Nonlinear Method Research Articles

Research on Variable Parameter Color Image Encryption Based on Five-Dimensional Tri-Valued Memristor Chaotic System.

To construct a chaotic system with complex characteristics and to improve the security of image data, a five-dimensional tri-valued memristor chaotic system with high complexity is innovatively constructed. Firstly, a pressure-controlled tri-valued memristor on Liu's pseudo-four-wing chaotic system is introduced. Through analytical methods, such as Lyapunov exponential map, bifurcation map and attractor phase diagram, it is demonstrated that the new system has rich dynamical behaviors with periodic limit rings varying with the coupling parameter of the system, variable airfoil phenomenon as well as transient chaotic phenomenon of chaos-periodic depending on the system parameter and chaos-quasi-periodic depending on the memristor parameter. The system is simulated with dynamic circuits based on Simulink. Secondly, the differently structured synchronous controls of chaotic systems are realized using a nonlinear feedback control method. Finally, based on the newly constructed five-dimensional chaotic system, a variable parameter color image encryption scheme is proposed to iteratively generate varying chaotic pseudo-random sequences by varying the system parameters, which will be used for repetition-free disambiguation, additive modulo left-shift diffusion and DNA encryption for the three components of RGB of the color image after chunking. The simulation results are analyzed by histogram, information entropy, adjacent pixel correlation, etc., and the images are tested using differential attack, noise attack and geometric attack, as well as analyzing the PSNR and SSIM of the decrypted image quality. The results show that the encryption method has a certain degree of security and can be applied to medical, military and financial fields with more complex environmental requirements.

Sharp lower bounds on the manifold widths of Sobolev and Besov spaces

We study the manifold n-widths of Sobolev and Besov spaces with error measured in the Lp-norm. The manifold widths measure how efficiently these spaces can be approximated by continuous non-linear parametric methods. Existing upper and lower bounds only match when the smoothness index q satisfies q≤p or 1≤p≤2. We close this gap, obtaining sharp bounds for all 1≤p,q≤∞ for which a compact embedding holds. In the process, we determine the exact value of the manifold widths of finite dimensional ℓqM-balls in the ℓp-norm when p≤q. Although this result is not new, we provide a new proof and apply it to lower bounding the manifold widths of Sobolev and Besov spaces. Our results show that the Bernstein widths, which are typically used to lower bound the manifold widths, decay asymptotically faster than the manifold widths in many cases.

The use of nonlinear analysis in understanding postural control: A scoping review

Nonlinear analyses have emerged as an approach to unraveling the intricate dynamics and underlying mechanisms of postural control, offering insights into the complex interplay of physiological and biomechanical factors. However, achieving a comprehensive understanding of the application of nonlinear analysis in postural control studies remains a challenge due to the various nonlinear measurement methods currently available. Thus, this scoping review aimed to identify existing nonlinear analyses used to study postural control in both dynamic and quiet tasks, and to summarize and disseminate the available literature on the use of nonlinear analysis in postural control. For this purpose, a scoping review was conducted and reported following the PRISMA Extension for Scoping Reviews (PRISMA-ScR) Checklist and Explanation. Searches were conducted up to July 2023 on PubMed/Medline, Embase, CINAHL, Web of Science, and Google Scholar databases, resulting in the inclusion of 397 unique studies. The main classes employed among the studies were entropy-based, fractal-based, quantification of recurrence plots, and quantification of stability, with a total of 91 different algorithms distributed among these classes. The most common condition used to study postural control was quiet standing, followed by dynamic standing and gait tasks. Although various algorithms were utilized for this purpose, sample entropy was employed in 43% of studies to explore mechanisms related to postural control. Among them, 28% were in quiet standing, 3.27% were in dynamic standing, and 4.78% to study postural control during the gait. The results also provide insights into nonlinear analysis for future studies, concerning the complexity and interactions within the postural control system across various task demands.

