Combined Effects Of Nonlinearity Research Articles

Study of multi solitons, breather soliton structures in the earth's magnetotail region

The investigation of wave packets with varying magnitudes, which predominantly carry energy across different physical mediums, proves to be highly intriguing and unveils numerous nonlinear characteristics within Earth's magnetotail region and magnetosphere, as confirmed by extensive space observations. Nonlinear features in wave dynamics are elucidated through diverse nonlinear structures, among which breather structures hold prominence and manifest across various wave fields. We have considered an unmagnetized collisionless homogeneous hydrodynamical governing equations set in an electron-ion plasma comprising hot and cold ions. In this study, we have explored 1-soliton, 2-soliton, and breather structures in the framework of the Gardner equation (GE). We have derived the GE from the normalized set of governing equations employing the reductive perturbation technique (RPT). The GE, an extension of the Korteweg-de Vries (KdV) equation, encompasses the combined effects of quadratic and cubic nonlinearities. By employing the Hirota bilinear method (HBM), we have obtained multi-soliton solutions and breather soliton solutions. We have noticed the variations in electron temperature ratios and density concentration ratios substantially impact and reshape breather soliton structures. Such alterations in breather structures, influenced by different electron temperatures and concentration ratios, hold potential significance in understanding energy transport within Earth's magnetotail region. The alteration of shapes and soliton structures may also be investigated in the dynamics of wave fields upon interaction such as hydrodynamics, optics, optic fibers, signal processing, etc.

Topological unwinding in an exciton-polariton condensate array

The phase distribution in a Bose-Einstein condensate can realize various topological states classified by distinct winding numbers. While states with different winding numbers are topologically protected in the linear Schrödinger equation, when nonlinearities are introduced, violations of the topological protection can occur, leading to unwinding. Exciton-polariton condensates constitute a nonlinear open-dissipative system that is well suited to studying such physics. Here we show that a one-dimensional array of exciton-polariton condensates displays a spontaneous phase unwinding from a π- to zero-state. We clarify that this collective mode transition is caused by the combined effect of nonlinearity and topological defects in the condensates. While the mode-switching phenomenon observed in our previous experiment was interpreted as the single-particle mode competition, we offer an alternative explanation in terms the collective phase unwinding and find its evidence by reanalyzing the experimental data. Our results open a route towards active control of the mode switching by manipulating the topological defects in prospective quantum polaritonic devices.

Existence and multiplicity of solutions for fractional p-Laplacian equation involving critical concave-convex nonlinearities

