The instability of traveling pulses in nonlinear diffusion problems is inspected on the example of Gunn domains in semiconductors. Mathematically the problem is reduced to the calculation of the "energy" of the ground state in Schrödinger equation with a complicated potential. A general method to obtain the bottom-part spectrum of such equations based on the approximation of the potential by square wells is proposed and applied. Possible generalization of the approach to other types of nonlinear diffusion equations is discussed.

Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to a HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here, we unveil the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states which are also BICs in a laser-written second-order topological lattice, and further demonstrate their nonlinear coupling with edge (but not bulk) modes under the proper action of both self-focusing and defocusing nonlinearities. Theoretically, we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by nonlinearity in such an HOTI. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.

This paper presents a study on the influence of the frequency variation of a nonlinear1 control allocation technique execution, developed by the author [1], named by Fast Control2 Allocation (FCA) for the Quadrotor Tilt-Rotor (QTR) aircraft. Then, through Software In The3 Loop (SITL) simulation, the proposed work considers the use of Gazebo, QGroundControl, and4 Matlab applications, where different frequencies of the FCA can be implemented separated in5 Matlab, always analyzing the QTR stability conditions from the virtual environment performed in6 Gazebo. TheresultsshowedthattheFCAneedsatleast200HzoffrequencyfortheQTRsafeflight7 conditions, i. e., 2 times smaller than the main control loop frequency, 400 Hz. Lower frequencies8 than this one would case instability or crashes during the QTR Operation.

The maximization of entropy S within a closed system is accepted as an inevitability (as the second law of thermodynamics) by statistical inference alone. The Maximum Entropy Production Principle (MEPP) states that not only S maximizes, but $\dot{S}$ as well: a system will dissipate as fast as possible. There is still no consensus on the general validity of this MEPP, even though it shows remarkable explanatory power (both qualitatively and quantitatively), and has been empirically demonstrated for many domains. In this theoretical paper I provide a generalization of entropy gradients, to show that the MEPP actually follows from the same statistical inference, as that of the 2nd law of thermodynamics. For this generalization I only use the concepts of super-statespaces and microstate-density. These concepts also allow for the abstraction of 'Self Organizing Criticality' to a bifurcating local difference in this density, and allow for a generalization of the fundamentally unresolved concepts of 'chaos' and 'order'.

As paradigm of complex behavior, Self-organized Criticality (SOC) reflects the ability of nonequilibrium dynamical systems to self-adjust into metastable states that are scale independent. The goal of this report is to tentatively show that the hierarchy of Standard Model masses and mixing angles follows from the universal scaling attributes of SOC.

The work is devoted to the study of a MEMS resonator dynamics under the action of phase-locked and automatic gain control loops. Particular attention is directed to the study of the nonlinearity factor of the resonator elastic restoring force. It was found that the determination of control system parameters based on the stability analysis of the operating resonant mode, in the general case, does not provide the required phase adjustment and stabilization of the oscillation amplitude. Stable multifrequency modes of oscillations are found, an analytical study of the mechanisms of their appearance and evolution is carried out under variation of the key parameters of the system. The real regions of the control system stable operation are determined (which do not coincide, as was found, with the regions of stability of the operating resonant mode, due to the presence of hidden attractors in the phase space of the system). A methodology has been developed for identifying such areas of stable operation. A significant complication of the structure of possible motions in the system with an increase in the Q-factor of the resonator is revealed.

In this manuscript, we present a high-fidelity physics-based truth model of a Single Machine Infinite Bus (SMIB) system. We also present reduced-order control-oriented nonlinear and linear models of a synchronous generator-turbine system connected to a power grid. The reduced-order control-oriented models are next used to design various control strategies such as: proportional-integral-derivative (PID), linear-quadratic regulator (LQR), pole placement-based state feedback, observer-based output feedback, loop transfer recovery (LTR)-based linear-quadratic-Gaussian (LQG), and nonlinear feedback-linearizing control for the SMIB system. The controllers developed are then validated on the high-fidelity physics-based truth model of the SMIB system. Finally, a comparison is made of the performance of the controllers at different operating points of the SMIB system.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

Using a nonclassical symmetry of nonlinear reaction-diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen-Cahn-Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near the critical temperature. Solutions are given for the changing phase of a cylindrical or spherical inclusion, allowing for a 'mushy zone' with mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture, depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions.

This paper studied the nonlinear vibrations of top tensioned cantilevered pipes conveying pressurized steady two-phase flow under thermal loading. The coupled axial and transverse governing partial differential equations of motion of the system were derived based on Hamilton’s mechanics with the centreline assumed to be extensible. Multiple scale perturbation method was used to resolve the governing equations, which resulted to an analytical approach for assessing the natural frequency, mode shape and the nonlinear coupled axial and transverse steady state response of the pipe. The analytical assessment reveals that at some frequencies the system is uncoupled, while at some frequencies a 1:2 coupling exists between the axial and the transverse frequencies of the pipe. Nonlinear frequencies versus the amplitude displacement of the cantilever pipe conveying two-phase flow at super critical mixture velocity for the uncoupled scenario exhibit a nonlinear hardening behaviour, an increment in the void fractions of the two-phase flow resulted to a reduction in the pipe’s transverse vibration frequencies and the coupled amplitude of the system. However, increasing the temperature difference, pressure and the presence of top tension were observed to increase the pipe’s transverse vibration frequencies without a significant change in the coupled amplitude of the system.

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind.

The results of shaking table tests from the literature on a one-story, two-bay reinforced concrete frame experiencing both shear and axial failures are compared with nonlinear dynamic analyses using simplified models designed for assessing the collapse of older reinforced concrete structures. To simulate the nonlinear behavior of columns—both those prone to shear failure and those more flexure-dominant—the one-component beam model was utilized. This model consists of a linear elastic element linked in series to a rigid-plastic linear hardening spring at each end, representing a concentrated plasticity element. To capture strength degradation through path-dependent plasticity, a negative kinematic hardening model was used, connecting points at shear and axial failure, respectively. Shear failure points were determined via pushover analysis of the shear-critical columns using Phaethon software. While the simplified model yielded reasonable predictions of the overall frame response and lateral strength degradation, the reduced computational cost of the modeling approach led to some deviations between the calculated and measured shear forces and drifts during portions of the time-history response.

