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

In this paper, we propose a system of nonlinear mixed variational inequality problems, which consists of two elliptic mixed variational inequality problems on Banach spaces. Under suitable assumptions, using the Kakutani-Ky Fan fixed point theorem and Minty techniques, we prove the solution set to the system of nonlinear mixed variational inequality problem is nonempty, weakly compact and unique. Additionally, we suggest a stability result for the system of nonlinear mixed variational inequality problem by perturbing the duality mappings. Furthermore, we present an optimal control problem governed by the system of nonlinear mixed variational inequality problems and establish a solvability result.

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.

Abstract—The static and fatigue analysis of plates with holes, made of 2D woven roving composites, is conducted. The parametrization of convex holes is proposed. Experimental results of specimens without holes and with different shapes of notches are discussed. The fatigue behaviour is considered with the use of the low cycle fatigue method. The analysis is supplemented by the numerical finite element modeling. The present work is an extension of the results discussed in the literature. The finite element modeling of plates with holes is presented in details in Ref [1-3] including also the problems of the accuracy. The experimental results and the form of specimens are shown in Ref [4]. Two parametrical description of static and fatigue behaviour of plates with holes characterizes the goal and the novelty of the paper. The fuzzy approach is employed to reduce the number of experimental data [5].

The penetrability and directivity of ultrasound in different media is of interest in engineering and medical applications (imaging, nondestructive testing, sonochemistry, among others). The nonlinearity of a liquid can be used in the parametric antenna framework to generate low-frequency components with particular features from several ultrasonic signals at the source. Bubbly liquids are dispersive liquids in which a small amount of tiny gas bubbles leads to the increase of the nonlinear parameter of the media over certain frequency ranges. Parametric antenna applied to this huge nonlinear media gives rise to low-frequency components with relatively small intensity at the source. The evolution of a low-frequency component (difference-frequency component obtained from two primary signals) during its propagation in a bubbly liquid is somehow unknown. It is thus interesting to analyse its characteristics to establish whether this component can benefit from the quality of its own frequency and from the primary frequencies in terms of directivity and penetrability into the medium. It must be noted that no such study in bubbly liquids exists in the litterature, but only for homogeneous media. To this end, several numerical models developed previously are used here to analyse the difference-frequency component obtained from a parametric antenna emitting from two ultrasonic signals at the source in one and two-dimensional domains. These models allow us to observe the behavior of this frequency component. An angle that measures the directivity of a beam is also defined. Our results show a point hardly found in the literature: the high directivity and the huge penetrability of the secondary beam associated to the difference-frequency component into the bubbly liquid, compared to the same frequency signal excited directly from the source in the bubbly liquid and to the parametric acoustic array in homogeneous fluids.

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.

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.

The Planetary Roller Screw Mechanisms (PRSMs), alongside Ball Screw Mechanisms (BSMs) and Electromechanical Actuators (EMAs), occupies a pivotal role in advancing the precision and efficiency of various industrial applications, including aerospace, automotive, and high-precision machining tools. Despite their critical advantages such as high load capacity, superior precision, and extended lifespan, the deployment of PRSMs in complex operational conditions reveals a landscape rife with challenges and opportunities for further research. This comprehensive review endeavors to dissect the multifaceted aspects of PRSMs, focusing on their mechanics and dynamics, tribology and thermal behavior, and the paramount importance of reliability and condition monitoring. By synthesizing current research findings, this paper highlights the significant advancements in understanding the static and dynamic characteristics of PRSMs, the intricate interplay between lubrication conditions and wear mechanisms, and the critical role of thermal effects on operational performance. Moreover, it delves into the dynamic models that address the impact of manufacturing imperfections, such as waviness and defects, on the reliability of these mechanisms. Despite the strides made, the review identifies critical gaps in the existing literature, particularly under conditions of extreme temperatures, large deformations, and multifaceted loads, advocating for a holistic approach to research. By proposing integrated thermo-mechanical models and emphasizing the need for empirical validations, this paper outlines a roadmap for future studies aimed at facilitating the development of more robust and reliable PRSMs, capable of meeting the demands of complex operational scenarios and advancing the field of high-precision applications in aerospace, robotics, and beyond.

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.

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.

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.

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.

We propose a theoretical method for the deterministic shaping of quantum light via photon number state selective interactions. Nonclassical states of light are an essential resource for high precision optical techniques that rely on photon correlations and noise reshaping. Notable techniques include quantum enhanced interferometry, ghost imaging, and generating fault tolerant codes for continuous variable optical quantum computing. We show that a class of nonlinear-optical resonators can transform many-photon wavefunctions to produce structured states of light with nonclassical noise statistics. The devices, based on parametric down conversion, utilize the Kerr effect to tune photon number dependent frequency matching, inducing photon number selective interactions. With a high amplitude coherent pump, the number selective interaction shapes the noise of a two-mode squeezed cavity state with minimal dephasing, illustrated with simulations. We specify the requisite material properties to build the device and highlight the remaining material degrees of freedom which offer flexible material design.

Rebar cages form the skeletal framework of reinforced concrete structural members. They comprise longitudinal and transverse reinforcing bars, usually connected by tie wires. Past studies have identified tie-wire connections as the "weak links" in large, prefabricated rebar cages, leading to their failure during site handling and construction stages. Recent research has explored the use of mechanical U-bolt connectors to bolster stability and safety of rebar cages while reducing their vulnerability and risk of failure. This paper presents a comprehensive experimental and numerical investigation of a new type of mechanical connector, referred to as "Cage Clamp", to enhance rebar cage stability and safety. Component-level experimental tests are conducted to determine the force-displacement response of Cage Clamp connectors for crossbar connections in different degrees of freedom. The results highlight the remarkable strength and stiffness of Cage Clamp connectors, significantly outperforming traditional tie-wire connections. Furthermore, full-scale experimental tests are performed on a circular underground pile-shaft rebar cage with Cage Clamp connectors to assess its behavior under various site handling conditions. The data obtained from these experiments are used to construct and refine detailed 3D finite element models of the rebar cages, capable of capturing the complex behavior of rebar cages with Cage Clamp connectors. Using the numerical model, a sensitivity analysis is performed to assess the effect of the number of Cage Clamps on the deflection and stability of the rebar cage. The findings show that using cage clamps to connect pick-up rebar with lateral reinforcement at every 8 to 10 feet is sufficient to ensure the stability of the cage during typical site handling conditions. The results of this study serve as a basis for establishing analysis, design, fabrication, and handling guidelines for rebar cages, contributing to safe and efficient construction practices.

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.

Tail-sitters aim to combine the advantages of fixed-wing and rotor-craft, but demand a robust and fast stabilization strategy to perform vertical maneuvers and transitions to and from aerodynamic flight. The research conducted in this work intends to assess the performance of nonlinear control strategies to stabilize the attitude of a X-Vert VTOL aircraft when hovering, comparing existing solutions to applications of Nonlinear Dynamics Inversion (NDI) and its incremental version, INDI. Such controllers are implemented and tuned in simulation in order to stabilize a model of the tail-sitter , complemented by estimation methods that allow to feed back the necessary variables. These estimators and controllers are then implemented in a microcontroller, validating them in a Hardware-in-the-Loop (HITL) scenario, with simple maneuvers in vertical flight. Lastly, the developed control solutions are used to stabilize the aircraft in experimental flight, being monitored by a motion capture system. The experimental results allow to validate the model of the X-Vert and compare the effectiveness of the different control solutions in stabilizing it, with the INDI presenting itself as a more robust control strategy, with better tracking capabilities and less actuator demands.

