is chosen such that the absolute error of the periodic solution is minimized. Full article

This paper examines oscillations governed by the generic nonlinear differential equation ${u^{″}=\omega }_{p0}^2\left(1-u\mp {\displaystyle \frac{2{\beta }^2}{u^{\gamma }}}\right),$ where ${\omega }_{p0},\beta$ and $\gamma$ are positive constants. The aforementioned differential equation is of particular importance, as it describes electron plasma oscillations influenced by temperature effects and large oscillation amplitudes. Since no analytical solution exists for the oscillation period in terms of ${\omega }_{p0},\beta ,\gamma$ and the oscillation amplitude, accurate approximations are derived. A modified He’s approach is used to account for the non-symmetrical oscillation around the equilibrium position. The motion is divided into two parts: $u_{min}\le u<u_{eq}$ and $u_{eq}<u\le u_{max}$, where $u_{min}$ and $u_{max}$ are the minimum and maximum values of $u$, and $u_{eq}$ is its equilibrium value. The time intervals for each part are calculated and summed to find the oscillation period. The proposed method shows remarkable accuracy compared to numerical results. The most significant result of this paper is that He’s approach can be readily extended to strongly non-symmetrical nonlinear oscillations. It is also demonstrated that the same approach can be extended to any case where each segment of the function $f\left(u\right)$ in the differential equation $u^{″}+f\left(u\right)=0$ (for $u_{min}\le u<u_{eq}$ and for $u_{eq}<u\le u_{max}$) can be approximated by a fifth-degree polynomial containing only odd powers. Full article

The quality of power signals is strongly influenced by nonlinear loads in Electrical Power systems. Representation of electrical signals using different Sparse techniques is an interesting area of research as it moderates the volume of data to be stored. The storage of signals in Sparse form will make data storage easier and more efficient. Earlier studies concentrated on blindly choosing Overcomplete Hybrid Dictionaries (OHDs) for Sparse representation. The effect of different dictionaries in representing electrical signals has also not been reviewed in them. This paper presents an investigation of the effect of various dictionaries and the sparsity constant on the representation of electrical signals. The validation for statements presented in this paper is carried out by representing power signals with diverse power line disturbances like Swell, DC offset, and random oscillation, with the help of various dictionaries in the simulation platform. The Sparse representation of the power signals was generated using the Orthogonal Matching Pursuit algorithm. The resultant Sparse representation was then compared with the original signal. The difference between them was found to be negligible with the help of different metrics. The ratio of the obtained signal from Sparse representation, the original signal (A/R ratio), and the Mean Squared Error were taken as the metrics. The MATLAB platform was used for performing the simulation study. Full article

Modern power systems are high-dimensional, strongly coupled nonlinear systems with complex and diverse dynamic characteristics. The polynomial model of the power system is a key focus in stability research. Therefore, this paper presents a study on the approximate transient stability solution targeting the fault process in power systems. Firstly, based on the inherent sinusoidal coupling characteristics of the power system swing equations, a generalized polynomial matrix description in perturbation form is presented using the Taylor expansion formula. Secondly, considering the staged characteristics of the stability process in power systems, the approximate solutions of the polynomial model during and after the fault are provided using coordinate transformation and regular perturbation techniques. Then, the structural characteristics of the approximate solutions are analyzed, revealing the mathematical basis of the stable motion patterns of the power grid, and a monotonicity rule of the system’s power angle oscillation amplitude is discovered. Finally, the effectiveness of the proposed methods and analyses is further validated by numerical examples of the IEEE 3-machine 9-bus system and IEEE 10-machine 39-bus system. Full article

Ultrafast pump–probe spectroscopic studies allow for deep insights into the mechanisms and timescales of photophysical and photochemical processes. Extracting valuable information from these studies, such as reactive intermediates’ lifetimes and coherent oscillation frequencies, is an example of the inverse problems of chemical kinetics. This article describes a consistent approach for solving this inverse problem that avoids the common obstacles of simple least-squares fitting that can lead to unreliable results. The presented approach is based on the regularized Markov Chain Monte-Carlo sampling for the strongly nonlinear parameters, allowing for a straightforward solution of the ill-posed nonlinear inverse problem. The software to implement the described fitting routine is introduced and the numerical examples of its application are given. We will also touch on critical experimental parameters, such as the temporal overlap of pulses and cross-correlation time and their connection to the minimal reachable time resolution. Full article

X-ray production through betatron radiation emission from electron bunches is a valuable resource for several research fields. The EuAPS (EuPRAXIA Advanced Photon Sources) project, within the framework of EuPRAXIA, aims to provide 1–10 keV photons (X-rays), developing a compact plasma-based system designed to exploit self-injection processes that occur in the highly nonlinear laser-plasma interaction (LWFA) to drive electron betatron oscillations. Since the emitted radiation spectrum, intensity, angular divergence, and possible coherence strongly depend on the properties of the self-injected beam, accurate preliminary simulations of the process are necessary to evaluate the optimal diagnostic device specifications and to provide an initial estimate of the source’s performance. A dedicated tool for these tasks has been developed; electron trajectories from particle-in-cell (PIC) simulations are currently undergoing numerical analysis through the calculation of retarded fields and spectra for various plasma and laser parameter combinations. The implemented forward approach evaluation of the fields could allow for the integration of the presented scheme into already existing PIC codes. The spectrum calculation is thus performed in detector time, giving a linear complex exponential phase; this feature allows for a semi-analitical Fourier transform evaluation. The code structure and some trajectories analysis results are presented. Full article