(1) Objective: This study aims to lay a foundation for non-contact intensive care monitoring of premature babies. (2) Methods: Arterial oxygen saturation and heart rate were measured using a monochrome camera and a time division multiplex controlled lightning with three different wavelengths (660 nm, 810 nm and 940 nm) on a piglet model. (3) Results: Using the camera system and our newly designed algorithm for further analysis, the detection of a heartbeat and the calculation of oxygen saturation was evaluated. In motionless individuals, heartbeat and respiration were separated clearly during light breathing and only minor intervention. In this case, the mean difference between non-contact and contact saturation measurements was 0.7% (RMSE = 3.8%, MAE = 2.93%). (4) Conclusions: The new sensor has proven effective under ideal animal experiment conditions. The results allow a systematic improvement for the further development of contactless vital sign monitoring systems. The results presented here are a major step towards the development of an incubator with non-contact sensor systems for use in the neonatal intensive care unit.

Wicked problems, such as climate change, systemic poverty, and healthcare inequalities, rep- resent the most pressing and intractable challenges facing society today. We propose a novel approach that leverages complex systems theory as a comprehensive framework for understanding and tackling these challenges. By applying concepts such as state space analysis, attractors, and nonlinear dynamics, we offer a sophisticated toolkit for mapping the intricate web of interactions defining wicked problems and exploring potential interventions. Our approach moves beyond tradi- tional reductionist methods, embracing the inherent complexity and dynamism of these issues. We demonstrate how this framework can lead to more nuanced, adaptive, and effective strategies for addressing persistent societal problems. Despite the prevalence of wicked problems and the avail- ability of complex systems theory, practical applications of this approach remain uncommon. This paper aims to bridge this gap, illustrating the potential of complex systems theory to transform our engagement with intractable problems and pave the way for more robust, holistic solutions. By synthesizing insights from mathematics, physics, and social sciences, we present a transdisci- plinary approach that promises to revolutionize how we conceptualize and address society’s most challenging issues.

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 $J(t)\le \jinf \ll 1$.

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.

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.

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.

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.

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.

Nonlinear electrodynamics is known as the generalizations of Maxwell electrodynamics at strong fields and presents interesting features such as curing the classical divergences present in the linear theory when coupled to general relativity. In this paper, we consider the asymptotically flat Reissner-Nordstr\"om black hole solution with higher-order magnetic correction in Einstein-nonlinear-Maxwell fields. We study the effect of the magnetic charge parameters on the black hole, viz. weak deflection angle of photons and massive particles using Gauss-bonnet theorem. Moreover, we apply the Keeton-Petters formalism to confirm our results of the weak deflection angle. Apart from vacuum, their influence in the presence of different media such as plasma and dark matter are probed as well. Finally, We examine the black hole shadow cast using the null-geodesics method and investigate its spherically in-falling thin accretion disk. Our inferences show how the magnetic charge parameter $p$ affects the other physical quantities; so, we impose some constraints on this parameter using the observations from the Event Horizon Telescope.

In this project, our foremost intention is to analyze the angle of deflection of photon by NED black holes with many horizons in the context of non-linear electrodynamics. For the accomplishment of our intention at first we manipulated the optical metric of the desired black holes for the calculation of Gaussian curvature. After that, the angle of deflection in leading orders is attained from the desired black holes in weak field limit by using the famous Gauss-Bonnet theorem. Moreover, we evince the effect of plasma medium on the angle of deflection. At last, the graphical impact of the angle of deflection for NED black holes with many horizons is examined with respect to black hole charge and impact parameter in both the plasma and non plasma medium. In addition, we discuss the rigorous bound for grey body factor of the desired black hole and also observer its graphical behavior.

Refinery planning optimization is a challenging problem as regards handling the nonconvex bilinearity mainly due to pooling operations in processes such as crude oil distillation and product blending. This work investigates the performance of several representative piecewise-linear (or piecewise-affine) relaxation schemes (referred to as McCormick, bm, nf5, nf6t, and de (which is a new approach proposed based on eigenvector decomposition) that mainly give rise to mixed-integer optimization programs to convexify a bilinear term using predetermined univariate partitioning for instances of uniform and non-uniform partition sizes. Computational results show that applying these schemes give improved relaxation tightness than only applying convex and concave envelopes as estimators. Uniform partition sizes typically perform better in terms of relaxation solution quality and convergence behavior. It is also seen that there is a limit on the number of partitions that contributes to relaxation tightness, which does not necessarily correspond to a larger number of partitions, while a direct relation between relaxation size and tightness does not always hold for non-uniform partition sizes.

Our earlier work has tentatively shown that the hierarchy of fermion masses and mixing angles follows from the universal behavior of nonlinear dynamics. In this brief sequel we survey a similar scenario in which the Cabibbo angle arises from the nonlinear dynamics of charged-current interactions.

In this paper, we study the third order semilocal convergence of the Newton-like method for finding the approximate solution of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis under ω-continuity condition, which is weaker than the Lipschitz and Hölder continuity conditions. Second, we apply our approach to solve Fredholm integral equations, where the first derivative of involved operator not necessarily satisfy the Hölder and Lipschitz continuity conditions. Finally, we also prove that the R-order of the method is 2p + 1 for any p $\in$ (0,1].

