Search Results (161)

In this article, we investigate the fractional soliton solutions as well as the chaotic analysis of the fourth-order nonlinear Ablowitz–Kaup–Newell–Segur wave equation. This model is considered an intriguing high-order nonlinear partial differential equation that integrates additional spatial and dispersive effects to extend the concepts to more intricate wave dynamics, relevant in engineering and science for understanding complex phenomena. To examine the solitary wave solutions of the proposed model, we employ sophisticated analytical techniques, including the generalized projective Riccati equation method, the new improved generalized exponential rational function method, and the modified F-expansion method, along with mathematical simulations, to obtain a deeper insight into wave propagation. To explore desirable soliton solutions, the nonlinear partial differential equation is converted into its respective ordinary differential equations by wave transforms utilizing $\beta$-fractional derivatives. Further, the solutions in the forms of bright, dark, singular, combined, and complex solitons are secured. Various physical parameter values and arrangements are employed to investigate the soliton solutions of the system. Variations in parameter values result in specific behaviors of the solutions, which we illustrate via various types of visualizations. Additionally, a key aspect of this research involves analyzing the chaotic behavior of the governing model. A perturbed version of the system is derived and then analyzed using chaos detection techniques such as power spectrum analysis, Poincaré return maps, and basin attractor visualization. The study of nonlinear dynamics reveals the system’s sensitivity to initial conditions and its dependence on time-decay effects. This indicates that the system exhibits chaotic behavior under perturbations, where even minor variations in the starting conditions can lead to drastically different outcomes as time progresses. Such behavior underscores the complexity and unpredictability inherent in the system, highlighting the importance of understanding its chaotic dynamics. This study evaluates the effectiveness of currently employed methodologies and elucidates the specific behaviors of the system’s nonlinear dynamics, thus providing new insights into the field of high-dimensional nonlinear scientific wave phenomena. The results demonstrate the effectiveness and versatility of the approach used to address complex nonlinear partial differential equations. Full article

In this article, we present a nonlocal Cahn–Hilliard (nCH) equation incorporating a space-dependent parameter to model microphase separation phenomena in diblock copolymers. The proposed model introduces a modified formulation that accounts for spatially varying average volume fractions and thus captures nonlocal interactions between distinct subdomains. Such spatial heterogeneity plays a critical role in determining the morphology of the resulting phase-separated structures. To efficiently solve the resulting partial differential equation, a Fourier spectral method is used in conjunction with a linearly stabilized splitting scheme. This numerical approach not only guarantees stability and efficiency but also enables accurate resolution of spatially complex patterns without excessive computational overhead. The spectral representation effectively handles the nonlocal terms, while the stabilization scheme allows for large time steps. Therefore, this method is suitable for long-time simulations of pattern formation processes. Numerical experiments conducted under various initial conditions demonstrate the ability of the proposed method to resolve intricate phase separation behaviors, including coarsening dynamics and interface evolution. The results show that the space-dependent parameters significantly influence the orientation, size, and regularity of the emergent patterns. This suggests that spatial control of average composition could be used to engineer desirable microstructures in polymeric materials. This study provides a robust computational framework for investigating nonlocal pattern formation in heterogeneous systems, enables simulations in complex spatial domains, and contributes to the theoretical understanding of morphology control in polymer science. Full article

This article investigates the inverse optimal fault-tolerant formation-containment control problem for a group of unmanned helicopters, where the leaders form a desired formation pattern under the guidance of a virtual leader while the followers move toward the convex hull established by leaders. To facilitate control design and stability analysis, each helicopter’s dynamics are separated into an outer-loop (position) and an inner-loop (attitude) subsystem by exploiting their multi-time-scale characteristics. Next, the serial-parallel estimation model, designed to account for prediction error, is developed. On this foundation, the composite updating law for network weights is derived. Using these intelligent approximations, a fault estimation observer is constructed. The estimated fault information is further incorporated into the inverse optimal fault-tolerant control framework that avoids tackling either the Hamilton–Jacobi–Bellman or Hamilton–Jacobi–Issacs equation. Finally, simulation results are presented to demonstrate the superior control performance and accuracy of the proposed method. Full article

