The study of different forms of preconditioners for solving a system of nonlinear equations, by using Newton’s method, is presented. The preconditioners provide numerical stability and rapid convergence with reasonable computation cost, whenever chosen accurately. Different families of iterative methods can be constructed by using a different kind of preconditioners. The multi-step iterative method consists of a base method and multi-step part. The convergence order of base method is quadratic and each multi-step add an additive factor of one in the previously achieved convergence order. Hence the convergence of order of an m-step iterative method is m + 1. Numerical simulations confirm the claimed convergence order by calculating the computational order of convergence. Finally, the numerical results clearly show the benefit of preconditioning for solving system of nonlinear equations.

This article introduces a novel two-step fifth-order Jacobian-free iterative method aimed at efficiently solving systems of nonlinear equations. The method leverages the benefits of Jacobian-free approaches, utilizing divided differences to circumvent the computationally intensive calculation of Jacobian matrices. This adaptation significantly reduces computational overhead and simplifies the implementation process while maintaining high convergence rates. We demonstrate that this method achieves fifth-order convergence under specific parameter settings, with a broad applicability across various types of nonlinear systems. The effectiveness of the proposed method is validated through a series of numerical experiments which confirm its superior performance in terms of accuracy and computational efficiency compared to existing methods.

This paper focuses on the problem of finite-time stabilization of homogeneous, non-Lipschitz systems with dilations. A key contribution of this paper is the design of a virtual recursive Hölder, non-Lipschitz state feedback which renders the non-Lipschitz systems in the special case dominated by a lower-triangular nonlinear system, finite-time stable. The proof is based on a recursive design algorithm developed recently, to construct the virtual Hölder continuous, finite-time stabilizer as well as a C¹ positive definite and proper Lyapunov function that guarantees finite-time stability of the non-Lipschitz non-linear systems.

The numerical implementation of the controllers allows the use of very complex algorithms with ease. However, in practice, due to its proven advantages, the PID controller (and its variants) is widely used in industrial control systems as well as in many other applications that require continuous control. Most of the methods for tuning the parameters of PID controllers are based on time-invariant linear models of the processes, which in practice can lead to poor performance of the control system. The paper presents an application of reinforcement learning algorithms in tuning of PID controllers for the control of some classes of continuous nonlinear systems. Tuning the parameters of PID controllers is done with the help of Twin Delayed Deep Deterministic Policy Gradients (TD3) algorithm which presents a series of advantages compared to other similar methods from Machine Learning dedicated to continuous state and action spaces. TD3 algorithm is an off-policy Actor-Critic based method and was used as it does not require a system model. The presented technique is applied for control of a biotechnological system which has a strongly nonlinear dynamic. The proposed tuning method is compared to the classical tuning methods of PID controllers. The performance of the tuning method based on the TD3 algorithm is demonstrated through simulation illustrating the effectiveness of the proposed methodology.

In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.

As an option to deal with the insulin-dependent disease, a recent commuted PD control strategy is designed and carefully analyzed for different clinic diabetic patients. This controller approach is mainly conceived to stabilize the glucose blood concentration in a diabetic patient around its basal value, hence avoiding extreme situations such as hypoglycemia and hyperglycemia. This control strategy receives two inputs carefully tuned to actuate when the measured variable is out of a prescribed healthy zone. Therefore, one of these variables is invoked to decrease the glucose concentration to insulin injection, and the other is employed to increase the glucose absorption, both by using a proper PD controller. According to our numerical experiments, our controller approach performs well, even when there is an external disturbance in the controlled system.

Most works related to the identification of mathematical nonlinear systems make one suppose that such approaches can always be directly applied to any nonlinear system. This misconception produces a great deal of discouragement when the obtained results are not the expected ones. Thus, the current work hypothesizes that the most information one has about the mathematical structure of the model, the most precise the identification result should be. Therefore, a variant of the Sparse Identification of Nonlinear Dynamics (SINDY) approach is presented to obtain the full mathematical nonlinear model of a high-order system with coupled dynamics, namely, a commercial quadcopter. Furthermore, due to its high sensitivity to inputs, a control system is devised using the identified model to stabilize the quadcopter. This illustrates the effectiveness of the proposed identification method.

The article is devoted to issues related to the propagation and transformation of vortexes in the optical range of frequency. Within the framework of the traditional and modified model of slowly varying envelope approximation (SVEA), the process of converting vortex beams of the optical domain into vortex beams of the terahertz radio range based on nonlinear generation of a difference frequency in a medium with a second-order susceptibility is considered. The modified SVEA splits a slowly varying amplitude into two factors, which makes it possible to more accurately describe the three-wave mixing process. The theoretical substantiation of the rule of vortex beams topological charges conversion is given – the topological charge of the output radio-vortex beam is equal to the difference between the topological charges of the input optical vortex beams. A numerical simulation model of the processes under consideration has been implemented and analyzed.

This article, we study the sufficient conditions for the controllability of second-order impulsive partial neutral evolution differential systems with infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

For a dynamical system, it is known that the existence of a Lyapunov density implies almost global stability of an equilibrium. It is then natural to ask whether the existence of a common Lyapunov density for a nonlinear switched system implies almost global stability, in the same way as a common Lyapunov function implies global stability for nonlinear switched systems. In this work, the answer to this question is shown to be affirmative as long as switchings satisfy a dwell-time constraint with an arbitrarily small dwell time. As a straightforward extension of this result, we employ multiple Lyapunov densities in analogy with the role of multiple Lyapunov functions for the global stability of switched systems. This gives rise to a minimum dwell time estimate to ensure almost global stability of nonlinear switched systems, when a common Lyapunov density does not exist. The results obtained for continuous-time switched systems are based on some sufficient conditions for the almost global stability of discrete-time non-autonomous systems. These conditions are obtained using the duality between Frobenius-Perron operator and Koopman operator.

In wireless sensor networks (WSNs) deployed in smart agriculture systems, accurately determining the locations of sensor nodes is crucial for efficient monitoring and control. However, in many cases, the exact positions of certain sensor nodes may be unknown. To address this challenge, this paper presents a novel method for localizing unknown sensor nodes in WSN-based smart agriculture systems using range measurements. The proposed method utilizes the Levenberg-Marquardt optimization algorithm to solve a nonlinear least squares problem and minimize the error in estimating the unknown node locations. By leveraging the known positions of a subset of sensor nodes and the inexact distance measurements between pairs of nodes, the localization problem is transformed into a nonlinear optimization problem. To validate the effectiveness of the approach, extensive simulations and experiments were conducted. The results demonstrate that the proposed method achieves accurate localization of the unknown sensor nodes, effectively enhancing the overall performance of the WSN-based smart agriculture system. Furthermore, the method demonstrates robustness against measurement noise and scalability for large-scale networks. The practical implications of this research extend beyond smart agriculture systems, as the proposed method can be applied to various WSN applications where precise node localization is essential.

This paper proposed an optimal tracking control scheme through adaptive dynamic programming(ADP) for a class of partially unknown discrete-time nonlinear systems based on radial basis function neural network(RBF-NN). In order to acquire the unknown system dynamics, we use two RBF-NNs, the one is used to construct the identifier, and the another is used to directly approximate the steady-state control input, where a novel adaptive law is proposed to update neural network weights. While the optimal feedback control and the cost function are derived via feedforward neural networks approximating, it is proposed to regulate the tracking error, the critic network and the actor network are then trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation being built under the ADP framework. Simulations verify the effectiveness of the optimal tracking control technique using the neural networks.

Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians for second-order nonlinear differential equations with damping is developed and the limitations of this method are explored. It is shown that the limitations do not exist only for those nonlinear dynamical systems that can be converted into linear ones. The obtained results are applied to selected population dynamics models for which non-standard Lagrangians and their corresponding null Lagrangians and gauge functions are derived, and their roles in the population dynamics are discussed.

The Eliezer and Gray physical interpretation of the Ermakov-Lewis invariant is applied as a guiding principle for the derivation of the special relativistic analog of the Ermakov-Milne-Pinney equation and associated first integral. The special relativistic extension of the Ray-Reid system and invariant is obtained. General properties of the relativistic Ermakov-Milne-Pinney are analyzed. The conservative case of the relativistic Ermakov-Milne-Pinney equation is described in terms of a pseudo-potential, reducing the problem to an effective Newtonian form. The non-relativistic limit is considered as well. A relativistic nonlinear superposition law for relativistic Ermakov systems is identified. The generalized Ermakov-Milne-Pinney equation has additional nonlinearities, due to the relativistic effects.

To describe the hysteresis nonlinearities in smart actuators, numerous models have been presented in the literature, among which the Preisach operator would be the most effective one due to its capability in capturing multi-loop or sophisticated hysteresis curves. When such an operator is coupled with uncertain nonlinear dynamics, especially in noncanonical form, it is a challenging problem to develop techniques to cancel out the hysteresis effects, and at the same time achieve asymptotic tracking performance. To resolve this problem, in this paper, we investigate the problem of iterative inverse-based adaptive control for an uncertain noncanonical nonlinear systems with unknown input Preiasch hysteresis, and a new adaptive version of the closest match algorithm is proposed to compensate for the Preisach hysteresis. With our scheme, the stability and convergence of the closed-loop system can be established. The effectiveness of the proposed control scheme is illustrated by simulation and experiment results.

Artificial intelligence (AI) systems of autonomous systems such as drones, robots and self-driving cars may consume up to 50% of total power available onboard, thereby limiting the vehicle’s range of functions and considerably reducing the distance the vehicle can travel on a single charge. Next-generation onboard AI systems need an even higher power since they collect and process even larger amounts of data in real time. This problem cannot be solved using the traditional computing devices since they become more and more power-consuming. In this review article, we discuss the perspectives of development of onboard neuromorphic computers that mimic the operation of a biological brain using nonlinear-dynamical properties of natural physical environments surrounding autonomous vehicles. Previous research also demonstrated that quantum neuromorphic processors (QNPs) can conduct computations with the efficiency of a standard computer while consuming less than 1% of the onboard battery power. Since QNPs is a semi-classical technology, their technical simplicity and low, compared with quantum computers, cost make them ideally suitable for application in autonomous AI system. Providing a perspective view on the future progress in unconventional physical reservoir computing and surveying the outcomes of more than 200 interdisciplinary research works, this article will be of interest to a broad readership, including both students and experts in the fields of physics, engineering, quantum technologies and computing.

