Influence Of Nonlinearity Research Articles

Settling velocity characteristics of inertial particles in turbulent and wave-induced environments

In the present study, a theoretical model is proposed to calculate the settling velocity of solid particles in turbulence generated by both oscillatory and nearly horizontal flow motions. In contrast to other previous models that typically compartmentalize two flow conditions in their studies, this study takes a more comprehensive approach by considering the combined effects of both conditions. Taking into account the influence of drag nonlinearity, virtual mass and Basset history forces, the new theoretical model is formulated. The proposed model is obtained by solving the particle motion in fluid flow under some reasonable assumptions. Accordingly, we obtain a new dimensionless term to better take into account the effect of turbulence anisotropy on the settling velocity and the role of the sediment damping coefficient. Application of this term for other conditions is discussed in the paper. The present model shows satisfactory agreement with a wide range of experimental and numerical data and with different flow conditions found in the existing literature. These data include homogeneous isotropic turbulence with high resolution direct numerical simulations (DNS), turbulent open channel and vertical oscillation.

Dynamic deformation behavior of Fe-0.22C-1.65Si-1.98Mn quenching and partitioning steel over a wide range of strain rates and constitutive model establishment

During traffic accidents, automobiles often experience rapid deformation at high strain rates spanning from 10² to 10³ s⁻¹. The dynamic deformation behavior and the constitutive model of the materials are crucial for precisely analyzing and simulating vehicle collisions and damage. This study focuses on a high-strength quenching-partitioning steel (Q&P steel) compositionally tailored for automotive applications, specifically Fe-0.22C-1.65Si-1.98Mn. Tensile tests were conducted under quasi-static (10⁻⁴–10⁻¹ s⁻¹) and dynamic (1–10³ s⁻¹) conditions to obtain stress-strain data, based on which the deformation behavior and instability mechanism of the Q&P steel were revealed. A Johnson-Cook (J-C) constitutive model was established to predict the stress-strain behavior. This model was further improved by incorporating the nonlinear influence of strain rate on stress, resulting in a significant reduction of prediction error by 60.9 % in the high strain rate range. Based on the modified J-C model, the finite element simulations of the high-speed collision for U-shaped and tubular components were conducted. The simulations exhibit excellent agreement with experimental results, thus confirming the accuracy of the model in predicting high-speed deformation behavior of the Q&P steel. This validation enables precise simulations of dynamic collision characteristics and energy absorption.

Mast Design Performance - Influence of the Non-Linear Elastic Behaviour of Carbon Fibres on the Accuracy of Fluid/Structure Interaction Models for Estimating Mast Bending

_ The masts of racing yachts are generally made of carbon fibre reinforced plastics (CFRP) and are subject to two main loads: dock tuning and the forces exerted by the sails. Both result in compression and bending of the mast. The mast design must ensure that for any given sailing configuration, the mast deflection is matched to the sail design to maximise the boat’s performance. Fluid/structure interaction models are generally employed by sail designers who use a stick model for the structural definition of the mast. The elastic properties of the CFRP plies involved in mast lamination are assumed to be constant in this latter model. However, stiffness increases under tension and decreases under compression (up to 30% at failure depending on the fibre type, standard modulus, intermediate modulus, etc) due to some reversible changes in the microstructure of the carbon fibres. As a result, the actual curvature of the mast can be very different from that calculated with the stick model, leading to a significant error in the actual shape of the sail during sailing. In this work, we use a series of three critical loading cases corresponding to those of an IMOCA mast. The influence of the elastic non-linearity of the CFRP plies on the performance of the racing yacht mast is quantified. It is concluded clearly that this elastic non-linear behaviour of carbon fibres is to be accounted for by sails designers to optimise performance. Such an influence is expected to be even more pronounced on spreader masts such as those used for America’s Cup. Keywords Yacht design; IMOCA mast; Carbon fibre composites; Non-linear elasticity