In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method to classify spatiotemporal processes based on entropy measurements. To test and validate the method, we selected four classes of similar processes related to the evolution of random patterns: dynamic colored noises ((i)~white and (ii)~red); (iii)~weak turbulence from reaction-diffusion; (iv)~hydrodynamic fully developed turbulence, and (v)~plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon Permutation Entropy ($S^p_H$) and a new approach based on Tsallis Spectral Permutation Entropy ($S^s_q$). Notably, our observations reveal the segregation of reaction terms in this $S^p_H \times S^s_q$ space, a result that identifies specific sectors for each class of dynamic process, and can be used to train machine learning models for automatic classification of complex spatiotemporal patterns.

The thick functionally graded material (FGM) circular cylindrical shells with advanced varied shear correction coefficient and third-order shear deformation theory (TSDT) under advanced thermal vibration are studied by the method of generalized differential quadrature (GDQ). The coefficient of displacement model of TSDT is applied to derive the equations of motion for the thick FGM circular cylindrical shells. The stiffness in simpler forms of thick FGM circular cylindrical shells and temperature rise in linear expression of the heat conduction equation are used. The differential equations in dynamic equilibrium state of thick FGM circular cylindrical shells can be obtained and rewritten into displacements and shear rotations in partial derivative expressions under dynamic thermal loads in partial derivative expressions. Parametric effect studies including advanced nonlinear varied shear correction coefficient, nonlinear coefficient c1 value, power law index and thermal temperature difference of external heating loads on the displacements and stresses of thick FGM cylindrical shells under thermal dynamic vibration are investigated.

The goal of this article is to provide a review of the experimental techniques and procedures using vibration methods for the Structural Health Monitoring (SHM) of Polymer-Matrix Composites (PMC). It aims to be a guide for any researchers to carry out vibration experiments. The linear methods are first introduced. But as PMC is a complex material, these classic methods showed some limits, such as low accuracy for small damages, and a high environmental dependency. This is why the nonlinear methods are secondly studied, considering that the complexity of PMC induces a nonlinear behavior of the structure after damage occurrence. The different damage mechanisms are well explained in order to evaluate the potential of each vibration method to detect them.

Electrospun fiber scaffolds are widely used in small diameter vascular tissue engineering because they mimick organizational structure and biological function of natural extracellular matrix. However, there is still one problem of low patency rate in the long term. The main reasons are the mismatch of compliance and the easy formation of thrombus. Therefore, it is very important to promote the rapid endothelialization of small diameter tissue engineering blood vessels by regulating the topological structure and biological properties of electrospun fiber scaffolds. Firstly, crimped polylactic acid (PLA) fibers were prepared by heat treatment to mimick the crimped structure and nonlinear mechanical properties of the elastic membrane of blood vessel wall. It improved effectively the aspect ratio of human umbilical vein endothelial cells (HUVECs) and promoted lateral alignment and growth. Then, crimped PLA fibers with three levels of pore structure were prepared by thermal induced phase separation, vapor induced phase separation and laser ablation to enhance the degree of HUVECs infiltrarion and realize patterned cell growth. Crimped PLA fibers with three levels of pore structure promote rapid endothelialization of blood vessels, which is of great significance to achieve long term patency rate of small diameter tissue engineering blood vessels.

In this paper, we consider an epidemiological Susceptible-Infected-Susceptible (SIS) model in which the individuals cured from the infection return back into the group of people endangered by the infection. Delay differential equations were introduced to create more realistic models since many processes depend on past history. Many different mathematical methods, including the Susceptible-Infected-Recovered (SIR) model as well as derivatives thereof, can be used to prognose the spread of many various infectious diseases, including Covid-19.We use a nonlinear differential system with time delay as a mathematical formulation of this model. It is examined by the existence of a positive solution which is bounded by two functions $k_1, k_2\in C([t_0,\infty),(0,\infty))$ with constants $\lambda_1 > 0,\,\lambda_2 > 0$ where $0<\lambda_1\leq \lambda_2$. The conditions are put in place for existence of a positive solution that approaches zero in infinity, if $t\to\infty$. Infectious diseases accompany a person throughout their entire life, and in the history of mankind often appeared in frequent epidemics caused high mortality. The occurrence of infectious diseases in the population represents a serious health, social and economic problem. There is a lot of ambiguity concerning the time span and final spread of the epidemic thus making it very demanding for the governing bodies, healthcare institutions, and economic sector to precisely judge the future development.Several examples are shown at the end of this paper.

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.

To identify the exchange coefficients of a nonlinear polynomial tricompartmental general system of α+β , we follow the procedure; firstly, the recommended solution is to introduce an adequate time t*&gt;0 in a determinable manner. That is, after injecting quantity a into the main compartment, wait a moment for the exchange in the polynomial α+β order nonlinear general system to settle, and then compare this compartment to compartment 2 at t*. Secondly, applying the Taylor formula will linearize the system and identify the exchange coefficients. Finally, we will prove that the linearization method is stable.

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.

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.

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.

Reservoir computing (RC) systems can efficiently forecast chaotic time series using nonlinear dynamical properties of an artificial neural network of random connections. The versatility of RC systems has motivated further research on both hardware counterparts of traditional RC algorithms and more efficient RC-like schemes. Inspired by the nonlinear processes in a living biological brain and using solitary waves excited on the surface of a flowing liquid film, in this paper we experimentally validate a physical RC system that substitutes the effect of randomness for a nonlinear transformation of input data. Carrying out all operations using a microcontroller with a minimal computational power, we demonstrate that the so-designed RC system serves as a technically simple hardware counterpart to the `next-generation’ improvement of the traditional RC algorithm.

In this paper, we present a three-step sixth-order iterative schemes to estimate the solutions of a nonlinear systems of equations, for predicting the shear strength of a reinforced concrete beam. This procedure is designed by means of a weight function technique. The values for the parameters of this system were randomly selected inside the prescribed ranges by technical standards for structural concrete; moreover, some of this parameters were fixed taking into consideration the solvability region of the adopted steel constitutive model. The efficiency of the new class is compared with other current schemes, with very good results.

The traditional receiver employs scalar tracking loops, resulting in degraded navigation performance in weak signal and high dynamic scenarios. An innovative design of a vector tracking receiver based on nonlinear Kalman filter (KF) tracking loops is proposed in this paper, which combines the strengths of both vector tracking and KF tracking loops. Firstly, a comprehensive description of the vector tracking receiver model is presented, and unscented Kalman filter (UKF) is applied to nonlinear tracking loop. Secondly, to enhance the stability and robustness of the KF tracking loop, we introduce square root filtering and an adaptive mechanism. The tracking loop based on square root UKF (SRUKF) can dynamically adjust its filtering parameters based on signal noise and feedback Doppler error. Finally, the proposed method is implemented on a software-defined receiver (SDR), and the field vehicle experiment demonstrates the superiority of this method over other receivers in complex dynamic environments.

In this paper, a swarm trajectory planning method is proposed for multiple autonomous surface vehicles (ASVs) in an unknown and obstacle-rich environment. Specifically, based on the point cloud information of the surrounding environment obtained from local sensors, a kinodynamic path searching method is used to generate a series of waypoints in the discretized control space at first. Next, after fitting B-spline curves to the obtained waypoints, a nonlinear optimization problem is formulated to optimize the B-spline curves based on gradient-based local planning. Finally, a numerical optimization method is used to solve the optimization problems in real-time to obtain collision-free, smooth and dynamically feasible trajectories relying on a shared network. Simulation results demonstrate the effectiveness and efficiency of the proposed swarm trajectory planning method for a network of ASVs.

