Intelligent transportation systems (ITS) have recently evolved rapidly, which requires development of highly trustworthy and effective communication technologies for uses, including vehicle-to-vehicle (V2V) and vehicle-to-everything (V2X) communication; where Orthogonal Frequency Division Multiplexing (OFDM) is regarded as a strong candidate and highly popular option technique among these methods. However, the movement of vehicles introduces Doppler frequencies which produce inter-carrier interference (ICI), that is frequently occurs in V2X channels. This interference has the potential to compromise the integrity of subcarrier orthogonality within OFDM, leading to lower-quality communication and an increased likelihood of data transmission errors. When employing channels with doubly dispersive fading, OFDM necessitates the usage of a complex equalization based on the minimum mean-square error (MMSE) equalizer, which requires channel matrix inversion. Several low-complexity equalizers for OFDM have been developed and are based on band factorization, time domain LSQR (Least-Square QR) iterative computing, and banded minimum mean squared error (BMMSE). This paper proposes Conjugate Gradient Least Squares (CGLS), which is a novel iterative computation algorithm integrated with nonlinear equalizers. The suggested nonlinear equalization technique determines the trade-off between computations and performance. According to simulation data, the suggested nonlinear equalizer performs better than the current BMMSE and linear CGLS algorithms across doubly dispersive fading channels.

We demonstrate a method for realization of highly nonlinear optical 4-(4-dimethylaminostyryl)-1-methylpyridinium tosylate (DAST) two-dimensional structures by a double step technique. The desired polymeric structures have been first fabricated by using the multiple-exposure of two-beam interference technique, and the DAST nanoscrystals were then prepared inside the air-voids of these photoresist templates, resulting in nonlinear periodic structures. The nonlinear properties were characterized by optical and scanning microscopies, as well as by second-harmonic generation technique. This nonlinear modulation is very promising for the enhancement nonlinear conversion rates, such as terahertz generation, by using the quasi-phase matching technique.

This paper investigates the energy dissipation level of a nonlinear vehicle suspension system. The suspension system is modelled as a mass-spring-damper system, which is designed using the output frequency response function (OFRF) method. This method enables the derivation of an explicit relationship, between the system output spectrum (or Performance metric) and the system nonlinear parameters of interest. The OFRF polynomial, of the energy dissipation level, was derived in terms of the nonlinear parameters of interest. The results obtained show that the OFRF model, of the energy dissipation level, could be used to estimate the amount of heat dissipated, for a set of design parameters. This has potentials of providing some insights, in the design of vibration-based energy harvesters, as some of the wasted heat energy could be converted to electrical energy.

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.

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

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.

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

The cubic nonlinearity of graphene oxide (GO) monolayer was characterized by open and closed Z-scan using a nano-second laser of 10 Hz repetition rate with a Gaussian spatial beam profile. The reverse saturable absorption or positive nonlinearity from open Z-scan and valley-peak traces or positive nonlinearity from closed Z-scan was displayed. The reverse saturable absorption could be from a two-photon or two-step excitation process due to the larger absorption in the lower visible and upper UV wavelength region compared with the excitation source. The nonlinear absorption and nonlinear refraction coefficient were estimated to be ~ 2.62x10-8 m/W and 3.9x10-15 m2/W, respectively. This study also reveals the effect of nonlinear absorption on nonlinear refraction traces.