The key objective of the present paper is to propose a numerical scheme based on the homotopy analysis transform technique to analyze the time-fractional nonlinear predator-prey population model. The population model is coupled fractional order nonlinear partial differential equations often employed to narrate the dynamics of biological systems in which two species interact, first is a predator and the second is a prey. The proposed scheme provides the series solution with great freedom and flexibility by choosing appropriate parameters. The convergence of results is free from small or large parameters. Three examples are discussed to demonstrate the correctness and efficiency of the used computational approach.

This paper presents a robust control strategy for trajectory tracking control of Skid-Steer Mobile Manipulators (SSMMs) using a Robust Nonlinear Model Predictive Control (R-NMPC) approach that minimizes trajectory tracking errors while overcoming model uncertainties and terra-mechanical disturbances. The proposed strategy aims to counteract disturbance effects caused by the slip phenomena through the wheel-terrain contact and bidirectional interactions propagated by the mechanical coupling between the SSMM base and arm. To capture such interactions, the mobile base dynamics and arm joints consider a coupled nonlinear model with bounded uncertainties based on principles of full-body energy balance and link torques. In addition, the SSMM dynamics stands by dynamical models, which are capable of capturing nonlinear speed relationships. Thus, a centralized control architecture integrates a nominal and ancillary controller based on the Active Disturbance Rejection Control (ADRC) to strengthen robustness of the Nonlinear Model Predictive Control (NMPC), operating the SSMM dynamics as a single robotic body. The NMPC is responsible for trajectory tracking control of a five Degrees of Freedom (DoF)’s SSMM. Meanwhile, the ADRC uses an Extended State Observer (ESO) to quantify the impact of external disturbances and uncertainties, generating compensation for unmeasurable disturbances. In addition, the proposed robust control strategy compensates for the model mismatch errors, which are generated by the difference between an SSMM nominal model (disturbance-free) and its real-time response. Results indicate that the approach is able to compensate for effects by 70% using pre-set trajectories and regulation tests against unmeasurable disturbances applied to simulated SSMR model.

Metal–organic framework materials show feature linear- and nonlinear optical responses such as laser damage threshold, outstanding mechanical properties, thermal stability, and optical transparency as innovative functional materials for nonlinear optical technologies. The non-centrosymmetric crystal structure is precondition for generation of second-order nonlinear optical response, which guarantees technological applications. The ZnII- and AgI-squarate complexes are attractive templates for these purposes due to good crystal growth, optical transparency, high thermal stability, etc. However, debatable is the space group type of catena-((μ2-squarato)-tetra-aqua-zinc(II)) complex ([Zn(C4O4)(H2O)4]) (1) showing centro- and non-centro-symmetric monoclinic C2/c and Cc phases. The same is valid to catena-((μ3-squarato)-(μ2-aqua)-silver(I)) complex (Ag2C4O4) (2) exhibiting, so far, only C2/c phase. This study reports first new crystallographic data on (1) and (2) re-determined at different temperatures (293(2) and 300(2)K) and non-centro-symmetric Cc phase of (2), having different number molecules per unit cell comparing with C2/c phase. There are high-resolution crystallographic measurements of single crystals, experimental electronic absorption and vibrational spectroscopic data together with ultra-high resolution mass spectrometric ones. Experimental results are supported for theoretical optical and nonlinear optical properties obtained via high accuracy quantum chemical static methods and molecular dynamics, using density functional theory as well as chemometrics.

The nonlinear dynamics exhibited by aircraft flying at high angle of attack (AOA) pose great challenges to the design of flight control. The control design based on nonlinear dynamic inversion (NDI) is to reversely find the required control input based on the current nonlinear dynamics of the aircraft and the control objectives to be achieved. Since it is derived from the nonlinear dynamics of the aircraft, a single NDI controller can cover the entire flight envelope without the need for controller switching or gain scheduling. This paper employs the layered structure of the flight control loop to implement the NDI controller through the combination of aerodynamic control and thrust vectoring control (TVC). The resulting NDI controller is applied to an experimental F-16 installed with TVC to verify its high AOA maneuverability in the post-stall region. The verification simulation shows that the experimental F-16 under the NDI control can effectively track the high AOA command and successfully demonstrate the Herbst maneuver by performing the heading reversal with 70° AOA.

Approximate entropy (ApEn) and sample entropy (SampEn) are statistical indices designed to quantify the regularity or predictability of time series data. Although ApEn has been a prominent choice for use in the analysis of non-linear data, it is currently unclear as to which method and parameter selection combination is optimal for its application in biomechanics. The goal of this research was to examine the differences between ApEn and SampEn related to center of pressure (COP) data during tandem standing balance tasks, while also changing the tolerance window, r. Six participants completed five, 30-second trials, feet-together and tandem standing with eyes-open and eyes-closed. COP data (fs = 60 Hz, downsampled from 1200 Hz) from ground reaction force platforms were collected. ApEn and SampEn were calculated using a constant vector length, i.e., m = 2, but differing values of r (tolerance window). For each of the participants, four separate one-way analysis of variance analyses (ANOVA) were conducted for ApEn and SampEn in the anterior-posterior (AP) and medial-lateral (ML) directions. Dunnett's intervals were applied to the one-way ANOVA analyses to determine which tandem conditions differed significantly from the baseline condition. ApEn and SampEn provided comparable results in the predictability of patterns for different stability conditions, with increasing instability, i.e., tandem eyes closed postures, being associated with greater unpredictability. The selection of r had a relatively consistent effect on mean ApEn and SampEn values across r = 0.15 * SD to r = 0.25 * SD, where both entropy methods tended to decrease as r increased. Mean SampEn values were generally lower than ApEn values. The results suggest that both ApEn and SampEn indices demonstrated relative consistency and were equally effective in quantifying the level of the center of pressure signal regularity during quiet tandem standing postural balance tests.