This research addresses the problem of the initial synthesis of kinematic chains with spherical kinematic pairs, which are essential in the design of spatial mechanisms used in robotics, aerospace, and mechanical systems. The goal is to establish the existence of solutions for defining the geometric and motion constraints of these kinematic chains, ensuring that the synthesized mechanism achieves the desired motion with precision. By formulating the synthesis problem in terms of nonlinear algebraic equations derived from the spatial positions and orientations of the links, we analyze the conditions under which a valid solution exists. We explore both analytical and numerical methods to solve these equations, highlighting the significance of parameter selection in determining feasible solutions. Specifically, our approach demonstrates the visualization of fixed points, such as A, B, and C, alongside their spatial differences with respect to reference points and transformation matrices. We detail methods for plotting transformation components, including rotation matrix elements (e, m, and n) and derived products from these matrices, as well as the representation of angular parameters (θ_i, ψ_i, and $\phi$_i) in a three-dimensional context. The proposed techniques not only facilitate the debugging and analysis of complex kinematic behaviors but also provide a flexible tool for researchers in robotics, computer graphics, and mechanical design. By offering a clear and interactive visualization strategy, this framework enhances the understanding of spatial relationships and transformation dynamics inherent in multi-body systems. Full article

The heart rate slow component (_scHR) is an intensity-dependent HR increment that emerges during constant exercises, partially dissociated from metabolism ($\dot{\mathrm{V}}$O₂). The _scHR has been observed during constant-workload exercise in young and older adults. Unless this _scHR is accounted for, exercise prescription using HR targets lead to an undesired reduction in metabolic intensity over time. Purpose: The purpose of this study is to characterize _scHR across intensities, sex, and age to develop and validate a predictive equation able to maintain the desired metabolic stimulus over time in a constant aerobic exercise session. Methods: In our study, 66 individuals (35 females; 35 ± 13 yrs) performed the following: (i) a ramp-test for respiratory exercise threshold (GET and RCP) and maximal oxygen uptake ($\dot{\mathrm{V}}$O_2max) detection, and (ii) 6 × 9-minute constant exercises at different intensities. The _scHR was calculated by linear fitting from the fifth minute of exercise (bpm⋅min⁻¹). A multiple-linear equation was developed to predict the _scHR based on individual and exercise variables. The validity of the equation was tested on an independent sample by a Pearson correlation and Bland–Altman analysis between the measured and estimated HR during constant exercises. Results: The _scHR increases with intensity and is larger in males (p < 0.05). A multiple-linear equation predicts the _scHR based on the relative exercise intensity to RCP, age, and sex (r² = 0.54, SEE = 0.61 bpm⋅min⁻¹). _scHR (bpm⋅min⁻¹) = −0.0514 + (0.0240 × relative exercise intensity to RCP) − (0.0172 × age) − (0.347 × Sex (males = 0 and females score = 1)). In the independent sample, we found an excellent correlation between the measured and estimated HR (r² = 0.98, p < 0.001) with no bias (−0.01 b·min⁻¹, z-score= −0.04) and a fair precision (±4.09 b·min⁻¹). Conclusions: The dynamic of the _scHR can be predicted in a heterogeneous sample accounting for the combined effects of relative intensity, sex, and age. The above equation provides the means to dynamically adapt HR targets over time, avoiding an undesired reduction in the absolute and relative training load. This strategy would allow the maintenance of the desired metabolic stimulus ($\dot{\mathrm{V}}$O₂) throughout an exercise session in a heterogeneous population. Full article