A dynamic analysis of capital, corruption, and labor market interactions

The complex relationship between corruption, economic growth, and labor dynamics has long been a challenge for policymakers. This study sheds new light on these dynamic interactions by constructing a novel economic model with saturation effects that integrate employment considerations. Unlike static or purely empirical models, our approach captures the system’s evolution over time, employing a logistic growth function to realistically reflect economic limitations and distinguishing between employed and unemployed labor segments. By incorporating a Holling type II function, the model captures the nonlinear influence of corruption on economic growth, acknowledging diminishing returns at higher corruption levels. Through advanced theoretical analysis, we establish the existence and stability conditions for three distinct long-term equilibria: stagnation, corruption-free growth with full employment, and a coexistent state where corruption persists alongside some economic activity. Our analysis goes beyond merely identifying these equilibria by revealing the specific conditions under which each state prevails, and we solidify these theoretical predictions with comprehensive numerical simulations depicting the system’s behavior under varying conditions. The findings underscore the importance of robust anti-corruption measures and a labor-intensive economic approach, highlighting that fostering growth outpacing resource depletion is crucial for escaping stagnation and achieving sustainable development. Overall, this research advances the field by integrating employment dynamics, a Holling type II function for corruption, and a focus on stability analysis, providing invaluable insights for policymakers aiming to promote sustainable economic development, combat corruption, and ensure healthy employment conditions.

Kerr nonlinearity induced nonreciprocity in dissipatively coupled resonators

Nonlinearity-induced nonreciprocity is studied in a system comprising two resonators coupled to a one-dimensional waveguide when the linear system does not exhibit nonreciprocity. The analysis is based on the Hamiltonian of the coupled system and includes the dissipative coupling between the waveguide and resonators, along with the input-output relations. We consider a large number of scenarios which can lead to nonreciprocity. We pay special attention to the case when the linear system does not exhibit nonreciprocal behavior. In this case, we show how very significant nonreciprocal behavior can result from Kerr nonlinearities. We find that the bistability of the nonlinear system can aid in achieving large nonreciprocity. Additionally, we bring out nonreciprocity in the excitation of each resonator, which can be monitored independently. Our results highlight the profound influence of nonlinearity on nonreciprocal behavior, offering an avenue for controlling light propagation in integrated photonic circuits. Nonlinearity-induced nonreciprocity would lead to significant nonreciprocity in quantum fluctuations when our system is treated quantum mechanically. Published by the American Physical Society 2024

The Dual Faces of growth: Linear and non-linear effects of industrialization, financial development and natural resource rents on China's economy

The literature on driving indicators of economic growth shows diverse findings and commonly derives symmetric relationships. The current research aims to observe the linear and non-linear influence of primary indicators of interest. The results reveal that industrial value-added positively, while urbanization negatively influences China's short and long-term economic growth. Conversely, natural resource rents exhibit no immediate positive effect but contribute to long-term economic growth. A positive change in industrial value and financial development enhances economic growth with a more profound positive shock in the short and long run. Simultaneously, their negative change reduces the economic growth in China. Whether positive or negative, fluctuations in natural resource rents contribute to economic growth, waving the asymmetric dynamic in the short and long run. Further, urbanization boosts economic expansion during negative shocks but lacks significance during positive shocks in both short and long runs. Moreover, the frequency domain causation approves the structural transformation. In the same scenario, notable discrepancies in wavelet decomposition show significant fluctuations across all series, contributing to economic growth. To boost both immediate and sustained economic growth, investing in industries focused on value addition and refining urban planning to balance growth between megacities and smaller emerging urban areas is essential.

An experimental and modeling study on extinction strain rate in C2HX flames with varied oxygen content

The extinction strain rates (ESR) is an important physical-chemical properties of fuels. Therefore, an experiment study on ESR is crucial for studying emission reduction techniques. In this work, the ESR and laminar burning velocity (LBV) of C2HX fuels under a wide range of conditions are determined experimentally. Moreover, a series of the reduced mechanisms for predicting ESR and LBV of C2 hydrocarbons (C2H2, C2H4, C2H6) is provided, because the research of mechanism reduction seldom pay attention to ESR and LBV. The contribution of this work is therefore the improvement of understanding of the oxidation characteristics of light C2 hydrocarbons and to provide reduced skeletal mechanisms for those fuels with different levels of accuracy for their interaction with reduced oxygen content. For these gas mixtures, the extinction strain rates (ESR) and the laminar burning velocity (LBV), two important physical-chemical properties, were investigated in a counterflow and a heat flux burner setup under atmospheric conditions (1 bar and 298 K). The LBV of the premixed flames, as well as the ESR of the non-premixed C2Hx/O2/N2 flames, are determined experimentally and compared to the numerical predictions of a detailed mechanism (USC II) and the seven corresponding reduced skeletal mechanisms. The present study highlights the non-linear influence on the ESR of C2 hydrocarbons that were found with decreasing fuel content and decreasing oxygen content in either case. Since C2H2 has a significantly higher reactivity than C2H4 and C2H6, this is manifested in lower ESR and higher LBV for the same conditions. The recently developed species-targeted global sensitivity analysis (STGSA) is used to develop reduced mechanisms, showing that they can reproduce the ESR trends and are within the determined measurement uncertainty in a wide range of operating conditions. In addition, these developed significantly reduced mechanisms remain good at predicting the laminar burning velocity. The research generated a unique experimental dataset of the ESR and LBV of C2Hx which was also used to develop reduced mechanisms. Sensitivity analysis for the ESR and LBV gives insight into the difference between ESR and LBV calculations.