We review some new approaches to the description of the evolution of states of many-particle quantum systems by means of the correlation operators. Using the denition of marginal correlation operators within the framework of dynamics of correlations governed by the von Neumann hierarchy, we establish that a sequence of such operators is governed by the nonlinear quantum BBGKY hierarchy. The constructed nonperturbative solution of the Cauchy problem to this hierarchy of nonlinear evolution equations describes the processes of the creation and the propagation of correlations in many-particle quantum systems. Moreover, we consider the problem of the rigorous description of collective behavior of many-particle quantum systems by means of a one-particle (marginal) correlation operator that is a solution of the generalized quantum kinetic equation with initial correlations, in particular, correlations characterizing the condensed states of systems.

In this paper, we introduce ResNetMF, a groundbreaking approach that harnesses the power of residual network matrix factorization to revolutionize recommendation systems. ResNetMF integrates residual networks, renowned for their ability to capture intricate patterns and features, with matrix factorization techniques that excel in modelling user-item interactions. This fusion presents a novel solution that surpasses the limitations of traditional recommendation systems. Through comprehensive experimentation and evaluation of diverse datasets, ResNetMF demonstrates remarkable enhancements in recommendation accuracy and efficiency. By effectively capturing both linear and nonlinear relationships in user-item interactions, ResNetMF provides superior recommendation quality. The outcomes from experiments unequivocally highlight the superiority of ResNetMF over existing state-of-the-art recommendation approaches, thereby validating its innovative nature and underscoring its potential to shape the future of recommendation systems. Through the integration of the deep residual network, ResNetMF approach facilitates the training of neural networks, enabling them to explore the underlying data layers more comprehensively. Extensive experimentation and evaluation across various datasets provide compelling evidence for the superiority of ResNetMF. Moreover, the proposed method utilized natural language processing (NLP) techniques for targeted information dissemination in recommendation systems, emphasizing the importance of personalized and relevant recommendations for user satisfaction and engagement.

In this paper, we present an innovative technique that improves the convergence order of iterative schemes that do not require the evaluation of Jacobian matrices. Using this procedure, we achieve a remarkable increase in the order of convergence, raising it from p to p + 3 units, which results in a remarkable improvement in the overall performance. We have conducted comprehensive numerical tests in various scenarios to validate the theoretical results, showing the efficiency and effectiveness of the new Jacobian-free schemes.

This study presents an innovative approach named Optimal Adaptive Continuous Barrier Function Terminal Sliding Mode Control (OACBF-TSMC) approach with a novel switching manifold, to control mathematical model of nonlinear systems under model uncertainties and external disturbances. The proposed OACBF-TSMC approach combines the advantages of adaptive control, continuous barrier functions, and terminal sliding mode control to achieve robust stability of the mathematical model of nonlinear systems, and by using a genetic algorithm that tries to optimize the controller parameters as much as possible so that the proposed controller is the most to have efficiency and performance. The proposed method is designed to address the challenges of systems and provide superior performance in terms of stabilization accuracy, disturbance rejection, and robustness against uncertainties. However, the critical challenge facing the proposed controller is the complete elimination of the chattering phenomenon, which is the most important problem of ordinary sliding mode controllers. The simulation results show that the system trajectories in the proposed approach have converged to the origin with minimal overshoot and under-shoot in a finite time; In addition, the chattering problem in the control inputs has been well eliminated, which makes the proposed method suitable for various systems, including chaotic systems, energy sources, and distributed production systems. Furthermore, the OACBF-TSMC approach has the potential to enhance the stability and reliability of control systems, contributing to the integration of the system states.

This study determines the threshold for the computational rate of actuator motor controllers for unmanned underwater vehicles necessary to accurately follow discontinuous square wave commands. Motors must track challenging square-wave inputs, and identification of key computational rates permit application of deterministic artificial intelligence (D.A.I.) to achieve tracking to a machine-precision degree of accuracy in direct comparison to other state-of-art approaches. All modeling approaches are validated in MATLAB simulations where the motor process is discretized at varying step-sizes (inversely proportional to computational rate). At a large step-size (fast computational rate), discrete D.A.I. shows a mean error more than three times larger than that of a ubiquitous model-following approach. Yet, at a smaller step size (slower computational rate), the mean error decreases by a factor of 10, only three percent larger than that of continuous D.A.I. Hence, the performance of discrete D.A.I. is critically affected by the sampling period for discretization of the system equations and computational rate. Discrete D.A.I. should be avoided when small step-size discretization is unavailable. In fact, continuous D.A.I. has surpassed all modeling approaches which makes it the safest and most viable solution to future commercial applications in unmanned underwater vehicles.

Not only does this paper present a novel type-2 fuzzy system for identification and behavior prognostication of an experimental solar cell set and a wind turbine, but also it brings forward an exquisite technique to acquire an optimal number of membership functions and the corresponding rules. It proposes a seven-layered NCPRT2FS. For fuzzification in the first two layers, Gaussian type-2 fuzzy membership functions with uncertainty in the mean, are exploited. The third layer comprises rule definition and the forth one embeds fulfillment of type reduction. The three last remained layers are the ones in which resultant left–right firing points, two end-points and output all get assessed correspondingly. It should not be neglected off the nutshell that recurrent feedback at the fifth layer exerts delayed outputs ameliorating efficiency of the suggested NCPRT2FS. Later in the paper, a modern structural learning, established on type-2 fuzzy clustering, is held forth. An adaptively rated learning back-propagation algorithm is extended to adjust the parameters ensuring the convergence as well. Eventually, solar cell photo-voltaic and wind turbine are deemed as case studies. The experimental data are exploited and the consequent yields emerge so persuasive.

Increasingly, there is a focus on utilising renewable energy resources in a bid to fulfil increasing energy requirements and mitigate the climate change impacts of fossil fuels. While most renewable resources are free, the technology used to usefully convert such resources is not and there is an increasing focus on improving the conversion economy and efficiency. To this end, advanced control technologies can have a significant impact and is already a relatively mature technology for wind turbines. Though hydroelectric plants can use simple regulation systems, significant benefits have been shown to accrue from the appropriate use of the same control methods designed for wind turbine plants. This represents the key point of the paper. In fact, to date, the application communities connected with wind and hydraulic energies have had little communication, resulting in little cross fertilisation of control ideas and experience, particularly from the more mature wind area to hydrodynamic systems. Therefore, this paper examines the models and the application of control technology across both domains, both from a comparative and contrasting point of view, with the aim of identifying commonalities in models and control objectives, as well as potential solutions. Key comparative reference points include the articulation of the exployed models, specification of control objectives, development of high--fidelity simulators, and development of solution concepts. Not least, in terms of realistic system requirements are the set of physical and constraints under which such renewable energy systems must operate, and the need to provide reliable and robust control solutions, which respect the often remote and relatively inaccessible location of many onshore and offshore deployments.

We demonstrate a method for realization of highly nonlinear optical 4-(4-dimethylaminostyryl)-1-methylpyridinium tosylate (DAST) two-dimensional structures by a double step technique. The desired polymeric structures have been first fabricated by using the multiple-exposure of two-beam interference technique, and the DAST nanoscrystals were then prepared inside the air-voids of these photoresist templates, resulting in nonlinear periodic structures. The nonlinear properties were characterized by optical and scanning microscopies, as well as by second-harmonic generation technique. This nonlinear modulation is very promising for the enhancement nonlinear conversion rates, such as terahertz generation, by using the quasi-phase matching technique.

Pursuing sustainable energy solutions has prompted researchers to focus on optimizing energy extraction from renewable sources. Control laws that optimize energy extraction require accurate modeling, often resulting in time-varying, nonlinear differential equations. An energy-maximizing optimal control law is derived for time-varying, nonlinear, second-order, energy harvesting systems. We demonstrate that sustaining periodic motion under this control law when subjected to periodic disturbances necessitates identifying appropriate initial conditions, inducing the system to follow a limit cycle. The general optimal solution is applied to two point absorber wave energy converter models: a linear model where the analytical derivation of initial conditions suffices and a nonlinear model demanding a numerical approach. A stable limit cycle is obtained for the latter when the initial conditions lie within an ellipse centered at the origin of the phase plane. This work advances energy-maximizing optimal control solutions for nonautonomous nonlinear systems with application to point absorbers. The results also shed light on the significance of initial conditions in achieving physically realizable periodic motion for periodic energy harvesting systems.

Intelligent transportation systems (ITS) have recently evolved rapidly, which requires development of highly trustworthy and effective communication technologies for uses, including vehicle-to-vehicle (V2V) and vehicle-to-everything (V2X) communication; where Orthogonal Frequency Division Multiplexing (OFDM) is regarded as a strong candidate and highly popular option technique among these methods. However, the movement of vehicles introduces Doppler frequencies which produce inter-carrier interference (ICI), that is frequently occurs in V2X channels. This interference has the potential to compromise the integrity of subcarrier orthogonality within OFDM, leading to lower-quality communication and an increased likelihood of data transmission errors. When employing channels with doubly dispersive fading, OFDM necessitates the usage of a complex equalization based on the minimum mean-square error (MMSE) equalizer, which requires channel matrix inversion. Several low-complexity equalizers for OFDM have been developed and are based on band factorization, time domain LSQR (Least-Square QR) iterative computing, and banded minimum mean squared error (BMMSE). This paper proposes Conjugate Gradient Least Squares (CGLS), which is a novel iterative computation algorithm integrated with nonlinear equalizers. The suggested nonlinear equalization technique determines the trade-off between computations and performance. According to simulation data, the suggested nonlinear equalizer performs better than the current BMMSE and linear CGLS algorithms across doubly dispersive fading channels.

This paper investigates the energy dissipation level of a nonlinear vehicle suspension system. The suspension system is modelled as a mass-spring-damper system, which is designed using the output frequency response function (OFRF) method. This method enables the derivation of an explicit relationship, between the system output spectrum (or Performance metric) and the system nonlinear parameters of interest. The OFRF polynomial, of the energy dissipation level, was derived in terms of the nonlinear parameters of interest. The results obtained show that the OFRF model, of the energy dissipation level, could be used to estimate the amount of heat dissipated, for a set of design parameters. This has potentials of providing some insights, in the design of vibration-based energy harvesters, as some of the wasted heat energy could be converted to electrical energy.