Advanced nanocomposite membranes incorporate nanomaterials within a polymer matrix to augment the mechanical strength of the resultant product. Characterizing these membranes through molecular modeling necessitates specialized approaches to accurately capture the length scales, time scales, and structural complexities inherent in polymers. To address these requirements, an efficient simulation protocol is proposed, utilizing coarse-grained (CG) molecular dynamics simulations to examine the mechanical properties of polyethylene/single-walled carbon nanotube (PE/SWCNT) composites. This methodology integrates CG potentials derived from the statistical associating fluid theory (SAFT-$\gamma$ Mie) equation of state and a modified Tersoff potential as a model for SWCNTs. A qualitative correspondence with benchmark classical all-atom models, as well as available experimental data, is observed, alongside enhanced computational efficiency. Employing this CG model, the focus is directed at exploring the mechanical properties of PE/SWCNT composites under both tensile and compressive loading conditions. The investigation covered the influence of SWCNT size, dispersion, and weight fraction. The findings indicate that although SWCNTs enhance the mechanical strength of PE, the extent of enhancement marginally depends on the dispersion, filler size, and weight fraction. Fracture strengths may be elevated by 20% with a minor incorporation of SWCNTs. Under compression, the incorporation of SWCNTs into the composites results in a transformation from brittle to tough materials. These insights contribute to the optimization of PE/SWCNT composites, emphasizing the importance of considering multiple factors to fine-tune the desired mechanical performance. Full article

Anguilliform locomotion, an efficient aquatic locomotion mode where the whole body is engaged in fluid–body interaction, contains sophisticated physics. We hypothesized that data-driven modeling techniques may extract models or patterns of the swimmers’ dynamics without implicitly measuring the hydrodynamic variables. This work proposes empirical kinematic control and data-driven modeling of a soft swimming robot. The robot comprises six serially connected segments that can individually bend with the segmental pneumatic artificial muscles. Kinematic equations and relations are proposed to measure the desired actuation to mimic anguilliform locomotion kinematics. The robot was tested experimentally and the position and velocities of spatially digitized points were collected using QualiSys^® Tracking Manager (QTM) 1.6.0.1. The collected data were analyzed offline, proposing a new complex variable delay-embedding dynamic mode decomposition (CDE DMD) algorithm that combines complex state filtering and time embedding to extract a linear approximate model. While the experimental results exhibited exotic curves in phase plane and time series, the analysis results showed that the proposed algorithm extracts linear and chaotic modes contributing to the data. It is concluded that the robot dynamics can be described by the linearized model interrupted by chaotic modes. The technique successfully extracts coherent modes from limited measurements and linearizes the system dynamics. Full article

The development of copper-based materials with a high efficiency and low cost is desirable for use in iodine (I₂) remediation. Herein, Cu⁰-nanoparticles-functionalized, ZIF-8 (Zeolite Imidazole Framework-8)-derived, nitrogen-doped carbon composites (Cu@Zn-NC) were synthesized by ball milling and pyrolysis processes. The as-prepared composites were characterized using SEM, BET, XRD, XPS, and FT-IR analyses. The results showed that the morphology of ZIF-8 changed from a leaf-like structure into an irregular structure after the introduction of a copper salt and carbonization. The copper in the pyrolysis samples was mainly in the form of Cu⁰ particles. The presence of an appropriate amount of Cu⁰ particles could increase the specific surface area of Cu@Zn-NC. The subsequent batch adsorption results demonstrated that the as-fabricated composites showed high I₂ adsorption amounts (1204.9 mg/g) and relatively fast dynamics in an iodine–cyclohexane solution when the Cu content was 30% and the pyrolysis temperature was 600 °C, outperforming the other Cu-based materials. The isothermal adsorption followed both Langmuir and Dubinin–Radushkevich isotherm models, while the kinetics of I₂ adsorption followed a pseudo-second-order kinetic model. The activation energy (E_α) of the adsorbent was determined to be 47.2 kJ/mol, according to the Arrhenius equation. According to the experimental and DFT analyses, I₂-Zn interactions and I₂-Cu⁰ chemisorption jointly promoted the elimination of iodine. In general, this study provided an operative adsorbent for the highly effective capture of iodine in solution, which might be worth applying on a large scale. Full article

