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.

Initial periods of adsorption kinetics play an important role in estimating the initial adsorption rate and rate constant of adsorption process. Several adsorption processes rapidly occur, and the experimental data of adsorption kinetics under the initial periods can contain potential errors. The pseudo-second-order (PSO) kinetic model has been popularly applied in the field of adsorption. The use of the nonlinear optimization method to obtain the parameters of the PSO model can minimize error functions during modelling compared to the linear method. However, the nonlinear method has limitations in that it cannot directly recognize potential errors in the experimental points of time-dependent adsorption, especially under the initial periods. In this study, for the first time, the different linear types (Types 1–6) of the PSO model are applied to discover the error points under the initial periods. The result indicated that the fitting method using its linear equations (Types 2–5) is really helpful for identifying the error (doubtful) experimental points from the initial periods of adsorption kinetics. The imprecise points lead to low adjusted R2 (adj-R2), high reduced χ2 (red-χ2), and high Bayesian information criterion (BIC) values. After removing those points, the experimental data were adequately fitted with the PSO model. statistical analyses demonstrated that the nonlinear method must be used for modelling the PSO model because its red-χ2 and BIC were lower than the linear method. Type 1 has been extensively applied in the literature because of its very high adj-R2 (0.9999) and its excellent fitting to experimental points. However, its application should be limited because the potential errors from experimental points were not identified by this type. For comparison, the other kinetic models (i.e., pseudo-first-order, pseudo-nth-order, Avrami, and Elovich) are applied. The modelling result using the nonlinear forms of those models indicated that the fault experimental points from the initial periods were not detected.

The concepts of fractional calculus and the related techniques have been gaining momentum in circuit system fields, and an increasing body of evidence suggests that fractional-order characteristics are widely distributed in electronic components. In this paper, we consider the fractional characteristics of non-solid aluminum electrolytic capacitors and focus on the nonlinear dynamic characteristics of peak-current-mode controlled (PCMC) dc-dc boost converters with such components. In the work, we establish a piecewise smooth non-commensurate fractional-order model to describe the converter, in which the fractional-order equivalent impedance model of capacitors is adopted and the detailed control loop is considered. In order to analyze the converter, we use the fractional Adams-Bashforth-Moulton typed method (F-ABM) and stroboscopic map technique to obtain the time-domain solutions and the bifurcation diagram. The results of bifurcation diagrams indicate that, with the change of different parameters, the converter enters chaotic state through period doubling bifurcation. In order to provide empirical evidence for the nonlinear dynamic analysis, we consider both circuit-level simulation and experiments in the work, the results of which further confirm the results of theoretical analysis.

This research work presents the nonlinear control framework to estimate and reject the mismatched lumped disturbances acting on the nonlinear uncertain system. It is an unfortunate fact that the conventional Extended State Observer (ESO) is not capable to estimate the mismatched lumped disturbance and its derivative simultaneously for the systems. Also, the basic ESO is only suitable for systems with Integral Chain Form (ICF) structure. Similarly, the conventional Feedback Linearizing Control (FLC) approach is not robust for stabilizing the systems in the presence of disturbances and uncertainties. Hence, the nonlinear control framework is proposed to overcome the above issues which are composed of, (a) Dual Extended State Observer (DESO), and (b) DESO based FLC. The DESO provides information on the unmeasured state, mismatched disturbance, and its derivative. While the DESO-FLC utilizes the information from DESO to counter the effect of such disturbances and to stabilize the nonlinear systems around the reference point. The detailed closed-loop analysis is presented for the proposed control framework in the presence of lumped disturbances. The performance robustness of the presented design has been validated for the third order, nonlinear, unstable, and disturbed Magnetic Levitation System (MLS). The results of the DESO-FLC approach are compared with the most popular Linear Quadratic Regulator (LQR) and nonlinear FLC approaches based on the integral error criterion and the average electrical energy consumption.

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

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.

With correct dynamic system parameters (embodied in self-awareness statements), a controller can provide precise signals for tracking desired state trajectories. If dynamic system parameters are initially guessed incorrectly, a learning method may be used to find the correct parameters. In the deterministic artificial intelligence method, self-awareness statements are formed as mathematical expressions of the governing physics. When the nonlinear, coupled expressions are precisely parameterized as the product of known matrix components and unknown victrix (i.e., a regression form) tracking errors may be projected onto the known matrix to update the unknown victrix in an optimal form (in a two-norm sense). In this work, a modified learning method is proposed and proved to have global convergence of both state error and parameter estimation error. The modified learning method is compared with those in the prequels using simulation experiments of three-dimensional rigid body dynamic rotation motion. The modified approach is two magnitudes better than the methods in the prequels in terms of state error convergence.

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.

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.

