Nonlinear Curve Research Articles

Measurement error in hydrostatic leveling system due to temperature effect and their reduction method.

Temperature is a crucial factor influencing the accuracy of the hydrostatic leveling system (HLS), necessitating a temperature compensation test for HLS. This paper investigates HLS temperature compensation through theoretical correction and experimental verification. The influence of temperature on the accuracy of hydrostatic level products is determined through temperature tests on 34 hydrostatic level products. The optimal temperature compensation formula is derived using the non-linear curve fitting method. The HLS is enhanced with a temperature compensation algorithm and temperature sensor, resulting in a new, high-precision, and high-stability hydrostatic leveling product with temperature compensation. Experimental findings reveal that the stability of the improved hydrostatic leveling product exceeds 30% compared to products on the market and surpasses 70% compared to the original products.

Nonlinear Curve Fitting to Measurement Points with WTLS Method Using Approximation of Linear Model

The paper presents an approximate method of fitting measurement points to parameterized arbitrary nonlinear curves described by complex equations, even implicit ones, the most commonly used method of least squares in general WTLS. An approximation of a linear model is used here, in which the laws of propagation of error and propagation of uncertainty are true, so that only the first derivative of the transforming function is relevant. The effectiveness of the method has been demonstrated in several numerical examples. The method was verified on several nonlinear functions using the iterative algorithm by Monte Carlo propagation of distribution and the classical method based on the Levenberg-Marquardt algorithm for nonlinear optimization.

Quantification and modeling of disinfectant inactivation of Listeria monocytogenes biofilms on stainless steel surfaces

The present study evaluates and models the efficacy of three different disinfectants-sodium hypochlorite (SH), peracetic acid (PAA), and chlorine dioxide (ClO2) solution in inactivating biofilm formation of Listeria monocytogenes on stainless steel (SS) surfaces. The nonlinear survival curves of L. monocytogenes biofilm cells treated with different disinfectants were fitted using the Weibull model and four supervised machine learning models (Artificial Neural Networks (ANN), Random Forest (RF), Support Vector Regression (SVR), and Gradient Boosting Decision Tree (GBDT)). RF model exhibited superior predictive ability compared to other methods (RMSE: 0.12, MAE: 0.10, MAPE: 2.38, and R2: 0.99). Both RF and ANN showed better predictive effectiveness than the Weibull model. This research quantifies and models the efficacy of three disinfectants on L. monocytogenes biofilm on SS surfaces, providing valuable insights into the disinfection process of equipment surfaces in food processing.

Theoretical nonlinear force-displacement constitutive model of triangular-plate steel damper

Utilizing the inelastic deformation of a steel damper to dissipate seismic energy and control structural damage is a prevalent design strategy in a passive control field. Such a design strategy requires an explicit force-displacement constitutive model of the steel damper in both the elastic and plastic deformation phases. Currently, the nonlinear force-displacement relationship of the steel damper is mainly determined by quasi-static tests or numerical simulations which are generally time-consuming, and there is a lack of a theoretical and straightforward approach to determine the nonlinear force-displacement constitutive model of the steel damper. This study thus theoretically derives the nonlinear force-displacement constitutive model for a commonly used triangular-plate steel damper. The theoretical formula is derived based on the equal curvature assumption commonly applied to the triangular plate and is further modified based on the curvature shape function proposed in this study for the first time. After that, the force-displacement curves obtained from the theoretical formula are compared with those obtained from a large number of numerical simulations and several sets of quasi-static tests. The result shows that the theoretical formula derived based on the curvature shape function can better predict the nonlinear force-displacement curve of the triangular-plate steel damper, which significantly outperforms the theoretical formula derived based on the equal curvature assumption especially as the triangular-plate steel damper has a large plastic deformation. Furthermore, the influence factors of the strain-hardening phenomenon existing in the force-displacement curve of the triangular-plate steel damper are analyzed based on the modified theoretical formula. The result implies that the thickness-to-height ratio of the plate is the most significant factor for the strain-hardening behavior of the triangular-plate steel damper.