The susceptible-infected-recovered/removed-vaccinated (SIRV) epidemics model is an important generalization of the SIR epidemics model as it accounts quantitatively for the effects of vaccination campaigns on the temporal evolution of epidemics outbreaks. Additional to the time-dependent infection ($a(t)$) and recovery ($\mu (t)$) rates, regulating the transitions between the compartments $S\to I$ and $I\to R$, respectively, the time-dependent vaccination rate $v(t)$ accounts for the transition between the compartments $S\to V$ of susceptible to vaccinated fractions. An accurate analytical approximation is derived for arbitrary and different temporal dependencies of the rates which is valid for all times after the start of the epidemics for which the cumulative fraction of new infections $J(t)\ll 1$. As vaccination campaigns automatically reduce the rate of new infections by transferring susceptible to vaccinated persons, the limit $J(t)\ll 1$ is even better fulfilled than in the SIR-epidemics model. The comparison of the analytical approximation for the temporal dependence of the rate of new infections $\jt(t)=a(t)S(t)I(t)$, the corresponding cumulative fraction $J(t)$, and $V(t)$, respectively, with the exact numerical solution of the SIRV-equations for different illustrative examples proves the accuracy of our approach. The considered illustrative examples include the cases of stationary ratios with a delayed start of vaccinations, and an oscillating ratio of recovery to infection rate with a delayed vaccination at constant rate. The proposed analytical approximation is self-regulating as the final analytical expression for the cumulative fraction $\jinf $ after infinite time allows us to check the validity of the original assumption $J(t)\le \jinf \ll 1$.

Stratified Taylor Couette Flow (STCF) undergoes transient growth. Recent studies have shown that there exists transient amplification in the linear regime of counter-rotating STCF. It is reported that as Gr increases, the maximum amplification factor ($G_0$) initially decays before it eventually starts growing after reaching a certain critical value Gr$_{c}$. Assuming other parameters of the model are kept constant, the value Gr$_{c}$ changes with respect to different speed ratios of the cylinders. The observed decay/growth pattern of $G_0$ is attributed to the interplay between the induced shear and buoyancy. In this study, the mechanism that triggers this observed pattern is investigated. The kinetic budget of the optimal transient perturbation is analysed numerically to simulate the interaction of the shear production (SP), buoyancy production (BP) and other energy components that contributes to the total optimal transient kinetic energy. These contributions affect the total energy by influencing the perturbation to extract kinetic energy (KE) from the mean flow. The decay of $G_0$ resulted from the positive amplification of both BP and SP, while the growth is attributed to the negative and positive amplification of BP and SP, respectively. The optimal SP is positively amplified, implying that there is the possibility of constant linear growth. These findings agree with the linear growth rate for increasing values of Gr.

Recent studies have shown that the mechanical properties of bioinspired periodic composite materials can be strongly influenced by finite deformation effects, leading to highly nonlinear static and dynamic behaviors at multiple length scales. For instance, in porous periodic nacre-like microstructures, microscopic and macroscopic instabilities may occur for a given uniaxial loading process and, as a consequence, wave attenuation properties may evolve as a function of the microstructural evolution, giving it the designation of metamaterials. The numerical outcomes provide new opportunities to design bioinspired soft composite metamaterials characterized by high deformability and enhanced elastic wave attenuation capabilities given by the insertion of voids and lead cores.

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.

Fractional calculus is defined by expanded integer order integration and differentiation. In this paper, multiple mathematical models of a nonlinear dual tank device are precisely formulated by fractional calculus. Using the accurate model, multivariable Fractional-Order Controller is designed for the nonlinear device. The merits of the fractional-order design include: 1) Control of multivariable nonlinearities, 2) Compensation of uncertainties, 3) Elimination of coupling effects. Simulations and experiments are conducted to verify the precision of the fractional order models and the effectiveness of the multivariable fractional-order control design.

We have investigated the canine of olive flounder in terms of the nonlinear optical signals of two-photon excitation autofluorescence (2PEF) and second harmonic generation (SHG), whereby two kinds of nonlinear microscope images of the canine were obtained using ~140 femtosecond pulses. For increasing excitation power of laser pulses, a photobleaching effect was found to be significant in the red and green ranges of autofluorescence, where a double-exponential decay of the intensity occurs within hundreds of second due to collagen fluorophores in the canine. In the blue range of autofluorescence, the photobleaching is suppressed due to an energy conversion of the incident laser pulse to SHG signal. As a result, the signal in blue range remains constant for long term exposure to laser. We have also found that the SHG intensity depends on the orienta-tion of linearly polarized excitation, and the optical anisotropy of SHG can be attributed to the collagen alignment of canines.

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.

This paper presents a new method to model the nonlinear behaviour of masonry double curvature structures, possibly reinforced by composite materials, by means of conventional elasto-plastic analyses. It is meant to be used in professional design, especially for assessment and retrofitting purposes, therefore based on the exploitation of the simplest nonlinear Finite Elements available in a commercial software, namely trusses with elasto-fragile and elasto-ductile behaviour (Cutoff Bars). The numerical static nonlinear analyses are carried out by considering elastic hexahedral elements for bricks and lumping nonlinearities on joints. These have been assumed in turn elastic-brittle and elastic-plastic by using 1D elements, respectively Point Contacts, under No-Tension Material hypothesis, and Cutoff Bars, assigning small tensile resistance to the material. The reinforcement, realised with FRP hooping strips, has been successfully modelled in a similar fashion, i.e. by applying perfectly bonded elastic-plastic Cutoff Bars at the extrados of the dome, where the debonding is accounted for in a conventional way limiting the tensile strength according to Italian Standards indications. The procedure is validated against benchmark models with the same geometry, using experimental data and more refined structural model results for comparison.

In this review we collect some recent achievements in the accurate and efficient solution of the Nonlinear Schrödinger Equation (NLSE), with the preservation of its Hamiltonian structure. This is achieved by using the energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs) after a proper space semi-discretization. The main facts about HBVMs, along with their application for solving the given problem, are here recalled and explained in detail. In particular, their use as spectral methods in time, which allows efficiently solving the problems with spectral space-time accuracy.

To estimate the progressive collapse resistance capacity of a multi-column frame tube structure with the assembled truss beam composite floor (ATBCF), the pushdown analysis, and the nonlinear dynamic analysis as well, are conducted for such a structure by using the alternate load path (ALP) method. The bearing capacities of the remaining structures at three different work conditions, which are the side middle column failure, the edge middle column failure, and the corner column failure, are individually studied, and the collapse mechanism for the remaining structures is analyzed from the aspects of the internal force redistribution and the failure mode of the second defense line. Simultaneously, the influence of the column failure time on the dynamic response of the remaining structure and the dynamic amplification coefficient are discussed. The results show that the residual bearing capacity of the remaining structure with the bottom corner column failure is higher than that of the one with the side or edge middle column failure, while the latter has a stronger plastic deformation capacity. When the ALP method is adopted to operate the progressive collapse analysis, it is reasonable to take the column failure time as 0.1 times of the first-order vertical vibration period of the remaining structure, and it is suitable to set the dynamic amplification coefficient as of 2.0, which is the ratio of the maximum dynamic displacement to the static displacement of the remaining structure under the transient loading condition.