Abstract We investigate the following fractional p-Laplacian convex-concave problem: ( P λ ) ( − Δ ) p s u = λ | u | q − 2 u + | u | p s * − 2 u in Ω , u = 0 in R n \ Ω , $$\left({P}_{\lambda }\right) \begin{cases}\begin{aligned}\hfill {\left(-{\Delta}\right)}_{p}^{s}u& =\lambda \vert u{\vert }^{q-2}u+\vert u{\vert }^{{p}_{s}^{{\ast}}-2}u\hfill & \hfill & \quad \text{in} {\Omega},\hfill \\ \hfill u& =0 \hfill & \hfill & \quad \text{in} {\mathbb{R}}^{n}{\backslash}{\Omega},\hfill \end{aligned}\quad \hfill \end{cases}$$ where Ω is a bounded C 1,1 domain in R n ${\mathbb{R}}^{n}$ , s ∈ (0, 1), p > q > 1, n > sp, λ > 0, and p s * = n p n − s p ${p}_{s}^{{\ast}}=\frac{np}{n-sp}$ is the critical Sobolev exponent. Our analysis extends classical works (A. Ambrosetti, H. Brezis, and G. Cerami, “Combined effects of concave and convex nonlinearities in some elliptic problems,” J. Funct. Anal., vol. 122, no. 2, pp. 519–543, 1994, B. Barrios, E. Colorado, R. Servadei, and F. Soria, “A critical fractional equation with concave-convex power nonlinearities,” Ann. Inst. Henri Poincare Anal. Non Lineaire, vol. 32, no. 4, pp. 875–900, 2015, J. García Azorero, J. Manfredi, and I. Peral Alonso, “Sobolev versus Hölder local minimizer and global multiplicity for some quasilinear elliptic equations,” Commun. Contemp. Math., vol. 2, no. 3, pp. 385–404, 2000) to fractional p-Laplacian. Owing to the nonlinear and nonlocal properties of ( − Δ ) p s ${\left(-{\Delta}\right)}_{p}^{s}$ , we need to overcome many difficulties and apply notably different approaches, due to the lack of Picone identity, the stability theory, and the strong comparison principle. We show first a dichotomy result: a positive W 0 s , p ( Ω ) ${W}_{0}^{s,p}\left({\Omega}\right)$ solution of (P λ ) exists if and only if λ ∈ (0, Λ] with an extremal value Λ ∈ (0, ∞). The W 0 s , p ( Ω ) ${W}_{0}^{s,p}\left({\Omega}\right)$ regularity for the extremal solution seems to be unknown regardless of whether s = 1 or s ∈ (0, 1). When p ≥ 2, p − 1 < q < p and n > s p ( q + 1 ) q + 1 − p $n{ >}\frac{sp\left(q+1\right)}{q+1-p}$ , we get two positive solutions for (P λ ) with small λ > 0. Here the mountain pass structure is more involved than the classical situations due to the lack of explicit minimizers for the Sobolev embedding, we should proceed carefully and simultaneously the construction of mountain pass geometry and the estimate for mountain pass level. Finally, we show another new result for (P λ ) and all p > q > 1: without sign constraint, (P λ ) possesses infinitely many solutions when λ > 0 is small enough. Here we use the Z 2 ${\mathbb{Z}}_{2}$ -genus theory, based on a space decomposition for reflexible and separable Banach spaces, which has its own interest.

Amplitude deflection in a nonlinear MEMS resonator under parametric excitation

In this paper, the dynamic characteristics of a parametrically excited MEMS micro-resonator incorporating high-order nonlinearity and nonlinear damping are investigated experimentally and theoretically. An intriguing phenomenon of amplitude deflection is observed when the parametric excitation strength exceeds a certain value. We establish a dynamic model of the micro-resonator under parametric excitation and employ the averaging method to obtain an approximate analytical solution. Then the theoretical study is made to explain the amplitude deflection under large excitation, attributing it to the combined effects of high-order nonlinearity and nonlinear damping. These findings contribute to a more comprehensive understanding of the characteristics of parametrically excited systems.

Symbol error rate minimization using deep learning approaches for short-reach optical communication networks

Short-reach optical communication networks have various applications in areas where high-speed connectivity is needed, for example, inter- and intra-data center links, optical access networks, and indoor and in-building communication systems. Machine learning (ML) approaches provide a key solution for numerous challenging situations due to their robust decision-making, problem-solving, and pattern-recognition abilities. In this work, our focus is on utilizing deep learning models to minimize symbol error rates in short-reach optical communication setups. Various channel impairments, such as nonlinearity, chromatic dispersion (CD), and attenuation, are accurately modeled. Initially, we address the challenge of modeling a nonlinear channel. Consequently, we harness a deep learning model called autoencoders (AEs) to facilitate communication over nonlinear channels. Furthermore, we investigate how the inclusion of a nonlinear channel within an autoencoder influences the received constellation as the optical fiber length increases. Another facet of our work involves the deployment of a deep neural network-based receiver utilizing a channel influenced by chromatic dispersion. By gradually extending the optical length, we explore its impact on the received constellation and, consequently, the symbol error rate. Finally, we incorporate the split-step Fourier method (SSFM) to emulate the combined effects of nonlinearities, chromatic dispersion, and attenuation in the optical channel. This is accomplished through a neural network-based receiver. The outcome of this work is an evaluation and reduction of the symbol error rate as the length of the optical fiber is varied.