This study proposes a nonlinear adaptive optimal control method, the adaptive H₂ control method, applied to the trajectory tracking problem of the wheeled mobile robot (WMR) with four-wheel mecanum wheels. From the perspective of solving mathematical problems, finding an analytical adaptive control solution that satisfies the adaptive H₂ performance criterion for the trajectory tracking problem of the WMR with four-wheel mecanum wheels is an extremely challenging task due to the high complexity of the dynamic system. To analytically derive the control law and adaptive control law for this trajectory tracking problem, a proportional-derivative (PD) type transformation is employed to formalize the trajectory tracking error dynamics between the WMR and the desired trajectory (DT). Based on an in-depth analysis of the trajectory tracking error dynamics, a closed-form adaptive control law is analytically derived from the highly complex nonlinear dynamic system equations. This control law provides a solution to the trajectory tracking problem of the WMR while satisfying the adaptive H₂ performance criterion. The proposed adaptive nonlinear control method offers a simple control structure and advantages such as improved energy efficiency. Finally, simulations and experimental implementations were conducted to verify the performance of the proposed adaptive H₂ control method and the H₂ control method in tracking the DT. The results demonstrate that, compared to the H₂ control method, the adaptive H₂ control method exhibits superior trajectory tracking performance, particularly in the presence of significant model uncertainties. Full article

Control delay phenomena, such as time delays and actuator lags, can compromise the control performance of autonomous mobility systems, leading to increased control errors. Therefore, it is essential to develop a control delay compensation algorithm. This paper proposes a Lyapunov-based backstepping steering control algorithm to compensate for control delays in autonomous mobility systems. To estimate the control delay in the steering system, the Recursive Least Squares (RLS) algorithm was employed to calculate the time constant in real time. The control delay was estimated using an RLS designed based on a first-order differential equation. A backstepping steering controller was developed to calculate the desired steering angle using simplified error dynamics for reference path tracking. The control errors, specifically the lateral preview and yaw angle errors, were derived by calculating the path error between the current position and the waypoint. The performance of the proposed control algorithm was evaluated using the DC motor and CarMaker software 8.1.1(IPG Automotive, Karlsruhe, Germany) under scenarios involving sinusoidal input and four-curved loop and S-curved paths respectively. Full article

The conventional approach to intensity-modulated radiation therapy treatment planning involves two distinct strategies: optimizing an evaluation function while accounting for dose constraints, and solving feasibility problems using feasibility-seeking projection methods that incorporate inequality constraints. This paper introduces a novel iterative scheme within the framework of continuous dynamical systems, wherein constraint conditions dynamically evolve to enhance the optimization process. The validity of dynamically varying dose constraints is theoretically established through the foundation of continuous-time dynamical systems theory. In particular, we formalize a system of differential equations, with both beam coefficients and dose constraints modeled as state variables. The asymptotic stability of the system’s equilibrium is rigorously proven, ensuring convergence to a solution. In practical terms, we leverage a discretized iteration formula derived from the continuous-time system to achieve rapid computational speed. The mathematical structure of the proposed approach, which directly incorporates dose-volume constraints into the objective function, facilitates significant computational efficiency and solution refinement. The proposed method has an inherent dynamics that approaches more desirable solutions within the set of solutions when the solution to the optimization problem is not an isolated point. This property guarantees the identification of optimal solutions that respect the prescribed dose-volume constraints while enhancing accuracy when such constraints are feasible. By treating dose constraints as variables and concurrently solving the optimization problem with beam coefficients, we can achieve more accurate results when compared with using fixed values for prescribed dose conditions. Full article

