Nonlinear Model Research Articles

Nanoscale nonlocal thermal transport and thermal field emission in high-current resonant tunnel structures

We present a nonlinear model of thermal field emission in resonant tunneling nanostructures with multiple barriers and potential wells, based on an accurate determination of the quantum potential shape and a rigorous solution of the Schrödinger equation, while considering thermal balance. The model applies to vacuum and semiconductor resonant tunnel diode and triode structures with two and three electrodes and to the general case of two-way tunneling with electrode heating. The complete balance of heat release and transfer is accounted for, with heat transport considered ballistic. This approach can also be extended to the non-stationary case, incorporating the influence of space charge. The short flight time of electrons in such structures makes them promising for the fabrication of THz devices.

On the Performance and Fiber Nonlinearity Modeling of Learned Digital Back-Propagation in the Presence of DAC and ADC Quantization Noise

On the Performance and Fiber Nonlinearity Modeling of Learned Digital Back-Propagation in the Presence of DAC and ADC Quantization Noise

Non-linear development in statistical learning of visual orthographic regularities

Statistical learning is a core ability for individuals in extracting and integrating regularities and patterns from linguistic input. Yet, the developmental trajectory of visual statistical learning has not been fully examined in the orthographic learning domain. Employing an artificial orthographic learning task, we manipulated three levels of positional consistency of radicals, i.e., high (100%), moderate (80%), and low (60%), embedded in pseudocharacters to investigate visual statistical learning across a wide age range between 4–12-year-olds and adults. The non-linear power-function models indicated that the rates of improvement in acquiring varying positional consistencies increased with age, particularly for high and moderate levels. Specifically, we observed a significant enhancement in statistical learning abilities between the ages of 4–5 years and 5–6 years, followed by a stabilization of performance after 8–9 years. Our findings support the age-dependent perspective that individuals’ visual statistical learning ability improves significantly in early childhood and then decelerates its improvement progressively until adulthood.

Comparative Analysis of Machine Learning Algorithms Used for Translating Aptamer-Antigen Binding Kinetic Profiles to Diagnostic Decisions.

Current approaches for classifying biosensor data in diagnostics rely on fixed decision thresholds based on receiver operating characteristic (ROC) curves, which can be limited in accuracy for complex and variable signals. To address these limitations, we developed a framework that facilitates the application of machine learning (ML) to diagnostic data for the binary classification of clinical samples, when using real-time electrochemical measurements. The framework was applied to a real-time multimeric aptamer assay (RT-MAp) that captures single-frequency (12.6 Hz) impedance data during the binding of viral protein targets to trimeric aptamers. The impedance data collected from 172 COVID-19 saliva samples were processed through multiple nonlinear regression models to extract nine key features from the transient signals. These features were then used to train three supervised ML algorithms─support vector machine (SVM), artificial neural network (ANN), and random forest (RF)─using a 75:25 training-testing ratio. Traditional ROC-based classification achieved an accuracy of 83.6%, while ML-based models significantly improved performance, with SVM, ANN, and RF achieving accuracies of 86.0%, 100%, and 100%, respectively. The ANN model demonstrated superior performance in handling complex and high-variance biosensor data, providing a robust and scalable solution for improving diagnostic accuracy in point-of-care settings.

Optimizing photovoltaic power plant forecasting with dynamic neural network structure refinement

Reliable prediction of photovoltaic power generation is key to the efficient management of energy systems in response to the inherent uncertainty of renewable energy sources. Despite advances in weather forecasting, photovoltaic power prediction accuracy remains a challenge. This study presents a novel approach that combines genetic algorithms and dynamic neural network structure refinement to optimize photovoltaic prediction. This methodology dynamically adjusts the neural network parameters during training, including the number of neurons, transfer functions, weights, and biases, to minimize the root mean square error. Evaluation was performed on twelve representative days using annual, monthly, and seasonal data, and a comparison was made with multiple linear regression and nonlinear autoregressive neural network models, demonstrating the approach’s effectiveness. Evaluation metrics such as mean square error, R-value, and mean percentage error reveal promising prediction accuracy. MATLAB is used for modeling, training, and testing, and a real 4.2 kW PV plant is used for validation. The results indicate significant improvements, with mean square errors as low as 20 W on cloudy days and 175 W on sunny days. The proposed methodology achieves prediction versus target regressions consistency, with R values ranging from 0.95824 to 0.99980, highlighting its efficiency in providing reliable predictions of PV power generation.