Strong diffraction of nonlinear surface acoustic waves in crystals

Nonlinear distortion and shock formation in planar surface acoustic waves in anisotropic crystals have been modeled without [Hamilton et al., JASA (1999)] and with [Cormack et al., JASA 2022] piezoelectricity. Weak diffraction has been included in the paraxial approximation for nonlinear surface wave beams in isotropic solids [Shull et al., JASA (1995)]. Here, a procedure for including strong diffraction, i.e., without the paraxial approximation, in the model for nonlinear surface waves in crystals is presented, which incorporates the angular spectrum approach described by Kharusi and Farnell (JASA 1970). Anisotropy is defined by expressing the phase speed of a plane wave, and therefore, the magnitude of the corresponding wavenumber, as a function of the direction of propagation. Next, an explicit expression relating the two wavenumber components in the planar surface along which the wave propagates must be obtained as a function of direction, requiring iterative solution of a transcendental relation. The beam is then propagated incrementally away from the source, advancing the angular spectrum in k-space and including nonlinear interactions in the spatial domain to characterize the combined effects of diffraction and nonlinearity. Preliminary results are presented for converging nonlinear surface waves in crystals. [Work supported by IR&D at ARL:UT.]

On an anisotropic $ \overset{\rightarrow }{p}(\cdot) $-Laplace equation with variable singular and sublinear nonlinearities

<p>In the present paper, we study an anisotropic $ \overset{\rightarrow }{p}(\cdot) $-Laplace equation with combined effects of variable singular and sublinear nonlinearities. Using the Ekeland's variational principle and a constrained minimization, we show the existence of a positive solution for the case where the variable singularity $ \beta(x) $ assumes its values in the interval $ (1, \infty) $.</p>

Propagation of spin waves in a lattice of laterally and vertically coupled YIG microwaveguides by changing the magnetization angle in linear and nonlinear modes

Purpose. Investigation of the joint manifestation of the effects of anisotropic signal propagation, coupling, and nonlinear power dependence of the medium parameters in a lattice of laterally and vertically coupled spin-wave (SW) microwaveguides. Consideration of the case of the influence of the rotation of the magnetization angle and the change of the lateral gap between microwaveguides located on the same substrate on the transverse profile of the spin-wave beam and the spatial localization of the SW amplitude. Methods. The method of micromagnetic modeling based on the numerical solution of the Landau–Lifshitz–Hilbert equation shows the possibility of controlling the direction of propagation of SW in an ensemble of laterally and vertically coupled iron yttrium garnet (YIG) microwaveguides by changing the magnetization angle. By the method of numerical integration of the system of coupled discrete nonlinear Schrodinger equations, the possibility of changing the transverse profile of the spin-wave beam by changing the level of the initial signal amplitude is shown. Results. The spatial distributions of the components of the dynamic magnetization of the SW excited in two microwaveguides located on the same substrate obtained in micromagnetic simulations indicate a change in the character of localization of the SW power in the output sections of the microwaveguides. At variation of the lattice magnetization angle, a shift of the threshold power value is observed, at which a characteristic curbing of the transverse width of the spin-wave beam in the nonlinear mode appears. Conclusion. When excitation of surface magnetostatic SW in a lattice of laterally and vertically coupled microwaveguides, a transformation of the transverse profile of the wave is observed at a deviation of the magnetization angle of the structure by 15º , which is manifested in the change of the SW length and its localization in each of the microwaveguides. The combined effects of dipole coupling, gyrotropy, and nonlinearity of the medium make it possible to control the value of the threshold power of the SW, at which the mode of diffractionless propagation of the spin-wave beam is realized in a single layer of the structure.