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

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

The COVID-19 pandemic has significantly impacted human health and daily life. Meteorological factors play a crucial role in virus transmission. Understanding these factors is critical for pandemic control, yet debates continue due to variations in research methods and data. This study uses a global dataset and focuses on administrative units smaller than 10,000 km². The relationship between daily COVID-19 incidence rates and meteorological factors—including temperature, relative humidity (RH), ultraviolet radiation (UVR), and diurnal temperature range (DTR)—was analyzed across 173 units in 62 countries. The results revealed significant nonlinear responses and lag effects between incidence rates and the meteorological factors. Key inflection points were observed at 0°C and 24°C for temperature, 63% for RH, 102 KJ/m² for UVR, and 15°C for DTR. Below 0°C, infection risk increased with rising temperatures; from 0°C to 24°C, risk decreased; and above 24°C, risk escalated rapidly. RH below 63% correlated inversely with infection risk, while above 63%, the correlation was positive. Infection risk decreased with UVR below 102 KJ/m² but increased beyond this threshold. These nonlinear responses are primarily driven by the differential effects of these factors on virus survival, transmission, and human immunity. Conditions around 24°C, 63% RH, 102 KJ/m² UVR, and DTR below 15°C appear optimal for human immunity, correlating with lower infection risk. High temperature and low UVR prompted immediate infection responses, while low temperatures, high UVR, and larger DTR showed delayed effects. These findings provide new, more reliable evidence for understanding the mechanisms driving COVID-19 pandemic dynamics and for preventing the future normalization of the epidemic.

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.

Non-linear superposition of solitons provide almost linear branches as well as ``quantum jumps" to stable particle-like cores. Can the quest for possible non--linearity of quantum mechanics and the ``collapse paradox" of the wave function in (non-)linear quantum mechanics be resolved by transitions between different quasi-linear branches of the corresponding Whitney surface?

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.

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.

Living processes are integral to open systems for multiple reasons. From a thermodynamic perspective, they reduce local entropy at the cost of increasing environmental entropy. Furthermore, these processes are inherently nonlinear owing to their feedback interactions with the environment. Nonlinear systems exhibit diverse behaviours: some stabilize at a constant value, whereas others display bifurcations and chaotic dynamics. This study introduces a model that describes living processes as the dynamics of nonlinear single-value diverging maps, whereas chaotic evolution is associated with the increasing entropy environment. This model enables us to describe the lifetime of different species simply by varying the model parameters. This model also simplifies explaining the transition from life to death.

Scattering of a probe laser pulse by an intense light spring in QED vacuum is considered. This new scattering configuration can be seen as the vacuum equivalent to the process originally associated with scattering of light by a rotating black hole, usually called Penrose superradiance. Here the rotating object is an intense laser beam containing two different components of orbital angular momentum. Due to these two components with slightly different frequencies, the energy profile of the intense laser beam rotates with a frequency that depends on the frequency difference. The nonlinear properties of quantum vacuum are described by first order Euler-Heisenberg Lagrangian. It is shown that, in such a configuration, nonlinear photon-photon coupling leads to scattered radiation, with frequency shift and angular dispersion. These two distinct properties, of frequency and propagation direction, could eventually be favourable for possible experimental observations. In principle, this new scattering configuration can also be reproduced in a nonlinear optical medium.

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

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

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

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

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.

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.

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.

In this paper, we constructed and analyzed a modified SIR-type model for the epidemic problem which considering waning-immunity class in the population, with the nonlinear incidence and recovery rates. Depending on the basic reproduction ratio, we investigated conditions for both non-endemic and co-existing cases. The RouthHurwitz criteria is used to verify the local stability of equilibria, whereas for the global stability, the suitable Lyapunov function is selected to analyze the behavioral stability for each equilibria. Moreover, we studied the optimal control problem for this case. Numerically, we give some simulations to support our analitycal findings.

This article introduces a novel two-step fifth-order Jacobian-free iterative method aimed at efficiently solving systems of nonlinear equations. The method leverages the benefits of Jacobian-free approaches, utilizing divided differences to circumvent the computationally intensive calculation of Jacobian matrices. This adaptation significantly reduces computational overhead and simplifies the implementation process while maintaining high convergence rates. We demonstrate that this method achieves fifth-order convergence under specific parameter settings, with a broad applicability across various types of nonlinear systems. The effectiveness of the proposed method is validated through a series of numerical experiments which confirm its superior performance in terms of accuracy and computational efficiency compared to existing methods.