Low-dose ionizing radiation and the exposure–lag response: protocol for a prospective cohort study on The Health Effects of Chongqing Occupational Radiation Workers

IntroductionAlthough the effects of ionizing radiation on radiation workers have been extensively studied in China, no prospective cohort study has been conducted in Chongqing. Furthermore, previous cohorts have not provided a broad-gauge assessment of the temporal relationship between low-dose occupational radiation exposure and the risk of health outcomes.MethodsA prospective cohort study will be carried out focusing on radiation workers in Chongqing. Health examination outcomes and radiation dose monitoring data will be collected and analyzed using the distributed lag non-linear model (DLNM) combined with generalized additive model (GAM) or generalized linear model (GLM) to evaluate the exposure-lag response relationship.DiscussionOur study will enhance our understanding of the exposure-lag response association between occupational radiation exposure and the health of radiation workers based on DLNM.Clinical trial registrationChinese Clinical Trials Registry, ChiCTR2400081804.

Model and mesh selection from a mCRE functional in the context of parameter identification with full-field measurements

Abstract In this paper, we propose a general deterministic framework to question the relevance, assess the quality, and ultimately choose the features (in terms of model class and discretization mesh) of the employed computational mechanics model when performing parameter identification. The goal is to exploit both modeling and data at best, with optimized model accuracy and computational cost governed by the richness of available experimental information. Using the modified Constitutive Relation Error concept based on reliability of information and the construction of optimal admissible fields, we define rigorous quantitative error indicators that point out individual sources of error contained in the identified computational model with regards to (noisy) observations. An associated adaptive strategy is then proposed to automatically select, among a hierarchical list with increasing complexity, some parameterized mathematical model and finite element mesh which are consistent with the content of experimental data. In addition, the approach is computationally enhanced by the complementary use of model reduction techniques and specific nonlinear solvers. We focus here on experimental information given by full-field kinematic measurements, e.g. obtained by means of digital image correlation techniques, even though the proposed strategy would also apply to sparser data. The performance of the approach is analyzed and validated on several numerical experiments dealing with anisotropic linear elasticity or nonlinear elastoplastic models, and using synthetic or real observations.

Investigation of infertility treatments on infertile couples through fractional-order modeling approach

In this paper, our aim is to construct a nonlinear mathematical model to study the impact of treatment on the infertility problem. We utilize a well-known Caputo derivative with fractional-order to decrease the issue of infertility treatments. Banach fixed-point theory is used to determine the existence and uniqueness of the suggested model. Equilibrium points have been calculated by generating reproduction numbers as a part of local stability analysis, and Ulam–Hyers–Rassias stability is discussed as a generalized form of system to prove global stability. We use a fractional-order Euler’s method to determine the numerical and graphical results. The result manifests the improvement of achieving a healthy pregnancy through hormonal and IVF treatment in women.

Collaborative Control and Intelligent Optimization of a Lead–Bismuth Cooled Reactor Based on a Modified PSO Method

Accelerator-driven subcritical (ADS) reactors with lead–bismuth eutectic (LBE) coolants are some of the Gen-IV nuclear energy systems that can generate clean electricity and potentially transmute spent fuel. The dynamic characteristics and control strategy of an ADS reactor are substantially different from those of traditional nuclear reactors. In this paper, a new collaborative control strategy is proposed using an accelerator beam and a control rod, and the control system’s parameters are optimized using a modified particle swarm optimization (PSO) method. To test the control performance, a simulation platform is developed with a nonlinear reactor dynamic model, a power compensation control system and a coolant temperature control system. Four typical control transients are used, including a ±10% full-power (FP) step change load and a ±5% FP/min linear variable load. The simulation results show that the collaborative control strategy has a better load tracking capability and a higher power control accuracy than the beam single-control strategy and the rod single-control strategy. The results also show that the performance of the collaborative control system in terms of the reactor’s power and coolant temperature is significantly improved based on the modified PSO parameter optimization.

Characteristic Wavelength Selection and Surrogate Monitoring for UV–Vis Absorption Spectroscopy-Based Water Quality Sensing

Ultraviolet-visible (UV–Vis) absorption spectroscopy for in situ water quality sensing has garnered increasing attention. However, the selection of the characteristic wavelengths for water quality indicators has been underexplored in existing studies, resulting in surrogate monitoring models with low accuracy and high complexity. This research used field data from the Maozhou River in Shenzhen. The accuracy of the surrogate model based on the wavelength selection method is 134.8%, 52.5%, and 13.5% improvement in accuracy compared to the single wavelength method, the PCA method, and the full spectrum method, respectively. We investigate seven characteristic wavelength optimisation algorithms and five machine learning models for surrogate monitoring of five water quality indicators: TOC, BOD5, COD, TN, and NO3-N. The results indicate that the competitive adaptive reweighted sampling (CARS) method for wavelength selection, combined with ridge regression as a surrogate monitoring model, achieved the best performance in this study. The determination coefficient (R2) of the five water quality indicators were 0.80, 0.64, 0.82, 0.97, and 0.96, respectively. The study shows that for watersheds with relatively stable water chemical components, there is no need to use overly complex nonlinear models, and the regression model with characteristic wavelength selection can achieve good prediction results. This study provides detailed technical information on river water quality spectral surrogate monitoring, offering an important practice reference.