In order to make full use of the complementarity of existing navigation systems to improve the navigation and positioning accuracy, this paper investigates the visual/INS integrated navigation system based on the factor graph optimization (FGO) algorithm. In the traditional visual/INS integrated navigation system, there is often the problem of image blurring due to the rapid change of light and shadow captured by the vision sensor and the attitude change of the carrier, which leads to the decrease of the positioning accuracy of the combined navigation system. Therefore, this paper firstly introduces Retinex algorithm and BID algorithm to carry out the design of image de-blurring method; then implements the visual/INS integrated navigation algorithm based on the factor graph optimization method; finally, the experimental scheme is designed, comparative experiments are carried out, and the researched method is verified by using the public dataset. The experimental results show that the combined navigation algorithm realized in this paper has high accuracy, and its positioning accuracy is improved by 40% compared with visual positioning.

This work explores state-of-the-art approaches for stabilizing an inverted pendulum on a cart system, which has been used for over a century to demonstrate ideas in nonlinear and linear control theory, owing to its simple practical implementation yet complex system dynamics. We introduce energy-based control methods and propose a simple linear controller to quickly force the system to the downward equilibrium before swing-up. By constraining the system to start from a stable equilibrium configuration, the problem of global stability is reduced to ensuring that the system can follow all heteroclinic orbits that start very close to the downward equilibrium. Multiple Lyapunov functions are employed to ensure non-zero tracking, increasing the system's domain of attraction than is achieved by traditional controllers based on a single Lyapunov function. We stabilize our inverted pendulum system in the upright configuration through pole placement using a linear quadratic regulator known for fast settling times and smooth system response and through sliding mode controllers known for their robustness to disturbances and model uncertainties. While sliding mode controllers exhibit faster stabilization of the pendulum angle, they fail to stabilize the cart position in a reasonable amount of time. The paper concludes by suggesting various controller techniques that can enhance the swing-up and stabilization controller architectures, leaving room for future exploration. To facilitate further research and education, an open-source MATLAB simulation code is provided, encapsulating the system dynamics and controller designs. This resource offers flexibility for customization, making it a valuable tool for both researchers and educators working with inverted pendulum systems.

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.

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.

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.

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.

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.

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.

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.

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

The shape of the knee is a chain-like structure of an ellipsoid. This suggests that, in the latest study, in addition to rolling, there is slippage in the motion of the knee. This paper selects a mechanical braking model for cattle based on two mechanical structures in different directions at the joints. The experimental results show that the modified dynamical system has strong chaotic properties. This can be one of the basis for judging various health states.

New modied Hayward metric of magnetically charged non-singular black hole spacetime in the framework of nonlinear electrodynamics is constructed. When the fundamental length introduced, characterising quantum gravity effects, vanishes one comes to the general relativity coupled with the Bronnikov model of nonlinear electrodynamics. The metric can have one (an extreme) horizon, two horizons of black holes, or no horizons corresponding to the particle-like solution. Corrections to the Reissner-Nordström solution are found as the radius approaches to innity. As r -> 0 the metric has a de Sitter core showing the absence of singularities. The asymptotic of the Ricci and Kretschmann scalars are obtained and they are nite everywhere. The thermodynamics of black holes, by calculating the Hawking temperature and the heat capacity, is studied. It is demonstrated that phase transitions take place when the Hawking temperature possesses the maximum. Black holes are thermodynamically stable at some range of parameters.

This paper studies on aeroelastic control for the two-dimensional airfoil-flap system with unknown gust disturbances and model uncertainties. Open loop limit cycle oscillation (LCO) happens at the post-flutter speed. Structural stiffness of the aeroelastic system is represented by nonlinear polynomials. To robustly suppress aeroelastic vibration within finite time, a backstepping terminal sliding mode control (BTSMC) is proposed. In addition a learning rate is incorporating into the backstepping TSMC to adjusthow fast the aeroelastic response converges to zero. In order to overcome the limitation of the BTSMC design that it is dependent on prior knowledge, a nonlinear disturbance-observer (DO) is designed to estimate the variable observable disturbances. The closed-loop aeroelastic control system is proved to be globally asymptotically stable and converge within finite time by using Lyapunov theory. Simulation results of an aeroelastic two-dimensional airfoil with both trailing-edge (TE) and leading-edge (LE) control surfaces show that the proposed DO-BTSMC is effective for flutter suppression, even when subjected to gusts and parameter uncertainties.

We investigate emergent conductive phenomena triggered by collinear antiferromagnetic orderings. We show that an up-down-zero spin configuration in a triangle cluster leads to linear and nonlinear spin conductivities even without the relativistic spin–orbit coupling; the linear spin conductivity is characterized by the Drude-type one, while the nonlinear spin conductivity is characterized by the Hall-type one. We demonstrate the emergence of both spin conductivities in the breathing kagome system consisting of a triangle cluster. The nonlinear spin conductivity becomes larger than the linear one when the Fermi level lies near the region where a small partial band gap opens. Our results indicate that collinear antiferromagnets with the triangle geometry give rise to rich spin conductive phenomena.

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 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.

Many problems in the fields of finance and actuarial science can be transformed into the problem of solving backward stochastic differential equations (BSDE) and partial differential equations (PDE) with jumps, which are often difficult to solve in high-dimensional cases. To solve this problem, this paper applies the deep learning algorithm to solve a class of high-dimensional nonlinear partial differential equations with jump terms and their corresponding backward stochastic differential equations (BSDE) with jump terms. Using the nonlinear Feynman-Kac formula, the problem of solving this kind of PDE is transformed into the problem of solving the corresponding backward stochastic differential equations with jump terms, and the numerical solution problem is turned into a stochastic control problem. At the same time, the gradient and jump process of the unknown solution are separately regarded as the strategy function and they are approximated respectively by using two multilayer neural networks as function approximators. Thus, deep learning-based method is used to overcome the “curse of dimensionality” caused by high-dimensional PDE with jump, and the numerical solution is obtained. In addition, this paper proposes a new optimization algorithm based on the existing neural network random optimization algorithm, and compares the results with the traditional optimization algorithm, and achieves good results. Finally, the proposed method is applied to three practical high-dimensional problems: Hamilton-Jacobi-Bellman equation, bond pricing under the jump Vasicek model and high-dimensional option pricing model with default risk. The proposed numerical method has obtained satisfactory accuracy and efficiency. The method has important application value and practical significance in investment decision-making, option pricing, insurance and other fields.