Spherically symmetric solution in 4D Einstein--Gauss--Bonnet gravity coupled to modified logarithmic nonlinear electrodynamics (ModLogNED) is found. This solution at infinity possesses the charged black hole Reissner--Nordstr\"{o}m behavior. We study the black hole thermodynamics, entropy, shadow, energy emission rate and quasinormal modes. It was shown that black holes can possess the phase transitions and at some range of event horizon radii black holes are stable. The entropy has the logarithmic correction to the area law. The shadow radii were calculated for variety of parameters. We found that there is a peak of the black hole energy emission rate. The real and imaginary parts of the quasinormal modes frequencies were calculated. The energy conditions of ModLogNED are investigated.

Chaotic systems are systems whose results are sensitive to the initial conditions. Chaotic systems generally have nonlinearities that can be difficult to model. One example of a chaotic system with nonlinearities is the Lorenz system. The Lorenz system can be used to model weather, wind disturbances, and electronic circuit design, among other applications. In this manuscript, the Lorenz system is modeled and various control methods are applied in an effort to dictate the system’s state and rate trajectories. The combination of the linear feedback and nonlinear feedforward controllers can show over an 80% improvement in state trajectory errors when compared to the baseline run. However, the improved state trajectory performance comes at a cost of as much as 1800% error in the rate trajectories.

As a derivative of graphene, graphene oxide (GO) was initially developed by chemists to emulate some of the key properties of graphene, but it was soon recognized as a unique material in its own right, addressing an application space that is not accessible to chemical vapor deposition based materials. Over the past decade, GO has emerged as a new frontier material with tremendous advances in its material fabrication and quality control over its properties. These in turn have led to rapid progress in GO based photonics, electronics, and optoelectronics concepts and devices, evoking new science and paving the way for many technological breakthroughs with exceptional performance. Here, we review the unique fundamental characteristics of GO, its thin film fabrication methods, patterning techniques, and mechanisms for tuning its material properties. This latter capability in particular has enabled novel advanced functional photonic, electronic, and optoelectronic devices. Understanding these insights is essential for designing and tailoring GO properties for state-of-the-art applications including solar energy harvesting, energy storage, medical diagnosis, image displays, and optical communications. We conclude by discussing the open challenges and exciting opportunities of this field, together with future prospects for major technological advancements and breakthroughs.

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 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.

For a decade, the studies of dynamic control for unmanned aerial vehicles took a large interest, where drones as a useful technology in different areas were always suffering from several issues like instability-high energy consumption of batteries - inaccuracy of tracking targets. Different approaches are proposed for dealing with the non-linearity issues which present the most important features of this system. This paper describes our focus on the most common control strategies, known as model predictive control MPC, by developing a model based on the sensors embedded in our Tello quadrotor used for indoor purposes. The original controller of Tello quadrotor is supposed to be a slave, where the designed model predictive controller is created in MATLAB and imported to another embedded system, considered as a master; the objective of this model is to track the reference trajectory, almost keeping the stability of the system and ensure the low energy consumption. In the first part, a profound description of the modelling process of a dynamic model for drones is presented, explaining the design of MPC controller with both linear and non-linear strategies built in MATLAB. In the final part, simulation and results are discussed regarding its behaviour and performance, highlighting the MPC model's important role on drones' energy consumption profile.

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

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.

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.

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.

Thermodynamics and phase transitions of magnetic Anti-de Sitter black holes are studied. We consider an extended phase space thermodynamics with the cosmological constant being a thermodynamic pressure and the black hole mass is treated as a chemical enthalpy. The extended phase space thermodynamics of black holes mimics the behavior of the Van der Walls liquid. Quantities conjugated to the coupling of nonlinear electrodynamics (NED) and a magnetic charge are obtained. Thermodynamic critical points of phase transitions are investigated. It is demonstrated that the first law of black hole thermodynamics and the generalized Smarr relation take place. The Joule--Thomson adiabatic expansion of NED-AdS black holes is studied. The dependence of inversion temperature on pressure and the minimum of inversion temperature are found.

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.

In this paper, we study the weak deflection angle using Gauss-Bonnet theorem and bounding greybody factor for electric and magnetic black holes in the background of nonlinear electrodynamics. Using Gibbons and Werner's approach, first we acquire the Gaussian optical curvature to use in Gauss-Bonnet theorem and calculate the bending angle for spherically symmetric electric and magnetic black holes in both non-plasma and plasma mediums in the weak field limits. Later, we calculate the rigorous bounds of the greybody factor for the given black holes. Furthermore, we look into the graphical behaviour of bending angles and greybody bounds at some specific values of multiple parameters as well as black holes charges. It is to be mention here that all the results for the electric and magnetic charged black holes solutions reduce into the Schwarzschild black hole solution in the absence of the black holes charges.

