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

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

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

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

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

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

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

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.

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.

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.

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.

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

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

Quantum loops are processes that constitute quantum objects. In the causal model of quantum loops and quantum objects presented here, the nonlinear processes involve the elementary units of spacetime and the associated elementary units of quantum fields. As such, quantum loop processes are the sources of gravitational fields (i.e., spacetime curvature) and of the quantum objects wave function. The model may be viewed as a derivative of loop quantum gravity, spin networks and causal dynamical triangulation, although significant deviations to these theories exist. The causal model of quantum loops is based on a causal model of spacetime dynamics where space(-time) consists of interconnected space points, each of which is connected to a small number of neighboring space points. The curvature of spacetime is expressed by the density of these space points and by the arrangement of the connections between them. The quantum loop emerges in a nonlinear collective behavioral process from a collection of space points that carry energy and quantum field attributes.

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

Statistical mechanics investigates how emergent properties of macroscopic systems (such as temperature and pressure) relate to microscopic state fluctuations. The underlying idea is that global statistical descriptors of order and variability can monitor the relevant dynamics of the whole system at hand. Here we test the possibility of extending such an approach to psychotherapy research investigating the possibility of predicting the outcome of psychotherapy on the sole basis of coarse-grained empirical macro-parameters. Four good-outcome and four poor-outcome brief psychotherapies were recorded, and their transcripts coded in terms of standard psychological categories (abstract, positive emotional and negative emotional language pertaining to patient and therapist). Each patient-therapist interaction is considered as a discrete multivariate time series made of subsequent word-blocks of 150-word length, defined in terms of the above categories. Static analysis (Principal Component Analysis) highlighted a substantial difference between good-outcome and poor-outcome cases in terms of mutual correlations among those descriptors. In the former, the patient’s use of abstract language correlated with therapist’s emotional negative language, while in the latter it co-varied with therapist’s emotional positive language, thus showing the different judgment of the therapists regarding the same variable (abstract language) in poor and good outcome cases. On the other hand, the dynamic analysis, based on five coarse-grained descriptors related to variability, degree of order and complexity of the series, demonstrated a relevant case-specific effect, pointing to the possibility of deriving a consistent picture of any single psychotherapeutic process. Overall, the results showed that the systemic approach to psychotherapy (an old tenet of psychology) is mature to shift from a metaphorical to a fully quantitative status.

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

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

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

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

This paper is intended at highlighting the main mechanical parameters controlling the behavior of the so-called "acceleration-sensitive" Non-Structural Components (NSCs). In the first part a short review of the current state of knowledge and the critical issues related to the prediction of the seismic response of NSCs is reported. Then, the paper presents the results of a numerical parametric analysis intended to capture the key features of the dynamic response of a two-degree-of-freedom (2DOF) system which is supposed to be representative of both the main structure and the "non-structural" component (NSC). Particularly, it allows to simulate the coupled behaviour of both main structure and NSC and evaluating their response. The main parameters controlling the dynamic response of NSCs emerge from this study, which could pave the way towards formulating more mechanically consistent relationships for evaluating the maximum accelerations induced by seismic shakings on NSCs.

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 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.

In this paper, we generalize the problems of finding simple polygons with the minimum area, maximum perimeter and maximum number of vertices so that they contain a given set of points and their angles are bounded by $\alpha+\pi$ where $\alpha$ ($0\leq\alpha\leq \pi$) is a parameter. We also consider the maximum angle of each possible simple polygon crossing a given set of points, and derive an upper bound for the minimum of these angles. The correspondence between the problems of finding simple polygons with the minimum area and maximum number of vertices is investigated from a theoretical perspective. We formulate the three generalized problems as nonlinear programming models, and then present a Genetic Algorithm to solve them. Finally, the computed solutions are evaluated on several datasets and the results are compared with those from the optimal approach.

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

In this 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.

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

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

In 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.

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

The article analyzes Bernoulli 's binary sequences in representation of empirical events about the distribution of natural resources and population sizes. Considering the event as a nonlinear system, and consisting of two dependent random variables, with memory and probabilities in maximum finite or infinite lengths, constant and equal to ½ for both variables (stationary process). The expressions of the possible trajectories remain constant in sequences that are repeated alternating the presence or absence of one of the variables at each iteration (asymmetric). There are constant oscillations in the event except if the variables X₁ and X₂ are regulated as a function of time Y. It is observed that the variables X₁ and X₂ assume in time T_k → ∞ specific behaviors (geometric variable) that can be used as management tools for random systems. In this way, the article seeks to know from this analyzes, the maximum entropy of information in the system by a theoretical view and how to model resources distribution or containment in the given problem.

In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.