The most common source of transformer failure is in the insulation, and the most prevalent warning signal for insulation weakness is partial discharge (PD). Locating positons of these partial discharges would help repair the transformer to prevent failures. This work investigates algorithms that could be deployed to locate the position of a PD event using data from ultra-high frequency (UHF) sensors inside the transformer. These algorithms typically proceed in two steps: first determine the signal arrival time and then locate the position based on time differences. This paper reviews available methods for each task and then propose new algorithms: a convolutional iterative filter with thresholding (CIFT) to determine the signal arrival time and a reference table of travel times to resolve the source location. The effectiveness of these algorithms are tested with a set of laboratory-triggered PD events and two sets of simulated PD events inside transfers in production use. Tests show the new approach provides more accurate locations than the best-known data analysis algorithms, and the difference is particularly large, 3.7X, when the signal sources are far from sensors.

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

We report the results of an analysis of the functional capabilities of the KTP crystal and its isomorphs for nonlinear-optical frequency conversion of all types of interaction in the transparency range of the crystal. The possibility of implementing angle-, wavelength- (frequency-) and temperature-noncritical phase matching is shown.

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

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

Germanium (Ge) is a system-forming material of IR photonics for the atmospheric transparency window of 8 – 14 µm. For optics of the 3 – 5 µm range, more widespread silicon (Si), which has phonon absorption bands in the long-wave region, is predominantly used. A technology for growing Ge single crystals has been developed, allowing the production of precision optical parts up to 500 mm in diameter. Ge is used primarily for the production of transparent optical parts for thermal imaging devices in the 8 – 14 µm range. In addition, germanium components are widely used in a large number of optical devices where such properties as mechanical strength, good thermal properties and climatic resistance are required. A very important area of application of germanium is nonlinear optics, primarily acousto-optics. The influence of doping impurities and temperature on the absorption of IR radiation in germanium is considered in detail. The properties of germanium photodetectors are reported, primarily on the effect of photon drag of holes. Optical properties in the THz range are considered. The features of optical properties for all five stable isotopes of germanium are studied. The isotopic shift of absorption bands in the IR region, caused by phonon phenomena, which was discovered by the authors for the first time, is considered.

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

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.

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.

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.

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.

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.

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.

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

The main idea of this paper is to investigate the exact solutions and dynamic properties in optical nanofibers, which is modeled by space-time fractional perturbed nonlinear schr\"odinger equation involving Kerr law nonlinearity with conformal fractional derivative. Firstly, by the complex fractional traveling wave transformation, the traveling wave system of the original equation is obtained, then a conserved quantity, namely the Hamiltonian is constructed, and the qualitative analysis of this system is conducted via this quantity by classifying the equilibrium points. Moreover, the prior estimate of the existence of the soliton and periodic solution is established via the bifurcation method. Furthermore, all exact traveling wave solutions are constructed to illustrate our results explicitly by the complete discrimination system for polynomial method.

In the present work we propose a dynamical mathematical model of the lung cells inflammation process in response to SARS-CoV-2 infection. In this scenario the main protease Nsp5 enhances the inflammatory process, increasing the levels of NF kB, IL-6, Cox2, and PGE2 with respect to a reference state without the virus. In presence of the virus the translation rates of NF kB and IkB arise to a high constant value, and when the translation rate of IL-6 also increases above the threshold value of 7 pg mL^-1 s^-1 the model predicts a persistent over stimulated immune state with high levels of the cytokine IL-6. Our model shows how such over stimulated immune state becomes autonomous of the signals from other immune cells such as macrophages and lymphocytes, and does not shut down by itself. We also show that in the context of the dynamical model presented here, Dexamethasone or Nimesulide have little effect on such inflammation state of the infected lung cell, and the only form to suppress it is with the inhibition of the activity of the viral protein Nsp5.To that end, our model suggest that drugs like Saquinavir may be useful. In this form, our model suggests that Nsp5 is effectively a central node underlying the severe acute lung inflammation during SARS-CoV-2 infection. The persistent production of IL-6 by lung cells can be one of the causes of the cytokine storm observed in critical patients with COVID19. Nsp5 seems to be the switch to start inflammation, the consequent overproduction of the ACE2 receptor, and an important underlying cause of the most severe cases of COVID19.

The simultaneous evaluation of heat/mass transference procures momentous significance in the polymer industry and engineering activities. Extensive utilization of such aspects includes propylene flares, heat exchangers, energy transfiguration in chilling towers, and amputation of post fortuitous heat in nuclear reactors. Owing to such prospective demands, we interpreted the Jeffrey liquid reactive flow under non-linear convection. We scrutinized the transference of heat/mass under generalized Fourier-Fick relations. Thermal conductivity depends on temperature while mass diffusivity is dependent on concentration. Besides, heat source along with first-order chemical reaction aspects are accounted for. Relevant transformations are exerted to achieve non-linear differential systems that are solved through the homotopy scheme. Influences of divers factors are exhibited via graphical benchmark.

Bayesian model calibration techniques are commonly employed in the characterization of nonlinear dynamic systems, as they provide a conceptual and effective framework to deal with model uncertainties, experimental errors and procedure assumptions. This understanding has resulted in the need to introduce a model discrepancy term to account for the differences between model-based predictions and real observations. Indeed, the goal of this work is to enhance model-driven Structural Health Monitoring procedures by incorporating the posterior uncertainty linked to updated model discrepancy, and thus make relevant considerations for its use in the Structural Health Monitoring. Specifically, the Bayesian inference has been applied to the calibration of nonlinear hysteretic systems to both provide: (i) most probable values (MPV) of the parameters following the calibration, and; (ii) estimates of the model discrepancy posterior distribution. The effect of the model discrepancy in the calibration is first illustrated recurring to a single degree of freedom Bouc-Wen type oscillator, and then applied for calibrating a reference nonlinear Bouc-Wen model, deriving from real data acquired on a monitored masonry building.