We report a large third-order nonlinear optical response of palladium diselenide (PdSe₂) films – a two-dimensional (2D) noble metal dichalcogenide material. Both open-aperture (OA) and closed-aperture (CA) Z-scan measurements are performed with a femtosecond pulsed laser at 800 nm to investigate the nonlinear absorption and nonlinear refraction, respectively. In the OA experiment, we observe optical limiting behaviour originating from large two photo absorption (TPA) in the PdSe₂ film of β = 3.26 ×10^-8 m/W. In the CA experiment, we measure a peak-valley response corresponding to a large and negative Kerr nonlinearity of n₂ = -1.33×10^-15 m²/W – two orders of magnitude larger than bulk silicon. We also characterize the variation of n₂ as a function of laser intensity, observing that n₂ decreases in magnitude with incident laser intensity, becoming saturated at n₂ = -9.96×10^-16 m²/W at high intensities. These results verify the large third-order nonlinear optical response of 2D PdSe₂ as well as its strong potential for high performance nonlinear photonic devices.

According to our current understanding of quantum mechanics, a `measurement' violates unitarity. In other words as the act of measurement `resets' the probabilities described by the Schrödinger equation, in the very `moment' of the collapse of the wavefunction, conservation of probability does not hold. To make progress in our understanding of the measurement problem it is thus expected that one must encompass in a single equation both otherwise mutually-exclusive processes of measurement and unitary evolution. In this light, turning to the continuity equation, we realize the possibility that if we allow for existence of sources and sinks in the `fluid of probability' we get closer to such a theory by arriving at nonlinear generalizations of Schrödinger and Klein-Gordon equations. The generalized equations derived are then shown to satisfy all conditions that are expected from a proper generalization: simplification to their linear counterparts by a well-defined dynamical condition, and Galilean and Lorentz invariance.

Traditional population-based metaheuristic algorithms are effective in solving complex real-world problems but require careful strategy selection and parameter tuning. Parameter-less population-based optimization algorithms have gained importance due to their simplicity and efficiency. However, research on their applicability for solving large systems of nonlinear equations is still incipient. In this paper, a systematic review and detailed description of metaphor-less optimization algorithms is made, including the Jaya algorithm, the main Jaya variants for continuous optimization problems, with a focus on the Enhanced Jaya (EJAYA) algorithm, the three Rao algorithms, the best-worst-play (BWP) algorithm, and the very recent max-min-greedy-interaction (MaGI) algorithm. This paper also discusses a few previous parallelizations of the Jaya optimization algorithm, as well as recent GPU-based massively parallel implementations of the Jaya, Enhanced Jaya (EJAYA), Rao, and BWP algorithms developed by the authors. In addition, a novel GPU-accelerated version of the MaGI algorithm is proposed. The GPU-accelerated versions of the metaphor-less algorithms developed by the authors were implemented using the Julia programming language and tested primarily on GeForce RTX 3090 and NVIDIA A100 GPUs, as well as on Tesla V100S and Tesla T4 GPUs, using a set of difficult, large-scale nonlinear equation system problems. The computational experiments carried out produced quite significant speedups, which highlights the efficiency of the GPU-based versions of the metaphor-less algorithms developed for solving large-scale systems of nonlinear equations.

An adaptive deep neural network is used in an inverse system identification setting to approximate the inverse of a nonlinear plant with the aim of constituting the plant controller by copying to the latter the weights and architecture of the converging deep neural network. This deep learning (DL) approach to the adaptive inverse control (AIC) problem is shown to outperform adaptive filtering techniques and algorithms normally used in adaptive control, especially when the plant is nonlinear. The deeper the controller the better the inverse function approximation, provided that the nonlinear plant have an inverse and that this inverse can be approximated. Simulation results prove the feasibility of this DL-based adaptive inverse control scheme. The DL-based AIC system is robust to parameter change of the nonlinear plant in that, under such change, the plant output reassumes the value of the reference signal considerably faster than with the adaptive filter counterpart of the deep neural network. Settling times and rise times of the step response are shown to improve in the DL-based AIC system.

This paper aims to address the exponential stability and stabilization problems for a class of delayed nonlinear Markov jump systems under randomly occurring Denial-of-Service (DoS) attack and packet loss. Firstly, the stochastic characteristics of DoS attack and packet loss are depicted by the attack success rate and packet loss rate. Secondly, a Period Observation Window (POW) method and a hybrid-input strategy are proposed to compensate for the impact of DoS attack and packet loss on the system. Thirdly, A Dynamic Event-triggered Mechanism (DETM) is introduced to save more network resources and ensure the security and reliability of systems. Then, by constructing a general common Lyapunov functional and combining with the DETM and other inequality analysis techniques, the less conservative stability and stabilization criteria for the underlying systems are derived. In the end, the effectiveness of our result is verified through a numerical example.

Full-order state-space models represent the starting point for the development of advanced control methods for wind turbine systems (WTSs). Regarding existing control-oriented WTS models, two research gaps must be noted: (i) There exists no full-order WTS model in form of one overall ordinary differential equation that considers all dynamical effects which significantly influence the electrical power output; (ii) all existing reduced-order WTS models are subject to rather arbitrary simplifications and are not validated against a full-order model. Therefore, in this paper, two full-order nonlinear state-space models (of 11th and 9th-order in the (a, b, c)- and (d, q)-reference frame, resp.) for variable-speed variable-pitch permanent magnet synchronous generator WTSs are derived. The full-order models cover all relevant dynamical effects with significant impact on the system’s power output, including the switching behavior of the power electronic devices. Based on the full-order models, by a step-by-step model reduction procedure, two reduced-order WTS models are deduced: A non-switching (averaging) 7th-order WTS model and a non-switching 3rd-order WTS model. Comparative simulation results reveal that all models capture the dominant system dynamics properly. The full-order models allow for a detailed analysis covering the high frequency oscillations in the instantaneous power output due to the switching in the power converters. The reduced-order models provide a time-averaged instantaneous power output (which still correctly reflects the energy produced by the WTS) and come with a drastically reduced complexity making those models appropriate for large-scale power grid controller design.

Photoplethysmography is a widely used technique to noninvasively assess heart rate, blood pressure, and oxygen saturation. This technique has a large potential for further applications, for example in the field of physiological and mental health monitoring. However, advanced applications of photoplethysmography have been hampered by the lack of accurate and reliable methods to analyze the characteristics of the complex nonlinear dynamics of the photoplethysmogram. Methods of nonlinear time series analysis may be used to estimate the dynamical characteristics of the photoplethysmogram but they are highly influenced by the length of the time series, which is often limited in practical photoplethysmography applications. The aim of this study was to evaluate the error in the estimation of the dynamical characteristics of the photoplethysmogram associated to the limited length of the time series. The dynamical properties were evaluated using recurrence quantification analysis, and the estimation error was computed as a function of the length of the time series. Results demonstrated that properties such as de-terminism and entropy can be estimated with an error lower than 1% even for short photople-thysmogram recordings. Additionally, the lower limit for the time series length to estimate the average prediction time was computed.

This study presents the substantiation, development, and analysis of a technique for planning the autonomous vehicle (AV) motion reference parameters. The trajectory plan, speed and acceleration distributions, including other AV's kinematic parameters, are determined using sequential optimization. The study objectives are based on an analysis of the fundamental problems of AV motion planning summarized in this area's latest publications. The proposed approach combines the basic principles of the finite element method (FEM) and nonlinear optimization with nonlinear constraints. First, the generalization on representing an investigated function by finite elements (FE) is briefly described. A one-dimension FE with two nodes and three degrees of freedom (DOF) in a node was chosen as the basic one, corresponding to the 5th-degree polynomial. Next, a method for determining the motion trajectory is presented. The following are considered: formation of a restricted space for the AV's allowable maneuvering, the geometry of motion trajectory and its relation with vehicle steerability parameters, cost functions and their influences on the desirable trajectory's nature, compliance of nonlinear restrictions of the node parameters with the motion area boundaries. At the second stage, a technique for optimizing AV speed and acceleration redistribution is presented. The model considers possible combinations of cost functions, conditions of limiting the kinematic parameters with the tire slip critical speed, maximum speed level, maximum longitudinal acceleration, and critical lateral acceleration. In the simulation section, several variants of trajectories were searched and compared. Several versions of distributing the longitudinal speed and acceleration curves are determined, and their comparative analysis is fulfilled. At the end of the paper, the advantages and drawbacks of the proposed technique are noted. The conclusion is made regarding the options for improving the method in further studies.

The cubic nonlinearity of graphene oxide (GO) monolayer was characterized by open and closed Z-scan using a nano-second laser of 10 Hz repetition rate with a Gaussian spatial beam profile. The reverse saturable absorption or positive nonlinearity from open Z-scan and valley-peak traces or positive nonlinearity from closed Z-scan was displayed. The reverse saturable absorption could be from a two-photon or two-step excitation process due to the larger absorption in the lower visible and upper UV wavelength region compared with the excitation source. The nonlinear absorption and nonlinear refraction coefficient were estimated to be ~ 2.62x10-8 m/W and 3.9x10-15 m2/W, respectively. This study also reveals the effect of nonlinear absorption on nonlinear refraction traces.

The non-linear analysis of hollow-core concrete slabs requires the use of advanced numerical techniques, proper constitutive models both for concrete and steel as well as particular computational skills. If prestressing, cracking, crack opening, material softening, etc. are also to be taken into account, then the computational task can far exceed the capabilities of an ordinary engineer. In order for the calculations to be carried out in a traditional design office, simplified calculation methods are needed. Preferably based on the linear finite element (FE) method with a simple approach that takes into account material nonlinearities. In this paper the simplified analysis of hollow-core slabs based on the generalized nonlinear constitutive law is presented. In the proposed method a simple decomposition of the traditional iterative linear finite element analysis and the non-linear algebraic analysis of the plate cross-section is used. Through independent analysis of the plate cross-section in different deformation states, a degraded plate stiffness can be obtained, which allows iterative update of displacements and rotations in the nodes of the FE model. Which in turn allows to update the deformation state and then correct translations and rotations in the nodes again. The results obtained from the full detailed 3D nonlinear FEM model and from the proposed approach are compared for different slab cross-sections. The obtained results from both models are consistent.