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

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.

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

The widespread integration and growing dependence among currency, stock and commodity markets make these markets often very vulnerable to shocks and at risk of collapse at the same time. As a result, these trends threaten the sustainability of the entire financial system. In this study, we explore the spillovers and nonlinear dependences between the seven major foreign ex-change rates, crude oil and gold prices, a global stock price index, and oil and stock implied volatility indices as proxy variables for global risk factors by em-ploying directional spillover network approach. We also use multi-scale de-composition method and nonlinear causality test between these variables to capture multi-level relationships at short and long horizons. Major findings are summarized as follows. First, from the multi-scale decomposition analysis, we identify that Granger causality test results and the direction and strength of return spillovers change with the level of decomposition. Second, the results of nonlinear causality tests show variation in both the significance and direction of Granger causality relationships between the decomposed currency and other series at different timescales, especially for the decomposed oil, gold, and OVX series. Third, the measured directional spillover indices identify the EUR as the largest contributor of connectedness to the other series. The central role of the EUR is a net transmitter of connectedness to gold, oil, the GBP, JPY, and CHF.

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.

We experimentally demonstrate enhanced spectral broadening of femtosecond optical pulses after propagation through silicon-on-insulator (SOI) nanowire waveguides integrated with two-dimensional (2D) graphene oxide (GO) films. Owing to the strong mode overlap between the SOI nanowires and the GO films with a high Kerr nonlinearity, the self-phase modulation (SPM) process in the hybrid waveguides is significantly enhanced, resulting in greatly improved spectral broadening of the femtosecond optical pulses. A solution-based, transfer-free coating method is used to integrate GO films onto the SOI nanowires with precise control of the film thickness. Detailed SPM measurements using femtosecond optical pulses are carried out, achieving a broadening factor of up to ~4.3 for a device with 0.4-mm-long, 2 layers of GO. By fitting the experimental results with theory, we obtain an improvement in the waveguide nonlinear parameter by a factor of ~3.5 and the effective nonlinear figure of merit (FOM) by a factor of ~3.8, relative to the uncoated waveguide. Finally, we discuss the influence of GO film length on the spectral broadening and compare the nonlinear optical performance of different integrated waveguides coated with GO films. These results confirm the improved nonlinear optical performance for silicon devices integrated with 2D GO films.

It is known that the class of p-normed spaces (0 < p ≤ 1) is an important generalization of usual normed spaces with rich topological and geometrical structure, but the most of tools and general principles in nature with nonlinearity have not been developed yet, thus the main goal of this paper is to develop tools for nonlinear analysis under the framework of p-vector spaces. In particular, we first develop the general fixed point theorems which provide solutions to answer Schauder conjecture since 1930’s in the affirmative for p-vector spaces when p = 1 (which is just general topological vector spaces); then the one best approximation result for upper semi-continuous mappings is given, which is used as a powerful tool to establish fixed points for non-self set-valued mappings with either inward or outward set conditions; and finally we establish comprehensive existence results of solutions for Birkhoff-Kellogg Problems, and the general principle of nonlinear alternative by including Leray-Schauder alternative and related results. The results given in this paper not only include the corresponding results in the existing literature as special cases, but also expected to be useful tools for the study of nonlinear problems arising from theory to practice.

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

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.

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.

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.

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

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

The article analyzes existing materials and structures with quadratic-nonlinear optical properties that can be used to generate a difference frequency in the terahertz and sub-terahertz frequency ranges. The principle of constructing a nonlinear optical-radio converter, based on an optical focon (a focusing cone), is proposed. Based on the assumption that this focon can be implemented from the metal-organic framework (MOF), we propose a technique for modeling its parameters. The mathematical model of the process of propagation and nonlinear interaction of waves inside the focon is based on a simplification of the nonlinear wave equation. Within the framework of the developed model, the following parameters are approximately determined: the 3D gradient of the linear refractive index and the function determining the geometric profile of the focon, which provide a few-mode-based generation of the difference frequency.

We report on the application of time-resolved inline digital holography to study the nonlinear optical properties of quantum dots deposited onto the sample glass. Fresnel diffraction patterns of the probe pulse due to noncollinear degenerate phase modulation induced by the femtosecond pump pulse were extracted from the set of inline digital holograms and analyzed. Absolute values of the nonlinear refractive index of both sample glass substrate and the deposited layer of quantum dots were evaluated using the proposed technique. To characterize the inhomogeneous distribution of samples’ nonlinear optical properties we proposed to plot an optical nonlinearity map calculated as a local standard deviation of diffraction patterns intensity induced by noncollinear degenerate phase modulation.