A system of simultaneous multi-variable nonlinear equations can be solved by the Newton’s method with local q-quadratic convergence if the Jacobian is analytically available. If this is not the case, then quasi-Newton methods with local q-superlinear convergence give solutions by approximating the Jacobian in some way. Unfortunately, the quasi-Newton condition (secant equation) doesn’t completely specify the Jacobian approximate in multi-dimensional case, so its full-rank update is not possible with classic variants of methods. The suggested new iteration strategy (“T-Secant”) allows full-rank update of the Jacobian approximate in each iteration by determining two independent approximates for the solution. They are used to generate a set of new independent trial approximates, then the Jacobian approximate can fully be updated. It is shown, that the T-Secant approximate is in the vicinity of the classic quasi-Newton approximate, providing that the solution is evenly surrounded by the new trial approximates. The suggested procedure increases the super-linear convergence of the secant method (φS = 1.618...) to super-quadratic (φT = φS + 1 = 2.618...) and the quadratic convergence of the Newton-method (φN = 2) to cubic (φT = φN + 1 = 3) in one dimensional case. The Broyden-type efficiency (mean convergence rate) of the suggested method in multi-dimensional case is an order higher than the efficiency of other classic low-rank update quasi-Newton methods as shown by numerical examples on a Rosenbrock-type test-function with up to 1000 variables. The geometrical representation (hyperbolic approximation) in single variable case helps explaining the basic operations and a vector-space description is also given in multi-variable case.

Doubly-fed induction generators (DFIG) find extensive application in variable-speed wind power plants, providing notable advantages such as cost-effectiveness, operational flexibility across varying speeds, and enhanced power quality. This research focuses on the control of DFIGs employed in variable-speed wind turbine configurations. A suitable mathematical model is chosen for representative systems following a comprehensive review of contemporary research. Subsequent analysis reveals the instability of the open-loop time response of the system. To address this instability, the initial approach involves the implementation of the conventional Model Predictive Controller (MPC). However, the outcomes indicate that this controller falls short of delivering satisfactory performance despite the enhanced stability. In the subsequent phase, efforts are made to mitigate the impact of wind input variability by utilizing the Kalman filter, given its effectiveness in handling high variability. Following this, a novel methodology is introduced, which combines nonlinear MPC with the Lyapunov function. This method is based on the nonlinear model of the system. By using the Lyapunov function in the nonlinear MPC structure, the stability of the designed controller is guaranteed. The simulation results conducted using MATLAB software show that the output variables of the modeled DFIG system achieve stability within a reasonable timeframe applying the input.

Ambient vibration energy is widely being harnessed as a source of electrical energy to drive low-power devices. The vibration energy harvester (VEH) of interest employs an electromagnetic transduction mechanism, whereby ambient mechanical vibration is converted to electrical energy. The limitations affecting the performance of VEHs, with an electromagnetic transduction structure, include its operational bandwidth as well as the enclosure-size constraint. In this study, an analysis and design of a nonlinear VEH system is conducted, using the Output Frequency Response Function (OFRF) representations of the actual system model. However, the OFRF representations are determined from the Generalised Associated Linear Equation (GALE) decompositions of the system of interest. The effect of both nonlinear damping and stiffness characteristics, to respectively extend the average power and operational bandwidth of the VEH device, is demonstrated.

Despite the fact that SMA restrainers exhibit a superelastic strain capacity of 7%, this capacity appears inadequate for isolated bridges due to the typically greater than 20cm relative dis-placements between girders during intense seismic events. In order to perform such a stroke, a SMA restrainer of greater than 3 metres in length might be required. In order to reduce the length of restrainers, a novel honeycomb damper constructed from superelastic shape memory alloy (SMA) is proposed. The proposed device, denoted as the superelastic SMA honeycomb damper (SHD), is comprised of steel plates to prevent the SMA plane from collapsing and superelastic SMA honeycomb to provide self-centering capability. By incorporating the large strain capacity of SMA and the geometrically nonlinear deformation of honeycomb structures, SHD has been developed to satisfy the requirements of bridge restrainers with large strokes. It is capable of functioning as a restrainer and energy dissipation device when subjected to dynamic tension and compression loads. The SHD was initially investigated from a theoretical perspective. Following this, a mul-ti-cell SHD specimen was manufactured. The specimen underwent axial tensile and compressive experiments in order to examine the mechanical properties of SHDs. Finally, experimental results were investigated through numerical simulation analyses of the SHDs using a three-dimensional high-fidelity finite element model. Additionally, a method for enhancing SHD was proposed. The findings indicate that SHD is capable of exhibiting superior self-centering capability and sta-ble hysteretic responses when subjected to earthquakes.

Practically important properties of real liquids, including seawater, are their nonlinear properties, which include a nonlinear acoustic parameter, as well as cavitation strength – a rupture of the continuity of a liquid at high intensities in an acoustic wave. The manifestation of nonlinear effects is greatly facilitated by the presence of various nuclei in the liquid – gas bubbles, foreign particles, and other inclusions of various origins. For practical applications, it is important to study the properties of real liquids with inclusions in them. Due to the difficulties of measuring cavitation strength by acoustic methods, other methods are being sought. It is proposed to use an optoacoustic method associated with the use of laser radiation that causes optical breakdown - optical cavitation, that accompanied by a strong sound generation effect. The connection between optical breakdown thresholds and acoustic cavitation thresholds has been established, which can later be used to identify cavitation thresholds at high static pressures (at great depths in the sea), where the use of acoustic emitters is extremely difficult. The paper studies the bubble size distribution function in seawater, combined with studies of the acoustic nonlinearity parameter and cavitation strength at various depths. The interrelation of these characteristics for seawater is shown.

We present multi-sensor measurements from satellites, unmanned aerial vehicle, marine radar, thermal profilers and repeated conductivity-temperature-depth casts made in the Kara Gates strait connecting the Barents and the Kara Seas during spring tide in August 2021. Analysis of the field data during an 18-hour period from four stations evidence that a complex sill in the Kara Gates is the site of regular production of intense large-amplitude nonlinear internal waves. Satellite data show a presence of a relatively warm northeastward surface current from the Barents Sea toward the Kara Sea attaining 0.8-0.9 m/s. Triangle-shaped measurements of three thermal profilers revealed pronounced vertical thermocline oscillations up to 40 m associated with propagation of short-period nonlinear internal waves of depression generated by stratified flow passing a system of shallow sills in the strait. The most intense waves were recorded during the ebb tide slackening and reversal when the background flow was predominantly supercritical. Observed internal waves had wavelength of ~100 m and travelled northeastward with phase speeds of 0.8-0.9 m/s. The total internal wave energy per unit crest length for the largest waves was estimated to be equal to 1.0-1.8 MJ/m.

Multiphoton microscopy (MPM) is a cutting-edge nonlinear microscopy technique known for its exceptional capabilities in imaging dense tissues, making it an ideal tool for exploring human kidney tissue. This study delves into the application of MPM in evaluating renal cell tumors and characterizing tumor capsules. MPM encompasses two core methods: two-photon excitation fluorescence (TPEF) and second harmonic generation (SHG). It leverages femtosecond lasers to provide deep tissue imaging while minimizing phototoxicity, making it well-suited for live tissue analysis. The study analyzed 100 formalin-fixed paraffin-embedded (FFPE) kidney tissue samples, ensuring compliance with ethical standards. Using a Ti:Sapphire laser for femtosecond pulses and a variety of optical components and filters, the researchers captured TPEF and SHG signals, facilitating image analysis. Normal kidney tissue exhibited distinctive structures like glomeruli and tubules under MPM. Renal cell carcinoma (ccRCC) displayed unique TPEF patterns with eccentrically located nuclei and indistinct cytoplasmic membranes. Papillary RCC (pRCC) exhibited a papillary pattern with dark nuclei, while chromophobe RCC (chRCC) showcased distinct features like thick cell membranes, strong TPEF signal in nuclei, and granular cytoplasm. Renal oncocytoma (RO) presented strong TPEF signals in cuboidal cells with microcyst-like arrangements. Overall, MPM proved invaluable in assessing human kidney tissue, offering distinct TPEF patterns for different renal cell tumor types. This non-invasive technique has the potential to enhance pathological examinations and advance our understanding of complex biological processes, ultimately contributing to improved diagnostics and treatment strategies for renal diseases.