This paper presents the common methods and corresponding drawbacks concerning nonlinear analysis of fluxgate excitation circuits and emphasizes the importance of nonlinear analysis for these circuits. With regard to the nonlinearity of the excitation circuit, this paper proposes the use of the core-measured hysteresis curve for mathematical analysis and the use of a nonlinear model that considers the coupling effect of the core and winding and influence of the historical magnetic field on the core for simulation analysis. The feasibility of mathematical calculations and simulation for the nonlinear study of fluxgate excitation circuit is verified via experiments. The results demonstrate that, in this regard, the simulation is better than a mathematical calculation. The simulation and experimental results of the excitation current and voltage waveforms under different excitation circuit parameters and structures are essentially consistent with each other, thereby verifying the effectiveness of the nonlinear excitation analysis method.

The COVID-19 pandemic has significantly impacted human health and daily life. Meteorological factors play a crucial role in virus transmission. Understanding these factors is critical for pandemic control, yet debates continue due to variations in research methods and data. This study uses a global dataset and focuses on administrative units smaller than 10,000 km². The relationship between daily COVID-19 incidence rates and meteorological factors—including temperature, relative humidity (RH), ultraviolet radiation (UVR), and diurnal temperature range (DTR)—was analyzed across 173 units in 62 countries. The results revealed significant nonlinear responses and lag effects between incidence rates and the meteorological factors. Key inflection points were observed at 0°C and 24°C for temperature, 63% for RH, 102 KJ/m² for UVR, and 15°C for DTR. Below 0°C, infection risk increased with rising temperatures; from 0°C to 24°C, risk decreased; and above 24°C, risk escalated rapidly. RH below 63% correlated inversely with infection risk, while above 63%, the correlation was positive. Infection risk decreased with UVR below 102 KJ/m² but increased beyond this threshold. These nonlinear responses are primarily driven by the differential effects of these factors on virus survival, transmission, and human immunity. Conditions around 24°C, 63% RH, 102 KJ/m² UVR, and DTR below 15°C appear optimal for human immunity, correlating with lower infection risk. High temperature and low UVR prompted immediate infection responses, while low temperatures, high UVR, and larger DTR showed delayed effects. These findings provide new, more reliable evidence for understanding the mechanisms driving COVID-19 pandemic dynamics and for preventing the future normalization of the epidemic.

Non-linear superposition of solitons provide almost linear branches as well as ``quantum jumps" to stable particle-like cores. Can the quest for possible non--linearity of quantum mechanics and the ``collapse paradox" of the wave function in (non-)linear quantum mechanics be resolved by transitions between different quasi-linear branches of the corresponding Whitney surface?

The decay of the low-mode internal tide due to the superharmonic energy cascade is investigated in a realistically forced global Hybrid Coordinate Ocean Model (HYCOM) simulation with 1/25 degrees (4 km) horizontal grid spacing. Time-mean and depth-integrated supertidal kinetic energy is found to be largest near low-latitude internal tide generation sites, such as the Bay of Bengal, Amazon Shelf, and Mascarene Ridge. The supertidal kinetic energy can make up to 50% of the total internal tide kinetic energy several hundred kilometers from the generation sites. As opposed to the tidal flux divergence, the supertidal flux divergence does not correlate with the barotropic to baroclinic energy conversion. Instead, the time-mean and depth-integrated supertidal flux divergence correlates with the nonlinear kinetic energy transfers from (sub)tidal to supertidal frequency bands as estimated with a novel coarse-graining approach. The regular spaced banding patterns of the surface-intensified nonlinear energy transfers are attributed to semidiurnal mode 1 and mode 2 internal waves that interfere constructively at the surface. This causes patches where both surface tidal KE and nonlinear energy transfers are elevated. The simulated internal tide off the Amazon shelf steepens significantly near these patches, generating solitary-like waves in good agreement with Synthetic Aperture Radar (SAR) imagery. Globally, we find that regions of high supertidal energy flux also show a high correlation with observed instances of solitary nonlinear internal waves.

Techniques for the controlled seeding and growth of cracks are urgently required for non-destructive testing technique evaluation, particularly for additive manufactured (AM) samples. This paper describes a method which uses a combination of tensile load and resonance excitation of notched AM samples, with in-situ monitoring of the resonance frequency serving to track crack dimensions. Mechanical low-cycle fatigue cracks, ranging in length from ~0.3 mm to ~5 mm, are successfully created in five AM samples using this technique. The samples are non-destructively characterized using optical microscopy and Nonlinear Resonance (NLR) testing. The exploitation of resonance enables the concentration of a significant number of stress cycles on the samples in much shorter timespans than conventional fatigue testing, enabling high throughput, while utilising compact components. Furthermore, the tracking of resonance frequency shift throughout the process enables non-invasive and non-contact real-time condition monitoring.

Living processes are integral to open systems for multiple reasons. From a thermodynamic perspective, they reduce local entropy at the cost of increasing environmental entropy. Furthermore, these processes are inherently nonlinear owing to their feedback interactions with the environment. Nonlinear systems exhibit diverse behaviours: some stabilize at a constant value, whereas others display bifurcations and chaotic dynamics. This study introduces a model that describes living processes as the dynamics of nonlinear single-value diverging maps, whereas chaotic evolution is associated with the increasing entropy environment. This model enables us to describe the lifetime of different species simply by varying the model parameters. This model also simplifies explaining the transition from life to death.

Scattering of a probe laser pulse by an intense light spring in QED vacuum is considered. This new scattering configuration can be seen as the vacuum equivalent to the process originally associated with scattering of light by a rotating black hole, usually called Penrose superradiance. Here the rotating object is an intense laser beam containing two different components of orbital angular momentum. Due to these two components with slightly different frequencies, the energy profile of the intense laser beam rotates with a frequency that depends on the frequency difference. The nonlinear properties of quantum vacuum are described by first order Euler-Heisenberg Lagrangian. It is shown that, in such a configuration, nonlinear photon-photon coupling leads to scattered radiation, with frequency shift and angular dispersion. These two distinct properties, of frequency and propagation direction, could eventually be favourable for possible experimental observations. In principle, this new scattering configuration can also be reproduced in a nonlinear optical medium.

Integrated photonic devices operating via optical nonlinearities offer a powerful solution for all-optical information processing, yielding processing speeds that are well beyond that of electronic processing as well as providing the added benefits of compact footprint, high stability, high scalability, and small power consumption. The increasing demand for high-performance nonlinear integrated photonic devices has facilitated the hybrid integration of novel materials to address the limitations of existing integrated photonic platforms, such as strong nonlinear optical absorption or an inadequate optical nonlinearity. Recently, graphene oxide (GO), with its large optical nonlinearity, high flexibility in altering its properties, and facile fabrication processes, has attracted significant attention, enabling many hybrid nonlinear integrated photonic devices with improved performance and novel capabilities. This paper reviews the applications of GO to nonlinear integrated photonics. First, an overview of GO’s optical properties and the fabrication technologies needed for its on-chip integration is provided. Next, the state-of-the-art GO nonlinear integrated photonic devices are reviewed, together with comparisons of the nonlinear optical performance of different integrated platforms incorporating GO. Finally, the challenges and perspectives of this field are discussed.

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

Purpose: Prostate cancer remains the 2nd leading cancer killer of men, yet it is also a disease with a high rate of overtreatment. Diffusion weighted imaging (DWI) has shown promise as a reliable, grade-sensitive imaging method, but it is limited by low image quality. Currently, DWI image quality is directly related to low gradient ampli-tudes, since weak gradients must be compensated with long echo times. Methods: We propose a new type of MRl accessory, an "inside-out" and nonlinear gradient, whose sole purpose is to deliver diffusion encoding to a region of interest. Performance was simulated in OPERA and the resulting fields were used to simulate DWI with two compartment and kurtosis models. Experiments with a nonlinear head gradient prove the accuracy of DWI and ADC maps diffusion encoded with nonlinear gradients. Results: Simulations validated thermal and mechanical safety while showing a 5 to 10-fold increase in gradient strength over prostate. With these strengths, lesion CNR in ADC maps approximately doubled for a range of anatomical positions. Proof-of-principle experiments show that spatially varying b-values can be corrected for accurate DWI and ADC. Conclusions: Dedicated nonlinear diffusion encoding hardware could improve prostate DWI.

We report a photonic-based radio frequency (RF) arbitrary waveform generator (AWG) using a soliton crystal micro-comb source with a free spectral range (FSR) of 48.9 GHz. The comb source provides over 80 wavelengths, or channels, that we use to successfully achieve arbitrary waveform shapes including square waveforms with a tunable duty ratio ranging from 10% to 90%, sawtooth waveforms with a tunable slope ratio of 0.2 to 1, and a symmetric concave quadratic chirp waveform with an instantaneous frequency of sub GHz. We achieve good agreement between theory and experiment, validating the effectiveness of this approach towards realizing high-performance, broad bandwidth, nearly user-defined RF waveform generation.

The pile foundation in the permafrost region is in a negative temperature environment, so the concrete is affected by the negative temperature of the surrounding soil.It not only affects the formation of concrete strength, but also leads to engineering quality accidents in serious cases.Based on the actual measurement of temperature at different strata depths and the comprehensive consideration of surface temperature, terrestrial heat flux and other parameters, the law curve of temperature change along depth in Greater Khingan is established.The calculated results of the curve are consistent with the measured results of ground temperature.The results show that the variation trend of ground temperature along the strata depth at different monitoring sites is basically the same. From June to November, the ground temperature at different depths tends to be constant.From December to May, the ground temperature at any depth within the depth range of 0 to 5.5m follows the law of the cosine function.Below 5.5m, the earth temperature no longer varies with depth.The research results can be used as reference for pile foundation construction under negative temperature environment.

Nonlinear ultrasonic testing has been accepted as a promising manner for evaluating material integrity in an early stage. Stress fatigue is the main threats to train safety, railways examinations for stress fatigue are more significant and necessary. A series of ultrasonic nonlinear wave experiments are conducted for rail specimens extracted from railhead with different degree of fatigue produced by three-point bent loading condition. The nonlinear parameter is the indicator of nonlinear waves for expressing the degree the fatigue. The experimental results show that the sensitivity of a third harmonic longitudinal wave is higher than second harmonic longitudinal wave testing. As the same time, collinear wave mixing shows strong relative with fatigue damages than a second longitudinal wave NDT method and provides more reliable results than third harmonic longitudinal waves nonlinear testing method.

