The principles of causality and unitarity are studied within rational nonlinear electrodynamics proposed earlier. We investigate dyonic and magnetized black holes and show that in the self-dual case, when the electric charge equals the magnetic charge, corrections to Coulomb's law and Reissner-Nordstrom solutions are absent. In the case of the magnetic black hole, the Hawking temperature, the heat capacity and the Helmholtz free energy are calculated. It is shown that there are second-order phase transitions and it was demonstrated that at some range of parameters the black holes are stable.

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.

This paper proposes a model based on gene expression programming for predicting discharge coefficient of triangular labyrinth weirs. The parameters influencing discharge coefficient prediction were first examined and presented as crest height ratio to the head over the crest of the weir (p/y), crest length of water to channel width (L/W), crest length of water to the head over the crest of the weir (L/y), Froude number (F=V/√(gy)) and vertex angle () dimensionless parameters. Different models were then presented using sensitivity analysis in order to examine each of the dimensionless parameters presented in this study. In addition, an equation was presented through the use of nonlinear regression (NLR) for the purpose of comparison with GEP. The results of the studies conducted by using different statistical indexes indicated that GEP is more capable than NLR. This is to the extent that GEP predicts the discharge coefficient with an average relative error of approximately 2.5% in such a manner that the predicted values have less than 5% relative error in the worst model.

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.

This paper presents the application of optimal control problem in modeling of stirred tank heater temperature control. The analysis of the open loop system shows that the system is not efficient without a controller. Linear Quadratic Gaussian (LQG) and Linear Quadratic Integral (LQI) controllers are used to increase the performance of the system. Comparison of the closed loop system with the proposed controllers have been done with Matlab/Simulink Toolbox and a promising results have been analyzed.

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.

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.

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.

In this paper, we define new kind of Daehee numbers, the degenerate Daehee numbers of the third kind, using degenerate log function as generating function. We obtain some identities for the degenerate Daehee numbers of the third kind associated with the Daehee, degenerate Daehee and degenerate Daehee numbers of the second kind. In addition, we derive a differential equation associated with the degenerate log function. We deduce some identities from the differential equation.

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.

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 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.

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.

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.

Reliable fatigue design rules affect the proactive identification of safety parameters in aerospace industry. Numerous fatigue crack initiation and propagation models, linear and nonlinear, have been developed for designing purposes or estimation of the remaining life of aging airplanes. Depending on the adopted assumptions, the accuracy varies for different loading histories, loading types, and materials. Semi empirical models are simple but yield significant inaccuracies. Models with better theoretical basis provide better accuracy, but implementation in real conditions is problematic. In the present work, a review of author’s recent fatigue crack initiation and propagation models based on physical mechanisms is presented and improvements are proposed. Verification of the models on test results is provided and discussed.

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

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

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.

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.

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

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

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.

This work presents a linear smoothing scheme over high-order triangular elements in the framework of a cell-based strain smoothed finite element method for two-dimensional nonlinear problems. The main idea behind the proposed linear smoothing scheme for strain-smoothed finite element method (S-FEM) is no subdivision of finite element cells to sub-cells while the classical S-FEM needs sub-cells. Since the linear smoothing function is employed, S-FEM is able to use quadratic triangular or quadrilateral elements. The modified smoothed matrix obtained node-wise is evaluated. In the same manner with the computation of the strain-displacement matrix, the smoothed stiffness matrix and deformation graident are obtained over smoothing domains. A series of benchmark tests are investigated to demonstrate validity and stability of the proposed scheme. The validity and accuracy are confirmed by comparing the obtained numerical results with the standard FEM using 2nd-order triangular element and the exact solutions.

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.

Different hypotheses of carcinogenesis have been proposed based on local genetic factors and physiologic mechanisms. It is assumed that changes of the metric invariants of a biologic system (BS) determine general mechanisms of cancer development. Numerous data demonstrate an existence of three invariant feedback patterns of BS: negative feedback (NFB), positive feedback (PFB) and reciprocal links (RL). These base patterns represent basis elements of a Lie algebra and imaginary part of coquaternion. Considering coquaternion as a model of a functional core of a BS, conditions of the system can be identified with the points of three families of hypersurfaces in R⁴₂: hyperboloids of one sheet, hyperboloids of two sheets and double-cones. Corresponding quadratic form relates negative and positive entropy contributions of base elements to the energy level of the system, so that anabolic states of the system will correspond to the points of a hyperboloid of one sheet, while catabolic conditions to the points of a hyperboloid of two sheets. Equilibrium states will lie in a double cone. Hypothetically anabolic and catabolic states dominate intermittently oscillating around the equilibrium. Deterioration of base elements increases positive entropy and causes domination of catabolic states which is the main metabolic determinant of cancer. Corresponding trajectory of a malfunctioning system will have a tendency to remain inside the double cone.

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.

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.

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

: 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 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.

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.