In this paper, we investigate the following chemotaxis-haptotaxis model $$\left\{ \begin{array}{ll} u_{t}=\nabla\cdot (D(u) \nabla u)- \nabla\cdot (H(u)\nabla v)- \nabla\cdot (I(u)\nabla w)+ u(a-\mu u^{k-1}-\lambda w),\\ v_{t}=\triangle v-v+u^{\gamma},\\ w_{t}=-v w \end{array}\right.\eqno(*) $$ under homogenous Neumann boundary condition and for a bounded domain $ \Omega \subset \mathbb{R}^{n} (n\geq2)$, with $\lambda, \mu, \gamma >0$, $k>1$, $a \in \mathbb{R}$, and $D(u)\geq K_{D} (u+1)^{m-1}$, $0\leq H(u)\leq \chi u(u+1)^{-\alpha}$, $0\leq I(u)\leq \xi u(u+1)^{-\beta}$ for $K_{D}, \chi, \xi>0, m, \alpha, \beta\in \mathbb{R}$. It has been demonstrated that (i) For $0\gamma-k+1$ and $\beta>1-k$, problem ($*$) admits a classical solution $(u, v, w)$ which is globally bounded. (ii) For $\frac{2}{n}\gamma-k+\frac{1}{e}+1$ and $\beta>\max\{\frac{(n\gamma-2)(n\gamma+2k-2)}{2n}-k+1, \frac{(n\gamma-2)(\gamma+\frac{1}{e})}{n}-k+1\}$ or $\alpha>\gamma-k+1$ and $\beta>\max\{\frac{(n\gamma-2)(n\gamma+2k-2)}{2n}-k+1, \frac{(n\gamma-2)(\alpha+k-1)}{n}-k+1\}$, problem ($*$) admits a classical solution $(u, v, w)$ which is globally bounded.

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

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.

Abstract: In this study, we present an analytical tool that can be used to predict the nonlinear structural response of seaplanes advancing through sinusoidal head-sea waves. Seaplanes exhibit a unique instability phenomenon known as porpoising, which is an oscillatory motion along the heave and pitch axes that can cause serious structural damage. The heaving and pitching equations of motion are presented in the form of coupled, forced, and nonlinear Duffing-type equations with cubic nonlinearity. The analytical model developed in this study leverages the Poincaré–Lindstedt perturbation method to express the amplitude and frequency of motion in terms of all physical parameters. The accuracy and reliability of the proposed model were validated through computational fluid dynamics (CFD) simulations based on incompressible unsteady Reynolds-averaged Navier–Stokes (RANS) equations. The results show a strong agreement between the analytical tool and the CFD simulations, with minor discrepancies due to assumptions inherent in the 2D simulations, particularly the assumption that seawater only passes beneath the hull, resulting in increased buoyancy forces and reduced damping. This study offers a novel and practical method for predicting the dynamic stability of seaplanes under realistic sea conditions, potentially enhancing safety and operational efficiency by mitigating the risks associated with porpoising.

We study the nonlinear absorptive and dispersive optical properties of molecular systems immersed in a thermal reservoir interacting with a Four-wave Mixing (FWM) signal. Residual spin-orbit Hamiltonians are considered in order to take into account the internal structure of the molecule. As system parameters in the dissipation processes, transverse and longitudinal relaxation times are considered for stochastic solute-solvent interaction processes. The intramolecular coupling effects on the optical responses are studied using a molecule model consisting of two coupled harmonic curves of electronic energies with displaced minima in nuclear energies and positions. In this study, it was considered the complete frequency space is considered through the pump-probe detuning, not restricting the derivations to only maximums of population oscillations. This approach opens the possibility of studying the behavior of optical responses, which is very useful in experimental design. Our results indicate the sensitivity of the optical responses to parameters of the molecular structure as well as to those derived from the photonic process of FWM signal generation.