Efficiency of Nitrate Removal from Groundwater by Adsorption on Raw and Treated Bentonite

The objective of this study was to treat groundwaters with a high initial nitrate (NO3−) content (125 mg/L, and 177 mg/L) by adsorption onto a local bentonite in its raw state (RB), treated with a ratio of H2SO4/bentonite = 0.2 (B0.2), and another treated with a ratio of H2SO4/bentonite = 0.6 (B0.6). Non-linear modelling of the nitrate adsorption kinetics of two water samples showed the pseudo-first-order model was the best fit, confirming that nitrate retention on each adsorbent was due to chemisorption. The intra-particle diffusion curves were multi-linear, indicating that there are other mechanisms influencing nitrate ion adsorption on bentonite than intra-particle diffusion. The effectiveness of the adsorbents tested was in the following order: B0.6 > B0.2 > RB. This finding demonstrates that acid activation of the clay improves its characteristics. The optimal adsorbent dose was found to be 1 g/L after changing the bentonite dose from 0.1 to 4 g/L. The pH of the treatment affects nitrate removal rates. The greatest results are achieved at pH levels close to 6. It also appears that the treatment was more effective for water with low initial nitrate levels.

Dynamical analysis of multi-soliton and interaction of solitons solutions of nonlinear model arise in energy particles of physics

Dynamical analysis of multi-soliton and interaction of solitons solutions of nonlinear model arise in energy particles of physics

Non-Linear Hyperelastic Model Analysis and Numerical Validation of 3D Printed PLA+ Material Incorporating Various Infill Densities

Additive manufacturing (AM) or 3D printing technology creates a tangible object by adding successive layers of materials. Nowadays, 3D printing is used for developing both metal and non-metal products. In the advancement of 3D printing technology, material specimen design, modification, and testing become very simple, especially for non-metal materials, such as hyperelastic, thermoplastic, or rubber-like materials. However, proper material modeling and validation are required for the analysis of these types of materials. In this study, 3D printed poly lactic acid (PLA+) material behavior is analyzed numerically for validation in the counterpart of experimental analysis to evaluate their behavior in both cases. The specimen was designed in SolidWorks by following ASTM D638 dimension standards with proper infill densities and raster angle or infill orientation angle. These infill layer densities and angles of orientation play an important role in the mechanical behavior of the specimen. This paper aims to present a numerical validation of five infill densities (20%, 40%, 60%, 80%, and 100%) for a ±45-degree infill angle orientation by incorporating a nonlinear hyperelastic model. Results indicate that infill densities affect the mechanical behavior of PLA+ material. The result also suggested that neo-Hookean and Mooney–Rivlin are the best-fitted hyperelastic material models for these five separate linear infill densities. However, neo-Hookean is easier to analyze, as it has only one parameter and a new equation is developed in this study for determining the parameter for different infill densities.

Second-order skewness of the maximum likelihood estimators in symmetric nonlinear regressions

The symmetric nonlinear regression model encompasses a wide class of models like the nonlinear normal, Student-t, and power exponential regression models, among others. We provide a simple closed-form expression, in matrix form, for the second-order skewness of the maximum likelihood estimators of the regression parameters, as well as a simple expression for the second-order skewness of the maximum likelihood estimator of the scale parameter in the symmetric nonlinear regression model. The matrix formula involves simple operations on matrices and vectors, which is quite suitable for computer implementation. We present Monte Carlo simulations to verify the behaviour of the second-order skewness in small-sized samples in this class of regression models. Real data applications are also considered to show the practical importance of our results.