Coupled vibration analysis of bolted variable angle tow plates under combined nonlinear effects

To establish a dynamical modal of variable angle tow (VAT) plate accurately, the fiber path and fiber orientation of the VAT plate are described by high-order polynomials. Then, a simplified nonlinear joint model with interface dynamic partitioning is proposed to simulate the interface mechanical behavior of bolted joints. Based on these, a nonlinear semi-analytic dynamic model of the bolted VAT plate is built, which considers both material and joint nonlinearity and can accurately predict nonlinear vibration response. After verifying the proposed modeling method, a special bolted VAT plate is used as the analysis object for free vibration and forced vibration analysis. Firstly, the frequency veering behavior of the VAT plate caused by variations in boundary stiffness, connection stiffness, and fiber orientation is studied. Then, by analyzing the forced vibration response of the bolted VAT plate, it is found that under the combined effect of the modal interaction, material nonlinearity, and joint nonlinearity, the bolted VAT plate exhibited complex but rule-based nonlinear dynamic behavior. More importantly, the research work done in this paper has certain guiding significance for the optimization design of vibration resistance of a bolted VAT thin-walled structure with variable stiffness parameters and joint parameters as design variables.

Tidal energy extraction modifies tidal asymmetry and transport in a shallow, well-mixed estuary

Tidal energy extraction is increasingly being studied as a potential renewable energy resource in estuaries worldwide. Although it is understood that energy extraction via tidal stream turbines can modify currents and transport within estuaries, it is not clear how the underlying nonlinear physical mechanisms dictating tidal hydrodynamics are modulated. This research investigates the influence of a hypothetical tidal stream turbine array on barotropic tidal processes in a shallow, well-mixed system: the Piscataqua River – Great Bay (PRGB) estuary, using a numerical model. The modeled turbine farm includes 180 turbines which would extract an estimated 44.7 GWh of energy, annually. The tidal hydrodynamic model for the existing condition is validated with in-situ observations of currents and water level before analyzing tidal asymmetry and transport with and without tidal turbines. Results indicate that the tidal turbine array will decrease tidal elevation and current magnitudes system-wide, but generally reduce ebb currents and transport more than flood over most of the estuary footprint, thereby diminishing tidal asymmetry. The smaller asymmetric distortion compared to the no-turbine case is attributed to reductions in the storage volume of water over the estuary’s extensive tidal flat regions between low and high waters which decreases the associated nonlinear intertidal storage mechanism up to 25%. This leads to weakened ebb dominance over estuary sections from the mouth to mid-reaches, where depths are deep enough to keep the combined nonlinear shallow water and frictional effects from asserting control over the storage mechanism. Even in upstream shallow regions where depth-dependent friction controls asymmetry in both cases, the frictional mechanism is reduced only by 10% with turbines. Some environmental considerations of this work are discussed, with focus on sediment transport, water quality, and ecology.

Nonlinear elliptic p-Laplacian equations in the whole space

In this paper the existence and multiplicity of non-zero solutions for nonlinear Dirichlet problems involving the p-Laplacian operator and which are defined in the whole space is established. In particular, the existence of two non-zero solutions, one with negative energy and other with positive one for equations having combined effects of concave and convex nonlinearities is obtained. The approach is based on variational methods.

Singular Anisotropic Problems with Competition Phenomena

We consider a Dirichlet problem driven by the anisotropic (p(z), q(z))-Laplacian, with a parametric reaction exhibiting the combined effects of singular and concave-convex nonlinearities. The superlinear term may change sign. Using variational tools together with truncation and comparison techniques, we prove a global (for the parameter lambda >0) existence and multiplicity theorem (a bifurcation-type theorem).