A score-based filter for nonlinear data assimilation

We propose a score-based generative sampling method for solving the nonlinear filtering problem with superior accuracy. A major drawback of existing nonlinear filtering methods, e.g., particle filters, is the low accuracy in handling high-dimensional nonlinear problems. To overcome this issue, we incorporate the score-based diffusion model into the recursive Bayesian filter framework to develop a novel score-based filter (SF). The key idea of SF is to store the information of the recursively updated filtering density function in the score function, instead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). By leveraging the reverse-time diffusion process, SF can generate unlimited samples to characterize the filtering density. An essential aspect of SF is its analytical update step, gradually incorporating data information into the score function. This step is crucial in mitigating the degeneracy issue faced when dealing with very high-dimensional nonlinear filtering problems. Three benchmark problems are used to demonstrate the performance of our method. In particular, SF provides surprisingly impressive performance in reliably capturing/tracking the 100-dimensional stochastic Lorenz system that is a well-known challenging problem for existing filtering methods.

Synthesis of CBO (Co3O4-Bi2O3) Heterogeneous Photocatalyst for Degradation of Fipronil and Acetochlor Pesticides in Aqueous Medium

The excessive use of pesticides has led to the harmful contamination of water reservoirs. Visible-light-driven photocatalysis is one of the suitable methods for the removal of pesticides from water. Herein, the development of CBO (Co3O4-Bi2O3) as a heterogeneous catalyst for the visible light-assisted degradation of Fipronil and Acetochlor pesticides is reported. After synthesis via coprecipitation using cobalt (II) nitrate hexahydrate (Co(NO3)2·6H2O), bismuth (III) nitrate pentahydrate (Bi(NO3)3·5H2O) and sodium hydroxide (NaOH) as precursor materials, the prepared CBO was characterized using advanced techniques including XRD, EDS, TEM, SEM, FTIR, and surface area and pore size analysis. Then, it was employed as a photocatalyst for the degradation of Fipronil and Acetochlor pesticides under visible light irradiation. The complete removal of Fipronil and Acetochlor pesticides was observed over CBO photocatalyst using 50 mL (100 mg/L) of each pesticide separately within 120 min of reaction. The reaction kinetics was investigated using a non-linear method of analysis using the Solver add-in. The prepared CBO exhibited a 2.8-fold and 2-fold catalytic performance in the photodegradation of selected pesticides than Co3O4 and Bi2O3 did, respectively.

An intelligent aortic valve model for complete cardiac cycle.

The aortic valve (AV) is crucial for cardiovascular (CV) hemodynamic, impacting cardiac output (CO) and left ventricular volumetric flow rate (LVQ). Its nonlinear behavior challenges standard LVQ prediction methods as well as CO one. This study presents a novel approach for modeling the AV in the CV system, offering an improved method for estimating crucial parameters like LVQ across various AV conditions, including aortic stenosis (AS). The model, based on AV channel length during the entire cardiac phase, introduces a time-varying AV resistance (TV-AVR) parameterized by the pressure ratio across the AV and LVQ, enabling the simulation of both healthy and AS-related conditions. To validate this model, in vitro measurements are compared using a hybrid mock circulatory loop device. An unconventional use of a convolutional neural network (CNN) corrects the model's estimates, eliminating the need for labeled datasets. This approach, incorporating real-time learning and transforming 1-D CV signals into 2-D tensors, significantly improves the accuracy of LVQ measurements, achieving an error rate of less than 3.41 ± 4.84% for CO in healthy conditions and 2.83 ± 1.35% in AS cases-a 33.13% enhancement over linear diode models. These results underscore the potential of this approach for enhancing the diagnosis, prediction, and treatment of AV diseases. The key contributions of the proposed method encompass nonlinear TV-AVR estimation, investigation of transient CV responses, prediction of instantaneous CO, development of a flexible framework for noninvasive measurements integration, and the introduction of an adjustable resistance model using an extended Kalman filter (EKF) and CNN combination, all without requiring labeled data.

Understanding racial differences in financial hardship among older adults surviving cancer.