The susceptible-infected-recovered-vaccinated-deceased (SIRVD) epidemic compartment model extends the SIR model to include the effects of vaccination campaigns and time-dependent fatality rates on epidemic outbreaks. It encompasses the SIR, SIRV, SIRD, and SI models as special cases, with individual time-dependent rates governing transitions between different fractions. We investigate a special class of exact solutions and accurate analytical approximations for the SIRVD and SIRD compartment models. While the SIRVD and SIRD equations pose complex integro-differential equations for the rate of new infections and the fractions as a function of time, a simpler approach considers determining equations for the sum of ratios for given variations. This approach enables us to derive fully exact analytical solutions for the SIRVD and SIRD models. For nonlinear models with a high-dimensional parameter space, such as the SIRVD and SIRD models, analytical solutions, exact or accurately approximative, are of high importance and interest: not only as suitable benchmarks for numerical codes, but especially as they allow us to understand the critical behavior of epidemic outbursts as well as the decisive role of certain parameters. In the second part of our study, we apply a recently developed analytical approximation for the SIR and SIRV models to the more general SIRVD model. This approximation offers accurate analytical expressions for epidemic quantities, such as the rate of new infections and the fraction of infected persons, particularly when the cumulative fraction of infections is small. The distinction between recovered and deceased individuals in the SIRVD model affects the calculation of the death rate, which is proportional to the infected fraction in the SIRVD/SIRD cases but often proportional to the rate of new infections in many SIR models using a posteriori approach. We demonstrate that the temporal dependence of the infected fraction and the rate of new infections differs when considering the effects of vaccinations and when the real-time dependence of fatality and recovery rates diverge. These differences are highlighted for stationary ratios and gradually decreasing fatality rates. \Revised{The case of stationary ratios allows one to construct a new powerful diagnostics method to extract analytically all SIRVD model parameters from measured COVID-19 data of a completed pandemic wave.

In this article, an iterative method of two step is proposed for finding all roots simultaneously of polynomial equations. The order of convergence of the proposed algorithm is 2m, by using any iterative scheme of order m. Numerical tests are performed to confirm the theoretical results and to compare the proposed scheme with existing methods for finding all roots simultaneously.

As a rapidly expanding family of two-dimensional (2D) materials, MXenes have recently gained considerable attention due to their appealing properties. Here, by developing a solution-based coating method that enables transfer-free and layer-by-layer film coating, we investigate the layer-dependent nonlinear optical absorption of Ti₃C₂T_x films ‒ an important member of the MXene family. By using the Z-scan technique, we characterize the nonlinear absorption of the prepared MXene films consisting of different numbers of monolayers. The results show that there is a strong and layer-dependent nonlinear absorption behavior, transitioning from revisable saturable absorption (RSA) to saturable absorption (SA) as the layer number increases from 5 to 30. Notably, the nonlinear absorption coefficient β varies significantly within this range, changing from ~7.13 × 10² cm/GW to ~-2.69 × 10² cm/GW. We also characterize the power-dependent nonlinear absorption of the MXene films at various incident laser intensities, and a decreasing trend in β is observed for increasing laser intensity. These results reveal the intriguing layer-dependent nonlinear optical properties of 2D MXene films, highlighting their versatility and potential for implementing high-performance nonlinear photonic devices.

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.

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

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.

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.

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.

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.

Scattering resonances play a crucial role in understanding wave behavior in various physical systems. While significant progress has been made in analyzing resonances in high-contrast and nonlinear media, a general characterization of resonances in small, high-contrast nonlinear media with the Kerr effect, particularly in layered configurations, has remained an open problem. In this paper, we present a novel asymptotic approach that addresses this gap by providing an approximation for resonances in terms of material properties, geometry, and nonlinearity. Our results offer new insights into the dependence of resonances on these factors, particularly for complex multilayered structures, making this the first general characterization of its kind.

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

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.

Optical communication systems pose significant challenges, including the effects of nonlinear noises. The nonlinearities, including Kerr-induced phase noise, become more problematic in m-QAM as the orden of the format increases becoming a highly densed set of data-symbols and therefore, requiring advanced signal processing for successful separation of symbols at the demodulation stage. Machine learning techniques have recently been applied to improve signal integrity in such scenarios. This paper explores the application of a spectral clustering algorithm adapted to deal with data streaming to mitigate nonlinear noise in long-haul optical channels dominated by nonlinear phase noise, offering a promising solution to a pressing issue. We demonstrate that the spectral clustering algorithm outperforms the k-means algorithm in the face of nonlinear phase noise in -90, -100, and -110 dBc/Hz scenarios at 1 MHz in a simulated 10 GHz symbol rate channel.