Downwash modelling for three-lifting-surface aircraft configuration design

This paper introduces a semi-empirical model to predict the downwash gradient at the horizontal tail of a three-lifting-surface aircraft. The superposition principle applied to well established formulations valid for two lifting surfaces is not a reasonable approach to calculate the downwash of a canard-wing-tail layout, and this paper demonstrates that such a basic technique leads to incorrect results. Therefore, an ad hoc prediction model is proposed that considers the combined nonlinear effects of canard and main wing inductions on tail downwash, being based on a full factorial design sweep of CFD simulations obtained by varying the main geometrical parameters of the three lifting surfaces. A suitable analytical formula for the downwash gradient is established through a process of data analysis and factor extraction. The presented model extends the validity of the available models for traditional two-lifting-surface designs by means of a correction factor. The engineering estimation method introduced here exhibits an acceptable accuracy, as well as relatively small prediction errors, and it is suitable for conceptual and preliminary studies of three-surface layouts. The value of this methodology is confirmed by the validation with the results of numerical and experimental investigations on a case study aircraft.

Adaptive Robust Servo Control for Vertical Electric Stabilization System of Tank and Experimental Validation

A tracking stability control problem for the vertical electric stabilization system of moving tank based on adaptive robust servo control is addressed. This paper mainly focuses on two types of possibly fast time-varying but bounded uncertainty within the vertical electric stabilization system: model parameter uncertainty and uncertain nonlinearity. First, the vertical electric stabilization system is constructed as an uncertain nonlinear dynamic system that can reflect the practical mechanics transfer process of the system. Second, the dynamical equation in the form of state space is established by designing the angular tracking error. Third, the comprehensive parameter of system uncertainty is designed to estimate the most conservative effects of uncertainty. Finally, an adaptive robust servo control which can effectively handle the combined effects of complex nonlinearity and uncertainty is proposed. The feasibility of the proposed control strategy under the practical physical condition is validated through the tests on the experimental platform. This paper pioneers the introduction of the internal nonlinearity and uncertainty of the vertical electric stabilization system into the settlement of the tracking stability control problem, and validates the advanced servo control strategy through experiment for the first time.

Numerical modeling and nonlinear analysis of semi-rigid jointed steel frames

This paper investigates the effect of semi-rigid connection, geometric nonlinearity and material nonlinearity in steel frame analysis. To study the independent and combined effects of different nonlinearities, elastic and inelastic analyses are carried out using general purpose finite element software SAP2000. Connections are modeled as rotational springs and frame as one dimensional beam element. Verification and application of the simplified numerical model developed in the present study is demonstrated by considering different examples and comparing the results of present study with those available in the published literature. Numerical alternatives, key features about modeling and necessary input parameters are discussed in detail. Rotational springs are characterized by linear, bilinear, multi-linear or nonlinear moment-rotation relationships of the connection. Results in terms of beam moment and nodal displacement are presented for both elastic and inelastic analyses. With the increase in connection flexibility, beam mid-span moments and displacements increase, but beam-end moments decrease. It is observed that the influence of connection nonlinearity dominates over material and geometric nonlinearities.

Large‐scale ground motion simulation of the 2016 Kumamoto earthquake incorporating soil nonlinearity and topographic effects

AbstractA large‐scale physics‐based simulation is conducted to investigate ground motion distribution in the Mw 7.0 2016 Kumamoto earthquake, Japan. The model simulates the earthquake scenario from fault rupture to wave propagation, and localized site response with consideration of the combined effect of soil nonlinearity and topographic amplification. The simulation domain is 51 km × 43 km × 25 km, and the obtained ground motion time histories are compared satisfactorily with recordings from KiK‐net and K‐NET. Ground motion distribution considering nonlinear soil response and topographic amplification is presented. A 3D equivalent linear model is developed to mimic the soil nonlinearity, and it is demonstrated that neglecting soil nonlinearity could over‐predict peak ground acceleration (PGA) and underestimate peak ground velocity (PGV) near the fault. The topographic amplification factors (TAFs) of PGA and PGV are found between 0.5 and 2.0, with a correlation coefficient of 0.7 between them. Predictive equations are proposed to correlate TAFs of PGA and PGV with topographic features, which are represented by relative heights obtained at different length scales. Finally, major earthquake damages are summarized with reference to the obtained ground motion intensity map.