Despite Medicare coverage, financial hardship is a prevalent issue among those diagnosed with cancer at age 65 years and older, particularly among those belonging to a racial or ethnic minority group. Sociodemographic, clinical, and area-level factors may mediate this relationship; however, no studies have assessed the extent to which these factors contribute to the racial/ethnic disparities in financial hardship. Surveys assessing financial hardship were completed by 721 White (84%) or Black (16%) patients (aged 65 years and older) who were diagnosed with breast (34%), prostate (27%), lung (17%), or colorectal (14%) cancer or lymphoma (9%) at the University of Alabama at Birmingham between 2000 and 2019. Financial hardship included material, psychological, and behavioral domains. Nonlinear Blinder-Oaxaca effect decomposition methods were used to evaluate the extent to which individual and area-level factors contribute to racial disparities in financial hardship. Black patients reported lower income (65% vs. 34% earning <$50,000) and greater scores on the Area Deprivation Index (median, 93.0 vs. 55.0). Black patients reported significantly higher rates of overall (39% vs. 18%), material (29% vs. 11%), and psychological (27% vs. 11%) hardship compared with White patients. Overall, the observed characteristics explained 51% of racial differences in financial hardship among cancer survivors, primarily because of differences in income (23%) and area deprivation (11%). The current results identify primary contributors to racial disparities in financial hardship among older cancer survivors, which can be used to develop targeted interventions and allocate resources to those at greatest risk for financial hardship.

A fourth-order accurate extrapolation nonlinear difference method for fourth-order nonlinear PIDEs with a weakly singular kernel

A fourth-order accurate extrapolation nonlinear difference method for fourth-order nonlinear PIDEs with a weakly singular kernel

Physicochemical properties and CO2 absorption performance of poly(ethylene glycol) 300 + hydroxyethyl ethylenediamine mixed solution

Density (ρ) and viscosity (η) data of the polyethylene glycol 300 (PEG300) and hydroxyethyl ethylenediamine (AEEA) mixed solution were measured at P = 1005 hPa and T = (298.15–318.15) K. Following these data, Jouyban-Acree model exhibited superior correlation to density in the mixed system compared to nonlinear least square method, while the McAllister four-body equation yielded a better fitting for kinematic viscosity than other models. Utilizing ρ and η data, the Redlich-Kister equation was employed for the systematic computation and analysis of excess molar volume (VmE), excess activation Gibbs free energy (ΔG*E), partial molar volumes (V1¯ and V2¯), and viscosity deviation (Δη) in the PEG300 (1) + AEEA (2) mixed solution. These excess properties indicated the advantageous nature of intermolecular binding in the PEG300 (1) + AEEA (2) mixed solution, further substantiated on the basis of various spectroscopic characterizations. Finally, under conditions of CO2 flow rate at 150 mL/min, absorption experiments were conducted for 4 h in the PEG300 (1) + AEEA (2) mixed solution, pure AEEA, and pure PEG300, which indicated that the mixed solution exhibited the highest CO2 absorption capacity of 0.95 mol CO2/mol AEEA, demonstrating superior absorption performance compared to the two pure substances.

Pointing correction based on limit cycles oscillators applied on a heliostats field digital twin

Digital twin models are an emerging topic that captures the dynamic response of physical systems to have a portrayal of digital representation. Complex systems such as heliostat fields for sustainable energy are good candidates for developing digital twins since the physical operation of facilities of this type can be highly time-consuming and weather-dependent. Therefore, a digital twin model of heliostat fields represents an adequate choice for the performance validation of new pointing correction algorithms with shorter assessing times. In this sense, one of the most important issues in the operation of heliostat fields for sustainable energy is to achieve a good accuracy of heliostats pointing to the target, even under physical errors of the solar field components and disturbances produced by external agents. However, since these types of disturbances have nonlinear characteristics, they should be dealt with by using nonlinear methods. This article presents a novel pointing correction technique based on nonlinear Limit Cycle Oscillators (LCOs) applied to the digital twin of a heliostat field. Analytical analysis, numerical verification, and further validation results are used to demonstrate the performance of the developed novel dynamic method.