Non-linear influences of track dynamic irregularities on vertical levelling loss of heavy-haul railway track geometry under cyclic loadings

Abstract With an emphasis on the combined degradation of railway track geometry and components, a new numerical-analytical method is proposed for predicting the track geometrical vertical levelling loss (VLL). In contrast to previous studies, this research unprecedentedly considers the influence of initial track irregularities (ITI) on VLL under cyclic loadings, elastic-plastic behaviour, and different operational dynamic conditions. The non-linear numerical models are simulated using an explicit finite element package known as LS-Dyna, and their results are validated by full-scale experimental and field measurement data. The outcomes are iteratively regressed by an analytical logarithmic function that cumulates permanent settlements, which innovatively extends the effect of ITI on VLL in a long-term behaviour. For a typical heavy-haul railway operating under 30 tons axle load and 60 km/h train velocity, the result indicates that the set of ITI with the highest standard deviation (SD) of vertical profile (VP) degrades faster (37% on average) than that with the lowest SD. Additionally, our new findings reveal that the worst scenario is related to a train running at 60 km/h and carrying a load of 20 tons/axle in an uneven track whose SD of VP evolves from 3.23 mm at N = 0 (ITI) to 7.20 mm, whereas the best one corresponds to a train at 60 km/h and 30 ton axle load in an uneven track whose SD of VP downgrades from 0.48 to 1.50 mm, both at 3 M cycles (or 60 million gross tons). These findings indicate the importance of considering the ITI for predicting track geometrical VLL under cyclic loadings. Therefore, based on this research, an acceptable condition (thresholds) of ITI can be redefined for a minimum effect on VLL, which can support the development of practical maintenance guidelines to extend the railway track service life.

Analysis of source second-harmonic-controlled wideband extended series of continuous modes power amplifiers

In this article, an in-depth analysis is presented for the first time by considering the impact of the input nonlinearity caused by gate-source capacitance (Cgs) on the performance and broadband design of extended series of continuous modes (ESCMs) power amplifiers (PAs). The conclusion of the analysis shows that the drain current waveforms of ESCMs will be altered, resulting in the overlapping region with the voltage waveform and theoretical efficiency becoming a function of the nonlinear factor γ under the influence of input nonlinearity. As a result, compared to the traditional ESCMs PAs, the introduction of nonlinear factor γ has given rise to a wider load design space and source second-harmonic manipulation space, which can achieve bandwidth expansion while reducing the design complexity of input and output matching networks. Subsequently, this conclusion was verified by using a commercially available 10W gallium nitride (GaN) device from Cree to design wideband high-efficiency PAs. The measured results show that in the target frequency band from 0.55 to 3.55 GHz, a drain efficiency of 60.5%–71.5 % and a gain of 9–12 dB can be obtained at a saturated output power of 39–42 dBm.

Deciphering the digital divide: the heterogeneous and nonlinear influence of digital economy on urban-rural income inequality in China

ABSTRACT This study investigates the heterogeneous and nonlinear impact of digital economy on the urban-rural income disparities in 30 Chinese provinces from 2013 to 2020. The results from moderated multiple regressions and panel threshold regressions consistently indicate that digital economy generally widens China’s urban-rural inequality, but this widening effect diminishes as the digital economy progresses. Furthermore, the influence of digital economy varies depending on local socio-economic factors, including economic development, industrial structure, education level, government expenditure, and openness. Digital economy exerts a stronger influence on exacerbating the inequality in economically developed regions with higher education levels and greater openness, but it helps prevent the inequality from expanding through its interactions with secondary industry development and fiscal expenditure. These findings provide a reference for formulating target strategies in line with local development conditions to bridge the inequality engendered by the digital divide.

