As a novel layered noble metal dichalcogenide material, palladium diselenide (PdSe₂) has attracted wide interest due to its excellent optical and electronic properties. In this work, a strong third-order nonlinear optical response of 2D PdSe₂ films is reported. We conduct both open-aperture (OA) and closed-aperture (CA) Z-scan measurements 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. In addition, the variation of n₂ as a function of laser intensity is also characterized, with n₂ decreasing in magnitude when increasing incident laser intensity, becoming saturated at n₂ = -9.96×10^-16 m²/W at high intensities. Our results show that the extraordinary third-order nonlinear optical properties of PdSe₂ have strong potential for high-performance nonlinear photonic devices. Keywords: 2D materials, PdSe₂ films, Z-scan technique, Kerr nonlinearity, nonlinear photonics.

In the present study, nonlinear vibration of a nanobeam resting on fractional order viscoelastic Winkler-Pasternak foundaion is studied using nonlocal elasticity theory. D'Alembert principle is used to derive the governing equation and the associated boundary conditions. The approximate analytical solution is obtained by applying the multiple scales method. Detailled parametric study is conducted, the effects of variation in different parameters belonging to the application problems on the system are calculated numerically and depicted. We remark that the order and the coefficient of the fractional derivative have significant effect on the natural frequency and the amplitude of vibrations

While numerous studies have explored the correlation between the built environment and ride-hailing demand, few have assessed their nonlinear interplay. Utilizing ride-hailing order data and multi-source built environment data from Nanjing, China, this paper uses the machine learning method, eXtreme Gradient Boosting (XGBoost), combined with SHapley Additive exPlanations (SHAP) and Partial Dependence Plots (PDP) to investigate the impact of built environment factors on ride-hailing travel demand, including their non-linear and threshold effects. The findings reveal that dining facilities have the most significant impact, with a contribution rate of 30.75%, on predicting ride-hailing travel demand. Additionally, financial, corporate, and medical facilities also exert considerable influence. The built environment factors need to reach a certain threshold or within a certain range to maximize the impact of ride-hailing travel demand. population density, land use mix and distance to the subway station collectively influence ride-hailing demand. The results are helpful for TNCs to allocate network ride-hailing resources reasonably and effectively.

On-chip integration of two-dimensional (2D) materials with unique structures and distinctive properties endow integrated devices with new functionalities and improved performance. With a high flexibility in modifying its properties and a strong compatibility with various integrated platforms, graphene oxide (GO) becomes an attractive 2D material for implementing functional hybrid integrated devices. Here, we demonstrate novel functionalities that go beyond the capabilities of conventional photonic integrated circuits, by harnessing the photo-thermal effects in 2D GO films integrated onto them. These include all-optical control and switching, optical power limiting, and non-reciprocal light transmission. The 2D layered GO films are on-chip integrated with precise control of their thicknesses and sizes. Benefitting from the broadband response of 2D GO films, all the three functionalities feature a very wide operational bandwidth. By fitting the experimental results with theory, we also extract the changes in material properties induced by the photo-thermal effects, which reveal interesting insights about 2D GO films. These results highlight the versatility of 2D GO films in implementing functional integrated photonic devices for a range of applications.

All-optical signal processing based on nonlinear optical devices is promising for ultrafast information processing in optical communication systems. Recent advances in two-dimensional (2D) layered materials with unique structures and distinctive properties have opened up new avenues for nonlinear optics and the fabrication of related devices with high performance. This paper reviews the recent advances in research on third-order optical nonlinearities of 2D materials, focusing on all-optical processing applications in the optical telecommunications band near 1550 nm. First, we provide an overview of the material properties of different 2D materials. Next, we review different methods for characterizing the third-order optical nonlinearities of 2D materials, including the Z-scan technique, third-harmonic generation (THG) measurement, and hybrid device characterization, together with a summary of the measured n₂ values in the telecommunications band. Finally, the current challenges and future perspectives are discussed.