The solution of structural problems with nonlinear material behaviour in a model order reduction framework is investigated in this paper. In such a framework, greedy algorithms or adaptive strategies are interesting as they adjust the reduced order basis (ROB) to the problem of interest. However, these greedy strategies may lead to an excessive increase in the size of the reduced basis, i.e. the solution is no more represented in its optimal low-dimensional expansion. Here, an optimised strategy is proposed to maintain, at each step of the greedy algorithm, the lowest dimension of the PGD basis using a randomised SVD algorithm. Comparing to conventional approaches such as Gram-Schmidt orthonormalisation or deterministic SVD, it is shown to be very efficient both in terms of numerical cost and optimality of the reduced basis. Examples with different mesh densities are investigated to demonstrate the numerical efficiency of the presented method.

The fault diagnosis of wind farms has been proven to be a challenging task and motivates the research activities carried out through this work. Therefore, this paper deals with the fault diagnosis of a wind park benchmark model, and it considers viable solutions to the problem of earlier fault detection and isolation. The design of the fault indicator involves data-driven approaches, as they can represent effective tools for coping with poor analytical knowledge of the system dynamics, noise, uncertainty and disturbances. In particular, the proposed data-driven solutions rely on fuzzy models and neural networks that are used to describe the strongly nonlinear relationships between measurement and faults. The chosen architectures rely on nonlinear autoregressive with exogenous input models, as they can represent the dynamic evolution of the system along time. The developed fault diagnosis schemes are tested by means of a high-fidelity benchmark model, that simulates the normal and the faulty behaviour of a wind farm installation. The achieved performances are also compared with those of a model-based approach relying on nonlinear differential geometry tools. Finally, a Monte-Carlo analysis validates the robustness and the reliability of the proposed solutions against typical parameter uncertainties and disturbances.

We discuss the dynamics of a roller coaster cart driven by a constant force along the suspended track of a winding roller coaster. The track is assumed arbitrarily long and specially shaped. It is made by semicircular track portions, in the form of valleys and hills, standing perfectly vertical in the same plane. This is a mechanical analog of a Josephson junction electrodynamics. To demonstrate the explanatory potential of the analogy, we focus particularly on the conditions of de-trapping of the cart from one of the valleys of the track. This mechanical process has its analog in a non-noise-generated premature switching to the finite voltage state of a Josephson junction.

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.

The main functions of the automated systems rely on the advanced sensors for detection and perception of the environment around the vehicle. Radars and cameras are commonly utilized to detect the potential obstacles and vehicles ahead on the road. Nevertheless, cameras can generate spurious detections in the extreme weather conditions such as fog, rain, dust, snow, dark, and heavy sunlight in the sky. Due to limitations in vertical field view of the radars, single radars are not reliable to detect the height of the targets precisely. In this paper, a triple radar arrangement (long-range, medium-range, and short-range radars) based on sensor fusion technique is proposed to detect objects with different size in level 2 Advanced Driver-Assistance (ADAS) system. The typical objects including truck, pedestrians, and animals are detected in different scenarios. The developed model considered ISO 26262 and ISO/PAS 21448 to reasonably address insufficient robustness and inability of the sensors. The models of sensor and level 2 ADAS systems are developed using MATLAB toolbox and Simulink. Sensor detection performance is determined by running simulations with triple radar setup. Obtained results demonstrate that the proposed approach generates accurate detections of targets in all tested scenarios.

Based on the nonlinear failure criterion and modified tangential technique, the upper bound solutions of supporting pressure on the deep tunnel face were obtained under pore water pressure conditions. The influence of parameters on the supporting pressure and collapse range was investigated according to the unlimited block failure mechanism. It is found that the upper bound solutions of supporting pressure increase with the growth of the nonlinear coefficient and pore water pressure coefficient. The collapse range of the tunnel face scales out with the increase of the nonlinear coefficient and shrinks when increasing the pore water pressure coefficient. Moreover, with the increase of the nonlinear coefficient, the impact strength on supporting pressure and collapse range declines gradually. According to the calculating results, it is manifest that both the pore water pressure and nonlinear criterion factors have negative impacts on the stability of the tunnel face. Thus, more attention should be paid to these parameters to ensure face stability in deep tunnel construction.

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].

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.

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 manuscript explores unmanned aerial vehicle DC motor control performance efficacy of deterministic artificial intelligence in comparison to model-following adaptation, particularly a direct self-tuner with filtering. The deterministic artificial intelligence model made use of self-awareness statements to overcome error in response to permutations of the multi-duty cycle square wave that served as the system input. It can be seen that (despite equivalently powerful estimation techniques) deterministic artificial intelligence provided far superior results: a reduction in peak initial transient error of 55%, and a mean error reduction over 81% with over 65% reduction in error standard deviation compared to a state-of-the-art nonlinear adaptive control method. Deterministic artificial intelligence also was able to very closely track at the switching of the input control, while the benchmark nonlinear adaptive control failed to respond as quickly at these points.

Gas bubbles present in liquids underpin many natural phenomena and human-developed technologies that improve the quality of life. Since all living organisms are predominantly made of water, they may also contain gas bubbles—introduced both naturally and artificially—that can serve as biomechanical sensors operating in hard-to-reach places inside a living body and emitting signals that can be detected by common equipment used in ultrasound and photoacoustic imaging procedures. This kind of biosensors is the focus of the present article, where we critically review the emergent sensing technologies based on acoustically driven oscillations of gas bubbles in liquids and bodily fluids. This review is intended for a broad biosensing community and transdisciplinary researchers translating novel ideas from theory to experiment and then to practice. To this end, all discussions in this review are written in a language that is accessible to non-experts in specific fields of acoustics, fluid dynamics and acousto-optics.