Training supervised machine learning models requires labeled examples. A judicious choice of examples is helpful when there is a significant cost associated with assigning labels. This article improves upon a promising extant method – Batch-mode Expected Model Change Maximization (B-EMCM) method – for selecting examples to be labeled for regression problems. Specifically, it develops and evaluates alternate strategies for adaptively selecting batch size in B-EMCM. By determining the cumulative error that occurs from the estimation of the stochastic gradient descent, a stop criteria for each iteration of the batch can be specified to ensure that selected candidates are the most beneficial to model learning. This new methodology is compared to B-EMCM via mean absolute error and root mean square error over ten iterations benchmarked against machine learning data sets. Using multiple data sets and metrics across all methods, one variation of AB-EMCM, the max bound of the accumulated error (AB-EMCM Max), showed the best results for an adaptive batch approach. It achieved better root mean squared error (RMSE) and mean absolute error (MAE) than the other adaptive and non-adaptive batch methods while reaching the result in nearly the same number of iterations as the non-adaptive batch methods.

Gol'denveizer's problem of a torus has been analyzed by Audoly and Pomeau (2002) and Sun (2021). However, all of the investigations of Gol'denveizer's problem of an elastic torus have been linear. In this paper, the finite element method is used to more accurately address this problem. Furthermore, Sun (2021) cannot be solved by nonlinear analysis. We research the nonlinear mechanical properties of Gol'denveizer's problem of circular and elliptic tori, and relevant nephograms are given. We study the buckling of Gol'denveizer's problem of an elastic torus, and propose failure patterns and force-displacement curves of tori in the nonlinear range. Investigations reveal that circular tori have more rich buckling phenomena as the parameter a increases. Gol'denveizer's problem of the buckling of an elliptic torus is analyzed, and we find a new buckling phenomenon called a "skirt." As a/b increases, the collapse load of an elliptic torus of the Gol'denveizer problem is enhanced gradually.

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

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

The 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 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.

Cellular Nonlinear Networks (CNN) are a concept introduced in 1988 by Leon Chua and Lin Yang as a bio-inspired architecture, capable of massively parallel computation. Later on, CNN have been enhanced by incorporating designs that incorporate memristors to profit from their processing and memory capabilities. In addition, Stochastic Computing (SC) can be used to optimize the quantity of required processing elements; thus it provides a lightweight approximate computing framework, quite accurate and effective, though. In this work, we propose utilization of SC in designing and implementing a memristor-based CNN. As a proof of the proposed concept, an example of application is presented. This application combines Matlab and a FPGA in order to create the CNN. The implemented CNN has then been used to perform three different real-time applications on a 512x512 gray-scale and a 768x512 color image: storage of the image, edge detection, and image sharpening. It has to be pointed out that the same CNN has been used for the three different tasks, with the sole change of some programmable parameters. Results show an excellent capability with significant accompanying advantages, like the low number of needed elements further allowing for a low cost FPGA-based system implementation, something confirming the system’s ability for real time operation.

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

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

Any effort to combat corruption can benefit from an examination of past and projected worldwide trends. In this paper, we forecast the level of corruption in countries by integrating an artificial neural network modeling and time series analysis. The data were obtained from 113 countries from 2007 to 2017. The study is carried out at two levels: (a) global level where all countries are considered as a monolithic group; and (b) cluster level, where countries are placed into groups based on their development-related attributes. For each cluster, we use the findings from our previous study on the cluster analysis of global corruption using machine learning methods that identified the four most influential corruption factors, and we use those as independent variables. Then, using the identified influential factors, we forecast the level of corruption in each cluster using a nonlinear autoregressive recurrent neural network with exogenous inputs (NARX), an artificial neural network technique. The NARX models were developed for each cluster, with the objective function in terms of the Corruption Perceptions Index (CPI). For each model, the optimal neural network is determined by finetuning the hyperparameters. The analysis was repeated for all countries as a single group. The accuracy of the models is assessed by comparing the mean square errors (MSE) of the time series models. The results suggest that the NARX artificial neural network technique yields reliable future values of CPI globally or for each cluster of countries. This can assist policymakers and organizations in assessing the expected efficacies of their current or future corruption control policies from a global perspective as well as for groups of countries.

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.

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

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.

The nonlinear deformation and stress analysis of a circular torus is a difficult undertaking due to its complicated topology and the variation of the Gauss curvature. A nonlinear deformation (only one term in strain is omitted) of Mindlin torus was formulated in terms of the generalized displacement, and a general Maple code was written for numerical simulations. Numerical investigations show that the results obtained by nonlinear Mindlin, linear Mindlin, nonlinear Kirchhoff-Love, and linear Kirchhoff-Love models are close to each other. The study further reveals that the linear Kirchhoff-Love modeling of the circular torus gives good accuracy and provides assurance that the nonlinear deformation and stress analysis (not dynamics) of a Mindlin torus can be replaced by a simpler formulation, such as a linear Kirchhoff-Love theory of the torus, which has not been reported in the literature.