Gain-scheduled autopilots have emerged as a dominant strategy to achieve adaptive control of coupled, non-linear engineering complexities, owing to an ability to adapt to changing operational conditions and uncertainties. This study focuses on utilizing bilinear interpolation of gain-scheduled autopilots, emphasizing enhanced system performance and robustness. Through a comprehensive investigation and comparative analysis using three disparate cases, advantages over conventional methods are revealed. Strengths and weaknesses of both simple and specialized variants (such as linear, and real-time gain-scheduling) are introduced. Three missile guidance case–studies utilize simulation time and miss distance figures of merit. Potential to achieve precise control across various mission scenarios, while ensuring reduced computational complexity is revealed by nearly two–hundred percent improved missile miss distances with comparable distances traveled and slightly improved computational burden.

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.

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.

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.

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.

We report a diode pumped solid state (DPSS) laser used for intracavity pump-enhanced difference frequency generation (DFG) to create a 3.5 micron laser. Using a 50 mm-long periodically poled lithium niobate (PPLN) crystal inside the cavity of an Nd:YVO4 solid state laser at 1064 nm with 4.5 W pump power at 808 nm, and a 310 mW C-band signal at 1529 nm, up to 31 mW of mid-infrared output power at 3499 nm is obtained. The cavity requires no active stabilization and/or locking, and the entire cavity is &lt;8 cm in length. The obtained output power corresponds to a black box efficiency of 2.20 %W-1, which is the highest value reported to date for continuous wave DFG based on a bulk nonlinear optical crystal with no active stabilization. Potential future applications in free space optical communication are discussed as well.

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.

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.

The tension cable-supported power transmission structure (TC-PTS) is a new type of power transmission structure suitable for mountainous terrain, which is sensitive to wind load. In this regard, a nonlinear finite element analysis model of wind-induced vibration is proposed for the TC-PTS, and the wind-induced vibration response of the structure is analyzed. Firstly, the tangent stiffness matrix of the three-dimensional truss element for the supporting suspension cable and transmission line, considering the geometric nonlinearity of structures, is derived through the relationship between the element elastic energy and its displacement. Subsequently, the element mass matrix and damping matrix of the supporting suspension cable and transmission line, as well as the element nodal load vector obtained from wind load equivalence are given. Then, based on the nonlinear finite element theory, the nonlinear dynamic equation of wind-induced vibration is established for the TC-PTS and solved by Newmark-β method combined with Newton-Raphson iterative method. Furthermore, the rain-flow counting method and Miner's linear fatigue cumulative damage theory were used for wind induced fatigue damage assessment. Finally, a two-span TC-PTS is selected as an example, and the wind-induced nonlinear vibration and fatigue damage assessment are analyzed through the proposed model. The results show that the proposed model has high computational accuracy and efficiency. With the increase of wind speed and wind direction angle, the maximum lateral displacement and tension of the supporting suspension cable and transmission line increase, and their degree of increase shows a nonlinear trend. In terms of the wind-induced fatigue analysis results of TC-PTS, the fatigue damage at the end of the supporting-conductor suspension cable is greater than the fatigue damage at its midpoint. Compared to the fatigue damage at the midpoint of the conductor, the fatigue damage at the end of the conductor is less affected by wind direction angle, and both are more significantly affected by the wind speed.

In this paper, to make the missile intercept the maneuvering target, the parallel approaching guidance law is developed. In order to estimate the target maneuver more accurately and reduce that’s influence on guidance accuracy, the distance-scalar disturbance observer is employed. Specifically, the estimation accuracy of the observer designed is regardless of the relative distance. The finite-time prescribed performance is employed to ensure that the line-of-sight angular rate is capable of converging to a predesigned small region in the specified finite time. All signals of interception system can guarantee ultimately uniformly boundedness proved by the Lyapunov stability theory. Finally, the availability of the parallel approaching guidance law is demonstrated by the numerical simulation.

The investigation of plasma channels induced by focused ultra-short 1030-nm laser pulses in bulk of synthetic HPHT diamond revealed strong dependence of their size and shape on the used numerical aperture of the lens (NA=0.15-0.45). It was shown that at loose focusing conditions, it is possible to significantly increase the length of the plasma channel with a slight increase in pulse power, while tight focusing allows to obtain more compact structures in the same range of used powers. Such dependence paves the way to new possibilities in 3D processing of transparent dielectrics, allowing, for example, to vary the spatial parameters of modified regions without changing the setup, but only by controlling the lens aperture, which seems very promising for industrial applications.

The generalized dynamic model of the rotor system, presented in the paper, is the first model that takes into account the interconnected oscillations of the “rotor - weakly conductive fluid – foundation” system under the action of such parameters as fluid and rotor motion, linear eccentricity, friction forces, foundation vibration and nonlinear characteristics of rolling bearings, as well as the action of a magnetic field on the fluid. Consistent equations of motion for the system “rotor - weakly conductive fluid – foundation” were derived and solved analytically. Forced and natural oscillations of the system were analyzed, and the distinctive features of the rotor system dynamics were revealed. The values of frequencies and amplitudes, which are one of the main factors determining the dynamic behavior of the system, were obtained and studied.

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.

Graphyne is a material that has unique mechanical properties, but little is known about how these properties change when the material has holes. In this work, the effect of hole geometry, considering circular, triangle, and rhombus hole configurations, on the mechanical nonlinear response of γ-graphyne structures is studied. Graphyne, graphdiyne, graphyne-3, and graphyne-4 structures are under investigation. An efficient nonlinear finite element analysis (FEA) method is adequately implemented under large deformations for this purpose. The study varied the size and shape of the holes to understand how these changes affect the nanostructure's mechanical response. The results indicate that the hole geometry significantly impacts the mechanical nonlinear response of γ-graphyne structures. The holes' size and shape affect the structures' elastic behavior, deformation, and strength. The findings can be used to optimize the design of γ-graphyne structures for specific mechanical applications. The study highlights the importance of considering the hole geometries in the design and fabrication of these materials.

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 paper presents the experimental and numerical study on a ductile beam-column connection between a composite reinforced concrete truss (CRCT) beam and Concrete Filled Tube (CFT) column subjected to bending and shear loads. Two experimental models with different beam-column joint testing schemes, extracted from the same prototype three-dimensional structure designed according to the rules of the capacity design provided by seismic code, were subjected to quasi-static cyclic tests by applying gravitational loads and the horizontal seismic force. The main objective of this paper is to verify the experimental ductile behavior of both specimens and to simulate the experimental global and local response by nonlinear static analysis considering different modelling approaches. The comparison between the experimental and numerical results highlights, for both models considered, the ductile and dissipative capacity of the connection system, designed following the criterion of the hierarchy of resistances proposed by the current Italian code. Different experimental setup showed similar results demonstrating the repeatability of the test and its reproducibility through the nonlinear numerical analysis.

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.

The motion of Unmanned Surface Vehicles (USVs) is frequently disturbed by the ocean wind, wave and current. A poorly designed controller will lead to failures and even safety problems during actual navigation. In order to obtain satisfied control performance of the motion for the USVs, a Model Predictive Control (MPC) based on improved Nonlinear Disturbance Observer (NDO) is proposed. Firstly, the USV model is approximately linearized and MPC is designed for the multivariable system with constraints. In order to compensate the influence of disturbances, an improved NDO is designed, with which the calculation time for the MPC saved a lot. Finally, comparison experiments are conducted between the MPC with NDO and the MPC with improved NDO, and the results show that they have similar performance to the USVs. However, the proposed method has less parameter to be tuned and it is much more time-saving compared to the MPC with traditional NDO.