The structural strain method for fatigue evaluation of welded components: Analytical treatment of reversed plasticity

The traction structural stress method has been adopted by various industry sectors, in addition to ASME Boiler and Pressure Code (B&PV), for fatigue life evaluation and assessment of welded components, especially for high-cycle fatigue applications. Its effectiveness has been validated and demonstrated by showing good data correlation in the form of the master S–N curve scatter band. For low cycle fatigue with the involvement of elastic-plastic deformation, the structural strain method has been recently developed by simply extending the current elastic-deformation-based structural stress method to more general elastic-plastic deformation. Closed-form structural strain solutions for elastic-perfectly plastic materials and numerical solutions for nonlinear strain hardening materials have been obtained under simple load-controlled loading and unloading cycling conditions. In this paper, the equations of nonlinear cyclic structural stress-strain curves under fully-reversed fatigue loading are analytically derived for the first time with a 3-bar model, which consists of three elastic-perfectly plastic bars. The general trends and patterns of the loading paths of the constructed cyclic structural stress-strain curves with the 3-bar model are validated with finite element analysis (FEA). Based on the insights gained from the 3-bar model and the FEA results, a simple procedure for constructing cyclic structural stress-strain curves from their corresponding monotonic loading curves are developed for both elastic-perfectly plastic model and the modified Ramberg-Osgood nonlinear strain hardening model. The effectiveness of this procedure is demonstrated by correlating low-cycle fatigue data of welded structures under pulsating and fully-reversed loading conditions.

Influence of electron–phonon interaction on linear and nonlinear magneto-optical absorption properties in monolayer transition metal dichalcogenides

In this study, we investigate the linear and non-linear magneto-optical properties of TMDC monolayer semiconductors MX2 (M = Mo/W, X = S/Se) in a perpendicular magnetic field by evaluating the magneto-optical absorption coefficients (MOACs) and the refractive index changes (RICs) subject to the influence of electron–phonon interaction (EPI). Our results are achieved by considering the influence of electron couplings with acoustic (AC) and optical (OP) phonons via the absorption (AB) and emission (EM) mechanisms. When compared to the neglected EPI case, the intensity of the linear MOAC and RIC increases about 2.6–4 times and 5.3–10.5 times, respectively. The absorption peaks exhibit the blue-shifts, with the largest blue-shift observed for the OP-EM phonon scatterings, followed by the AC phonons and the smallest for the OP-AB phonon scatterings. Meanwhile, the greatest contribution to MOAC and RIC comes from the OP-AB phonons, which is followed by that of the AC phonons and the OP-EM phonons, respectively. The MoX2 group is more significantly affected by the scattering mechanism compared to the WX2 one. Although the OP-EM phonons contribution for the MoX2 group is much smaller than that of the other two interaction mechanisms, it nevertheless produces a very noticeable blue-shift. Meanwhile, for the WX2 group, all three mechanisms erect comparable results. The biggest (smallest) value of the linear MOAC and RIC are both founded in MoSe2 (MoS2). Notably, the absolute values of the non-linear MOAC and RIC terms increase by tens to hundreds of times, leading to the total MOAC terms being negative, contrary to when EPI is not taken into account, while the characteristics of the non-linear RIC curves also undergo considerable changes. Among the four TMDC materials, MoX2 is more significantly affected by the EPI effect than WX2.