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 this paper, modelling design and analysis of a triple inverted pendulum have been done using Matlab/Script toolbox. Since a triple inverted pendulum is highly nonlinear, strongly unstable without using feedback control system. In this paper an optimal control method means a linear quadratic regulator and pole placement controllers are used to stabilize the triple inverted pendulum upside. The impulse response simulation of the open loop system shows us that the pendulum is unstable. The comparison of the closed loop impulse response simulation of the pendulum with LQR and pole placement controllers results that both controllers have stabilized the system but the pendulum with LQR controllers have a high overshoot with long settling time than the pendulum with pole placement controller. Finally the comparison results prove that the pendulum with pole placement controller improve the stability of the system.

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.

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 brain, rather than being homogeneous, displays an almost infinite topological genus, because is punctured with a very high number of topological vortexes, i.e., .e., nesting, non-concentric brain signal cycles resulting from inhibitory neurons devoid of excitatory oscillations. Starting from this observation, we show that the occurrence of topological vortexes is constrained by random walks taking place during self-organized brain activity. We introduce a visual model, based on the Pascal’s triangle and linear and nonlinear arithmetic octahedrons, that describes three-dimensional random walks of excitatory spike activity propagating throughout the brain tissue. In case of nonlinear 3D paths, the trajectories in brains crossed by spiking oscillations can be depicted as the operation of filling the numbers of the octahedrons in the form of “islands of numbers”: this leads to excitatory neuronal assemblies, spaced out by empty area of inhibitory neuronal assemblies. These procedures allow us to describe the topology of a brain of infinite genus, to assess inhibitory neurons in terms of Betti numbers, and to highlight how non-linear random walks cause spike diffusion in neural tissues when tiny groups of excitatory neurons start to fire.

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

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.

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.

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.

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

In this paper, an electromechanical mass lifter system is designed, analyzed and compare using optimal and robust control theories. LQR and μ -synthesis controllers are used to improve the lift displacement by comparison method for tracking the desired step and sinusoidal wave signals input. Finally, the comparison simulation result prove the effectiveness of the electromechanical mass lifter system with μ -synthesis controller for improving the rise time, percentage overshoot, settling time and peak value of tracking the desired step displacement signal and improving the peak value for tracking the desired sinusoidal displacement signal with a good performance.

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.

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

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.

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.

In the present paper we investigate the conservative conditions in Quadratic Gravity. It is shown explicitly that the Bianchi identities lead to the conservative condition of the left-hand-side of the (gravitational) field equation. Therefore, the total energy-momentum tensor is conservative in the bulk (like in General Relativity). However, in Quadratic Gravity it is possible to have singular hupersurfaces separating the bulk regions with different behavior of the matter energy-momentum tensor or different vacua. They require special consideration. We derived the conservative conditions on such singular hypersurfaces and demonstrated the very possibility of the matter creation. In the remaining part of the paper we considered some applications illustrating the obtained results.

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.

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.

We investigate the tunneling of quasiparticles through a potential barrier of finite height and width, in a system with a band structure consisting of a quadratic band crossing point (QBCP). We compute the results of the transmission coefficient at various incident angles, and also the conductivity and the Fano factor. We discuss the distinguishing signatures of these transport properties in comparison with other semimetals, as well as electrons in normal metals.

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

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.

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.

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.

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

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.

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.

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

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.

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 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.

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

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

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

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

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

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

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.

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.

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

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

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

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.

This paper presents a cascade predictive control structure based on the field-oriented control (FOC) in the dq rotor reference frame for the synchronous reluctance machine (SynRM). The constant d-axis current control strategy was used and thus, the electromagnetic torque was directly controlled by the q-axis current. Because the model of the two axes currents from the inner loop is a coupled non-linear multivariable one, to non-interaction linear control the two currents, their decoupling was achieved through feedforward components. Following the decoupling, two independent monovariable linear systems resulted for the two currents dynamics that were controlled using model predictive control (MPC) algorithms, considering their ability to automatically handle the state bounds. The most important bounds for SynRM are the limits imposed on currents and voltages, which in the dq plane correspond to a circular limit. To avoid computational effort, linear limitations were adopted through polygonal approximations, resulting in rectangular regions in the dq plane. For the outer loop that controls the angular speed with a constrained MPC algorithm, as plant was considered the q-axis current closed loop dynamics and the torque linear equation. To evaluate the performances of the proposed cascade predictive control structure, a simulation study using MPC controllers versus PI ones was conducted.

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.

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

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

In engineering practice, one can often encounter issues related to optimization where the goal is to minimize material consumption, minimize stresses or deflections of the structure. In most cases, these issues are addressed with finite element analysis software and simple optimization algorithms. However, in the case of optimization of certain structures, it is not co straightforward. An example of such constructions are bubble deck ceilings, where in order to reduce the dead weight, air cavities are used, which are regularly arranged over the entire surface of the ceiling. In the case of these slabs, the flexural stiffness is not constant in all its cross-sections, which means that the use of structural finite elements (plate or shell) for static calculations is not possible, and therefore the optimization process becomes more difficult. The paper presents a minimization procedure of the weight of bubble deck slabs using numerical homogenization and sequential quadratic programming with constraints. Homogenization allows to determine the effective stiffnesses of the floor, which in the next step are sequentially corrected by changing the geometrical parameters of the floor and voids in order to achieve the assumed deflection. The presented procedure allows to minimize the use of material in a quick and effective way by automatically determining the optimal parameters describing the geometry of the bubble deck floor cross-section.