Micro-grids’ operations offer local reliability; in the event of faults or low voltage/frequency events on the utility side, micro-grids can disconnect from the main grid and operate autonomously while providing the continued supply of power to local customers. With the ever-increasing penetration of renewable generation, however, the operations of micro-grids become increasingly complicated because of the associated fluctuations of voltages. As a result, transformer taps are adjusted frequently, thereby leading to the fast degradation of expensive tap-changer transformers. In the islanding mode, the difficulties also come from the drop of voltage and frequency upon disconnecting from the main grid. To appropriately model the above, the nonlinear AC power flow constraints are necessary. Computationally, the discrete nature of tap-changer operations and the stochasticity caused by renewables add two layers of difficulty on top of a complicated AC-OPF problem. To resolve the above computational difficulties, the main principles of the recently-developed "l1-proximal" Surrogate Lagrangian Relaxation are extended. Testing results based on 9-bus system demonstrate the efficiency of the method to obtain the exact feasible solutions for micro-grid operations thereby avoiding approximations inherent to existing methods, while demonstrating that through the optimization, 1. the number of tap changes is drastically reduced, and 2. the method is capable of handling networks with meshed topologies.

The paper presents the design and the implementation of different advanced control strategies that are applied to a nonlinear model of a thermal unit. A data–driven grey–box identification approach provided the physically meaningful nonlinear continuous–time model, which represents the benchmark exploited in this work. The control problem of this thermal unit is important since it constitutes the key element of passive air conditioning systems. The advanced control schemes analysed in this paper are used to regulate the outflow air temperature of the thermal unit by exploiting the inflow air speed, whilst the inflow air temperature is considered as an external disturbance. The reliability and robustness issues of the suggested control methodologies are verified with a Monte–Carlo analysis for simulating modelling uncertainty, disturbance and measurement errors. The achieved results serve to demonstrate the effectiveness and the viable application the suggested control solutions to air conditioning systems. The benchmark model represents one of the key issues of this study, which is exploited for benchmarking different model–based and data–driven advanced control methodologies through extensive simulations. Moreover, this work highlights the main features of the proposed control schemes, while providing practitioners and heating, ventilating and air conditioning engineers with tools to design robust control strategies for air conditioning systems.

A system of two nonlinear difference equations under stochastic perturbations is considered. Nonlinearity of the exponential type in each equation of the system under consideration depends on all variables of the system. The stability in probability of a positive equilibrium of the system is studied via the general method of Lyapunov functionals construction and the method of linear matrix inequalities (LMIs). The obtained results are illustrated via examples and figures with numerical simulations of solutions of a considered system of stochastic difference equations. The proposed way of investigation can be applied to nonlinear systems of higher dimension and with other types of nonlinearity, for both difference equations and for delay differential equations.

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.

In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illsutrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.

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.

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

: In the last years, materializations of neuromorphic circuits based on nanophotonic arrangements have been proposed, which contain complete optical circuits, laser, photodetectors, photonic crystals, optical fibers, flat waveguides, and other passive optical elements of nanostructured materials, which eliminate the time of simultaneous processing of big groups of data, taking advantage of the quantum perspective and thus highly increasing the potentials of contemporary intelligent computational systems. This article is an effort to record and study the research that has been conducted concerning the methods of development and materialization of neuromorphic circuits of Neural Networks of nanophotonic arrangements. In particular, an investigative study of the methods of developing nanophotonic neuromorphic processors, their originality in neuronic architectural structure, their training methods and their optimization has been realized along with the study of special issues such as optical activation functions and cost functions.

The Landau damping effect was observed in collisionless plasma, as a microscopic resonant mechanism between electromagnetic radiation and the collective modes. In this paper we demonstrate the occurrence of the Landau damping at macroscopic scale in the interaction between water waves and anharmonic lattice of magnetic buoys. By coupling the Navier-Stokes equations for incompressible fluid with the nonlinear dynamics of an anharmonic magnetic lattice we obtain a resonant transfer of momentum and energy between the two systems. The velocity of the flow is obtained in the Stokes approximation with Basset type of drag force. The dynamics of the buoys is calculated in the surfactant approximation for a specific frequency, then we use Fourier analysis to obtain the general time variable interaction. After involving an integral Dirichlet transform we obtain the time dependent expression of the drag force, the interaction waves-lattice with a new term in the form of a Caputo fractional derivative. We compare the results of the model with experiments performed in a wave tank with free floating magnetic buoys under the action of small amplitude gravitational waves. This configuration can be applied in studies for the attenuation with resonant damping of rogue waves, storms or tsunamis.

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

This text deals with exploring random solutions for generalized nonlinear variational inequality problems. Using the Fan-KKM theorem and Aumann's measurable selection theorem, we are able to prove the existence and uniqueness of random solution sets under the conditions of monotonicity and convexity. Additionally, we use Minty's lemma to demonstrate the compactness and convexity of the random solution sets.

Frequency combs (FCs)—spectra containing equidistant coherent peaks—have enabled researchers and engineers to measure the frequencies of complex signals with high precision thereby revolutionising the areas of sensing, metrology and communications and also benefiting the fundamental science. Although mostly optical FCs have found widespread applications thus far, in general FCs can be generated using waves other than light. Here, we review and summarise recent achievements in the emergent field of acoustic frequency combs (AFCs) including phononic FCs and relevant acousto-optical, Brillouin light scattering and Faraday wave-based techniques that have enabled the development of phonon lasers, quantum computers and advanced vibration sensors. In particular, our discussion is centred around potential applications of AFCs in precision measurements in various physical, chemical and biological systems in conditions, where using light, and hence optical FCs, faces technical and fundamental limitations, which is, for example, the case in underwater distance measurements and biomedical imaging applications. This review article will also be of interest to readers seeking a discussion of specific theoretical aspects of different classes of AFCs. To that end, we support the mainstream discussion by the results of our original analysis and numerical simulations that can be used to design the spectra of AFCs generated using oscillations of gas bubbles in liquids, vibrations of liquid drops and plasmonic enhancement of Brillouin light scattering in metal nanostructures. We also discuss the application of non-toxic room-temperature liquid-metal alloys in the field of AFC generation.