Coarse particulate air pollution and mortality in a multidrug-resistant tuberculosis cohort

RationaleThe association between ambient coarse particulate matter (PM2.5–10) and mortality in multi-drug resistant tuberculosis (MDR-TB) patients has not yet been studied. The modifying effects of temperature and humidity on this association are completely unknown. ObjectivesTo evaluate the effects of long-term PM2.5–10 exposures, and their modifications by temperature and humidity on mortality among MDR-TB patients. MethodsA Chinese cohort of 3469 MDR-TB patients was followed up from diagnosis until death, loss to follow-up, or the study's end, averaging 2567 days per patient. PM2.5–10 concentrations were derived from the difference between PM10 and PM2.5. Cox proportional hazard models estimated hazard ratios (HRs) per 3.74 μg/m3 (interquartile range, IQR) exposure to PM2.5–10 and all-cause mortality for the full cohort and individuals at distinct long-term and short-term temperature and humidity levels, adjusting for other air pollutants and potential covariates. Exposure-response relationships were quantified using smoothed splines. ResultsHazard ratios of 1.733 (95% CI, 1.407, 2.135) and 1.427 (1.114, 1.827) were observed for mortality in association with PM2.5–10 exposures for the full cohort under both long-term and short-term exposures to temperature and humidity. Modifying effects by temperature and humidity were heterogenous across sexes, age, treatment history, and surrounding environment measured by greenness and nighttime light levels. Nonlinear exposure-response curves suggestes a cumulative risk of PM2.5–10-related mortality starting from a low exposure concentration around 15 μg/m3. ConclusionLong-term exposure to PM2.5–10 poses significant harm among MDR-TB patients, with effects modified by temperature and humidity. Immediate surveillance of PM2.5–10 is crucial to mitigate the progression of MDR-TB severity, particularly due to co-exposures to air pollution and adverse weather conditions.

Thermal resistance of Listeria monocytogenes, Escherichia coli O157:H7 and Salmonella in animal fat – Kinetic analysis and mathematical modeling

The objective of this study was to evaluate the effect of fat on thermal resistance of L. monocytogenes, E. coli O157:H7, and Salmonella spp. A 4-strain cocktail of each microorganism was inoculated to beef tallow and heated isothermally at temperatures between 55 and 80℃. All survival curves did not follow the 1st-order inactivation kinetics but conformed to a two-stage linear pattern. The first stage was markedly less heat-resistant than the second, as manifested by significantly lower D values. The z values of E. coli O157 H7 and Salmonella spp. were 11.8 °C and 12.3 °C in the first stage (z1) but increased to 23.7 °C and 20.8 °C in the second stage (z2), respectively. For L. monocytogenes, while the z values were similar for both stages (z1 = 19.6 °C and z2 = 18.5 °C), the second stage D values are 3.6–5.9 times of those in the first stage. One-step analysis was used to fit the nonlinear curves to the Weibull model, yielding < 1 exponents for the model (0.495, 0.362, and 0.282, respectively, for L. monocytogenes, E. coli O157:H7, and Salmonella spp.), suggesting gradually increased thermal resistance during heating. The experimental results showed that these microorganisms could resist heating for longer time and at higher temperatures in tallow than they do in regular meats containing lower levels of fat. The kinetic models can be used to develop thermal processes to properly inactivate pathogens contaminated in the fat portions of meat products or other high fat products.

Spatial Prediction of Diameter Distributions for the Alpine Protection Forests in Ebensee, Austria, Using ALS/PLS and Spatial Distributional Regression Models

A novel Bayesian spatial distributional regression model is presented to predict forest structural diversity in terms of the distributions of the stem diameter at breast height (DBH) in the protection forests in Ebensee, Austria. The distributional regression approach overcomes the limitations and uncertainties of traditional regression modeling, in which the conditional mean of the response is regressed against explanatory variables. The distributional regression addresses the complete conditional response distribution, instead. In total 36,338 sample trees were measured via a handheld mobile personal laser scanning system (PLS) on 273 sample plots each having a 20 m radius. Recent airborne laser scanning (ALS) data were used to derive regression covariates from the normalized digital vegetation height model (DVHM) and the digital terrain model (DTM). Candidate models were constructed that differed in their linear predictors of the two gamma distribution parameters. In the distributional regression approach, covariates can enter the model in a flexible form, such as via nonlinear smooth curves, cyclic smooths, or spatial effects. Supported by Bayesian diagnostics DIC and WAIC, nonlinear smoothing splines outperformed linear parametric slope coefficients, and the best implementation of spatial structured effects was achieved by a Gaussian process smooth. Model fitting and posterior parameter inference was achieved by using full Bayesian methodology and MCMC sampling algorithms implemented in the R-package BAMLSS. With BAMLSS, spatial interval predictions of the DBH distribution at any new geo-locations were enabled via straightforward access to the posterior predictive distributions of the model terms and by offering simple plug-in solutions for new covariate values. A cross-validation analysis validated the robustness of the proposed method’s parameter estimation and out-of-sample prediction. Spatial predictions of stem count proportions per DBH classes revealed that regeneration of smaller trees was lacking in certain areas of the protection forest landscape. Therefore, the intensity of final felling needs to be increased to reduce shading from the dense, overmature shelter trees and to promote sunlight for the young regeneration trees.