The evidence is presented for the long-range previtreous changes of two static properties: dielectric constant ( ) and its strong electric field related counterpart - the nonlinear dielectric effect (NDE). Notable is the evidence for the functional characterizations of (T) temperature changes by the ‘Mossotti Catastrophe’ formula, and NDE vs. T evolution by the relations resembling one developed for critical liquids. The analysis of dynamic properties based on the activation energy index excluded the Vogel-Fulcher-Tammann (VFT) relation as a validated tool for portraying the evolution of the primary relaxation time. Such a result questions the commonly applied ‘Stickel operator’ routine as the reliable tool for determining the dynamic crossover temperature. It is worth stressing that the strong electric field radically affects the distribution of relaxation times, the form of the evolution of the primary relaxation time as well as the fragility. Obtained results support the concept of a possible semi-continuous phase transition hidden below Tg. Studies were carried out in supercooled squalene, the material with extremely low electric conductivity, strongly elongated molecule, and vitally important for biology and medicine related issues.

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 paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

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

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

Neural networks models are mostly represented by oriented graphs where only the components, constitutive elements of the graph, are transcribed into mathematical xpression. Indeed, accurate knowledge of the full expression of the model is required in certain situations such as selecting among several reference models, the one that best fits the available data or comparing the explanatory and predictive performance of an established model with respect to some reference models. In this paper, we establish a formalism of the mathematical expression for multilayer perceptron neural network in a general framework, MLP-p-n-q, with p, n and q natural integers and show its restriction to cases where one has a hidden layer and multivariate outputs (MLP-p-1-q), and then a single output (MLP-p-1-1). Then, we give some specific cases of the most commonly used models. An application case is presented in the context of solving a nonlinear regression problem.

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

Since December 2019, the coronavirus disease (COVID-19) has rapidly spread worldwide. The Mexican government has implemented public safety measures to minimize the spread of the virus. In this paper, the authors use statistical models in two stages to estimate the total number of coronavirus (COVID-19) cases per day at the state and national level in Mexico. Two types of models are proposed: first, a polynomial model of the growth for the first part of the outbreak until the inflection point of the pandemic curve and then a second nonlinear growth model is used to estimate the middle and the end of the outbreak. Model selection will be performed using Vuong’s test. The proposed models show overall fit similar to predictive models (e.g. time series, and machine learning); however, the interpretation of parameters is less complex for decision-makers and the residuals follow the expected distribution when fitting the models without autocorrelation being an issue.

In a bid to resolve lingering problems in cosmology, more focus is being tilted towards cosmological models in which physical constants of nature are not necessarily real constants, but varying with cosmic time. In this paper we have study cosmology in nonlinear electrodynamics with the Newton's gravitational constant $G$ not a constant but vary in form of power-law of the scale factor of the universe. The evolution of the scale factor $a (t)$ is studied in this model which depends on nonlinear electrodynamics fine tuning term of $\alpha$. Then we check the stability of the model using the speed of sound.

The logarithmic correction to Bekenshtein$-$Hawking entropy in the framework of 4D Einstein - Gauss - Bonnet gravity coupled with nonlinear electrodynamics is obtained. We explore the black hole solution with the spherically symmetric metric. The logarithmic term in the entropy has a structure similar to the entropy correction in the semi-classical Einstein equations which mimics the quantum correction to the area low. The energy emission rate of black holes and energy conditions are studied. The quasinormal modes of a test scalar field are investigated. The gravitational lensing of light around BHs was studied. We calculated the deflection angle for some model parameters.

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.

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

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.

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'.

We report enhanced nonlinear optics in complementary metal-oxide-semiconductor (CMOS) compatible photonic platforms through the use of layered two-dimensional (2D) graphene oxide (GO) films. We integrate GO films with silicon-on-insulator nanowires (SOI), high index doped silica glass (Hydex) and silicon nitride (SiN) waveguides and ring resonators, to demonstrate an enhanced optical nonlinearity including Kerr nonlinearity and four-wave mixing (FWM). The GO films are integrated using a large-area, transfer-free, layer-by-layer method while the film placement and size are controlled by photolithography. In SOI nanowires we observe a dramatic enhancement in both the Kerr nonlinearity and nonlinear figure of merit (FOM) due to the highly nonlinear GO films. Self-phase modulation (SPM) measurements show significant spectral broadening enhancement for SOI nanowires coated with patterned films of GO. The dependence of GO’s Kerr nonlinearity on layer number and pulse energy shows trends of the layered GO films from 2D to quasi bulk-like behavior. The nonlinear parameter of GO coated SOI nanowires is increased 16 folds, with the nonlinear FOM increasing over 20 times to FOM > 5. We also observe an improved FWM efficiency in SiN waveguides integrated with 2D layered GO films. FWM measurements for samples with different numbers of GO layers and at different pump powers are performed, achieving up to ≈7.3 dB conversion efficiency (CE) enhancement for a uniformly coated device with 1 layer of GO and ≈9.1 dB for a patterned device with 5 layers of GO. These results reveal the strong potential of GO films to improve the nonlinear optics of silicon, Hydex and SiN photonic devices.