The phenomena of light absorption, fluorescence and laser emission are accounted for within a unique picture. The atomic dipole is dealt with in a quantum framework, whereas the electromagnetic field is assumed to be a classical sine-wave. The on and off resonance cases are investigated. This is achieved owing to a novel application of Poynting's theorem. Observable predictions are made, regarding absorption of the electromagnetic energy and the frequency bandwidth of light emitted either by fluorescence or laser effect.

Nonlinear optimization (NOPT) is a meaningful tool for solving complex tasks in fields like engineering, economics, and operations research, among others. However, NOPT has problems when it comes to dealing with data variability and noisy input measurements that lead to incorrect solutions. Furthermore, nonlinear constraints may result in outcomes that are either infeasible or suboptimal, such as non-convex optimization. This paper introduces a novel regularized physics-informed neural network (RPINN) framework as a new NOPT tool for both supervised and unsupervised data-driven scenarios. By using custom activation functions and regularization penalties in an artificial neural network (ANN), RPINN can handle data variability and noisy inputs. Besides, it uses physics principles to build the network architecture, computing the optimization variables based on network weights and learned features. In addition, it uses automatic differentiation training to make the system scalable and cut down on computation time through batch-based back-propagation. The test results for both supervised and unsupervised NOPT tasks show that our RPINN can provide solutions that are competitive compared to state-of-the-art solvers. In turn, RPINN’s robustness against noisy input measurements makes it particularly valuable in environments with fluctuating information. Additionally, RPINN’s ANN-based foundation offers significant flexibility and scalability.

A one-dimensional model for fluid and solute transport in poroelastic materials (PEM) is studied. Although the model was recently derived and some exact solutions, in particular steady-state solutions and their applications, were studied, special cases occurring when some parameters vanish were not analysed earlier. Since the governing equations are nonintegrable in nonstationary case, the Lie symmetry method and modern tools for solving ODE systems are applied in order to construct time-dependent exact solutions. Depending on parameters arising in the governing equations, several special cases with new Lie symmetries are identified. Some of them have a highly nontrivial structure that cannot be predicted from a physical point of view or using Lie symmetries of other real-world models. Applying the symmetries obtained, multiparameter families of exact solutions are constructed, including those in terms of elementary and special functions (hypergeometric, Whittaker, Bessel and modified Bessel functions). A possible application of the solutions obtained is demonstrated and it is shown that some exact solutions can describe (at least qualitatively) the solute transport in PEM. The obtained exact solutions can also be used as test problems for estimating the accuracy of approximate analytical and numerical methods for solving relevant boundary value problems.

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

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

The numerical implementation of the controllers allows the use of very complex algorithms with ease. However, in practice, due to its proven advantages, the PID controller (and its variants) is widely used in industrial control systems as well as in many other applications that require continuous control. Most of the methods for tuning the parameters of PID controllers are based on time-invariant linear models of the processes, which in practice can lead to poor performance of the control system. The paper presents an application of reinforcement learning algorithms in tuning of PID controllers for the control of some classes of continuous nonlinear systems. Tuning the parameters of PID controllers is done with the help of Twin Delayed Deep Deterministic Policy Gradients (TD3) algorithm which presents a series of advantages compared to other similar methods from Machine Learning dedicated to continuous state and action spaces. TD3 algorithm is an off-policy Actor-Critic based method and was used as it does not require a system model. The presented technique is applied for control of a biotechnological system which has a strongly nonlinear dynamic. The proposed tuning method is compared to the classical tuning methods of PID controllers. The performance of the tuning method based on the TD3 algorithm is demonstrated through simulation illustrating the effectiveness of the proposed methodology.