Experimental and constitutive model investigation on the tensile mechanical properties of polyurea at wide strain-rate range

Polyurea is extensively utilized as a protective coating material for structures under impact and blast loadings, owing to its significant large tensile deformation capability and strain hardening effect. In this study, the tensile performance of polyurea was experimentally and theoretically investigated. Firstly, rational geometric shapes and dimensions were designed, and a series of quasi-static and dynamic uniaxial tensile tests were conducted to obtain the nonlinear stress-strain curves at different strain rates. The results indicated a notable strain-rate effect in polyurea, with an increase in elastic modulus and tensile stress as the strain rate increased. Moreover, as the strain rate escalates, the strain hardening effect becomes more pronounced, thereby enhancing the protective capabilities of polyurea. Subsequently, an existing hyperelastic model, namely the Mooney-Rivlin (MR) model, was modified to incorporate the strain rate effect, resulting in a non-linear visco-hyperelastic constitutive model. Furthermore, the proposed constitutive model and parameters were validated by simulating existing tensile and blast tests using the finite element (FE) program LS-DYNA. This work could provide a reference for the design of structural protection.

Quantifying reaction rates in methane oxidation: atomistic simulations at high temperature

This study presents a comprehensive analysis of methane oxidation at high temperatures (2500 K–3500 K)—a critical process in atmospheric chemistry and energy production. Employing reactive molecular dynamics simulations, the research bridges the knowledge gap in understanding the complex reaction networks at these elevated temperatures. Key features include the identification of intermediate species and the simplification of the reaction networks through advanced simulation and post-processing techniques. Another focus of the study is on employing the Arrhenius equation for nonlinear curve fitting to determine activation energy and pre-exponential factors for various reactions. The analysis reveals that, despite temperature variations, there are 121 common reactions among the reduced reaction systems. This discovery revealed the underlying consistency in methane oxidation pathways across a range of high temperatures. The results of this research are vital for enhancing current models of methane oxidation, particularly in the context of improving combustion processes and deepening our understanding of atmospheric dynamics involving methane.

A nonlinear analysis of electrically forced vibrations of piezoelectric plates with viscous damping near the thickness-shear mode

Based on the theory of nonlinear piezoelectricity, an approximate solution for electrically forced nonlinear thickness-shear vibrations of piezoelectric plates is introduced. The model considers an infinite piezoelectric plate subjected to an alternative voltage, incorporating 3rd-order and 4th-order elastic constants and viscous damping under finite deformation. The system's differential equations for steady-state forced vibrations are derived from the nonlinear pure thickness-shear vibration problem, and transformed so that the new electrical boundary conditions are free. After the application of Galerkin's method, the transformed differential equations lead to a cubic equation, capturing the nonlinear current-frequency curves of AT-cut quartz plates without the need of the quality factor Q, due to the introduced viscous damping. When the damping effect is ignored, the frequency response curves of the AT-cut quartz plate under a specific voltage are confirmed with the existing literature. The study emphasizes the presence of the critical voltage and the importance of the fourth-order elastic constant (c6666) in the stability, revealing lower c6666 values correspond to improved stability. Additionally, a proposed algorithm efficiently determines critical voltages for resonator stability.