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.

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

Satellite Image Time Series (SITS) is a data set which includes satellite images across several years with a high acquisition rate. Radiometric normalization is a fundamental and important preprocessing method for remote sensing applications using SITS due to the radiometric distortion caused by noise between images. Normalizing the subject image based on the reference image is a general strategy when using traditional radiometric normalization methods to normalize multi-temporal imagery (usually two scenes or three scenes in different time phases). However, these methods are not suitable for calibrating SITS because they cannot minimize the radiometric distortion between any pair of images in SITS. The existing relative radiometric normalization methods for SITS are based on linear assumptions which cannot effectively reduce nonlinear radiometric distortion caused by continuously changing noise in SITS. To overcome this problem and obtain a more accurate SITS, this study proposed a Nonlinear Radiometric Normalization Model (named NMAG) for SITS based on Artificial Neural Networks (ANN) and Greedy Algroithm (GA) . In this method, GA was used to determine the correction order of SITS and calculate the error between the image to be corrected and normalized images, which avoided the selection of a single reference image. ANN was used to obtain the optimal solution of error function, which minimized the radiometric distortion between different images in SITS. SITS composed of 21 Landsat-8 images in Tianjin City from October 2017 to January 2019 were selected to test the method. We compared NMAG with other two contrasting method (refered as CM1 and CM2), and found that the average of root mean square error $(\mu_{RMSE})$ of NMAG $(497.22)$ was significantly smaller than those of CM1 $(641.39)$ and CM2 $(543.47)$, and the accuracy of normalized SITS obtained by using NMAG has increased by 22.4\% and 8.5\% toward CM1 and CM2, respectively. These experimental results confirmed the effectiveness of NMAG in the reduction of radiometric distortion caused by continuously changing noise between images in SITS.

This study addresses an alternative use of viscous dampers (VDs) associated with buckling restrained braces (BRBs) as the innovative seismic protection devices. For this, 4, 8 and 12 storey steel frames were designed with 6.5 m equal span length and 4 m storey height. Thereafter, the VDs and BRBs were placed over the height of each frame considering three different configurations. The structures were modeled using SAP2000 finite element program and evaluated by the nonlinear time history analyses subjected to the six natural accelerograms (1976 Gazlı, 1978 Tabas, 1987 Superstition Hills, 1992 Cape Mendocino, 1994 Northridge and 1999 Chi-Chi). The structural response of the structures with and without VDs and BRBs were studied in terms of variation in the displacement, interstorey drift, absolute acceleration, maximum base shear, time history of roof displacement. The results clearly indicated that the application of VDs and BRBs had remarkable improvement in the earthquake performance of the case study frames by reducing the local/global deformations in the main structural systems and satisfied the serviceability.

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.

An adaptive control technique has been implemented for DSTATCOM for power quality enhancement in three phase four wires(3P4W) distribution system. The reference source currents are extracted from active components of load current for each phase by using this technique. It has also been used for load balancing, harmonic suppression, power factor improvement and reactive power compensation in distribution system. The adaptive control technique has been tested at varying load in steady state and dynamic conditions. This technique is developed using MATLAB/Simulink and source side harmonics are mitigated under different load conditions which are acceptable in accordance with IEEE standard.

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.

An exact spherically symmetric and magnetically charged black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics (NED) is obtained. The NED Lagrangian is given by ${\cal L}_{NED} = -{\cal F}/(1+\sqrt[4]{2\beta{\cal F}})$, where ${\cal F}$ is the field invariant. We study the thermodynamics calculating the Hawking temperature and the heat capacity of the black hole. The phase transitions take place when the Hawking temperature has an extremum and the heat capacity is singular. We demonstrate that black holes are thermodynamically stable in some range of event horizon radii where the heat capacity is positive. The BH shadow radii are calculated. It is shown that when increasing the nonlinearity parameter $\beta$ the BH shadow radius is decreased.

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.