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.

Curcumin, a nontoxic and cheap natural medicine, has high therapeutic efficacy for many diseases including diabetes and cancers. Unfortunately, its exceedingly low water-solubility and rapid degradation in the body severely limit its bioavailability. In this work, we prepare a series of biocompatible poly(vinyl anisole)@nonlinear poly(ethylene glycol) (PVAS@PEG) core-shell nanogels with different PEG gel shell thickness to provide high water solubility, good stability, and controllable sustained release of curcumin. The PVAS nanogel core is designed to attract and store curcumin molecules for high drug loading capacity and the hydrophilic nonlinear PEG gel shell is designed to offer water dispersibility and thermo-responsive drug release. The obtained nanogels are monodispersed in spherical shape with clear core-shell morphology. The size and shell thickness of the nanogels can be easily controlled by changing the core-shell precursor feeding ratios. The optimized PVAS@PEG nanogels display a high curcumin loading capacity of 38.0 wt%. The nanogels can stabilize the curcumin from degradation at pH =7.4 and release the curcumin in response to heat in the physiologically important temperature range. The nanogels can enter cells effectively and exhibit negligible cytotoxicity to both the B16F10 and HL-7702 cells at a concentration up to 2.3 mg/mL. Such designed PVAS@PEG nanogels have a great potential to be used for delicate drug delivery.

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 vacuum preloading method effectively strengthens the soft soil foundations with vertical drainage, which will produce a smear effect when laying sand drains. Meanwhile, the seepage of pore water and soil deformation during consolidation exhibits nonlinear characteristics. Therefore, based on Gibson's 1D large strain consolidation theory, this paper developed a more generalized large strain radical consolidation model of sand-drained soft foundations under free strain assumption. In this system, the double logarithmic compression permeability relationships for soft soils with large strain properties, the variation of the radical permeability coefficient in the smear zone, and the effect of the non-Darcy flow were all included. Then, the partial differential control equations were numerically solved by the finite difference method and validated with existing radical consolidation test results and derived analytical solutions. Finally, the influences of relevant model parameters on consolidation are discussed. The analysis shows that the greater the maximum dimensionless vacuum negative pressure P0, the faster the consolidation rate of sand-drained foundations. Meanwhile, the decrease in the negative pressure transfer coefficient k1 will result in a decreasing final settlement amount. Moreover, the consolidation rate of sand-drained foundations is slower considering the non-Darcy flow, but the final settlement is unaffected.

The effectiveness of a recently proposed methodology in the identification of damage in planar, multi-storey, Reinforced Concrete (RC) moment-frames, which develop a plastic-yield mechanism on their beams, is showcased here via the examining of a group of such existing multi-storey frames with three or more unequal spans. According to the methodology, the diagram of the instantaneous Eigen-Frequencies of the frame in the nonlinear regime is drawn as a function of the inelastic seismic roof displacement by performing a sequence of pushover and instantaneous modal analyses with gradually increasing target displacement. Using this key-diagram, the locations of severe seismic damage in an existing moment-frame can be evaluated if the instantaneous fundamental eigen-frequency of the damaged frame, at an analysis step within the nonlinear area, is known in advance by “the monitoring and the identification of frequencies” using a local network of uniaxial accelerometers. This is a hybrid technique because both procedures, the instrumental Monitoring of the structure and the Pushover analysis on the frame (M and P technique), are combined. Moreover, the damage image of the planar multi-storey moment-frame is illustrated, and the lateral stiffness matrix of the damaged frame is calculated with high accuracy.

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.

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.

This paper studies the trajectory tracking control of an autonomous underwater vehicle (AUV) based on a stochastic uncertain nonlinear system. We investigate the time-varying gain adaptive control method looking for possible approaches to alleviate the heavy computational burden. Under nonlinear growth, conditions satisfy polynomial growth conditions. These two problems are resolved the fast response time and good path tracking, respectively. Novel adaptive algorithms are developed exploiting the dynamic properties of the AUV motion. By appropriately turning the original controller design problems into parameters choosing problems and then solving them in a functional time-varying observer technical theorem. In order to deal with the station error of system converges to arbitrarily small domains with stochastic uncertain disturbance. A coordinate transformation is proposed for all system states to meet boundedness. We show that the convergence of the AUV trajectory errors can be guaranteed by the proposed contraction constraints in the stability analysis, closed-loop stability is proved, and the system is asymptotically probabilistic in the global scope. They are taking advantage of the guaranteed stability. Extensive simulation studies on the AUV model demonstrate the effectiveness and robustness of the proposed approach. A real-time time-varying gain constructive control strategy is further developed for the Hardware-in-the-loop simulation; the controller design results are imported into the AUV actuator model to verify the effectiveness of the controller design.

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.

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.

This paper discusses the mathematical modelling of exothermic explosions in a slab. This model is based on a nonlinear equation containing a nonlinear term related to Arrhenius, bimolecular, and sensitised laws of reaction kinetics. The absolute temperature can be obtained by solving the nonlinear equation using Akbari-Ganji’s method. The influence of the parameters Frank-Kamenetskii, activation energy and numerical exponent on temperature is discussed. The analytical results are compared with previous available analytical and numerical results ( Matlab). A satisfactory agreement is noted.

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.

This paper presents a novel algorithm, the multi-objective nonlinear interval PageRank (MONIPR) Algorithm. This algorithm extends the conventional PageRank (PR) algorithm, integrating nonlinear interval computation and multi-objective considerations into the computation process. The MONIPR algorithm bridges a research gap in integrating nonlinear interval approaches and multi-objective problems into the PR algorithm, which were traditionally treated separately. In addition, this research adopts the constrained interval arithmetic proposed to address the limitations of the conventional PR algorithm, which tends to overlook uncertainties and results in deterministic outcomes. In addition, we use a numerical example to demonstrate the proposed algorithm, contrasting it with the conventional approaches. A numerical example demonstrates the algorithm's performance by comparing the rank intervals obtained with the traditional crisp Markov chain and PR algorithm. The results highlight the ability of the proposed algorithm to provide a range of possible rank intervals, considering both uncertainty and multi-objectives. The findings suggest potential applications in decision-making, uncertainty quantification, and systems analysis.

The total tree height (h) and diameter at breast height (dbh) relationship is an essential tool in forest management and planning. The height—diameter (h-dbh) relationship had been studied with several approaches and for several species worldwide. The nonlinear mixed effect modeling (NLMEM) has been extensively used and lately the resilient backpropagation artificial neural network (RBPANN) approach has been a trend topic for modeling this relationship. The artificial neural network (ANN) is a computing system based in artificial intelligence and inspired in biological neural network for supervised learning. In this study the NLMEN and RBPANN approaches were used for modeling the h—dbh relationship for Durango pine species (Pinus durangensis Martínez) in mixed-species forest from Mexico. The total dataset considered 1,000 (11,472 measured trees) randomly selected from 14,390 temporary forest inventory plots and the dataset was randomly divided into two parts; 50% for training and 50% for testing. An unsupervised clustering analysis was used to grouped the dataset into 10 clusters based on k-means clustering method and plot-variables like density, basal area, mean dbh, mean h, quadratic mean diameter, altitude and aspect. The RBPANN was performed for tangent hyperbolicus (RBPANN-tanh), softplus (RBPANN-softplus), and logistic (RBPANN-logistic) activation functions for functions in cross product of the covariate or neurons and the weights for the ANN analysis. For both training and testing, 10 classical statistics (e.g., RMSE, R2, AIC, BIC, logLik) were computed for the residual values and assess the approaches for h—dbh relationship. For training and testing, the ANNs approach outperformed the NLMEM approach, and the RBPANN-tanh has the best performance in both training and testing phases.