Prognosis recovery score of apical surgery Guided Bone Regeneration using cone beam computed tomography and digital bioinformatics

ObjectiveGuided Bone Regeneration (GBR) is a dental surgical procedure that uses barrier membranes to prevent soft tissue invasion and conduct new bone growth. This study aimed to define a Prognosis Recovery score (PR score) to objectively classify post-surgery responders from non-responder patients who underwent GBR using Cone Beam Computed Tomography (CBCT). MethodsThis prospective-observational-longitudinal-cohort study recruited 250 individuals who were assigned to: Conventional-Apical-Surgery (CAS, n = 39), Apical-Surgery using human fascia lata Membrane placement (ASM, n = 42), and Apical-Surgery using human fascia lata Membrane placement and lyophilized allograft Bone powder (ASMB, n = 39); and Apical-Surgery using collagen membrane Porcine origin and Bovine Bone-matrix (ASPBB, n = 130), an independent external validation cohort. Surgery was performed, and evolution was monitored by CBCTs at 0, 6-, 12-, 18-, and 24 months post-surgery. ResultsNormalized lesion volumes were calculated, and non-linear time evolution morphology curves were characterized. The three-time evolution bone growth patterns were: a linear tendency (PR0), “S'' shaped log-logistic (PR1), and “C" cellular growth (PR2). The treatment success rates were PR2-46 %, PR2-88 %, and PR2-95 %/PR1-5% for CAS, ASM, and ASMB groups. The xenograft ASPBB counterpart achieved PR2-92 % and PR1-8%. The score PR had a sensitivity, specificity, and accuracy of 100 %. ConclusionsPatients' treatment success can be quantitatively, objectively, and precisely predicted with the Prognosis Recovery score (using only two CBCTs), according to their biological response to allograft or xenograft materials (time-evolution bone growth curves), reducing cost and radiation exposure. Clinical significanceThrough digital imaging and bioinformatic analysis of bone regeneration observed in CBCTs, we defined a Prognosis Recovery (PR) score using only two CBCT volume assessments (0 and 6 months). The PR score allowed us to define three time-evolution curves depending on the biomaterials used and to classify patients in a quantitative, objective, and accurate way.

A comprehensive performance analysis of advanced hybrid MPPT controllers for fuel cell systems

The present power generation corporations are working on Renewable Power Systems (RPS) for supplying electrical power to the automotive power industries. There are several categories of RPSs available in the atmosphere. Among all of the RPSs, the most general power network used for Electric Vehicles (EVs) is hydrogen fuel which is available in nature. The H2 fuel is fed to the Proton Exchange Membrane Fuel Stack (PEMFS) for producing electricity for the EV stations. The advantages of this selected fuel system are more power conversion efficiency, environmentally friendly, low carbon emissions, more power density, less starting time, plus able to work at very low-temperature values. However, this fuel stack faces the issue of a nonlinear power density curve. Due to this nonlinear power supply from the fuel stack, the functioning point of the overall network changes from one position of the I–V curve to another position. So, the peak voltage extraction from the fuel stack is not possible. In this article, there are various metaheuristic optimization-based Maximum Power Point Tracking (MPPT) methodologies are studied along with the conventional methods for obtaining the Maximum Power Point (MPP) position of the PEMFS. From the simulative investigation, the Continuous Different Slope Value-based Cuckoo Search Method (CDSV with CSM) provides better efficiency with more output power. Also, for all the MPPT methods comprehensive analysis has been made by utilizing the simulation results.