To study the coupling mechanism and dynamic response of the end-face movable gear trans-mission system under complex excitation, a specific configuration of end-meshing movable gear reduction mechanism was used to achieve predetermined rigid thrust transmission and mis-matched gear meshing functions, which solved the inherent defects of traditional harmonic gear mechanism thin-wall flexible wheel easy to be damaged by fatigue. Considering the phenomenon of elastic deformation of live teeth accompanied by significant changes in meshing characteristics in the transmission process of end-meshing harmonic reducer, the influence of dynamic meshing parameters, live tooth deformation, time-varying stiffness of tooth meshing, and time-varying backlash on nonlinear dynamic performance was explored, as well as the mechanism of mul-ti-parameter coupling on transmission performance. The nonlinear dynamics model of the end-meshing harmonic reducer is established to solve the chattering prediction problem. Finally, a comprehensive test bed for the transmission system of harmonic reducer with meshing type with adjustable characteristic end was built to verify the correctness of the theoretical model and provide the theoretical and technical basis for exploring the optimal parameter selection of pas-sive vibration suppression problem.

In this paper, we present an innovative technique that improves the convergence order of iterative schemes that do not require the evaluation of Jacobian matrices. Using this procedure, we achieve a remarkable increase in the order of convergence, raising it from p to p + 3 units, which results in a remarkable improvement in the overall performance. We have conducted comprehensive numerical tests in various scenarios to validate the theoretical results, showing the efficiency and effectiveness of the new Jacobian-free schemes.

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.

For deep-penetrating geochemistry, there is a frontier issue as to how to explore ore-bearing information deep in covered areas, while it is, too, important to investigate the geochemical migration of ore-forming elements for the development of exploration geochemistry. In this study, a 380-day migration column experiment was conducted with surface soil and pure Cu powder collected from the Yujiashan study area in Wuhan City, Hubei Province taken as the object of research to simulate the migration process of ore-forming elements under natural conditions. The results showed obvious vertical migration of the ore-forming elements and conversion of mobile metal forms in the process; further, according to 6 groups of simulation experiments that took 45 days to conduct on migration column samples and the surface oil and Cu powder collected from the Pulang mining area in Yunnan Province, the vertical migration of the ore-forming element was still visible, and the exogenous substance (pure Cu powder) could enhance the anomaly without changing the basic migration mechanism. This indicates that Cu might migrate in a stable manner in soil cover in the Pulang mining area, and its migration was mostly driven by the transformation of Fe-Mn oxide bound state and organic bound state; finally, a multifractal analysis was conducted, revealing that the ore-forming elements presented a nonlinear and complex structure during their upward migration, which caused anomalies in the covered area, and multiple parameters exerted a certain indicative effect on different source intensities and properties of soil. In this study, laboratory simulations were performed to summarize the active-state evolution pattern and migration mechanism of ore-forming elements with a view to providing technical support and theoretical guidance for geochemical prospecting in the covered region.

An algorithm for the treatment of images affected by both blurring and salt&pepper noise is proposed with a cost only proportional to the number of pixels. The methodology uses a discretization scheme for the Laplace operator multiplied by a suitable nonlinear term depending on the gradient. Even if this approach resembles a diffusion type algorithm, only one step of the procedure is applied, leading to significant time savings. The procedure is successfully tested on some standard black&white natural images.

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

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

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

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 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.

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.

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.

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 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.

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.

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 this work, numerical and experimental implementation of a state observer applied to an Erbium-Doped Fiber Laser (EDFL) has been developed. The state observer is designed through the mathematical model of the EDFL to estimate the non-measurable variable; however, in numerical estimation, the state variables can be measurable given the mathematical model. Only the laser intensity variable was experimentally measured. The state observer estimated the population inversion through the obtained experimental laser intensity time series fitted with their numerical laser intensity using the mean square error (MSE) tool. A bifurcation diagram of the population inversion time series local maximum was built from the state observer. The state space of the experimental laser intensity versus observed population inversion was built.

This paper employs the Finite Element Method (FEM) to simulate and analyze the effects of corrosion defect parameters on the stress and failure pressure of pipelines. It investigates how the boundary conditions of the pipeline model influence stress and examines the sensitivity of failure pressure to corrosion defect parameters. A nonlinear regression equation has been developed from a dataset obtained through simulation experiments to predict the failure pressure of corroded pipelines. To validate the effects of corrosion defect parameters on failure pressure, a hydrostatic test platform for an API 5L X65 pipeline with corrosion defects was established to measure stress levels and failure pressures across varying corrosion defects. The study reveals that failure pressure is negatively correlated with corrosion length and depth, while positively correlated with corrosion width. Among these parameters, corrosion depth exerts a more significant influence on the pipeline's failure pressure than corrosion length and width. Within the range of corrosion defect parameters examined, the maximum deviation of the prediction equation's results from the simulation results is 8.71%, with an average deviation of 5.81%. The standard deviation of the fitted residuals is 0.01837. Additionally, the maximum deviation between the predicted results and experimental measurements is 8.39%, with an average deviation of 7.77%. The strong agreement between the predicted results from the equation and the actual measured data underscores the effectiveness of the nonlinear regression equation.