The Kerr nonlinear optical performance of silicon nanowire waveguides integrated with 2D layered graphene oxide (GO) films is theoretically studied and optimized based on experimentally measured linear and nonlinear optical parameters of the GO films. The strong mode overlap between the silicon nanowires and highly nonlinear GO films yields a significantly enhanced Kerr nonlinearity for the hybrid waveguides. A detailed analysis for the influence of waveguide geometry and GO film thickness on the propagation loss, nonlinear parameter, and nonlinear figure of merit (FOM) is performed. The results show that the effective nonlinear parameter and nonlinear FOM can be increased by up to ≈52 and ≈79 times relative to bare silicon nanowires, respectively. Self-phase modulation (SPM)-induced spectral broadening of optical pulses is used as a benchmark to evaluate the nonlinear performance, examining the trade-off between enhancing Kerr nonlinearity and minimizing loss. By optimizing the device parameters to balance this, a high spectral broadening factor of 27.6 can be achieved ‒ more than 6 times that achieved in previous experiments. Finally, the influence of pulse chirp, material anisotropy, and the interplay between saturable absorption and SPM is also discussed. These results provide useful guidance for optimizing the Kerr nonlinear optical performance of silicon waveguides integrated with 2D layered GO films.

The complexity of modern power grids, exacerbated by integrating diverse energy sources, espe-cially inverter-based resources (IBRs), presents a significant challenge to grid operation and plan-ning since linear models fail to capture the intricate IBR dynamics. This study employs the Sparse Identification of Nonlinear Dynamics (SINDy) method to bridge the gap between theoretical un-derstanding and practical implementation in power system analysis. It introduces the novel Volterra-based Nonlinearity Index (VNI) to examine system-level nonlinearity comprehensively. The distinction of dynamics into first-order linearizable terms, second-order nonlinear dynamics, and third-order noise elucidates the intricacy of power systems. The findings demonstrate a fundamental shift in system dynamics as power sources transit to IBRs, revealing system-level nonlinearity compared to module-level nonlinearity in conventional syn-chronous generators. The VNI quantifies nonlinear-to-linear relationships, enriching our comprehension of power system behavior and offering a versatile tool for distinguishing between different nonlinearities and visualizing their distinct patterns through the proposed VIN profile.

This paper aims to search for lump waves in a spatial symmetric (2+1)-dimensional dispersive wave model. Through an ansatz on positive quadratic functions, we conduct symbolic computations with Maple to generate lump waves for the proposed nonlinear model. A line of critical points of the lump waves is computed, whose two spatial coordinates travel at constant speeds. The corresponding maximum and minimum values are evaluated in terms of the wave numbers, and interestingly, all those extreme values do not change with time, either. The last section is the conclusion.

We discuss methods for calculation of critical indices and amplitudes from the perturbative expansions. Several important examples of the Stokes flow through 2D and 3D channels are brought up. Power series for the permeability derived for small values of amplitude are employed to calculation of various critical exponents in the regime of large amplitudes. Special nonlinear approximations valid for arbitrary values of the wave amplitude are derived from the expansions. The technique developed for critical phenomena is applied then for relaxation phenomena. The concept of time-translation invariance is discussed, its spontaneous violation and restoration considered. Emerging probabilistic patterns correspond to a local breakdown of time-translation invariance. Their evolution leads to the timetranslation symmetry complete (or partial) restoration. We estimate typical time extent, amplitude and direction for such restorative process. The new technique is based on explicit introduction of origin in time. After some transformations we come to the exponential and generalized, exponential-type solution with explicit finite time scale, which was only implicit in initial parametrization with polynomial approximation. The concept of crash as a relaxation phenomenon, consisting of time-translation invariance breaking and restoration, is put forward. COVID-19 related mini-crash in the time series for Shanghai Composite is discussed as an illustration.

We experimentally demonstrate, for the first time, blind nonlinearity compensation using the Density-Based Spatial-Clustering of Applications with Noise (DBSCAN) algorithm for a 40-Gb/s 16-quadrature amplitude modulated being transmitted at 50 km of standard single-mode fiber. At high launched optical powers, DBSCAN offers up to 0.83- and 8.84-dB enhancement in Q-factor when compared to conventional K-means clustering and linear equalization, respectively.