Development of the scientific and pedagogical school of the department “Ground Transport and Technological Complexes”

The scientific article reflects the main stages of the historical development of the scientific and pedagogical school of the cycle “Technology of structural metals. Materials Science”, which is one of the areas of the department “Ground transport and technological complexes”. Employees of the department made a significant contribution to solving practical problems in assessing the effectiveness of existing technological processes for restoring the tread surface profile of wheel pairs of wheels, the proposed processes of face milling and turning when restoring the wheel rim profile, including the use of preliminary induction annealing to improve machinability, optimization of cutting conditions wheels based on linear and nonlinear programming methods. A large amount of research and implementation work has been carried out to improve the repair technology and increase the reliability of the wheel-motor unit of rail crews of railway rolling stock. Issues related to surfacing operations during repairs and increasing the wear resistance of deposited surfaces were considered.At the same time, the teachers of the department conduct training sessions on disciplines at a high methodological level, without which it is impossible to imagine a modern engineer.Over the years of work of the cycle “Technology of Structural Metals. Materials Science” a large number of textbooks, teaching aids, guidelines and manuals on laboratory work and course design, as well as collections of scientific papers, articles and monographs on the main areas of research work were published.The historical digression presented in this article gives an idea of the scientific potential of the department accumulated over many years, which can serve as a reliable basis for further development of new scientific directions.

Unique Operating Conditions Analysis of Turboshaft Engines Based on Nonlinear Integrated Model

The unique mission of the helicopter compared to the fixed-wing aircraft introduces challenges to the aerodynamic stability of the turboshaft engine. Thus, the assessment of the availability of stability margin for special operating conditions in the envelope of this equipment is required to guarantee flight safety. In this paper, a rapid nonlinear complete engine method is developed to investigate the effect of helicopter ground-effect operation and high-altitude hovering on aerodynamic stability by considering factors including inlet distortion and component matching. Research indicated that the most dangerous point of stability margin in a unique section of the flight envelope is high altitude hovering, with about a 16.7% reduction in available stability margin compared to standard ground test conditions. This paper also investigates the effects of typical helicopter ground effects on a turboshaft engine and shows that the stability margin will be reduced by a maximum of 1.43% in hovering if the influence of ground effects in the flight envelope is not considered in the design.

Phase field modeling of ductile fracture with isotropic hardening and radius return method

Phase field model has been investigated for brittle fracture in many static and dynamic scenarios, but its applications to ductile fracture is not as common as brittle fracture, especially implementing in software LS-DYNA with explicit scheme. In this study, an efficient LS-DYNA implementation of the phase field modeling of ductile fracture is presented and both with and without the split of elastic strain energy have been considered for the damage evolution. In more detail, plasticity formulation of ductile material with isotropic hardening is briefly presented first and then the governing equations of the classical phase field model are derived, which gives the displacement-phase coupled problem. For with the split of elastic strain energy, the shear component of elastic strain energy is considered for the damage evolution. The influence of degradation function on stress–strain curve is also investigated by using three kinds of function (polynomial function, algebraic fraction function and sigmoid function), which leads to linear and nonlinear finite element method (FEM) formulation of the phase field model and Newton–Raphson method is used to solve the nonlinear FEM formulation of the phase field model. A tensile bar test shows the influence of critical energy release rate and degradation function on stress–strain curve. Mode Ⅰ failure of three-point bending test, Mode Ⅱ failure of single-edge notched plate and mixed-mode failure of asymmetrical double-notched plate verify the proposed model in this study. From these simulations, with the split of elastic strain energy shows improvements on plastic deformation than without the split of elastic strain energy.

Stress and Strain Characteristics in Flexible Pavement Using Three-Dimensional Nonlinear Finite Element Analysis

AbstractA new numerical simulation was developed to obtain various structural parameters by employing a nonlinear finite element method using ABAQUS: stress, strain, and the displacement response of five layers on the flexible pavement. The primary purpose of this study was to develop a new simulation that can accurately and effectively characterize stress and strain problems in flexible pavement. New constitutive model equations were developed based on Hooke’s law the three-dimensional model for stress and strain. 40 kN wheel load was used to represent a set of dual tires, assuming a uniformly distributed contact area between the tire-pavement surfaced using linear viscoelastic and nonlinear viscoelastic materials. Four tire-inflation pressures were used 380, 490, 630, and 700 kPa. Results indicated that each flexible pavement layer created with a nonlinear viscoelastic material exhibited a 40% vertical plastic strain reduction compared to linear viscoelastic materials after 7000 s and repeated for 30,000 cyclic loadings. The implication of this newly developed constitutive model was verified against published experimental data. Analyses were completed to simplify the results model results considering the effects of stress and strain on flexible pavement layers. The newly developed constitutive model for solving stress and strain characterization problems can predict the effects on flexible pavement layers and various types of observed flexible pavement failure.