In this study, we evaluate the nonlinear dynamics of convection flow using the thermodynamic variational principle, focusing on scenarios where multiple external forces, such as a thermal gradient and rotational field, are applied to a shallow annular pool. We observed that with the increase in the thermal gradient, the flow changed from an axial flow to a rotational oscillatory flow with the wave amplitudes aligned. Further increasing the temperature difference led to a rotational oscillatory flow characterized by alternating wave generation and annihilation. Our analysis of the flow, considering heat fluxes orthogonal to the thermal gradient, allowed us to describe the flow state as a phase at equilibrium. The state transition of the flow was accompanied by a discontinuous jump in the heat flux, which occurred at the intersection of the entropy production curves.

Most works related to the identification of mathematical nonlinear systems make one suppose that such approaches can always be directly applied to any nonlinear system. This misconception produces a great deal of discouragement when the obtained results are not the expected ones. Thus, the current work hypothesizes that the most information one has about the mathematical structure of the model, the most precise the identification result should be. Therefore, a variant of the Sparse Identification of Nonlinear Dynamics (SINDY) approach is presented to obtain the full mathematical nonlinear model of a high-order system with coupled dynamics, namely, a commercial quadcopter. Furthermore, due to its high sensitivity to inputs, a control system is devised using the identified model to stabilize the quadcopter. This illustrates the effectiveness of the proposed identification method.

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 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.

Backgrounds Linear association has widely been assumed for prediction of aging-related fractional anisotropy (FA) decline in white matter of the brain. While useful for testing significance of the aging effect, it fails to identify a threshold age before and after which the age-FA association changes. Identification of such a threshold is often of clinical interest for timely intervention. Methods We employed a sigmoidal growth function to test a threshold effect in age triggering onset of cerebral decline in 21 white matter tracts, and compared its fitting performance to those of linear, and power regression. The study sample was a normal healthy cohort of 106 participants with ages in mid-life ranging from 18 to 60 years. Results Of the 21 white matter tracts analyzed, the posterior thalamic radiation showed better fit with sigmoidal curve model, compared to a linear or power regression. The estimated threshold age in years (95% confidence interval) were 47.2 (44.1-48.4). Conclusion While available evidence regarding the presence of a specific age threshold for cerebral decline in mid-life based on FA was limited, the posterior thalamic radiation exhibited a threshold age of 47.2. Beyond this age point, we observed a significant change in the FA risk pattern.

In this paper, a robust nonlinear dynamic controller is designed for a wind turbine with a permanent magnet synchronous generator. The wind turbine is subject to variations in all the parameters appearing in its mathematical model. Furthermore, the wind velocity is considered unavailable for direct measurement. This situation is of particular interest in practical applications, where only the nominal parameter values are known, and accurate wind velocity measurement is challenging due to perturbations caused by the turbine itself, even with appropriate sensors. The problem addressed in this work involves tracking the reference angular velocity corresponding to the wind velocity. To achieve accurate tracking, appropriate compensation of the perturbation terms resulting from parameter uncertainties and wind estimation errors is required. To address this problem, an estimator of the wind velocity is utilized, along with high–order sliding mode parameter estimators, to ensure high–performance operation of the turbine.