Membrane materials are most widely applied in construction engineering with small mass and high flexibility, it presents strong geometric nonlinearity in the process of vibration. In the paper, an improved multi-scale perturbation method is used to solve the aeroelastic stability of closed and open membrane roofs for quantify the effect of geometric nonlinearity on the single-mode aeroelastic instability wind speed of membrane roofs. The results show that the critical wind speed values of the two models are small when the geometrical nonlinearity of membrane material is neglected. In addition, under normal wind load, the influence of geometrical nonlinearity of membrane on the aerodynamic stability of roof can be neglected, However, under strong wind load, when the roof deformation reaches 3% of the span, the influence of geometric nonlinearity should be considered and the influence increases with the decrease of transverse and downwind span of membrane roof. The results obtained in this paper have important theoretical reference value for the design the membrane structures.

In this paper, the current technologies of the regenerative shock absorber systems have been categorized and evaluated. Three drive modes of the regenerative shock absorber systems, namely the direct drive mode, the indirect drive mode and hybrid drive mode are reviewed for their readiness to be implemented. The damping performances of the three different modes are listed and compared. Electrical circuit and control algorithms have also been evaluated to maximize the power output and to deliver the premium ride comfort and handling performance. Different types of parameterized road excitations have been applied to vehicle suspension systems to investigate the performance of the regenerative shock absorbers including that of the nonlinear regenerative shock absorber. The research gaps for comparison of the different drive modes and the nonlinearity analysis of the regenerative shock absorbers are identified and, the corresponding research questions have been proposed for future work.

In this paper, we study the fractional pseudo-parabolic equations u_t + (−△)^s u + (−△)^s u_t = u log |u|. Firstly, we recall the relationship between the fractional Laplace operator (−△)^s and the fractional Sobolev space H^s and discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we derive a threshold result of existence of global weak solution: for the low initial energy J(u₀) < d, the solution is global in time with I(u₀) > 0 or ∥u₀∥X_0(Ω) = 0 and blows up +∞ with I(u₀) < 0; for the critical initial energy J(u₀) = d, the solution is global in time with I(u₀) ≥ 0 and blows up at +∞ with I(u₀) < 0. The decay estimate of the energy functional for the global solution is also given.

This study analyzes the modeling and dynamics of a novel passive in Multi-Degree-of-Freedom (MDOF) vibration isolation platform which can achieve significant isolation effect. Symmetrical Scissor-Like structures (SLSs) are utilized in the proposed MDOF isolation platform as the supporting and isolation elastic components. Based on the mathematical modeling and theoretical analysis of the MDOF vibration isolation system with SLSs, the effect of structural parameter and joint friction on stiffness and damping properties is investigated. It is shown that due to geometric relations within the SLSs, the natural frequencies can be reduced via adjusting structural parameters of the SLS for different direction vibration isolation. Theoretical and experimental results show that the SLS isolation platform can achieve much better loading capacity and vibration isolation performance simultaneously by only using linear passive components because of the MDOF adjustable stiffness property. Therefore, with low costing and energy consumption, the proposed novel isolation platform can provide the improvement of vibration suppression in various engineering practices.

We discuss the optimal control formulation for enhancement and denoising of satellite multiband images and propose to take it in the form of an L1-control problem for quasi-linear parabolic equation with non-local p[u]-Laplacian and with a cost functional of a tracking type. The main characteristic feature of the considered class of parabolic problems is the fact that the variable exponent p(t,x) and the anisotropic diffusion tensor D(t,x) are not well predefined a priori, but instead these characteristic non-locally depend on a solution of this problem, i.e., pu=p(t,x,u) and Du=D(t,x,u). We prove the existence of optimal pairs with sparse L1-controls using for that the indirect approach and a special family of approximation problems.

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

In this paper, a kind of single-walled carbon nanotube nonlinear model is developed, and the strongly nonlinear dynamic characteristics of such carbon nanotubes subjected to random magnetic field are studied. The nonlocal effect of microstructure is considered based on the theory of nonlocal elasticity. The natural frequency of the strongly nonlinear dynamic system is obtained by the energy function method, the drift coefficient and the diffusion coefficient are verified. The stationary probability density function of the system dynamic response is given and the fractal boundary of the safe basin is provided. Theoretical analysis and numerical simulation show that stochastic resonance occurs when varying the random magnetic field intensity. The boundary of safe basin has fractal characteristics and the area of safe basin decreases when the intensity of the magnetic field permeability increases.