Variational Auto-Encoders (VAEs) are deep generative models used for unsupervised learning, however their standard version is not topology-aware in practice since the data topology may not be taken into consideration. In this paper, we propose two different approaches with the aim to preserve the topological structure between the input space and the latent representation of a VAE. Firstly, we introduce InvMap-VAE as a way to turn any dimensionality reduction technique, given an embedding it produces, into a generative model within a VAE framework providing an inverse mapping into original space. Secondly, we propose the Witness Simplicial VAE as an extension of the Simplicial Auto-Encoder to the variational setup using a witness complex for computing the simplicial regularization, and we motivate this method theoretically using tools from algebraic topology. The Witness Simplicial VAE is independent of any dimensionality reduction technique and together with its extension, Isolandmarks Witness Simplicial VAE, preserves the persistent Betti numbers of a data set better than a standard VAE.

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.

The influence of linear and nonlinear modes of ADC driver on the operational amplifier (Op-Amp), which has different values of maximum output voltage slew rate, on the effective number of bits of ADC is considered. It is shown that the effective number of bits of ADC when op-amps on bipolar transistors with input signal amplitudes exceeding 50-100 mV is determined by the nonlinear modes of its input differential stage.

The weakness of the dispersion-managed link combined with optical phase conjugation to compensate for optical signal distortion caused by chromatic dispersion and nonlinear Kerr effect of standard single mode fiber is its limited structural flexibility. We propose dispersion map that can simultaneously compensate for the distorted wavelength division multiplexed signal while increasing the configurational flexibility. Each residual dispersion per span (RDPS) in the former half of the proposed link is randomly determined, and in the latter half, the arrangement order of RDPS is the same as or inverted in the former half. We confirm that the dispersion maps in which the RDPS distribution pattern in the latter half is opposite to the arrangement order in the former half are more effective in compensation, and rather, the compensation effect is better than in the dispersion map of the conventional scheme. The notable result of this paper is that the increase of flexibility can be achieved through random arrangement of RDPS in the former half, and the compensation improvement can be achieved by through inverse arrangement in the latter half which make the distribution profile of each half link roughly symmetric with respect to the midway optical phase conjugator.

Abstract: Nonlinear spectrum distortions are caused by the peculiarities of the operation of charge-coupled device elements (CCD), in which the signal exposition time (TINT) is one of the significant parameters. A change of TINT on a CCD leads to a nonlinear distortion of the resulting spectrum. Nonlinear distortion of the spectrum, in its turn, leads to errors in determining the central wavelength of Fiber Bragg Gratings (FBG) and spectrally sensitive sensors, which, in general, negatively affects the accuracy of measuring systems. The paper proposes an algorithm for correcting nonlinear distortions of the spectrum obtained on a spectrum analyzer using CCD as a receiver. It is shown that preliminary calibration of the optical spectrum analyzer with subsequent mathematical processing of the signal makes it possible to make corrections in the resulting spectrum, thereby leveling the errors caused by measurements at different TINT.

In the paper, by the Faά di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers and discover inverses of fifteen closely related lower triangular integer matrices.

This paper presents three approaches to estimating battery parameters of the electrical equivalent circuit model (ECM) based on electrochemical impedance spectroscopy (EIS); these approaches are referred to as (a) least squares (LS), (b) exhaustive search (ES), and (c) nonlinear least squares (NLS). The ES approach is assisted with the LS method for the rough determination of the lower and upper bound of the ECM parameters, and the NLS approach is incorporated with the Monte Carlo run such that different initial guesses can be assigned to improve the goodness of EIS fitting. The proposed approaches are validated using both simulated and real EIS data. Compared to LS approach, the ES and NLS approaches show better fitting accuracy at various noise levels; whereas both in the validation using simulated EIS data and actual EIS data collected from LG 18650 and Molicel 21700 batteries, the NLS approach shows better fitting accuracy than that of LS and ES approaches. In all cases, compared with the ES approach, the computational time of the NLS approach is significantly faster, and compared with the LS approach, the NLS approach shows a minimal difference in computational time and considerably better fitting performance.

This paper discusses approaches to the numerical integration of the coupled nonlinear Schrödinger equations system in case of few-mode wave propagation. The wave propagation assumes the propagation of up to nine modes of light in an optical fiber. In this case, the light propagation is described by the non-linear coupled Schrödinger equation system, where propagation of each mode is described by own Schrödinger equation with other modes interactions. In this case, the non-linear coupled Schrödinger equation system solving becomes increasingly complex, because each mode affects the propagation of other modes. The suggested solution is based on the direct numerical integration approach, which is based on a finite-difference integration scheme. The well-known explicit finite-difference integration scheme approach fails, due to the non-stability of the computing scheme. Due to this fact, the combined explicit/implicit finite-difference integration scheme, based on the implicit Crank–Nicolson finite-difference scheme, is used. It allows ensuring the stability of the computing scheme. Moreover, this approach allows separating the whole equation system on the independent equation system for each wave mode at each integration step. Additionally, the algorithm of numerical solution refining at each step and the integration method with automatic integration step selection are used. The suggested approach has performance gains (or resolutions) up to three or more orders of magnitude in comparison with the split-step Fourier method due to the fact that there is no need to produce direct and inverse Fourier transforms at each integration step. The main advantage of the proposed method is the ability to calculate the propagation of an arbitrary number of modes in the fiber.