Neural network driven sensitivity analysis of diffraction-based overlay metrology performance to target defect features

Overlay (OVL) is one significant performance indicator for the lithography process control in semiconductor manufacturing. The accuracy of the OVL metrology is extremely critical for guarantee the lithography quality. Currently, diffraction-based overlay (DBO) is one of the mainstream OVL metrology techniques. Unfortunately, the accuracy of the DBO metrology is largely affected by the defect features of the OVL target. Therefore, there is a strong need to investigate the impacts of these target defects on the DBO metrology performance. However, efficiently investigating the statistical and interactive impacts of various DBO target defects remains challenging. This study aims to address this issue through proposing an intelligent sensitivity analysis approach. A cumulative distribution based global sensitivity analysis (GSA) method is utilized to assess the nonlinear influences of multiple defects in the OVL target on the DBO inaccuracy. The scenarios with both known and unknown distributions of the OVL target defects are considered. For the former, a neural network driven forward model is constructed for fast calculating the optical diffraction responses to accelerate the GSA process. For the latter, another neural network based inverse model are built for efficiently estimating the distribution of the target defects. Finally, a series of simulation experiments are conduct for typical DBO targets with multiple common defect features. The results demonstrate the effectiveness and robustness of the proposed approach as well as give valuable insights into the DBO defect analysis. Our study provides a strong tool to assist the practitioners in achieving intelligent and efficient DBO analysis and thus in enhancing OVL metrology performance.

Data-driven modeling of equatorial atmospheric waves: The role of moisture and nonlinearity on global-scale instabilities and propagation speeds.

The equatorial region of the Earth's atmosphere serves as both a significant locus for phenomena, including the Madden-Julian Oscillation (MJO), and a source of formidable complexity. This complexity arises from the intricate interplay between nonlinearity and thermodynamic processes, particularly those involving moisture. In this study, we employ a normal mode decomposition of atmospheric reanalysis ERA-5 datasets to investigate the influence of nonlinearity and moisture on amplitude growth, propagation speed, and mode coupling associated with equatorially trapped waves. We focus our analysis on global-scale baroclinic Kelvin and Rossby waves, recognized as crucial components contributing to the variability of the MJO. We examine the dependence of wave amplitudes on the background moisture field in the equatorial region, as measured by total column water vapor. Our analysis demonstrates the crucial role of moisture in exciting these waves. We further investigate the dependence of the propagation speed of the waves on their amplitudes and the background moisture field. Our analysis reveals a robust correlation between the phase speed of the normal modes and their corresponding amplitude, whereas a weaker correlation is found between the eigenmodes' phase speed and the moisture field. Hence, our findings suggest that moisture plays a role in exciting the global-scale Rossby-Kelvin structure of the MJO. In this context, the propagation speed of the eigenmodes is mainly influenced by their amplitudes, underscoring the significant role of nonlinearity in wave propagation.

Toward a sustainable agricultural system in China: exploring the nexus between agricultural science and technology innovation, agricultural resilience and fiscal policies supporting agriculture

IntroductionThis study delves into the intricate dynamics between fiscal policies supporting agriculture and the non-linear influence of agricultural science and technology innovation on enhancing agricultural resilience. We conducted research across 31 provinces (including autonomous regions and municipalities) in China from 2007 to 2021.MethodBy constructing the evaluation index system of agricultural resilience, the entropy value method is used to measure the value of agricultural resilience, and then standard deviation ellipse and center of gravity migration analysis, benchmark regression model, heterogeneity analysis, threshold regression model are used to analyze the relationship between agricultural science and technology innovation, fiscal policies supporting agriculture and agricultural resilience.Result(1) The analysis of the spatio-temporal evolution trend shows that the overall development of China’s agricultural resilience is relatively stable, the resilience range is expanding, and the geographical area with the southeast as the center of gravity presents a stronger pulling effect; (2) The benchmark regression model shows that agricultural science and technology innovation has a significant positive effect on agricultural resilience; (3) Agricultural science and technology innovation plays a nonlinear role in increasing agricultural resilience when fiscal policies supporting agriculture are used as a threshold variable. (4) Heterogeneity analysis highlights stronger promotion of agricultural resilience through science and technology innovation in non-main producing areas and economically underdeveloped regions.DiscussionTo address this, policymakers should leverage the resilience of the Southeast, boost innovation capacity, tailor innovation to local needs, and reinforce fiscal policies supporting agriculture. These insights provide valuable direction for policymakers in crafting effective measures to enhance agricultural resilience.