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

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

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

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

Increasing of the imaging rate of conventional atomic force microscopy (AFM) is almost impossible without impairing of the imaging quality, since the probe tip tends to lose contact with the sample. We propose to apply the additional nonlinear force on the upper surface of a cantilever, which will help to keep the tip and surface in contact. In practice this force can be produced by the precisely regulated airflow. Such an improvement affects the AFM system dynamics, which were evaluated using a mathematical model presented in this paper. The model defines the relationships between the additional nonlinear force, the pressure of the applied air stream and the initial air gap between the upper surface of the cantilever and the end of the air duct. It was found that the nonlinear force created by the stream of compressed air (aerodynamic force) prevents the contact loss caused by the high scanning speed or higher surface roughness, and at the same time has minimal influence on the interaction force, thus maintaining stable contact between the probe and the surface. This improvement allows to effectively increase the scanning speed by at least 10 times using a soft (spring constant of 0.2 N/m) cantilever by applying the air pressure of 40 Pa. If a stiff cantilever (spring constant of 40 N/m) is used, the potential of accuracy improvement reaches 92 times. This method is suitable for use with different types of AFM sensors and can be implemented practically without essential changes in AFM sensor design.

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

During speciation-with-gene-flow, a transition from single-locus to multi-locus processes can occur, as strong coupling of multiple loci creates a barrier to gene flow. Testing predictions about such transitions with empirical data requires building upon past theoretical work and the continued development of quantitative approaches. We simulated genomes under different evolutionary scenarios of gene flow and divergent selection, extending previous work with the additions of neutral sites and coupling statistics, allowing us to investigate if and how selected and neutral sites differ in the conditions they require for transitions during speciation. As the per-locus strength of selection grew and/or migration decreased, it became easier for selected sites to show divergence – and thus to rise in linkage disequilibrium (LD) with each other as a statistical consequence – farther in advance of the conditions under which neutral sites could diverge. Indeed, even very low rates of gene flow were sufficient to prevent differentiation at neutral sites. However, once strong enough, coupling among selected sites eventually reduced gene flow at neutral sites as well. To explore whether similar transitions might be detectable in empirical data, we used published genome resequencing data from three taxa of Heliconius butterflies. We found that allele-frequency outliers and F ST outliers exhibited stronger patterns of LD than the genomic background, as expected. The statistical characteristics of LD – likely indicative of the strength of coupling of barrier loci – varied between chromosomes and taxonomic comparisons. Broad qualitative agreement between the patterns we observed in the empirical data and our simulations suggests that selection drives rapid genome-wide transitions to multi-locus coupling, illustrating how divergence and gene flow interact along the speciation continuum.

Backward electromagnetic waves are extraordinary waves with contra-directed phase velocity and energy flux. Unusual properties of the coherent nonlinear optical coupling of the phase-matched ordinary and backward electromagnetic waves with contra-directed energy fluxes are described which enable greatly-enhanced frequency and propagation direction conversion, parametrical amplification, as well as control of shape of the light pulses. Extraordinary transient processes that emerge in such metamaterials in pulsed regimes are described. The results of the numerical simulation of particular plasmonic metamaterials with hyperbolic dispersion are presented, which prove the possibility to match phases of such coupled guided ordinary and backward electromagnetic waves. Particular properties of the outlined processes in the proposed metamaterial are demonstrated through numerical simulations. Potential applications include ultra-miniature amplifiers, frequency changing reflectors, modulators, pulse shapers, and remotely actuated sensors.

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

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

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

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

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

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

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

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

MEMS (Micro-electromechanical Systems) becomes important increasingly due to the smarter and smaller fuze used in OICW (Objective Individual Combat Weapon). MEMS Safety and Arming (S&A) device is employed in different platforms and regions for small caliber projectile. Therefore, it is necessary to make a parametric study of the MEMS S&A device in different apply environments and explore the main sensitive factors of the MEMS S&A device to provide reference for designs. In this paper, based on the MEMS S&A device designed by our term, theory and finite element models are established, and the centrifugal insurance mechanism of the MEMS S&A device is parametric studied under the different speeds, temperature and thickness of the model by nonlinear dynamic method. By comparing the experimental and predicted results, the established FEM model is verified, and the conclusion is that the temperature and the centrifugal force are the main sensitive factors in the centrifugal insurance mechanism. In summary, we can suggest that the application environment, which the MEMS S&A device is suitable for, is the temperature equal to or slightly greater than normal temperature and the rotating speed higher than35000r/min of small caliber projectile.

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |u_t|^m-2u_t and source term |u|^p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T_max is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

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

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

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

Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion of nano-beam. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ) method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of value and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency ratio and imperfection sensitivity of a curved SWCNT for various boundary conditions are investigated. The results show that the geometric imperfection plays a significant role in the nonlinear vibration characteristics of curved SWCNTs.

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