Machine learning-based modeling of interface creep behavior of grouted soil anchors with varying soil moistures

The interface creep behavior of the grouted soil anchor subject to varying soil moisture was investigated using the combined incorporation of experimental and data-driven modeling methods to establish an efficient and robust forecasting framework. This study carried out the rapid and creep pullout tests of element anchor specimens at various saturations and then utilized machine learning methods to predict the development of interface creep displacement. The stepwise loading strategy and nonlinear superposition method were combined to generate the interface shear creep curves of the element anchor specimens. A total of 936 data groups of the interface shear displacement were collected with changing soil moisture contents, interface shear time, and interface shearing stress. Next, this study explored the Back Propagation Neural Network (BPNN) and four other machine learning algorithms in predicting the interface creep behavior of the grouted soil anchor under various moisture conditions. As for the hyperparameters, the beetle antennae search (BAS) approach was employed to optimize the BPNN and random forest (RF) models. Finally, the boxplot and Taylor diagrams proved the BAS-BPNN demonstrated a better performance than BAS-RF in predicting the interface creep behavior. The consequent correlation coefficients ranged from 0.9613 to 0.9805 for BPNN, indicating the accuracy and reliability of the interface creep prediction. A partial dependence plot (PDP) was also introduced to visualize the established machine learning model. The threshold of moisture content near 28.7 % is found to switch the interface shear stress-displacement response from strain-stabilizing to strain-softening behavior and to result in the main moisture-increase-induced interface strength degradation. The soil moisture fluctuation leads to the development of interface shear displacement mainly observed in the early phase of 20 h after the onset of moisture change. The uncovered coupled impact of soil moisture condition and interface shear stress state can provide insights into the evaluation of the time-dependent in-service performance of grouted soil anchors embedded in clayey soils.

Geothermal resources and deep tectonic in Leh Ladakh (NW Himalaya), India: Inference from magnetotelluric studies

The geothermal resources and their connectivity with the deep tectonic are meaningful to understand through their structural geometry in the NW Himalayas. Therefore, over the NW-SE profiles, 23 audio Magnetotelluric (AMT) sites and over the SW-NE profile, 15 broadband Magnetotelluric (BBMT) sites were carefully chosen to provide the detailed structure. The electrical models were produced from a 2-D inversion algorithm based on the non-linear conjugate gradient method. The Chumathang-Mahe and Puga-Sumdo regions offer excellent geothermal potential as heat/fluid passes through the Mahe Fault (MF), Zildat Fault (ZF) and Kiagor Tso Fault (KTF). These faults are well revealed in the electrical models beneath the subsurface. The Puga Valley has an excellent geothermal resource at shallow depth. A ∼1000 m thick sulfide mineral body is defined with high conductivity (∼1 Ω-m). The crustal structure shows a highly conductive mid-crust beneath the Ladakh batholiths with no manifestation roots. The signs of the Indus-Tsangpo Suture Zone (ITSZ) and Shyok Suture Zone (SSZ) are well represented in the crustal model and are associated with the steep-dipping faults. The Chumathang-Mahe and Puga-Sumdo geothermal regions are connected with low resistivity body (C1) at shallow depths in the crustal model along the SW-NE profile and offer a path for deep fluid flow. The frictional heat generated in the process of the Indian plate subducting beneath the Tibetan plateau and the collision zone between India and Asia carried to melt. The high heat surface flow indicates the thermal origin of low resistivity. Thus, a ∼10 sq. km low resistivity reservoir is identified beneath the Tso Morari dome in the crustal model that overlies a resistivity feature. The high conductivity at mid-crust determined at active tectonic fabric may be potential geothermal resources yielding high well-productivity.