Combined nonlinear effects of urbanization and economic growth on CO2 emissions in Malaysia. An application of QARDL and KRLS

Despite adequate literature on the nonlinear nexus between economic growth-environment and urbanization-environment in Malaysia, yet study on the combined nonlinear effect is lacking. Therefore, this work investigates the existence of a combined nonlinear impact of both urbanization and economic growth utilizing the Environmental Kuznets Curve (EKC) hypothesis with the help of yearly data from 1965 to 2018. This study employs the novel Quantile Autoregressive Distributed Lag (QARDL) technique. In addition, the Kernel-based Regularized Least Squares (KRLS) machine learning method is used to test robustness. The available evidence indicates that the observed association is quantile-dependent, which may have led to erroneous conclusions in prior studies relying on traditional models that focus on averages. Overall, the results endorse the legitimacy of EKC and a U-shape linkage between urbanization and the environment in the long and short run. Furthermore, the KRLS estimates also support the findings of QARDL results. Based on the results of the study, a comprehensive policy recommendation for planners and government officials. Urban development and environmental protection issues must be appropriately addressed so that the urbanization development and changes may better adapt to new social development demands.

Acoustic solitons in a periodic waveguide: Theory and experiments

We study the propagation of high-amplitude sound waves, in the form of pulse-like solitary waves, in an air-filled acoustic waveguide of periodically varying cross section. Our numerical simulations, solving the compressible Navier–Stokes equations in two dimensions, as well as our experimental results, strongly suggest that nonlinear losses, originated from vortex shedding (at the segment changes) are crucial in the dynamics of high amplitude pulses. We find that, even in the presence of strong dissipation, the solitary wave roughly retains its characteristics (as described by the amplitude–velocity–width relations), obtained by the derivation and analysis of an effective Boussinesq equation. In addition, we propose a transmission-line based numerical scheme, able to capture well the experimental results. The proposed design offers a new playground for the study of the combined effects of dispersion, nonlinearity and dissipation in air-borne acoustics, while, due to its simplicity, it can be extended to higher dimensions.

Robust Nonlinear Control of DFIG-Based Wind Farms for Damping Inter-Area Oscillations of Power Systems

This article presents a perturbation observer–based robust nonlinear damping control (RNDC) scheme for a doubly fed induction generator (DFIG)–based wind farm to damp the inter-area oscillations of multi-area power systems. In the RNDC scheme, the perturbation term is introduced to describe the combined effects of nonlinearities, uncertainties, and disturbances of multi-area power systems with wind farms. The feedback linearization control is realized for reactive power control loops of the DFIG based on state estimation and perturbation estimation derived from a perturbation observer, thus achieving the damping control of the DFIG. The proposed RNDC scheme only needs one measurement signal, and it does not require any model parameters of the power grid and wind farm. Simulation studies are carried out on a two-area power system model connected with the wind farm to validate the control performance of the RNDC scheme under the conditions of three-phase-to-ground faults, parameter variations, and time delays.

Effects of rotation and topography on internal solitary waves governed by the rotating Gardner equation

Abstract. Nonlinear oceanic internal solitary waves are considered under the influence of the combined effects of saturating nonlinearity, Earth's rotation, and horizontal depth inhomogeneity. Here the basic model is the extended Korteweg–de Vries equation that includes both quadratic and cubic nonlinearity (the Gardner equation) with additional terms incorporating slowly varying depth and weak rotation. The complicated interplay between these different factors is explored using an approximate adiabatic approach and then through numerical solutions of the governing variable depth, i.e., the rotating Gardner model. These results are also compared to analysis in the Korteweg–de Vries limit to highlight the effect of the cubic nonlinearity. The study explores several particular cases considered in the literature that included some of these factors to illustrate limitations. Solutions are made to illustrate the relevance of this extended Gardner model for realistic oceanic conditions.