In mobile applications such as geomagnetic surveying, two major effects hamper the use of optically pumped magnetometers: dead zones, sensor orientations where the sensors signal amplitude drops; and heading errors, a dependence of the measured magnetic field value on the sensor orientation. We present a concept for an omnidirectional magnetometer to overcome both these effects. The sensor uses two cesium vapor cells, interrogated by circularly-polarized amplitude-modulated laser light split into two beams running perpendicular to each other. This configuration is experimentally investigated using a setup wherein the laser beam and magnetic field direction can be freely adjusted relative to each other within a magnetically shielded environment. We demonstrate that a dead-zone free magnetometer can be realized with nearly isotropic magnetic-field sensitivity. While in the current configuration we observe heading errors emerging from light shifts and due to the nonlinear Zeeman effect, we introduce a straightforward approach to suppress these systematic effects in an advanced sensor realisation.

This research investigates the effects of torsional moments on the mechanical behavior of thin-walled open-ended vertical pile foundations subjected to lateral wind loads. The warping and torsion effect generated over the piles due to the resultant lateral load impact outside the shear center is analyzed in-field tests. Complementarily, a two-dimensional finite element model based on the simple bending stress-strain state as well as a three-dimensional finite element model considering torsional effects were implemented and their results analyzed. Finally, a comparative analysis between the in-field lateral loading tests and the finite element model approaches was established and correlations between the errors and the parameters of influence were highlighted. From the results, it has been ascertained that the slender thin-walled open-ended pile foundations are particularly sensitive to small load deviations from their center of gravity, this leads to the fact that the slenderer and the more eccentricity of the load, the more it affects the torsion and warping of the pile. Calculation methodologies usually consider a simple in-plane bending behavior which conducts to errors between 44 and 58% of the experimental results.

In the last years, a recent growing line of research has been developed with fruitful results by using fractional and conformable derivatives in the iterative procedures of classical methods for solving nonlinear equations. In that sense, the use of conformable derivatives has shown better behavior than fractional ones, not only in the theory, but also in the practice. In this work, we adapt the approximation of conformable derivatives in order to design the first conformable derivative-free iterative schemes to solve nonlinear equations: a Steffensen’s type method and a Secant type method; the latter with memory. Convergence analysis is made, preserving the order of classical cases, and the numerical performance is studied in order to confirm the results in the theory. It is shown that these methods can present some numerical advantages versus their classical partners, with wide sets of converging initial estimations.

In this paper, an iterative procedure to find the solution of a nonlinear structural model is introduced. The model presents different multiplicities where parameters are randomly selected within a solvability region. To achieve this aim, a class of multipoint fixed-point iterative schemes for single roots is modified to find multiple roots, reaching the fourth order of convergence. Complex discrete dynamics techniques are employed to select the members with the most stable performance. The structural problem, as well as some academic problems involving multiple roots, are solved numerically to verify the theoretical analysis, robustness and applicability of the proposed scheme.

At present paper, we aim to study the long-time behavior of a stochastic semi-linear degenerate parabolic equation on bounded or unbounded domain and driven by a nonlinear noise and defined. Since the theory of pathwise random dynamical systems can not be applied directly to the equation with nonlinear noise, first, we establish the existence of weak pullback mean random attractors for the equation by applying the theory of mean-square random dynamical systems; then, we prove the existence of (pathwise) pullback random attractors for the Wong-Zakai approximate system of the equation. In addition, we establish the upper semicontinuity of pullback random attractors for the Wong-Zakai approximate system of the equation under consideration driven by a linear multiplicative noise.

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.

The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical kinetic and potential energy-like terms. A method to derive these Lagrangians is presented and applied to selected theoretical models of the population dynamics. The role of the derived Lagrangians and the energy-like terms in the population dynamics is investigated, and it is shown that the obtained standard Lagrangians can be used to study oscillatory behavior of the models and the period of their oscillations, which may have ecological and environmental implications. These and other physical and biological insights gained from the derived standard Lagrangians are discussed.

This research investigates the impact of oil price fluctuations on food prices in Saudi Arabia between 1979 and 2020 using Nonlinear Autoregressive Distributed Lags (NARDL) methodology. The study employs Augmented Dickey-Fuller (ADF) and Phillip Perron (PP) tests to determine the integration order of the variables and Bounds testing to confirm the existence of long-run cointegration relationships between each variable. The results indicate that oil shocks influence food prices through several mechanisms. Firstly, the cost of energy increases due to the rise in oil prices, affecting the agricultural commodity market, including farm equipment, food processing, packaging, and distribution costs. Secondly, the demand for agricultural commodities to produce biofuels affects food availability and, thus, food prices. Thirdly, as an oil-based economy, the oil price shock affects food prices through its impact on government spending, which affects aggregate demand and liquidity. Therefore, Saudi Arabia should adopt appropriate policies to mitigate the impact of oil price shocks on food prices, including investing in renewable energy sources, diversifying its economy, and improving food production and supply chain efficiency. Additionally, implementing appropriate fiscal policies to ensure sufficient budget allocation for food support programs is crucial. However, investing in groundwater exploration can contribute significantly to the development of Saudi agriculture and to gradually achieving food self-sufficiency.

This paper applied the space-time generalized finite difference scheme for solving the nonlinear dispersive shallow water waves as the modified Camassa−Holm equation, modified Degasperis-Procesi equation, Fornberg-Whitham equation, and its modified form. The proposed meshless numerical scheme was composed of the space-time generalized finite difference method, the two-step Newton-Raphson method, and the time-marching method. The space-time approach can treat the temporal derivative as one of the spatial derivatives. This numerical technique enables all the partial derivatives in the governing equation can be discretized by a spatial discretization method, and the mixed derivative can efficiently deal with using the proposed meshless numerical scheme. The space-time generalized finite difference method is advanced from the Taylor series expansion and the moving-least square method. The numerical discretization process is only related to functional data and weighting coefficients on the central node and its nearby nodes. Thus, the matrix system composed of nonlinear algebraic equations will be a sparse matrix and can be efficiently solved by the two-step Newton-Raphson method. Furthermore, the time-marching method was utilized to proceed with the space-time domain along the time axis. In this paper, several numerical examples were tested to verify the capability of the proposed space-time generalized finite difference scheme.

The complexity of objects and control systems increases the requirements for mathematical models. The structural identifiability (SI) assessment of nonlinear systems is one of the identification problems. Until now, this problem solves by parametric methods using various approximation methods. This approach is not always effective under uncertainty. We apply an approach to SI estimation based on the analysis of virtual structures. The requirements form for the system input based on the expansion of the excitation constancy property and S-synchronizability. The approach generalization to structural identifiability used in the analysis of systems with symmetric nonlinearity is given. homothety and identifiability conditions for systems with non-symmetric nonlinearities (SNN) obtained. The detectability and recoverability proofed for virtual frameworks (VF) guaranteed the SI estimation under uncertainty. The conditions under which the non-symmetric nonlinearity is hypothetical symmetric nonlinearity obtained. SI estimation examples considered for closed nonlinear systems under uncertainty.