Most systems that are the subject of control engineering studies have some non-linearity. An example of this is the horizontal cylindrical tank, commonly used in process industries. To deal with cases like this, several control theories have been developed over time, each one presenting better results in certain systems. This work presents an alternative for the control of nonlinear systems, without necessary modeling or previous information about the system, based on a new optimization law for the artificial neural network training in real time.

In this paper, we constructed and analyzed a modified SIR-type model for the epidemic problem which considering waning-immunity class in the population, with the nonlinear incidence and recovery rates. Depending on the basic reproduction ratio, we investigated conditions for both non-endemic and co-existing cases. The RouthHurwitz criteria is used to verify the local stability of equilibria, whereas for the global stability, the suitable Lyapunov function is selected to analyze the behavioral stability for each equilibria. Moreover, we studied the optimal control problem for this case. Numerically, we give some simulations to support our analitycal findings.

In this paper, we investigate the following chemotaxis-haptotaxis model $$\left\{ \begin{array}{ll} u_{t}=\nabla\cdot (D(u) \nabla u)- \nabla\cdot (H(u)\nabla v)- \nabla\cdot (I(u)\nabla w)+ u(a-\mu u^{k-1}-\lambda w),\\ v_{t}=\triangle v-v+u^{\gamma},\\ w_{t}=-v w \end{array}\right.\eqno(*) $$ under homogenous Neumann boundary condition and for a bounded domain $ \Omega \subset \mathbb{R}^{n} (n\geq2)$, with $\lambda, \mu, \gamma >0$, $k>1$, $a \in \mathbb{R}$, and $D(u)\geq K_{D} (u+1)^{m-1}$, $0\leq H(u)\leq \chi u(u+1)^{-\alpha}$, $0\leq I(u)\leq \xi u(u+1)^{-\beta}$ for $K_{D}, \chi, \xi>0, m, \alpha, \beta\in \mathbb{R}$. It has been demonstrated that (i) For $0\gamma-k+1$ and $\beta>1-k$, problem ($*$) admits a classical solution $(u, v, w)$ which is globally bounded. (ii) For $\frac{2}{n}\gamma-k+\frac{1}{e}+1$ and $\beta>\max\{\frac{(n\gamma-2)(n\gamma+2k-2)}{2n}-k+1, \frac{(n\gamma-2)(\gamma+\frac{1}{e})}{n}-k+1\}$ or $\alpha>\gamma-k+1$ and $\beta>\max\{\frac{(n\gamma-2)(n\gamma+2k-2)}{2n}-k+1, \frac{(n\gamma-2)(\alpha+k-1)}{n}-k+1\}$, problem ($*$) admits a classical solution $(u, v, w)$ which is globally bounded.

In the paper, a modified nonlinear finite element method for analysis of trapezoidal plates geometrically reduced to shallow-shell Reissner-Mindlin formulation is presented. Due to the method proposed the complex plate cross-section and nonlinear materials may be modelled and no implementation of advanced constitutive law via user subroutines is needed. The generalized nonlinear constitutive law is used to update the stiffness of the plate element. The method enables modeling of complicated cross-sections, such as steel trapezoidal sheets, metal facing sandwich panels or reinforced concrete. Additionally, for those geometrically complex sections an advanced nonlinear material may be adopted. To verify the proposed method, a selected trapezoidal sheets were modeled in a commercial software as full 3D shell structures. By comparing displacements and forces, it was shown that both models behave almost identically, however, the simplified model has about 300-400 times less degrees of freedom, thus it is much more efficient.

In present work an opportunity of nearly single-cycle THz pulse generation in aperiodically poled lithium niobate (APPLN) crystal is studied. A radiating antenna model is used to simulate the THz generation from chirped APPLN crystal pumped by a sequence of femtosecond laser pulses with chirped delays m (m = 1, 2, 3 …) between adjacent pulses. It is shown that by appropriative choosing m it is possible to obtain temporally overlap of all THz pulses generated from positive (or negative) domains. It results in the formation of a nearly single-cycle THz pulse, if the chirp rate of domain length  in the crystal is sufficiently large. In opposite case, a few cycle THz pulses are generated with the number of the cycles depending on . The closed form expression for THz pulse form is obtained. The peak THz electric field strength of 0.3 MV/cm is predicted for APPLN crystal pumped by the sequence of laser pulses with peak intensity of the separate pulse in the sequence about 20 GW/cm2. By focusing the THz beam and by increasing the pump power the field strength can reach values of an order of few MV/cm.

Herein, we examined the effects of weather parameters and individual clinicodemographic risk factors on hemorrhagic stroke (HS) incidence, severity on admission, and disability at discharge in a harsh desert climate. In a retrospective design we studied patients admitted to a stroke unit in Arab Emirates in 2016-2019. With a distributed lag nonlinear model we explored immediate and delayed effects of weather on stroke incidence. Supervised machine learning was used to build models predictive of scores in NIHSS and mRS scales. We assessed model performance by calculating ROC AUC, F1 scores, specificity, and sensitivity. HS risk increased after a significant change in any weather parameter. The risk was reduced below baseline after 1-week adjustment to environmental changes. Climate input from the previous 3 days yielded reliable classification models. Humidex was a better predictor of severity than air temperature, whereas body mass index, age, and time of day at stroke onset were the strongest clinical predictors. Weather parameters before admission were stronger predictors of disease severity than individual clinical factors. We addressed limitations of previous studies by analyzing a full set of climate parameters: ambient temperature, relative humidity, humidex, atmospheric pressure, and wind speed. Predictive models may help to optimize patient management and develop preventative strategies.

Recently, more wind turbine systems are being installed in deep waters far from the coast. Several concepts of floating wind turbine systems (FWTSs) are developed, among which the semisubmersible platform, due to its applicability in different water depths, good hydrodynamic performance, and facility in the installation process, constitutes the most explored technology compared to the others. However, a significant obstacle to the industrialization of this technology is a design of a cost-effective FWTS, which can be achieved by optimizing the geometry, size and weight of the floating platform, along with the mooring system. This is only possible by selecting a method capable of accurately analyzing the FWTS coupled hydro-aero-structural dynamics at each design stage. Accordingly, this paper aims at providing a detailed overview of the most common coupled numerical and physical methods, including their basic assumptions, formulations, limitations, and costs, used for analyzing the dynamics of FWTSs, mainly those supported by a semisubmersible, to assist the choice of the most suitable method at each design phase of FWTSs. Finally, the article discusses possible future research to address challenges in modeling FWTSs dynamics that persist to date.

Abstract: In this study, we present an analytical tool that can be used to predict the nonlinear structural response of seaplanes advancing through sinusoidal head-sea waves. Seaplanes exhibit a unique instability phenomenon known as porpoising, which is an oscillatory motion along the heave and pitch axes that can cause serious structural damage. The heaving and pitching equations of motion are presented in the form of coupled, forced, and nonlinear Duffing-type equations with cubic nonlinearity. The analytical model developed in this study leverages the Poincaré–Lindstedt perturbation method to express the amplitude and frequency of motion in terms of all physical parameters. The accuracy and reliability of the proposed model were validated through computational fluid dynamics (CFD) simulations based on incompressible unsteady Reynolds-averaged Navier–Stokes (RANS) equations. The results show a strong agreement between the analytical tool and the CFD simulations, with minor discrepancies due to assumptions inherent in the 2D simulations, particularly the assumption that seawater only passes beneath the hull, resulting in increased buoyancy forces and reduced damping. This study offers a novel and practical method for predicting the dynamic stability of seaplanes under realistic sea conditions, potentially enhancing safety and operational efficiency by mitigating the risks associated with porpoising.

We study the nonlinear absorptive and dispersive optical properties of molecular systems immersed in a thermal reservoir interacting with a Four-wave Mixing (FWM) signal. Residual spin-orbit Hamiltonians are considered in order to take into account the internal structure of the molecule. As system parameters in the dissipation processes, transverse and longitudinal relaxation times are considered for stochastic solute-solvent interaction processes. The intramolecular coupling effects on the optical responses are studied using a molecule model consisting of two coupled harmonic curves of electronic energies with displaced minima in nuclear energies and positions. In this study, it was considered the complete frequency space is considered through the pump-probe detuning, not restricting the derivations to only maximums of population oscillations. This approach opens the possibility of studying the behavior of optical responses, which is very useful in experimental design. Our results indicate the sensitivity of the optical responses to parameters of the molecular structure as well as to those derived from the photonic process of FWM signal generation.

The susceptible-infected-recovered-vaccinated-deceased (SIRVD) epidemic compartment model extends the SIR model to include the effects of vaccination campaigns and time-dependent fatality rates on epidemic outbreaks. It encompasses the SIR, SIRV, SIRD, and SI models as special cases, with individual time-dependent rates governing transitions between different fractions. We investigate a special class of exact solutions and accurate analytical approximations for the SIRVD and SIRD compartment models. While the SIRVD and SIRD equations pose complex integro-differential equations for the rate of new infections and the fractions as a function of time, a simpler approach considers determining equations for the sum of ratios for given variations. This approach enables us to derive fully exact analytical solutions for the SIRVD and SIRD models. For nonlinear models with a high-dimensional parameter space, such as the SIRVD and SIRD models, analytical solutions, exact or accurately approximative, are of high importance and interest: not only as suitable benchmarks for numerical codes, but especially as they allow us to understand the critical behavior of epidemic outbursts as well as the decisive role of certain parameters. In the second part of our study, we apply a recently developed analytical approximation for the SIR and SIRV models to the more general SIRVD model. This approximation offers accurate analytical expressions for epidemic quantities, such as the rate of new infections and the fraction of infected persons, particularly when the cumulative fraction of infections is small. The distinction between recovered and deceased individuals in the SIRVD model affects the calculation of the death rate, which is proportional to the infected fraction in the SIRVD/SIRD cases but often proportional to the rate of new infections in many SIR models using a posteriori approach. We demonstrate that the temporal dependence of the infected fraction and the rate of new infections differs when considering the effects of vaccinations and when the real-time dependence of fatality and recovery rates diverge. These differences are highlighted for stationary ratios and gradually decreasing fatality rates. \Revised{The case of stationary ratios allows one to construct a new powerful diagnostics method to extract analytically all SIRVD model parameters from measured COVID-19 data of a completed pandemic wave.