Abstract: The article proposes to consider the possibility of connecting the problems of engineering synthesis of frequency control systems for asynchronous electric drives with the basic provisions of the theory of identification of asynchronous electric motors based on the equations of a generalized AC electric machine.The article presents the results of experimental studies of load parrying processes in asynchronous electric drives with vector and scalar controls. These results indicate the absence of fundamental advantages as processes in a drive with vector control. This advantage should have manifested itself in a more efficient formation of the moment and fast transients. It is suggested that the reason for this is in too significant errors, assumptions and simplifications of the equations adopted in the derivation of vector control and which are its theoretical basis. A method is proposed for describing asynchronous electric motors by nonlinear transfer functions, which made it possible to formulate the principle of correction of electric drives and a method for assessing their efficiency.The article shows. that the correction based on the proposed nonlinear transfer functions of the induction motor is much more efficient than the traditional vector control, which was confirmed by detailed experiments and modeling. The results of the most important of which are given in the article. An assumption was made. that the advantage in efficiency is due to a more accurate identification of the dynamics of an asynchronous electric motor with a gear function instead of vector equations.

Driving simulators are widely used for understanding human-machine interaction, driver behavior and in driver training. The effectiveness of simulators in these process depends largely on their ability to generate realistic motion cues. Though the conventional filter-based motion cueing strategies have provided reasonable results, these methods suffer from poor workspace management. To address this issue, linear MPC-based strategies have been applied in the past. However, since the kinematics of the motion platform itself is non-linear and the required motion varies with the driving conditions, this approach tends to produce sub-optimal results. This paper presents a nonlinear MPC-based algorithm which incorporates the nonlinear kinematics of the Stewart platform within the MPC algorithm in order to increase the cueing fidelity and utilize maximum workspace. Further, adaptive weights-based tuning is used to smoothen the movement of the platform towards its physical limits. Full-track simulations were carried out and performance indicators were defined to objectively compare the response of the proposed algorithm with classical washout filter and linear MPC-based algorithms. The results indicate a better reference tracking with lower root mean square error and higher shape correlation for the proposed algorithm. Lastly, the effect of the adaptive weights-based tuning was also observed in the form of smoother actuator movements and better workspace utilization.

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.

Stability considerations play a central role in structural dynamics to determine states that are robust against perturbations during the operation. Linear stability concepts, such as the complex eigenvalue analysis, constitute the core of analysis approaches in engineering reality. However, most stability concepts are limited to local perturbations, i.e. they can only measure a state’s stability against small perturbations. Recently, the concept of basin stability has been proposed as a global stability concept for multi-stable systems. As multi-stability is a well-known property of a range of nonlinear dynamical systems, this work studies the basin stability of bi-stable mechanical oscillators that are affected and self-excited by dry friction. The results indicate how the basin stability complements the classical binary stability concepts for quantifying how stable a state is given a set of permissible perturbations.

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.

We report on space-selective crystallization of congruent and polar Sr2TiSi2O8 crystals in a stoichiometric SrO-TiO2-SiO2 glass induced by (1030 nm, 300 fs) femtosecond laser irradiation. This allows us to compare with non-congruent laser induced crystallization of polar LiNbO3, in non stoichiometric Li2O-Nb2O5-SiO2 glass and gain information on the mechanism of nanocrystals orientation with the laser polarization that we pointed out previously. Using scanning electron microscopy (SEM), Second-harmonic generation (SHG) and electron backscattered diffraction (EBSD), we studied the laser induced crystallization according to the laser processing parameters (pulse energy, pulse repetition rate, scanning speed). We found 1) a domain where the laser track is filled with crystals not perfectly textured (low energy), 2) a domain where an amorphous volume remain surrounded by a crystallized shell (high energy). This arises from Sr out-diffusion and may gives rise to crystallization of both SrTiO3 and Sr2TiSi2O8 phases at low speed. In the one-phase domain (at higher speed), it is found the possibility to elaborate a tube with a perfect fresnoite texture. Significant difference in size and morphology whereas crystallization threshold remains similar are discussed based on glases thermal propeties. Contrarily to Li2O-Nb2O5-SiO2 (LNS) glass, no domain of oriented nanocrystallization controlled by the laser polarization has been found in SrO-TiO2-SiO2 (STS) glass, which is attributed to the larger crystallization speed in STS glass. No nanogratings have also been found that is likely due to the congruency of the glass.

Hasselmann and coauthors proposed the discrete interaction approximation (DIA) as the best tool replacing the nonlinear evolution term in a numerical wind-wave model. Much later, Polnikov and Farina radically improved the original DIA by means of location all the interacting four wave vectors, used in the DIA configuration, exactly at the nodes of the numerical frequency-angular grid. This provides nearly two-times enhancing the speed of numerical calculation for the nonlinear evolution term in a wind-wave model. For this reason, the proposed version of the DIA was called as the fast DIA (FDIA). In this paper we demonstrate all details of the FDIA concept for several frequency-angular numerical grids of high resolution, with the aim of active implementation the FDIA in modern versions of world-wide used wind-wave models.

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.