Modeling the growth curve in ducks: a sinusoidal model as an alternative to classical nonlinear models

The present study aimed to apply a sinusoidal model to duck body weight records in order to introduce it to the field of poultry science. Using 8 traditional growth functions as a guide (Bridges, Janoschek, logistic, Gompertz, Von Bertalanffy, Richards, Schumacher, and Morgan), this study looked at how well the sinusoidal equation described the growth patterns of ducks. By evaluating statistical performance and examining model behavior during nonlinear regression curve fitting, models were compared. The data used in this study came from 3 published articles reporting 1) body weight records of Kuzi ducks aged 1 to 70 d, 2) body weight records for Polish Peking ducks aged 1 to 70 d, and 3) average body weight of Peking ducks aged 1 to 42 d belonging to 5 different breeds. The general goodness-of-fit of each model to the various data profiles was assessed using the adjusted coefficient of determination, root mean square error, Akaike's information criterion (AIC), and Bayesian information criterion. All of the models had adjusted coefficient of determination values that were generally high, indicating that the models generally fit the data well. Duck growth dynamics are accurately described by the chosen sinusoidal equation. The sinusoidal equation was found to be one of the best functions for describing the age-related changes in body weight in ducks when the growth functions were compared using the goodness-of-fit criteria. To date, no research has been conducted on the use of sinusoidal equations to describe duck growth development. To describe the growth curves for a variety of duck strains/lines, the sinusoidal function employed in this study serves as a suitable substitute for conventional growth functions.

Cross-sectional relationship between dietary protein intake, energy intake and protein energy wasting in chronic kidney disease patients.

The potential threshold for dietary energy intake (DEI) that might prevent protein-energy wasting (PEW) in chronic kidney disease (CKD) is uncertain. The subjects were non-dialysis CKD patients aged ≥ 14 years who were hospitalised from September 2019 to July 2022. PEW was measured by subjective global assessment. DEI and dietary protein intake (DPI) were obtained by 3-d diet recalls. Patients were divided into adequate DEI group and inadequate DEI group according to DEI ≥ 30 or < 30 kcal/kg/d. Logistic regression analysis and restricted cubic spline were used in this study. We enrolled 409 patients, with 53·8 % had hypertension and 18·6 % had diabetes. The DEI and DPI were 27·63 (sd 5·79) kcal/kg/d and 1·00 (0·90, 1·20) g/kg/d, respectively. 69·2 % of participants are in the inadequate DEI group. Malnutrition occurred in 18·6 % of patients. Comparing with patients in the adequate DEI group, those in the inadequate DEI group had significantly lower total lymphocyte count, serum cholesterol and LDL-cholesterol and a higher prevalence of PEW. For every 1 kcal/kg/d increase in DEI, the incidence of PEW was reduced by 12·0 % (OR: 0·880, 95 % CI: 0·830, 0·933, P < 0·001). There was a nonlinear curve relationship between DEI and PEW (overall P < 0·001), and DEI ≥ 27·6 kcal/kg/d may have a preventive effect on PEW in CKD. Low DPI was also significantly associated with malnutrition, but not when DEI was adequate. Decreased energy intake may be a more important factor of PEW in CKD than protein intake.

Finite element modeling of the magnetic property behaviors of electrical steels in rotating fields considering their crystallographic textures

In magnetic device modeling, the crystallographic textures and microstructures of electrical steels critically influence their magnetic properties. Yet, these aspects are often neglected or inadequately represented in finite element (FE) models, leading to inaccuracies in predicting electrical steel performance, especially in complex electromagnetic environments. This paper presents a multi-scale modeling approach, integrating a macroscopic FE model of a magnetic device with a microstructural scalar permeability model that accounts for the crystallographic textures of electrical steels. This approach demonstrates proficiency in predicting nonlinear anisotropic permeability and capturing magnetic anisotropy of electrical steels within a rotational tester, especially when anisotropy is predominantly governed by crystallographic texture and the angles between the B and H vectors are minimal. Furthermore, the model effectively captures the magnetic anisotropy in complex magnetic fields and geometric configurations of a permanent magnet motor. A comparative analysis of this model is conducted against three other material models: an isotropic model, a two-axis model, and a general-vector model. These models are based on different approaches, ranging from a single non-linear BH curve to comprehensive vector BH curves covering all directions. Among them, the general-vector model, reliant on extensive 2D vector BH measurements, is the most accurate but requires substantial experimental data.