Coefficient of Restitution in a Low-Velocity Normal Impact Using Elastoplastic Contact Stiffness

Abstract Elastoplastic deformation during particle impact occurs widely in many engineering applications. The material properties characterizing both the elastic and plastic behavior play an important role in particle impact. A non-linear contact stiffness-based model representing the elastic and plastic deformation of the material is used to obtain the coefficient of restitution during the impact of a sphere on a deformable substrate. The model consists of the Maxwell combination of perfectly plastic component and a non-linear elastic component. The proposed model is used to estimate the plastic energy dissipation during the impact. An analytical solution is obtained for residual contact radius and coefficient of restitution expressed in terms of experimentally determinable parameters. Our approach yields a single dimensionless parameter referred to as the “indentation parameter,” Λ, and it is shown that the impact response and coefficient of restitution for various impact situations can be determined based on this indentation parameter. The proposed model accurately predicts the residual contact radius and coefficient of restitution, validated through experimental results of low-velocity impacts (1–4 m/s) over a flat sample of aluminum alloy (Al6061) impacted by steel and zirconia balls. The present model is further compared with other existing theoretical contact models for the elastoplastic impact and the extension of the present model for other dissipative systems is also discussed.

An Actual Case Study of a Deterministic Multi-Objective Optimization Model in a Defined Contribution Faculty Pension System

The optimal management of pension funds has become increasingly critical. As the population ages, the effective management of pension funds is essential for the social security system. The primary goal of this paper is to develop a deterministic nonlinear multi-objective optimization model to determine the contribution rates in a defined contribution pension system. The computational optimization model was implemented using the LINGO language. In the first part of this study, three main scenarios were analyzed considering different inflation rates, focusing on the objective function that minimizes the salary percentages workers pay when saving for a specified period while aiming to achieve a certain number of coverage years. The first scenario assumes that the worker desires an economic quality equivalent to their working life, showing that contribution rates range from 10% to 30% (with a 3% inflation rate). The second scenario posits that the worker only requires 80% of their equivalent salary during retirement, resulting in contribution rates directly proportional to those in scenario 1 (using the same parameters). The third scenario speculates that inflation may reach 7% per year, causing contribution rates to rise significantly from 40% to 80%. Finally, the Pareto front illustrates the trade-off between the contribution rate and the coverage years based on scenario 1 parameters.

A Mathematical Programming Approach for Joint Optimization of Wind Farm Layout and Cable Routing Based on a Three‐Dimensional Gaussian Wake Model

ABSTRACTWind energy is currently one of the most promising alternative energy sources. The optimization of the wind farm layout and the cable layout are two important elements in the design of wind farms. Since increasing the distance between turbines can reduce wake loss but increase cable cost, these two optimizations are coupled and jointly affect the revenue of wind farms. In this paper, we propose a novel nonlinear mathematical programming model based on the 3D Gaussian wake model and use a mathematical programming approach to optimize the layout of the wind farm and the cable layout together, considering both power generation and cable cost. In this method, some of the constraints were linearized to facilitate the solution process. The optimization results show that profit increased by 9.07% when using annual economic efficiency as the objective function, compared with using energy production as the objective function.

The fractional analysis of (2+1)-dimensional nonlinear time-fractional Rosenau-Hyman model using Natural homotopy transform method

The fractional analysis of (2+1)-dimensional nonlinear time-fractional Rosenau-Hyman model using Natural homotopy transform method

Novel exploration of machine learning solutions with supervised neural structures for nonlinear cholera epidemic probabilistic model with quarantined impact

Novel exploration of machine learning solutions with supervised neural structures for nonlinear cholera epidemic probabilistic model with quarantined impact

Pressure-Dependent Nonlinearities of a Compact Hydropneumatic Strut with Integrated Gas–Oil Chamber

<div>Hydropneumatic Struts (HPS) are widely implemented in automobile, aerospace, and construction industries, mainly for the purpose of vibration and shock absorption. The HPS design with integrated gas–oil chamber is relatively more compact and robust, while mixing gas and oil inside the HPS generates gas–oil emulsion and more nonlinearities. This study formulated a nonlinear analytical model of the compact HPS with gas–oil emulsion, considering the real gas law and pressure-dependent LuGre friction model. The polytropic version of the van der Waals (vdW) method for real gas is applied to represent the thermodynamic behavior of nitrogen. The experimental data were collected at a near temperature of 30°C with three charging pressures under excitations in the frequency range of 0.5–6 Hz, considering two flow connection configurations between chambers as one- and two-bleed orifice. The nonlinear behavior of the gas volume fraction of the emulsion was identified based on peak strut velocity and charge pressure. Discharge coefficients of bleed and check valves were determined as a function of the instantaneous pressure difference between chambers. The parameters of the pressure-dependent LuGre model, such as the stiction force and Coulomb force apart from stiffness and damping coefficient of bristle deflection, were also investigated considering the effect of pressure variation. Compared to the generally used ideal gas and models, the proposed model considerably improved the prediction accuracy of the total force and pressures of HPS, with normalized root-mean-square deviations of about 8%.</div>