We consider rational nonlinear electrodynamics with the Lagrangian ${\cal L} = -{\cal F}/(1+2\beta{\cal F})$ (${\cal F}=(1/4)F_{\mu\nu}F^{\mu\nu}$ is the Lorentz-invariant), proposed in \cite{Krug2}, coupled to General Relativity. The effective geometry induced by nonlinear electrodynamics corrections are found. We determine shadow's size of regular non-rotating magnetic black holes and compare them with the shadow size of the super-massive M87* black hole imaged by the Event Horizon Telescope collaboration. Assuming that the black hole mass has a pure electromagnetic nature, we obtain the black hole magnetic charge. The size of the shadow obtained is very close to the shadow size of non-regular neutral Schwarzschild black holes. As a result, we can interpret the super-massive M87* black hole as a regular (without singularities) magnetized black hole.

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the Gauss-Bonnet theorem for finding deflection angle in weak field limits. The effect of non-linear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

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

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.

In this paper, a capacitor microphone system is presented to improve the conversion of mechanical energy to electrical energy using a nonlinear auto regressive moving average-L2 (NARMA-L2) and model predictive control (MPC) controllers for the analysis of the open loop and closed loop system. The open loop system response shows that the output voltage signal need to be improved. The comparison of the closed loop system with the proposed controllers have been analyzed and a promising result have been obtained using Matlab/Simulink.

Layered 2D graphene oxide (GO) films are integrated with silicon nitride (SiN) waveguides to experimentally demonstrate an enhanced Kerr nonlinearity via four-wave mixing (FWM). Owing to the strong light–matter interaction between the SiN waveguides and the highly nonlinear GO films, the FWM performance of the hybrid waveguides is significantly improved. SiN waveguides with both uniformly coated and patterned GO films are fabricated based on a transfer-free, layer-by-layer GO coating method together with standard photolithography and lift-off processes, yielding precise control of the film thickness, placement and coating length. Detailed FWM measurements are carried out for the fabricated devices with different numbers of GO layers and at different pump powers. By optimizing the trade-off between the nonlinearity and loss, we obtain a significant improvement in the FWM conversion efficiency of ≈7.3 dB for a uniformly coated device with 1 layer of GO and ≈9.1 dB for a patterned device with 5 layers of GO. We also obtain a significant increase in FWM bandwidth for the patterned devices. A detailed analysis of the influence of pattern length and position on the FWM performance is performed. Based on the FWM measurements, the dependence of GO’s third-order nonlinearity on layer number and pump power is also extracted, revealing interesting physical insights about the 2D layered GO films. Finally, we obtain an enhancement in the effective nonlinear parameter of the hybrid waveguides by over a factor of 100. These results verify the enhanced nonlinear optical performance of SiN waveguides achievable by incorporating 2D layered GO films.

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

A mathematical model is proposed for quantitative description of the outbreak of novel coronavirus COVID-19 Although the model is relatively simple, the comparison with the public data shows that an exact solution solution of the model (with the correctly-specified parameters) leads to the results, which are in good agreement with the measured data in China and Austria. Prediction of the total number of the COVID-19 cases is discussed and examples are presented using the measured data in Austria, France and Poland.

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

This study suggests a novel cooperative multi-simplex algorithm that generalizes a local search optimizer to design a novel global search heuristic algorithm. The proposed algorithm exploits the vertex sharing strategy to enhance the search abilities of the working simplexes. The vertex sharing among the simplexes is carried out through cooperative step that is based on fitness of the underlying simplex. The proposed algorithm is applied to solve some systems of nonlinear equations by transforming them to optimization problems. Comparative analysis of results shows that the proposed method is practical and effective.

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

This study presents a new kinetic scheme for the mass yield prediction of waste lignocellulosic biomasses treated by Hydrothermal Carbonization (HTC). The proposed reactions are based on the decomposition, solubilization, and polymerization of each main fraction of the biomass: cellulose, hemicellulose, and lignin. The ash content was assumed to be inert. The kinetic parameters have been obtained by non-linear adjustment using a data set with 220 experimental runs collected from the literature. The results indicate that the pre-exponential factors range was from 7.33 x10¹ to 1.412x10⁵ min^-1, and activation energies were between 33.75 y 225.3 kJ/mol. A good fit is achieved between the observed and predicted data with an R² of 0.81 and an RMSE of 7.7 %. The proposed scheme was validated with the experimental data obtained by the HTC of sawdust (Pinus radiata) and rapeseed (Brassica napus). The experiments were carried out at temperatures of 190, 220, and 250 ºC and reaction times of 0, 30, 60, 90, and 120 min. The predicted values showed an average error of 2.3 and 3.5 %, respectively. Therefore, the kinetic scheme is a useful tool in the conversion analysis of waste biomass treated by HTC.

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

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

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