In this article, an iterative method of two step is proposed for finding all roots simultaneously of polynomial equations. The order of convergence of the proposed algorithm is 2m, by using any iterative scheme of order m. Numerical tests are performed to confirm the theoretical results and to compare the proposed scheme with existing methods for finding all roots simultaneously.

As a rapidly expanding family of two-dimensional (2D) materials, MXenes have recently gained considerable attention due to their appealing properties. Here, by developing a solution-based coating method that enables transfer-free and layer-by-layer film coating, we investigate the layer-dependent nonlinear optical absorption of Ti₃C₂T_x films ‒ an important member of the MXene family. By using the Z-scan technique, we characterize the nonlinear absorption of the prepared MXene films consisting of different numbers of monolayers. The results show that there is a strong and layer-dependent nonlinear absorption behavior, transitioning from revisable saturable absorption (RSA) to saturable absorption (SA) as the layer number increases from 5 to 30. Notably, the nonlinear absorption coefficient β varies significantly within this range, changing from ~7.13 × 10² cm/GW to ~-2.69 × 10² cm/GW. We also characterize the power-dependent nonlinear absorption of the MXene films at various incident laser intensities, and a decreasing trend in β is observed for increasing laser intensity. These results reveal the intriguing layer-dependent nonlinear optical properties of 2D MXene films, highlighting their versatility and potential for implementing high-performance nonlinear photonic devices.

Enhanced supercontinuum generation (SCG) is experimentally demonstrated in integrated silicon nitride (Si₃N₄) waveguides incorporating highly nonlinear graphene oxide (GO) in the form of two-dimensional (2D) films. On-chip integration of the 2D GO films with precise control of their thickness is realized by using a transfer-free and layer-by-layer coating method. The control of the film length and coating position is achieved via window opening in the upper silica cladding of the photonic integrated chips. Detailed SCG measurements are performed using the fabricated devices with different waveguide geometries and GO film thicknesses, and the results are compared with devices without GO. Significantly improved spectral broadening of ultrashort optical pulses with ultrahigh peaks powers exceeding 1000 W is observed for the hybrid devices, achieving up to 2.4 times improvement in the spectral bandwidth relative to devices without GO. Theoretical analyses for the influence of GO film thickness, coating length, coating position, and waveguide geometry are also provided by fitting the experimental results with theory, showing that there is still significant room for further improvement. This work opens up a promising new avenue towards improving the SCG performance of photonic integrated devices by incorporating functional 2D materials.

The article presents a modified finite element (FE) based algorithm for nonlinear analysis of 2D beam structures, which takes into account the influence of the shear forces. The method proposed enables using complex materials with nonlinearities without the need of implementing advanced constitutive models in FE routines. It can be directly integrated with commonly available FE software for linear analysis of beam structures, so its functionality can be easily extended also with material nonlinearities. The presented approach adopts the generalized constitutive law algorithm to iteratively modify the stiffness of beam element. To address an influence of a shear stiffness, a Timoshenko beam element was used. The methodology was implemented and its performance was verified on several numerical examples. For validation, the displacements and the ultimate loads were compared with the values from a commercial FE software. The results shown a good correlation between the reference model and the method proposed.

We show that Universe inflation occurs when Einstein's gravity couples to nonlinear electromagnetic fields with cosmic stochastic magnetic fields background. Nonlinear electrodynamics with two parameters is used. The strength of magnetic fields to have the Universe inflation is obtained. It is shown that singularities of the energy density and pressure are absent for any scale factors. At large scale factors one arrives at equation of state for ultra-relativistic case. It is demonstrated that the curvature invariants do not have singularities. By computing the deceleration parameter we show that graceful exit takes place with reasonable e-folding number. The duration of Universe inflation as a function of model parameters is obtained. The classical stability and causality are analyzed by calculating the speed of the sound.

Endothelial disorders are related to various diseases. An initial endothelial injury is characterized by endothelial glycocalyx injury. We aimed to evaluate endothelial glycocalyx injury by measuring serum syndecan-1 concentrations in patients during comprehensive medical examinations. A single-center, prospective, observational study was conducted at Asahi University Hospital. The participants enrolled in this study were 1313 patients who underwent comprehensive medical examinations at Asahi University Hospital from January 2018, to June 2018. One patient undergoing hemodialysis was excluded from the study. At enrollment, blood samples were obtained, and study personnel collected demographic and clinical data. No treatments or exposures were conducted except for standard medical examinations and blood sample collection. Laboratory data were obtained by collection of blood samples at the time of study enrolment. According to nonlinear regression, the concentrations of serum syndecan-1 were significantly related to age (p = 0.016), aspartic aminotransferase concentration (AST, p = 0.020), blood urea nitrogen concentration (BUN, p = 0.013), triglyceride concentration (p < 0.001), and hematocrit (p = 0.006). These relationships were independent associations. Endothelial glycocalyx injury, which is reflected by serum syndecan-1 concentrations, is related to age, hematocrit, AST concentration, BUN concentration, and triglyceride concentration.

A number of third order nonlinear processes can occur in single-mode fibres and an understanding of such phenomena is almost a prerequisite for actual lightwave-system designers. In this paper we review the main limitations imposed by several nonlinear effects, namely the self- and cross-phase modulation, four-wave mixing, stimulated Raman scattering and stimulated Brillouin scattering, on the performance of optical fiber communication systems.

This paper addresses the analysis for the nonlinear vibration response of a rectangular tube with a flexible end and non-rigid acoustic boundaries. This is a further work of the linear structural acoustic problem in a well-known acoustic book. In fact, the acoustic boundaries of an enclosed space sometimes are non-rigid and the structural vibration responses are nonlinear. These two points are the focuses of this paper. The multi-level residue harmonic balance method is applied to this nonlinear structural acoustic problem. The results obtained from the multi-level residue harmonic balance method and numerical method are generally in good agreement. The effects of excitation magnitude, tube length, and phase shift parameter etc. are examined.

Scattering resonances play a crucial role in understanding wave behavior in various physical systems. While significant progress has been made in analyzing resonances in high-contrast and nonlinear media, a general characterization of resonances in small, high-contrast nonlinear media with the Kerr effect, particularly in layered configurations, has remained an open problem. In this paper, we present a novel asymptotic approach that addresses this gap by providing an approximation for resonances in terms of material properties, geometry, and nonlinearity. Our results offer new insights into the dependence of resonances on these factors, particularly for complex multilayered structures, making this the first general characterization of its kind.

Bayesian nonlinear mixed effects models for data in the form of continuous, repeated measurements from a population, also known as Bayesian hierarchical nonlinear models, are a popular platform for analysis when interest focuses on individual specific characteristics and relevant uncertainty quantification. Due to the limitation of computational power, this framework was relatively dormant until the late 1980s, but in recent years, the statistical research community saw vigorous development of new methodological and computational techniques for these models, the emergence of software, and wide application of the models in numerous industrial and academic fields. This article presents an overview of the formulation, interpretation, and implementation of Bayesian nonlinear mixed effects models and surveys recent advances and applications.

This article presents a concise survey of basic discrete and semi-discrete nonlinear models which produce two- and three-dimensional (2D and 3D) solitons, and a summary of main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ⁽²⁾) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of basic species of multidimensional discrete modes, including fundamental and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

Optical communication systems pose significant challenges, including the effects of nonlinear noises. The nonlinearities, including Kerr-induced phase noise, become more problematic in m-QAM as the orden of the format increases becoming a highly densed set of data-symbols and therefore, requiring advanced signal processing for successful separation of symbols at the demodulation stage. Machine learning techniques have recently been applied to improve signal integrity in such scenarios. This paper explores the application of a spectral clustering algorithm adapted to deal with data streaming to mitigate nonlinear noise in long-haul optical channels dominated by nonlinear phase noise, offering a promising solution to a pressing issue. We demonstrate that the spectral clustering algorithm outperforms the k-means algorithm in the face of nonlinear phase noise in -90, -100, and -110 dBc/Hz scenarios at 1 MHz in a simulated 10 GHz symbol rate channel.

The phenomena of light absorption, fluorescence and laser emission are accounted for within a unique picture. The atomic dipole is dealt with in a quantum framework, whereas the electromagnetic field is assumed to be a classical sine-wave. The on and off resonance cases are investigated. This is achieved owing to a novel application of Poynting's theorem. Observable predictions are made, regarding absorption of the electromagnetic energy and the frequency bandwidth of light emitted either by fluorescence or laser effect.

Nonlinear optimization (NOPT) is a meaningful tool for solving complex tasks in fields like engineering, economics, and operations research, among others. However, NOPT has problems when it comes to dealing with data variability and noisy input measurements that lead to incorrect solutions. Furthermore, nonlinear constraints may result in outcomes that are either infeasible or suboptimal, such as non-convex optimization. This paper introduces a novel regularized physics-informed neural network (RPINN) framework as a new NOPT tool for both supervised and unsupervised data-driven scenarios. By using custom activation functions and regularization penalties in an artificial neural network (ANN), RPINN can handle data variability and noisy inputs. Besides, it uses physics principles to build the network architecture, computing the optimization variables based on network weights and learned features. In addition, it uses automatic differentiation training to make the system scalable and cut down on computation time through batch-based back-propagation. The test results for both supervised and unsupervised NOPT tasks show that our RPINN can provide solutions that are competitive compared to state-of-the-art solvers. In turn, RPINN’s robustness against noisy input measurements makes it particularly valuable in environments with fluctuating information. Additionally, RPINN’s ANN-based foundation offers significant flexibility and scalability.

A one-dimensional model for fluid and solute transport in poroelastic materials (PEM) is studied. Although the model was recently derived and some exact solutions, in particular steady-state solutions and their applications, were studied, special cases occurring when some parameters vanish were not analysed earlier. Since the governing equations are nonintegrable in nonstationary case, the Lie symmetry method and modern tools for solving ODE systems are applied in order to construct time-dependent exact solutions. Depending on parameters arising in the governing equations, several special cases with new Lie symmetries are identified. Some of them have a highly nontrivial structure that cannot be predicted from a physical point of view or using Lie symmetries of other real-world models. Applying the symmetries obtained, multiparameter families of exact solutions are constructed, including those in terms of elementary and special functions (hypergeometric, Whittaker, Bessel and modified Bessel functions). A possible application of the solutions obtained is demonstrated and it is shown that some exact solutions can describe (at least qualitatively) the solute transport in PEM. The obtained exact solutions can also be used as test problems for estimating the accuracy of approximate analytical and numerical methods for solving relevant boundary value problems.