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

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

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.

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

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

The study on graphs emerging from different algebraic structures like groups, rings, fields, vector spaces, etc. is a prominent area of research in mathematics, as algebra and graph theory are two mathematical fields that focuses on creating and analysing structures. There are numerous studies linking algebraic structures and graphs, which began with the introduction of Cayley graphs of groups. Several algebraic graphs have been defined on rings, which have huge-growing literature. In this article, we systematically review the literature on some variants of Cayley graphs that are defined on rings, to understand the research in this area.

Remote patient monitoring systems are helpful since they can provide timely and effective healthcare facilities. Such online telemedicine are usually achieved with the help of sophisticated and advanced wearable sensor technologies. The modern type of wearable connected devices enables the monitoring of vital sign parameters such as: heart rate variability (HRV) also known as electrocardiogram (ECG), blood pressure (BLP), Respiratory rate and body temperature. The ubiquitous problem of wearable devices is power demand for signal transmission, such devices require frequent battery charge which causes serious limitations to the continuous monitoring of vital data. To overcome this, the current study provides a primary report for collecting kinetic energy from human daily activities for monitoring Human vital signs, the harvested energy is used to sustain the battery autonomy of wearable devices, which enables longer monitoring time of vital data. A thorough review of available commercial ECG devices is first provided, and different methods evaluated in other literature to improve the monitoring time of wearable IOT devices. Besides, a novel type of Stress or exercise ECG monitoring device based on Microcontroller PIC18F4550 and Wi-Fi device ESP8266 is proposed in this study, which is cost effective and enables real time monitoring of heart rate on cloud during normal daily activities. In order to achieve both portability and maximum power, the harvester has smallest structure and low friction. Neodymium magnets are chosen for their highest magnetic force. Due to nonlinear magnetic force interaction of the magnets, the nonlinear part of the dynamic equation has inverse quadratic form. Electromechanical damping is considered in this study and the quadratic non linearity is approximated using MacLaurin expansion, which enables to find the law of motion for general case of studies using classical methods for dynamic equations and find the suitable parameters for the harvester. The oscillations are enabled by applying an initial force and there is loss of energy due to the electromechanical damping. A typical numerical application is computed with Matlab software and ODE45 solver is used to verify the accuracy of the method.

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

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

Cultural Tourism (CT), which enhances the economic development of a region, aids a country in reinforcing its identities, enhancing cross-cultural understanding, and preserving the heritage culture of an area. Designing a proper tourism model assists the tourists in understanding the point of interest without the help of a local guide. However, owing to the need for the analysis of different factors, designing such a model is a complex process. Therefore, this article proposes a CT model for Riyadh for peak visitor time. Primarily, the map data and cultural event dataset are processed for location, such as grouping with Kriging Interpolation-based Chameleon (KIC), tree forming, and feature extraction. After that, the event dataset’s attributes are processed with word embedding. Meanwhile, the Social Network Sites (SNS) data like reviews and news are extracted with an external Application Programming Interface (API). The review data is processed with keyword extraction and word embedding, whereas the news data is processed with score value estimation. Lastly, the data are fused corresponding to a historical site and given to the Multi-Quadratic-Long Short Term Memory (MQ-LSTM) Recommendation System (RS); also, the recommended result with the map is stored in a database. Lastly, the database security is maintained with Locality Sensitive Hashing (LSH); moreover, by attaining higher performance values, the proposed model is experimentally verified.

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

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

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

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

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

Different hypotheses of carcinogenesis have been proposed based on local genetic factors and physiologic mechanisms. It is assumed that changes of the metric invariants of a biologic system (BS) determine general mechanisms of cancer development. Numerous data demonstrate an existence of three invariant feedback patterns of BS: negative feedback (NFB), positive feedback (PFB) and reciprocal links (RL). These base patterns represent basis elements of a Lie algebra sl(2,R) and imaginary part of coquaternion. Considering coquaternion as a model of a functional core of a BS, conditions of the system can be identified with the points of three families of hypersurfaces in R42: hyperboloids of one sheet, hyperboloids of two sheets and double-cones. Corresponding quadratic form relates negative and positive entropy contributions of base elements to the energy level of the system, so that anabolic states of the system will correspond to the points of a hyperboloid of one sheet, while catabolic conditions to the points of a hyperboloid of two sheets. Equilibrium states will lie in a double cone. Hypothetically anabolic and catabolic states dominate intermittently oscillating around the equilibrium. Deterioration of base elements increases positive entropy and causes domination of catabolic states which is the main metabolic determinant of cancer. Corresponding trajectory of a malfunctioning system will have a tendency to remain inside the double cone.

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.

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

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

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