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 firstly present two popular space discretization models of the Nonlinear Schrödinger Equation in dark solitons motion : the Direct-Discrete model and the Ablowitz-Ladik model. Applying the midpoint scheme to the space discretization models, we get two time-space discretization models: the Crank-Nicolson method and the New-Difference method. Secondly, we demonstrate that the solutions of the two space discretization models converge to the solution of the Nonlinear Schrödinger Equation. Also, we prove that the convergence order of the two time-space discretization models are O(h2+τ2) in discrete L2-norm error estimates. Finally, the numerical experiments agree well with the proven theoretical results.

A nonlinear MEMS multimass sensor is investigated. The MEMS design consists of an array of nonlinear microcantilevers clamped to a shuttle mass which, in turn, is attached to a linear spring and a dashpot. The microcantilevers are made of a polymeric hosting matrix reinforced by aligned carbon nanotubes (CNT) with different CNT volume fractions in each cantilever so as to suitably tune the frequency bandwidth of the device. The advantages of a single input-single output (SISO) system are here exploited for the design, actuation and detection principles as in previous literature.

This study presents the solution of the second type of a two-dimensional nonlinear integral equation in Banach space. Also, the existence and uniqueness of this equation’s solution are discussed. We utilize a numerical approach involving hybrid and block-pulse functions to obtain the approximate solution of a two-dimensional nonlinear integral equation. Nonlinear integral equation in two dimensions is reduced numerically to a system of nonlinear algebraic equations that can be solved using numerical methods. This study focuses on showing the convergence analysis for the numerical approach and obtaining an error estimate. Some numerical examples have been provided to demonstrate the approach’s viability and efficacy

A deterministic compartment model for the transmission dynamics of onchocerciasis with nonlinear incidence functions in two interacting populations is studied. The model is quantitatively analyzed to investigate it's local asymptotic behavior with respect to disease-free and endemic equilibria. It is shown, using Routh-Hurwitz criteria, that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number is less than the unity. When the reproduction number is greater than the unity, we prove the existence of a locally asymptotically stable endemic equilibrium. Furthermore, bifurcation analysis was done by investigating the possibility of the co-existence of the equilibria of the model at R0<0 but near R0=0 by Center Manifold Theory.

Winter frost injury is a major limiting factor for olive cultivation in temperate regions. The response of olive shoots to freezing stress can be used for selecting resistant genotypes to freezing. The electrolyte leakage (EL) and tetrazolium tests (TZ) are commonly used to evaluate dead tissues in cold stress studies. The temperature-response curve of dead tissues to lethal temperature (LT) is measured with models to calculate LT50 and LT90. In this study, we evaluated the accuracy and efficiency of eighteen non-linear regression models (NLRs) in calculating LT50 and LT90 of freezing stress in different olive cultivars at various stages of dormancy. After evaluating the prediction performance of NLR models, it was found that only eight models were suitable for the purpose of this research out of the 18 models examined. The 2p-logistic and Gompertz models were selected for modeling EL and TZ, respectively. Our research findings indicate that the Roughani, Kawi, and Zard varieties of olive trees exhibit the best performance in cold weather conditions. Our findings provide valuable insights into selecting frost-resistant cultivars and designing effective strategies for cold acclimation in olive cultivation.

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.

Being one of the most critical phases of a flight, landing deserves specific attention, especially when the aircraft is subject to external disturbances such as wind. A notable concern associated with touchdown events, especially when crosswind is present is tire wear. This work is aimed first at developing a nonlinear flight simulator able to handle the entire landing maneuver in non-null wind conditions, considering the airborne phase, ground run, and the transition between them. Then, the simulator is included in an optimal process to define the landing technique associated with the minimum tire wear. The methodology is tested in a simulation environment with a realistic model of a reference aircraft, showing that a significant reduction of tire wear can be obtained by optimizing the sideslip angle at touchdown and the lateral-directional controls after the airplane touches the runway with both legs of the main landing gear.

The heat release response of the flame to acoustic excitation is a critical factor for understanding combustion instability. In the present work, the nonlinear heat release response of a methane-air non-premixed flame to the low frequency acoustic excitations is experimentally investigated. The flame describing function (FDF) was measured based on the overall CH* chemiluminescence intensity and the velocity fluctuations obtained by two-microphone method. The CH* chemiluminescence images and the schlieren images were analyzed to reveal the mechanism of nonlinear response. The excitation frequency ranges from 10Hz to 120Hz. The forced relative velocity fluctuation amplitude ranges from 0.10 to 0.50. The corresponding flame Strouhal number (Stf) ranges from 0.43 to 4.67. The study has shown that the flame length responds more sensitively to changes in excitation amplitude when subjected to relatively high frequency excitations. The normalized flame length (Lf/D) decreases from 3.79 to 2.37 with the increase of excitation amplitude at excitation frequency of 100Hz. The number of oscillation zones along the flame increases with increasing excitation frequency, which is consistent with the increase of the Stf. The low-pass filtering characteristic of FDF is caused by the dispersion of multiple oscillation zones, as well as the cancellation effect of the adjacent oscillation zones under relatively high frequency excitation. The cancellation effect of the positive and negative oscillation zones with various Stf is main mechanism for the local gain peak and valley. When two adjacent oscillation regions have approximate amplitudes, the overall phase-lag becomes more sensitive to changes in excitation frequency and amplitude. This sensitivity leads to nonlinear anomalous changes in the phase-lag near the frequency corresponding to the gain valley. The calculated disturbance convection time is consistent with the measured time delay in the short flame scenario. Future research is necessary to establish whether the observed agreement occurs due to the oscillation zone consistently occurring proximate to the flame's center of mass, coupled with a precise determination of the average convective velocity.

Broadband reverse saturable absorption is systematically investigated via Z-scan, transient absorption spectrum (TAS). The excited state absorption and negative refraction of Orange IV are observed in the Z-scan experiment at 532 nm. Meanwhile, two-photon induced excited-state absorption and pure two-photon absorption are observed at 600 nm and 700 nm with the pulse width of 190 fs, respectively. An ultrafast broadband absorption in visible wavelength region is observed via TAS. The different nonlinear absorption mechanism at multiple wavelengths is discussed and interpreted from the results of TAS. In addition, the ultrafast dynamics of negative refraction in the excited state of Orange IV is investigated via degenerate phase object pump probe, from which the weak long-lived excited state is extracted. All studies indicate that Orange IV has the potential to be further optimized into a superior broadband reverse saturable absorption material and also has certain reference significance for the study of optical nonlinearity in organic molecules containing azobenzene groups.

The near-infrared (NIR) organic dyes with strong ultrafast nonlinear optical (NLO) activities are of importance for various applications. However, such kinds of dyes are still scarce. In this work, we have compared the NLO properties of two NIR Aza-BODIPY derivatives, in which the strong electron-donating groups, namely 4-(N, N-dimethylamino) phenyl and 1-ethyl-1,2,3,4-tetrahydroquinoline groups, are connected with the cores of Aza-BODIPY. Z-Scan experimental results show that two Aza-BODIPY derivatives exhibit strong saturation absorption and large modulation depth under the excitation of femtosecond pulses at 800 nm. Under 1300 nm excitation, two derivatives exhibit strong nonlinear refraction. In addition, the Aza-BODIPY derivatives also display effective two-photon excited fluorescence emission in the wavelength range of 1200-1600 nm. Based on the experimental results, it is found that 1-ethyl-1,2,3,4-tetrahydroquinoline group can more effectively enhance the NLO properties of Aza-BODIPY derivatives compared with the 4-(N, N-dimethylamino) phenyl group, thus providing new possibilities for the design and development of NIR NLO materials.