This research aims to explore factors that influence sustainable music learning system from psychological perspective, and innovatively constructs a combination of qualitative and quantitative approaches. For first time, combines nonlinear system and identifies relevant factors affecting music learning by establishing data system for questionnaire answering and a quantitative model for actual academic performance. Existing research mainly looks at several factors that affect fragmented music learning system from perspective of teachers' teaching rules, emphasizing phased teaching state and learning goals of teachers as main body, thus ignoring music learning students, who are a large group of music learning objects. The research fills gap in this type of research object, focusing on sustainable music learning system from emotional perspective and students who occupy a dominant position in music learning, so as to more accurately explore impact of their emotional influencing factors on music learning system. The most prominent innovation of this study lies in construction of stochastic nonlinear system for psychological influencing factors of student music learning and a quantitative model for actual learning effect. Through analysis of nonlinear system, weight values of several negative emotions on music learning system are obtained. The comprehensive impact of emotional factors and practical learning on music learning system can be obtained by weighting them together.

This research aims to explore factors that influence sustainable music learning system from psychological perspective, and innovatively constructs a combination of qualitative and quantitative approaches. For first time, combines nonlinear system and identifies relevant factors affecting music learning by establishing data system for questionnaire answering and a quantitative model for actual academic performance. Existing research mainly looks at several factors that affect fragmented music learning system from perspective of teachers' teaching rules, emphasizing phased teaching state and learning goals of teachers as main body, thus ignoring music learning students, who are a large group of music learning objects. The research fills gap in this type of research object, focusing on sustainable music learning system from emotional perspective and students who occupy a dominant position in music learning, so as to more accurately explore impact of their emotional influencing factors on music learning system. The most prominent innovation of this study lies in construction of stochastic nonlinear system for psychological influencing factors of student music learning and a quantitative model for actual learning effect. Through analysis of nonlinear system, weight values of several negative emotions on music learning system are obtained. The comprehensive impact of emotional factors and practical learning on music learning system can be obtained by weighting them together.

To study the coupling mechanism and dynamic response of the end-face movable gear trans-mission system under complex excitation, a specific configuration of end-meshing movable gear reduction mechanism was used to achieve predetermined rigid thrust transmission and mis-matched gear meshing functions, which solved the inherent defects of traditional harmonic gear mechanism thin-wall flexible wheel easy to be damaged by fatigue. Considering the phenomenon of elastic deformation of live teeth accompanied by significant changes in meshing characteristics in the transmission process of end-meshing harmonic reducer, the influence of dynamic meshing parameters, live tooth deformation, time-varying stiffness of tooth meshing, and time-varying backlash on nonlinear dynamic performance was explored, as well as the mechanism of mul-ti-parameter coupling on transmission performance. The nonlinear dynamics model of the end-meshing harmonic reducer is established to solve the chattering prediction problem. Finally, a comprehensive test bed for the transmission system of harmonic reducer with meshing type with adjustable characteristic end was built to verify the correctness of the theoretical model and provide the theoretical and technical basis for exploring the optimal parameter selection of pas-sive vibration suppression problem.

Commonly, professors, students and researchers from universities around the world use software distributed under a license agreement for computer simulation purposes, which requires a computer with considerable hardware capabilities. Consequently, this implies a high cost to conduct simulations that require implementing numerical methods in all areas of engineering, particularly in the field of robotics and nonlinear control. This paper presents the design and results analysis of a low-cost and open-source frugal computer simulation tool with applications to robotic nonlinear control, for instance, for numerical simulations of manipulator robot control based on dynamic models. Using a single board minicomputer with with reduced computing power, Raspberry Pi, together with free software, GNU-Octave, trajectory tracking control simulations in the joint space of a Selective Conformal Assembly Robot Arm (SCARA) are achieved by solving a system of nonlinear differential equations, represented in matrix form, which includes the control law and the system model. The results of the proposed alternative are compared by running the same simulation code on a laptop computer using MATLAB and GNU Octave, which show minimal deviations and reasonable time complexity. Moreover, considering the frugality curve calculated for this approach, in addition to the low acquisition cost of the simulation software tool, it would allow the creation of a simulation laboratory in some universities with budgetary constraints for educational and research purposes.

For deep-penetrating geochemistry, there is a frontier issue as to how to explore ore-bearing information deep in covered areas, while it is, too, important to investigate the geochemical migration of ore-forming elements for the development of exploration geochemistry. In this study, a 380-day migration column experiment was conducted with surface soil and pure Cu powder collected from the Yujiashan study area in Wuhan City, Hubei Province taken as the object of research to simulate the migration process of ore-forming elements under natural conditions. The results showed obvious vertical migration of the ore-forming elements and conversion of mobile metal forms in the process; further, according to 6 groups of simulation experiments that took 45 days to conduct on migration column samples and the surface oil and Cu powder collected from the Pulang mining area in Yunnan Province, the vertical migration of the ore-forming element was still visible, and the exogenous substance (pure Cu powder) could enhance the anomaly without changing the basic migration mechanism. This indicates that Cu might migrate in a stable manner in soil cover in the Pulang mining area, and its migration was mostly driven by the transformation of Fe-Mn oxide bound state and organic bound state; finally, a multifractal analysis was conducted, revealing that the ore-forming elements presented a nonlinear and complex structure during their upward migration, which caused anomalies in the covered area, and multiple parameters exerted a certain indicative effect on different source intensities and properties of soil. In this study, laboratory simulations were performed to summarize the active-state evolution pattern and migration mechanism of ore-forming elements with a view to providing technical support and theoretical guidance for geochemical prospecting in the covered region.

An algorithm for the treatment of images affected by both blurring and salt&pepper noise is proposed with a cost only proportional to the number of pixels. The methodology uses a discretization scheme for the Laplace operator multiplied by a suitable nonlinear term depending on the gradient. Even if this approach resembles a diffusion type algorithm, only one step of the procedure is applied, leading to significant time savings. The procedure is successfully tested on some standard black&white natural images.

We experimentally demonstrate enhanced self-phase modulation (SPM) in silicon nitride (Si₃N₄) waveguides integrated with 2D graphene oxide (GO) films. GO films are integrated onto Si₃N₄ waveguides using a solution-based, transfer-free coating method that enables precise control of the film thickness. Detailed SPM measurements are carried out using both picosecond and femtosecond optical pulses. Owing to the high Kerr nonlinearity of GO, the hybrid waveguides show significantly improved spectral broadening compared to the uncoated waveguide, achieving a broadening factor of up to ~3.4 for a device with 2 layers of GO. By fitting the experimental results with theory, we obtain an improvement in the waveguide nonlinear parameter by a factor of up to 18.4 and a Kerr coefficient (n₂) of GO that is about 5 orders of magnitude higher than Si₃N₄. Finally, we provide a theoretical analysis for the influence of GO film length, coating position, and its saturable absorption on the SPM performance. These results verify the effectiveness of on-chip integrating 2D GO films to enhance the nonlinear optical performance of Si₃N₄ devices.

For a given material, different shapes correspond to different rigidities. In this paper, the radii of the oblique elliptic torus are formulated, a nonlinear displacement formulation is presented and numerical simulations are carried out for circular, normal elliptic, and oblique tori, respectively. Our investigation shows that both the deformation and the stress response of an elastic torus are sensitive to the radius ratio, and indicate that the analysis of a torus should be done by using the bending theory of shells rather than membrance theory. A numerical study demonstrates that the inner region of the torus is stiffer than the outer region due to the Gauss curvature. The study also shows that an elastic torus deforms in a very specific manner, as the strain and stress concentration in two very narrow regions around the top and bottom crowns. The desired rigidity can be achieved by adjusting the ratio of minor and major radii and the oblique angle.

The PI3K/mTOR signalling pathway plays a central role in the governing of cell growth, survival and metabolism. As such, it must integrate and decode information from both external and internal sources to guide efficient decision-making by the cell. To facilitate this, the pathway have evolved an intricate web of complex regulatory mechanisms and elaborate crosstalk with neighbouring signalling pathways, making it a highly non-linear system. Here, we describe the mechanistic biological details that underpin these regulatory mechanisms, covering a multitude of negative and positive feedback loops, feed-forward loops, competing protein interactions, and crosstalk with major signalling pathways. Further, we highlight the non-linear and dynamic network behaviours that arise from these regulations, uncovered through both computational and experimental studies. Given the pivotal role of the PI3K/mTOR network in cellular homeostasis and its frequent dysregulation in pathologies including cancer and diabetes, a coherent and systems-level understanding of the complex regulation and consequential dynamic signalling behaviours within this network is imperative for advancing biology and development of new therapeutic approaches.

Motivated by the way animals react in nature, we introduce a fully-connected neural-network model, which incorporates the external pattern presented to the system as a fundamental tool of the recognition process. In this new scenario, in the absence of this external field, memories are not attractors inside basins of attraction, as in usual attractor neural networks, although basins may be created according to the external pattern, thus allowing storing a much larger number of memories. The key point consists in calibrating the influence of the external pattern such as to cancel the noise generated by those memories not correlated with the external pattern.We illustrate how this proposal works by including this new contribution in the standard Hopfield model, showing a significant increase in its recognition capacity (typically by a factor $10^{2}$). As an additional feature of this model, we show its ability to react promptly to changes in the external environment, a crucial attribute of living beings. This procedure can be applied to a wide variety of neural-network models to increase considerably their recognition and reaction capabilities.

In 1895, Korteweg and de Vries (KdV), derived their celebrated equation describing the motion of waves of long wavelength in shallow water. In doing so they made a number of quite reasonable assumptions, incompressibility of the water and irrotational fluid. The resulting equation, the celebrated KdV equation, has been shown to be a very reasonable description of real water waves. However there are other phenomena which have an impact on the shape of the wave, that of vorticity and viscosity. This paper examines how a constant vorticity affects the shape of waves in electrohydrodynamics. For constant vorticity, the vertical component of the velocity obeys a Laplace equation and also has the usual lower boundary condition. In making the vertical component of the velocity take central stage, the Burns condition can be thus bypassed.