Low-frequency oscillation (LFO) of the synchronous generators in power systems by wind power is boring. To improve the robustness of the damping control scheme, this paper applies the sliding mode control (SMC) at the doubly fed induction generator (DFIG), with the parameter of the SMC optimized by the eigen-sensitivity. The originalities lie in, (1) the states strongly associated with the critical modes are newly applied to design the sliding surface, (2) the closed-loop model of the power system with the improved equivalent control is derived to analyze the damping effect on the critical modes and the undesirable effect on the noncritical modes, (3) the gain in the improved equivalent control is optimized to damp the critical and noncritical modes, and (4) the eigenvector sensitivity is improved to derive the second-order eigen- sensitivity to solve the nonlinear optimization. Numerical results show that the proposed model damps the critical modes effectively for different wind speeds, while the undesirable effect on the noncritical modes is avoided. Full article

The concept of polaron quasiparticles was first introduced in the pioneering papers by Landau and Feynman in the 1930s and 1940s. It describes the phenomenon of an external particle producing a bound state in an embedded medium. Since then, the study of polaron quasiparticles has been an active area of research in condensed matter physics, with a wide range of applications in magnetic phenomena and lattice deformation properties. In this paper, we provide a comprehensive review of the polaron quasiparticle phenomenon, including its historical origins, theoretical developments, and current research. We also study the various applications of polaron quasiparticles in condensed matter physics, including in magnetic phenomena and lattice deformation properties. The review concludes with an outlook on future directions of research in this field. In particular, we study the motion of external embedded particles in a quasi-two-dimensional Bose–Einstein condensate confined by the quantum harmonic oscillator. We found that the dynamics of attracting particles with static Bose–Einstein condensate exhibit circular and precessional elliptic trajectories due to centripetal force. Polaron-forming embedded particles in the condensate lead to a strongly nonlinear trajectory of the polaron and dynamics of condensate depending on the initial parameters of the condensate and polaron. Full article

Agriculture in the southeastern United States (SEUS) is heavily reliant upon water resources provided by precipitation during the warm season (June–August). The convective and stochastic nature of SEUS warm season precipitation introduces challenges in terms of water availability in the region by creating localized maxima and minima. Clearly, a detailed and updated warm season precipitation climatology for the SEUS is important for end users reliant on these water resources. As such, a nonlinear unsupervised learning method (kernel principal component analysis blended with cluster analysis) was used to develop a NARR-derived SEUS warm season precipitation climatology. Three clusters resulted from the analysis, all of which strongly resembled the mean spatially (r > 0.9) but had widely variable precipitation magnitude, as one cluster denoted a mean pattern, one a dry pattern, and one a wet pattern. The clusters were related back to major SEUS warm season precipitation moderators (tropical cyclone landfall and the El Niño–southern oscillation (ENSO)) and revealed a clearer ENSO relationship when discriminating among the cluster patterns. Ultimately, these updated SEUS precipitation patterns can help end users identify areas of notable sensitivity to different climate phenomena, helping to optimize the economic use of these critical water resources. Full article

In order to improve the Lindstedt-Poincaré method to raise the accuracy and the performance for the application to strongly nonlinear oscillators, a new analytic method by engaging in advance a linearization technique in the nonlinear differential equation is developed, which is realized in terms of a weight factor to decompose the nonlinear term into two sides. We expand the constant preceding the displacement in powers of the introduced parameter so that the coefficients can be determined to avoid the appearance of secular solutions. The present linearized Lindstedt-Poincaré method is easily implemented to provide accurate higher order analytic solutions of nonlinear oscillators, such as Duffing and van Der Pol nonlinear oscillators. The accuracy of analytic solutions is evaluated by comparing to the numerical results obtained from the fourth-order Runge-Kotta method. The major novelty is that we can simplify the Lindstedt-Poincaré method to solve strongly a nonlinear oscillator with a large vibration amplitude. Full article

This paper proceeds from the perspective that most strongly nonlinear oscillators of fractional-order do not enjoy exact analytical solutions. Undoubtedly, this is a good enough reason to employ one of the major recent approximate methods, namely an Optimal Homotopy Asymptotic Method (OHAM), to offer approximate analytic solutions for two strongly fractional-order nonlinear benchmark oscillatory problems, namely: the fractional-order Duffing-relativistic oscillator and the fractional-order stretched elastic wire oscillator (with a mass attached to its midpoint). In this work, a further modification has been proposed for such method and then carried out through establishing an optimal auxiliary linear operator, an auxiliary function, and an auxiliary control parameter. In view of the two aforesaid applications, it has been demonstrated that the OHAM is a reliable approach for controlling the convergence of approximate solutions and, hence, it is an effective tool for dealing with such problems. This assertion is completely confirmed by performing several graphical comparisons between the OHAM and the Homotopy Analysis Method (HAM). Full article