ДИНАМІЧНА МОДЕЛЬ ІТЕРАЦІЙНОГО ЕЛЕКТРОПРИВОДА ПОДАЧІ З ДВОМА ГВИНТОВИМИ ПЕРЕДАЧАМИ ДЛЯ ПРЕЦИЗІЙНИХ ВЕРСТАТІВ ТА ОБРОБНИХ ЦЕНТРІВ

A variant of a simplified design diagram is proposed and the corresponding kinematic diagram of a two-motor gearless drive mechanism with two screw gears (SG) is given for an iterative two-channel electric drive for the longitudinal feed of the working tool (worktable with a product) of a coordinate multi-purpose metal-cutting machine of especially high precision, model 24K70AF4. Compensators of the negative dynamic interaction of load control channels have been determined. A generalized dynamic model of the cutting process has been constructed, taking into account both the inertia of the cutting process and the influence of the machine “WT-cutter” elastic system dynamics. A dynamic model of a conditional compensator for the cutting process is determined and calculated. A refined mathematical model of motion in steady-state feed modes of the two-channel electric drive has been obtained, taking into account the compensation of the dynamic interaction of the channels on the load and the influence of friction nonlinearities in the drive mechanism and the working tool of the machine. A structural-algorithmic diagram of an iterative two-channel compensated feed electric drive with two SGs and subordinated adjustment of control channels has been designed. The diagram includes a generalized dynamic model of the cutting process and a dynamic model of the corresponding conditional compensator for the cutting process, and also takes into account the main static moments of resistance and nonlinearity of friction in the drive load. References 13, tables 2, figures 5.

An electrical analogy model for performance evaluation of natural air-cooled TEG modules considering nonlinear effect of heat convection

With the outstanding merits of the simple principle and low computational cost, the electrical analogy model of thermoelectric generator (TEG) modules plays an important role in evaluating the performance of thermoelectric energy harvesting systems. However, owing to the simplification of the heat dissipation structure and difficulty in determining the heat dissipation parameters, it is difficult to accurately describe the nonlinear influence of thermal convection on the heat dissipation performance of the TEG module under natural air-cooled conditions, thereby reducing the estimation accuracy of the module temperature and output. A new nonlinear electrical analogy model to evaluate the performance of natural air-cooled TEG modules was proposed in this study. The proposed model more accurately describes the nonlinear influence of thermal convection on the thermal dynamic characteristics of the TEG module by introducing a heat transfer branch between the cold and hot side surfaces of the TEG module and the environment. A parameter extraction method based on multi-objective optimization and the non-dominated sorting genetic algorithm II (NSGA-II) was proposed to overcome the problem of the heat dissipation parameters of natural air-cooled TEG modules. The experimental results show that under natural convection conditions, the maximum estimation errors of the temperature and output voltage evaluated by the proposed model and parameter identification method are less than 6.18 % and 9.14 %, respectively. Under forced convection, the maximum estimation errors of the temperature and output voltage were less than 7.36 % and 8.71 %, respectively. The above estimation errors are significantly lower than the traditional model.

An assessment on the new impetus of green energy development and its impact on climate change: a non-linear perspective.

The purpose of this article is to investigate the new driving forces behind China's green energy and further assess the impact of green energy on climate change. The existing literature has used linear methods to investigate green energy, ignoring the non-linear relationships between economic variables. The nonparametric models can accurately simulate nonlinear relationships between economic variables. This paper constructs a nonparametric additive model and uses it to explore green energy. The empirical results show that the impact of green finance on green energy is more prominent in the later stage (a U-shaped impact). Fiscal decentralization also exerts a positive U-shaped impact, meaning that expanding local fiscal autonomy has contributed to green energy growth in the later stage. Similarly, the impact of oil prices and foreign direct investment demonstrates a positive U-shaped pattern. However, the nonlinear impact of environmental pressure displays an inverted U-shaped pattern. Furthermore, this article explores the impact of green energy on climate change and its impact mechanisms. The results exhibit green energy generates a positive U-shaped impact on climate change, meaning that the role of green energy in mitigating climate change gradually becomes prominent over time. Mechanism analysis exhibits that industrial structure and energy structure both produce a nonlinear influence on climate change.