To describe the hysteresis nonlinearities in smart actuators, numerous models have been presented in the literature, among which the Preisach operator would be the most effective one due to its capability in capturing multi-loop or sophisticated hysteresis curves. When such an operator is coupled with uncertain nonlinear dynamics, especially in noncanonical form, it is a challenging problem to develop techniques to cancel out the hysteresis effects, and at the same time achieve asymptotic tracking performance. To resolve this problem, in this paper, we investigate the problem of iterative inverse-based adaptive control for an uncertain noncanonical nonlinear systems with unknown input Preiasch hysteresis, and a new adaptive version of the closest match algorithm is proposed to compensate for the Preisach hysteresis. With our scheme, the stability and convergence of the closed-loop system can be established. The effectiveness of the proposed control scheme is illustrated by simulation and experiment results.

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

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.

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

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

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

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

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

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

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

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.

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

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

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.

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.

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.

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 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.

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.

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.

Incremental control strategies provide undeniable advantages for controlling Uncrewed Aerial Vehicles (UAVs) due to their reduced model dependency and accurate tracking capacities. This is of particular relevance for hybrid UAVs, specially for tail-sitters, which perform complex manoeuvres when transitioning to and from aerodynamic flight. This paper summarizes the research undertaken in the application of the Incremental Nonlinear Dynamics Inversion (INDI) and Incremental Backstepping (IBKS) to a small tail-sitter UAV. After the application of these control strategies in a simulated scenario, the implementation in a Micro-Controller Unit was validated in a Hardware-in-the-Loop scenario. Following such validation, indoor experimental trials were undertaken in order to evaluate the capacity of these controllers to stabilize and control the real aircraft. The stabilization in the flight trials was successfully implemented and allow to conclude that both INDI and IBKS are control strategies suited to control a tail-sitter in vertical flight, providing accurate tracking capabilities under smooth actuation. Furthermore, it was found that the IBKS is significantly more computationally demanding than the INDI, although having a global proof of stability that is of interest in aircraft control.

Abstract. This paper proposes a Second Order Terminal Sliding Mode (2TSM) approach to the trajectory tracking of Differential Drive Mobile Robot (DDMR). Within this cascaded control scheme, the 2TSM dynamic controller, at the inner most loop, tracks the robot’s velocity quantities; while a kinematic controller, at the outer most loop, regulates the robot’s positions. In this manner, chattering is greatly attenuated and finite time convergence is guaranteed by the second order TSM manifold which involves higher order derivatives of the state variables, resulting in inherently robust as well as fast and better tracking precision. The simulation results demonstrate the merit of the proposed control methods.

This study presents the complexity and sensitivity of chaotic system dynamics in the case of the double pendulum. It applied detailed numerical analyses of the double pendulum in multiple computing platforms in order to demonstrate the complexity in behavior of the system of double pendulums. The equations of motion were derived from the Euler-Lagrange formalism, in order to capture the system's dynamics, which is coupled nonlinearly. These were solved numerically using the efficient Runge-Kutta-Fehlberg method, implemented in Python, R, GNU Octave, and Julia, while runtimes and memory usage were extensively benchmarked across these environments. Time series analyses, including the calculation of Shannon entropy and the Kolmogorov-Smirnov test, quantified the system's unpredictability and sensitivity to infinitesimal perturbations of the initial conditions. Phase space diagrams illustrated the intricate trajectories and strange attractors, as further confirmation of the chaotic nature of the double pendulum. All the findings have a clear indication of the importance of accurate measurements of the initial condition in a chaotic system, contributing to an increased understanding of nonlinear dynamics. Future research directions are faster simulations using Numba and GPU computing, stochastic effects, chaotic synchronization, and applications in climate modeling. This work will be useful for understanding chaos theory and efficient computational approaches in complex systems of dynamical nature.

This paper proposed an optimal tracking control scheme through adaptive dynamic programming(ADP) for a class of partially unknown discrete-time nonlinear systems based on radial basis function neural network(RBF-NN). In order to acquire the unknown system dynamics, we use two RBF-NNs, the one is used to construct the identifier, and the another is used to directly approximate the steady-state control input, where a novel adaptive law is proposed to update neural network weights. While the optimal feedback control and the cost function are derived via feedforward neural networks approximating, it is proposed to regulate the tracking error, the critic network and the actor network are then trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation being built under the ADP framework. Simulations verify the effectiveness of the optimal tracking control technique using the neural networks.

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