Frictional effect on the mechanical properties of bridge's semi-parallel stay cables under axial tensile loads

A novel analytical model is proposed to evaluate the influence of adjacent wire friction on the mechanical properties of semi-parallel stay cables. This model considers the bending and torsional stiffness of semi-parallel wires and the friction between adjacent contact wires. The finite difference method and nonlinear least squares method are used to solve the angle between the principal torsion-flexure axes and Frenet–Serret axes of the wires numerically, and each wire is solved sequentially according to the equation of the force transmission. The helical radius and angle of all wires after deformation are derived according to the angle, and the problem is iteratively solved until convergence of all wires. The effectiveness of the proposed model is verified via the refined finite element model of a 19-wire stay cable. The proposed method accurately evaluated the mechanical properties of adjacent wire friction on stay cable by analyzing the influence of angle on the semi-parallel wires, which is more conducive to understanding the fretting wear and fatigue behavior of wires and quantifying their damage.

Optimizing the Location of Supports under a Monolithic Floor Slab

Monolithic reinforced concrete floor slabs are one of the most common types of building structures, and their optimization is an urgent task. The article presents the methodology for finding the optimal position of point supports under a reinforced concrete floor slab of arbitrary configuration at arbitrary load. The slab is considered thin, elastic and isotropic, with constant over-the-area stiffness, that is, the reinforcement is not taken into account or is constant. The solution is performed using the finite element method in combination with the nonlinear optimization methods. Finite element analysis is implemented by authors in MATLAB (R2024a) environment in such a way that the location of the columns may not coincide with the nodes of the finite element mesh of the slab. This allows to significantly increase the efficiency of solving the optimization problem compared to previously used algorithms, including the Monte Carlo method. Boundary conditions are taken into account using the Lagrange multiplier method. As an optimization criterion, the maximum deflection value is used, as well as the value of the potential strain energy. The effectiveness of six nonlinear optimization methods is compared in the example of a square slab under the action of a uniformly distributed load. For solutions obtained using the pattern search, simulated annealing and internal point methods, the maximum deflections are at least 1.2 times higher than for solutions obtained using the particle swarm method and genetic algorithm. An example of real object optimization is also presented. By changing the position of seven columns, it was possible to reduce the maximum deflection of the floor slab by 1.6 times.

A Liouville optimal control framework in prostate cancer

In this work we present a new stochastic framework for obtaining optimal treatment regimes in prostate cancer. We model the realistic scenario of randomized clinical trials for incorporating randomness related to interaction between a prostate cancer cell and androgen cell quota, due to cancer heterogeneities, across different patients in a given group, using a Liouville partial differential equation. We then solve two optimization problems: one for determining the model parameters to fit the measured data and the second to determine the optimal androgen deprivation therapy. The optimization problems are implemented using a positive, stable, and conservative finite volume solver for the Liouville equations and the projected non-linear conjugate gradient method. Several numerical results, including comparison with ordinary differential equations modeling framework, demonstrate the robustness and accuracy of our proposed framework to obtain optimal treatment regimes in real time.

Synergistic activation of peroxymonosulfate by 3D CoNiO2/Co core-shell structure biochar catalyst for sulfamethoxazole degradation

In this study, a 3D CoNiO2/Co core–shell structure biochar catalyst derived from walnut shell was synthesized by hydrothermal and ion etching methods. The prepared BC@CoNi-600 catalyst exhibited exceptional peroxymonosulfate (PMS) activation. The system achieved 100 % degradation of sulfamethoxazole (SMX). The reactive oxygen species in the BC@CoNi-600/PMS system included SO4−, OH, and O2−. Density functional theory calculations explored the synergistic effects between nickel–cobalt bimetallic and carbon matrix during PMS activation. The unique 3D core–shell structure of BC@CoNi-600 features an outer nickel–cobalt bimetallic layer with exceptional PMS adsorption capacity, while protecting the zero-valence Co of the inner layer from oxidation. Based on the experimental-data, machine learning modeling mechanism, and information theory, a nonlinear modeling method was proposed. This study utilizes a machine learning approach to investigate the degradation of SMX in complex aquatic environments. This study synthesized a novel biochar-based catalyst for activated PMS and provided unique insights into its environmental applications.