Layered two-dimensional (2D) GO films are integrated with silicon-on-insulator (SOI) nanowire waveguides to experimentally demonstrate an enhanced Kerr nonlinearity, observed through self-phase modulation (SPM). The GO films are integrated with SOI nanowires using a large-area, transfer-free, layer-by-layer coating method that yields precise control of the film thickness. The film placement and coating length are controlled by opening windows in the silica cladding of the SOI nanowires. Owing to the strong mode overlap between the SOI nanowires and the highly nonlinear GO films, the Kerr nonlinearity of the hybrid waveguides is significantly enhanced. Detailed SPM measurements using picosecond optical pulses show significant spectral broadening enhancement for SOI nanowires coated with 2.2-mm-long films of 1−3 layers of GO, and 0.4-mm-long films with 5−20 layers of GO. By fitting the experimental results with theory, the dependence of GO’s n₂ on layer number and pulse energy is obtained, showing interesting physical insights and trends of the layered GO films from 2D monolayers to quasi bulk-like behavior. Finally, we show that by coating SOI nanowires with GO films the effective nonlinear parameter of SOI nanowires is increased 16 fold, with the effective nonlinear figure of merit (FOM) increasing by about 20 times to FOM > 5. These results reveal the strong potential of using layered GO films to improve the Kerr nonlinear optical performance of silicon photonic devices.

In this manuscript we report new effects of resonance detuning on various dynamical parameters of a generic 3-wave system. Namely, for suitably chosen values of detuning the variation range of amplitudes can be significantly wider than for exact resonance. Moreover, the range of energy variation is not symmetric with respect to the sign of the detuning. Finally, the period of the energy oscillation exhibits non-monotonic dependency on the magnitude of detuning. These results have important theoretical implications where nonlinear resonance analysis is involved, such as geophysics, plasma physics, fluid dynamics. Numerous practical applications are envisageable e.g. in energy harvesting systems.

Recently a new class of experiments in the field of surface gravity waves has emerged. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.

The relative dislocation density of aluminum and copper samples is quantitatively measured using linear Resonant Ultrasound Spectroscopy (RUS). For each metallic group, four samples were prepared with different thermomechanical treatments in order to induce changes in their dislocation densities. The RUS results are compared with Nonlinear Resonant Ultrasound Spectroscopy (NRUS) as well as Second Harmonic Generation (SHG) measurements. NRUS has a higher sensitivity by a factor of two to six and SHG by 14% to 62%. The latter technique is, however, faster and simpler. As main a result we obtain a quantitative relation between the changes in the nonlinear parameters and the dislocation density variations, which in a first approximation is a linear relation between these differences. We also present a simple theoretical expression that explains the better sensitivity to dislocation content of the nonlinear parameters with respect to the linear ones. X-Ray diffraction measurements, although intrusive and less accurate, support the acoustics results.

In this letter, it is proposed that cryogenic quantum bits could operate based on the nonlinearity due to the quantum capacitance of two-dimensional Dirac materials, and in particular graphene. The anharmonicity of a typical superconducting quantum bit is calculated and the sensitivity of quantum bit frequency and anharmonicty with respect to temperature are found. Reasonable estimates reveal that a careful fabrication process could reveal the expected properties, thus putting the context of quantum computing hardware into new perspectives.

Nonlinear rheological properties of chiral crystal cholesteryl oleyl carbonate (COC) in blue phase III are investigated under different shear deformations; large amplitude oscillatory shear, step shear deformation, and continuous shear flow. Rheology of the liquid crystal is significantly affected by structural rearrangement of defects under shear flow. One of the examples on the defect-mediated rheology is the blue phase rheology. Blue phase is characterized by three dimensional network structure of the disclination lines. It has been numerically studied that the rheological behavior of the blue phase is dominated by destruction and creation of the disclination networks. In this study, we find that the nonlinear viscoelasticity of BPIII is characterized by the fracture of the disclination networks. Depending on the degree of the fracture, the nonlinear viscoelasticity is divided into two regimes; the weak nonlinear regime where the disclination network locally fractures but still show elastic response, and the strong nonlinear regime where the shear deformation breaks up the networks, which results in a loss of the elasticity. Continuous shear deformation reveals that a series of the fracture process delays with shear rate. The shear rate dependence suggests that force balance between the elastic force acting on the disclination lines and the viscous force determines the fracture behavior.

Based on the fractional order of nonlinear system for love model with a periodic function as an external force, analyzed the characteristics of the chaotic dynamic in this study. The relationship between the chaotic dynamic of the fractional-love model with the external force and the fractional-order system was analyzed when the parameters are fixed. Further, we also studied the relationship between the chaotic systemic dynamic and the parameters when the fractional-order system is fixed. The results show that when the parameters are fixed, the fractional-order system exhibited segmented chaotic states for the different fractional orders of the system. When fixed the fractional-order system, the system exhibited the periodic and chaotic states as parameter changes.

In this work, numerical and experimental implementation of a state observer applied to an Erbium-Doped Fiber Laser (EDFL) has been developed. The state observer is designed through the mathematical model of the EDFL to estimate the non-measurable variable; however, in numerical estimation, the state variables can be measurable given the mathematical model. Only the laser intensity variable was experimentally measured. The state observer estimated the population inversion through the obtained experimental laser intensity time series fitted with their numerical laser intensity using the mean square error (MSE) tool. A bifurcation diagram of the population inversion time series local maximum was built from the state observer. The state space of the experimental laser intensity versus observed population inversion was built.

This paper employs the Finite Element Method (FEM) to simulate and analyze the effects of corrosion defect parameters on the stress and failure pressure of pipelines. It investigates how the boundary conditions of the pipeline model influence stress and examines the sensitivity of failure pressure to corrosion defect parameters. A nonlinear regression equation has been developed from a dataset obtained through simulation experiments to predict the failure pressure of corroded pipelines. To validate the effects of corrosion defect parameters on failure pressure, a hydrostatic test platform for an API 5L X65 pipeline with corrosion defects was established to measure stress levels and failure pressures across varying corrosion defects. The study reveals that failure pressure is negatively correlated with corrosion length and depth, while positively correlated with corrosion width. Among these parameters, corrosion depth exerts a more significant influence on the pipeline's failure pressure than corrosion length and width. Within the range of corrosion defect parameters examined, the maximum deviation of the prediction equation's results from the simulation results is 8.71%, with an average deviation of 5.81%. The standard deviation of the fitted residuals is 0.01837. Additionally, the maximum deviation between the predicted results and experimental measurements is 8.39%, with an average deviation of 7.77%. The strong agreement between the predicted results from the equation and the actual measured data underscores the effectiveness of the nonlinear regression equation.

In this study, we evaluate the nonlinear dynamics of convection flow using the thermodynamic variational principle, focusing on scenarios where multiple external forces, such as a thermal gradient and rotational field, are applied to a shallow annular pool. We observed that with the increase in the thermal gradient, the flow changed from an axial flow to a rotational oscillatory flow with the wave amplitudes aligned. Further increasing the temperature difference led to a rotational oscillatory flow characterized by alternating wave generation and annihilation. Our analysis of the flow, considering heat fluxes orthogonal to the thermal gradient, allowed us to describe the flow state as a phase at equilibrium. The state transition of the flow was accompanied by a discontinuous jump in the heat flux, which occurred at the intersection of the entropy production curves.

The influence of applied loads on free vibrations analysis of plates and shells panels made of functionally graded materials is analyzed in the present work. Formulations for the static analysis considering geometrically nonlinear behavior, as well as linear buckling and free vibrations analyses are considered. The calculation of the through-thickness stress distribution is also performed. A finite element model based on a higher order shear deformation theory and using a non-conforming triangular flat plate/shell element with 3 nodes, and 8 degrees of freedom per node is used in the numerical implementation. The results obtained with this numerical model are presented, discussed, and compared with alternative solutions published by other authors in some benchmark applications.

The oscillation of an elastically mounted rigid cylinder excited by steady fluid flow is investigated. Regarding the nonlinearity of real practical structures like marine risers and the stay cable of a long-span bridge, the dynamic behavior of the circular cylinder is described by double Duffing equations and the aerodynamic force performance of the wake flow is expressed by wake oscillator equation. Unlike previous studies, in the present investigation, attention is focused on coupling the wake oscillator equations, taking into account quadratic terms. Following this approach, the cylinder's combined cross-flow and in-line Vortex-Induced Vibrations (VIV) are modeled more accurately. Empirical coefficients are adjusted through comparison with previous credible experimental studies and the effects of changing coefficients of the quadratic terms on major VIV parameters are investigated. The oscillating amplitude calculated by the present model is close to that of the experiment. The relative error of results obtained by the present coupled model is lower than the previous model. Moreover, the present model successfully predicts the moving trajectories of a circular cylinder under VIV in a figure-of-eight shape.

Backgrounds Linear association has widely been assumed for prediction of aging-related fractional anisotropy (FA) decline in white matter of the brain. While useful for testing significance of the aging effect, it fails to identify a threshold age before and after which the age-FA association changes. Identification of such a threshold is often of clinical interest for timely intervention. Methods We employed a sigmoidal growth function to test a threshold effect in age triggering onset of cerebral decline in 21 white matter tracts, and compared its fitting performance to those of linear, and power regression. The study sample was a normal healthy cohort of 106 participants with ages in mid-life ranging from 18 to 60 years. Results Of the 21 white matter tracts analyzed, the posterior thalamic radiation showed better fit with sigmoidal curve model, compared to a linear or power regression. The estimated threshold age in years (95% confidence interval) were 47.2 (44.1-48.4). Conclusion While available evidence regarding the presence of a specific age threshold for cerebral decline in mid-life based on FA was limited, the posterior thalamic radiation exhibited a threshold age of 47.2. Beyond this age point, we observed a significant change in the FA risk pattern.

In this paper, a robust nonlinear dynamic controller is designed for a wind turbine with a permanent magnet synchronous generator. The wind turbine is subject to variations in all the parameters appearing in its mathematical model. Furthermore, the wind velocity is considered unavailable for direct measurement. This situation is of particular interest in practical applications, where only the nominal parameter values are known, and accurate wind velocity measurement is challenging due to perturbations caused by the turbine itself, even with appropriate sensors. The problem addressed in this work involves tracking the reference angular velocity corresponding to the wind velocity. To achieve accurate tracking, appropriate compensation of the perturbation terms resulting from parameter uncertainties and wind estimation errors is required. To address this problem, an estimator of the wind velocity is utilized, along with high–order sliding mode parameter estimators, to ensure high–performance operation of the turbine.