Raw infrared image enhancement via an inverted framework based on infrared basic prior

Existing raw infrared image enhancement methods can effectively compress image and improve contrast. However, there still exist limitations. First, enhanced images are often over-exposed. Second, a high contrast but low noise enhanced image is difficult to be obtained due to the fact that the noise level increases with contrast. Third, the targets are not sufficiently salient in enhanced image. In this paper, we design an inverted enhancement framework to address the three limitations simultaneously. Specifically, we analyze the widely recognized features of raw infrared image and call them infrared image basic prior. That is, infrared detectors are often used to detect targets under special conditions and our attention mechanism is to focus on high radiation objects, but there are few targets in the scene. Then we modify the traditional image enhancement framework into an inverted framework based on infrared image basic prior and design an inverted nonlinear gray mapping curve, which avoids over-exposure and noise over-amplification. Furthermore, result is further improved by using layer decomposition model and gamma correction. Enhanced result yields the targets of our main interest. Finally, the extended applications are performed and show ability to stimulate the effectiveness of algorithms of related fields. Experiments show that our approach yields better results than state-of-the-art methods. A video of results is provided at https://github.com/wangyuro/Datashare1.

Numerical Analysis of High Frequency Transverse Instabilities in a Can-Type Combustor

Abstract Dry low emissions (DLE) systems are well-known to be susceptible to thermoacoustic instabilities. In particular, transverse, spinning modes of high frequency may appear, and lead to severe damage in a matter of seconds. The thermoacoustic response of an engine is usually specific to the combustor geometry, operating conditions and difficult to reproduce at the lab-scale. In this work, details of high frequency dynamics (HFD) observed during the early development phase of a new DLE system are provided, where a multipeaked spectrum was noticed during testing. Beginning with an analysis of the measured pressure spectra from three different concepts, an analytical model of the clockwise and anticlockwise transverse waves was fitted to the experimental data using a nonlinear curve fitting approach to produce a simple yet useful understanding of the phenomena. A flamelet-based large eddy simulation (LES) of the entire combustion system was used to complement this analysis and confirm the mode shapes using dynamic mode decomposition (DMD). Both approaches independently identified a spinning second-order mode as the dominant one in the high frequency regime. The LES indicates the coupling of a distortion of swirl profile with a precessing vortex core as a possible cause for the onset of instability. With regard to modeling sensitivities, it is shown that subgrid scale combustion modeling has a strong impact on predicted amplitudes. Ultimately, a thickened-flame model with a modified efficiency function provided consistent results.

Nonlinear statics of magneto-electro-elastic nanoplates considering flexomagnetoelectric effect based on nonlocal strain gradient theory

The nonlinear static behavior of hygrothermal magnetoelectroelastic(MEE) nanoplates considering the flexomagnetoelectric (FME) effect is researched by engaging the first-order shear deformation theory (FSDT). The constitutive equations of MEE nanoplates take into account the FME effect and hygrothermal effect. Leveraging the FSDT, von Karman's nonlinear equation and Hamilton's principle, the nonlinear control equation for hygrothermal MEE nanoplates can be derived by using the variational approach. The nonlocal strain gradient theory (NSGT) has application in the size effect of MEE nanoplates. The nonlocal nonlinear term in the control equation is handled by employing the Airy stress function, and then the non-linear mechanical model is solved by the Galerkin method. Thus, the nonlinear load-deflection curves (NLDC) of the MEE nanoplate are obtained via the introduction of material parameters, enabling an examination of the impact of various factors such as the FME effect, two small size parameters of NSGT and other parameters on the nonlinear bending behavior of MEE nanoplates. In conclusion, this study offers a theoretical foundation for taking into account the FME effect in the development of nanodevices, thereby contributing to advancements in this field.