Direct femtosecond laser writing or inscription is a useful technique, and it has been 1 employed to engineer various materials in many applications including nonlinear photonic crystals, 2 which are of periodically patterned second-order nonlinearity to get and control the coherent light at 3 new frequencies. By manipulation of second-order nonlinearity, either erased or poled, quasi-phase 4 matching has been achieved in several crystals, especially three-dimensional nonlinear photonic 5 crystals have been originally proposed and proved to be truly three-dimensional. Here we shortly 6 review on the recent advances in the research field of nonlinear photonic crystals inscribed by 7 femtosecond laser. We also discuss some phenomena that not understood yet and the future possible research topics in this field.

Optical parametric amplification (OPA) represents a powerful solution to achieve broadband amplification in wavelength ranges beyond the scope of conventional gain media, for generating high-power optical pulses, optical microcombs, entangled photon pairs and a wide range of other applications. Here, we demonstrate optical parametric amplifiers based on silicon nitride (Si₃N₄) waveguides integrated with two-dimensional (2D) layered graphene oxide (GO) films. We achieve precise control over the thickness, length, and position of the GO films using a transfer-free, layer-by-layer coating method combined with accurate window opening in the chip cladding using photolithography. Detailed OPA measurements with a pulsed pump for the fabricated devices with different GO film thicknesses and lengths show a maximum parametric gain of ~24.0 dB, representing a ~12.2 dB improvement relative to the device without GO. We perform a theoretical analysis of the device performance, achieving good agreement with experiment and showing that there is substantial room for further improvement. This work demonstrates a new way of achieving high photonic integrated OPA performance by incorporating 2D materials.

Layered two-dimensional (2D) graphene oxide (GO) films are integrated with micro-ring resonators (MRRs) to experimentally demonstrate enhanced nonlinear optics in the form of four-wave mixing (FWM). Both uniformly coated and patterned GO films are integrated on CMOS-compatible doped silica MRRs using a large-area, transfer-free, layer-by-layer GO coating method together with photolithography and lift-off processes, yielding precise control of the film thickness, placement, and coating length. The high Kerr nonlinearity and low loss of the GO films combined with the strong light-matter interaction within the MRRs results in a significant improvement in the FWM efficiency in the hybrid MRRs. Detailed FWM measurements are performed at different pump powers and resonant wavelengths for the uniformly coated MRRs with 1−5 layers of GO as well as the patterned devices with 10−50 layers of GO. The experimental results show good agreement with theory, achieving up to ~7.6-dB enhancement in the FWM conversion efficiency (CE) for an MRR uniformly coated with 1 layer of GO and ~10.3-dB for a patterned device with 50 layers of GO. By fitting the measured CE as a function of pump power for devices with different numbers of GO layers, we also extract the dependence of GO’s third-order nonlinearity on layer number and pump power, revealing interesting physical insights about the evolution of the layered GO films from 2D monolayers to quasi bulk-like behavior. These results confirm the high nonlinear optical performance of integrated photonic resonators incorporated with 2D layered GO films.

Continuation methods are presented that are capable of treating frequency-domain flutter equations including multiple nonlinearities represented by describing functions. A small problem demonstrates how a series of continuation processes can find all limit-cycle oscillations within a specified region with a reasonable degree of confidence. Curves of the limit-cycle amplitude variation with velocity, indicating regions of stability and instability with colors give a compact view of the nonlinear behavior throughout the flight regime. A continuation technique for reducing limit-cycle amplitudes by adjusting various system parameters is presented. These processes are economical enough to be a routine part of aircraft design and certification.

The complexity of objects and control systems increases the requirements for mathematical models. The structural identifiability (SI) assessment of nonlinear systems is one of the identification problems. Until now, this problem solves by parametric methods using various approximation methods. This approach is not always effective under uncertainty. We apply an approach to SI estimation based on the analysis of virtual structures. The requirements form for the system input based on the expansion of the excitation constancy property and S-synchronizability. The approach generalization to structural identifiability used in the analysis of systems with symmetric nonlinearity is given. homothety and identifiability conditions for systems with non-symmetric nonlinearities (SNN) obtained. The detectability and recoverability proofed for virtual frameworks (VF) guaranteed the SI estimation under uncertainty. The conditions under which the non-symmetric nonlinearity is hypothetical symmetric nonlinearity obtained. SI estimation examples considered for closed nonlinear systems under uncertainty.

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