The influence of coupling nonlinearities on the dynamic behavior of a beam-plate system

Considering the wide application of beam-plate systems in engineering, this work studies the dynamic behavior of the beam-plate system connected by coupling nonlinearities. The governing equations of the beam-plate system are derived and then solved by employing the Galerkin truncation method (GTM). The correctness and stability of dynamic responses of the beam-plate system with coupling nonlinearities are studied, where a four-truncation number of the beam combined with a six-truncation number of the plate can guarantee the stability of the system's dynamic responses. Then, the influence of coupling nonlinearities on the dynamic behavior of the beam-plate system is studied. By analyzing the numerical results, the dynamic behavior of the beam-plate system with coupling nonlinearities can be effectively controlled by adjusting the parameters of coupling nonlinearities in a reasonable range. Complicated responses of the beam-plate system are motivated by coupling nonlinearities, where the working state of complex responses is quasi-periodic. The employment of coupling nonlinearities provides a possible way to control the frequency components of the vibration signal belonging to the beam-plate system. A reasonable use of coupling nonlinearities plays a positive effect on the vibration control of the beam-plate system.

Fracture mechanics approach to minimum reinforcement design of fibre-reinforced and hybrid-reinforced concrete beams

The problem of the minimum reinforcement condition in fibre-reinforced and hybrid-reinforced concrete flexural elements is addressed in the framework of fracture mechanics by means of the Updated Bridged Crack Model (UBCM). The model describes the crack propagation process occurring in the critical cross-section of the reinforced member, by assuming the composite as a multiphase material, whereby the toughening contribution of the cementitious matrix and of the reinforcements are independently evaluated. The key-point of the discussion is that, when the influence of the matrix nonlinearities on the response is neglected, the minimum reinforcement condition is defined by a linear relationship between the critical values of two dimensionless numbers: (i) the bar- reinforcement brittleness number, NP , proportional to the steel-bar area percentage, ρ; (ii) the fibre- reinforcement brittleness number, NP,f, proportional to the fibre volume fraction, Vf. The model is applied to several experimental campaigns of the literature, in order to assess its suitability in the minimum reinforcement design of reinforced members in a unified fracture mechanics-based framework.

Exploring non-linear effects of environmental factors on the volume of pedestrians of different ages using street view images and computer vision technology

Creating pedestrian-friendly neighborhoods and encouraging walking activities not only improves urban liveliness but also delivers health and environmental benefits. Previous research has largely focused on individual walking behavior, which often exhibits stronger associations with personal traits than with built environment characteristics. Pedestrian volume, a significant indicator of urban vitality and collective walking behavior, may have a stronger relationship with environmental characteristics. Moreover, prior studies often hypothesize a linear relationship between built environmental determinants and walking behavior. The exploration of potential non-linear influences may help policy makers and urban planners by identifying minimum, maximum, and optimal values of built environmental variables conducive for walking. Furthermore, studies focusing on the collective walking of older pedestrians remain scarce in the context of aging societies.In this study, we utilize street view imagery and advanced computer vision algorithms to estimate citywide pedestrian volumes and their corresponding age classifications (older adults vs. all). Additionally, we assessed both micro and macro built environmental factors. The possible non-linear impact is examined using Gradient Boosting Decision Tree (GBDT). Our findings reveal disparities in the influence of environmental determinants on the volume of older pedestrians versus that of all pedestrians. Also, the significance of environmental elements exhibits variations across different spatial resolutions. Further, both eye-level vegetation and building level show an inverted U-shaped influence on the pedestrian count.

Effect of nonlinearity of discrete Langevin model on behavior of extremes in generated time series

In this work we analyze the influence of nonlinearity on the behavior of extremal values of time series generated by two discrete Langevin models: fixing the diffusion function in the first (M1), the probability distribution function in the second (M2). The extremes were generated by applying the run theory. A mathematical relationship was found between nonlinearity of models and means and distributions of run lengths and inter-extreme times as well as with the clustering of extremes. Furthermore, the Allan factor curves of the extremes suggest that the sequences of extremes are fractal for timescales up to the mean inter-extreme time. Our main findings are that the variation of the nonlinearity parameter in model M1 (leading to the increase of the distribution tail length) can cause a significant variation of the extreme characteristics and an increase of the clustering while the variation of the nonlinearity parameter in model M2 (with fixed distribution) has a little effect on extremes.