A recently developed differential geometric representation of redundant serial robot kinematics is employed to create a new extended operational space dynamics and control formulation that explicitly accounts for redundant robot degrees of freedom. This formulation corrects deficiencies in kinematics and dynamics of redundant serial robots that have relied for over half a century on error-prone generalized inverse velocity-based kinematics for redundancy resolution. New ordinary differential equations of robot operational space dynamics are obtained, without the need for ad hoc derivation, in terms of task coordinates and self-motion coordinates that represent robot redundancy. A new extended operational space control approach is presented that exploits ordinary differential equations of motion in terms of task and self-motion coordinates, enabling enforcement of desired output trajectories, obstacle avoidance, and performance constraints. Four examples are presented with a one-degree-of-redundancy robot that demonstrate the validity and superior performance of the new formulation, relative to the traditional task space method used for redundant serial robot control. Finally, an example with eight degrees of redundancy is presented that further illustrates superior performance of the new operational space formulation. Full article

Delay partial differential equations have significant applications in numerous fields, such as population dynamics, control systems, neuroscience, and epidemiology, where they are required to efficiently model the effects of past states on current system behavior. This work presents an RBF-based localized meshless method for the numerical solution of delay partial differential equations. In the suggested numerical scheme, the localized meshless method is combined with the Laplace transform. The main attractive features of the localized meshless method are its simplicity, adaptability, and ease of implementation for complex problems defined on complex shaped domains. In a localized meshless scheme, a linear system of equations is solved. The Laplace transform, which is one of the most powerful techniques for solving integer- and non-integer-order problems, is used to represent the desired solution as a contour integral in the complex plane, known as the Bromwich integral. However, the analytic inversion of contour integral becomes very laborious in many situations. Therefore, a contour integration method is utilized to numerically approximate the Bromwich integral. The aim of utilizing the Laplace transform is to handle the costly convolution integral associated with the Caputo derivative and to avoid the effects of time-stepping techniques on the stability and accuracy of the numerical solution. We also discuss the convergence and stability of the suggested scheme. Furthermore, the existence and uniqueness of the solution for the considered model are studied. The efficiency, efficacy, and accuracy of the proposed numerical scheme have been demonstrated through numerical experiments on various problems. Full article

This research is devoted to the development of a method for helicopter turboshaft engine energy characteristics control by regulating the free turbine rotor speed and fuel consumption using neural network technologies. A mathematical model was created that links the main rotor and free turbine rotor speed parameters, based on which a relation with the engine output power was established. In this research, a differential equation was obtained that links fuel consumption, output power, and rotor speed, which makes it possible to monitor engine dynamics in various operating modes. A fuel consumption controller was developed based on a neuro-fuzzy network that processes input data, including the desired and current rotor speed, which allows real-time adjustments to improve the operational efficiency. In the research, based on the flight data analysis obtained during the Mi-8MTV helicopter with a TV3-117 turboshaft engine flight test, improved signal processing quality was obtained due to time sampling and adaptive quantisation methods (this is confirmed by assessing the homogeneity and representativeness of the training and test datasets). A comparative analysis of the developed and traditional controllers showed that the neuro-fuzzy network use reduces the transient fuel consumption process time by 8.92% while increasing the accuracy and F1 score by 18.28% and 21.32%, respectively. Full article

We present a new formulation of the central moment lattice Boltzmann (LB) method based on a minimal continuous Fokker-Planck (FP) kinetic model, originally proposed for stochastic diffusive-drift processes (e.g., Brownian dynamics), by adapting it as a collision model for the continuous Boltzmann equation (CBE) for fluid dynamics. The FP collision model has several desirable properties, including its ability to preserve the quadratic nonlinearity of the CBE, unlike that based on the common Bhatnagar-Gross-Krook model. Rather than using an equivalent Langevin equation as a proxy, we construct our approach by directly matching the changes in different discrete central moments independently supported by the lattice under collision to those given by the CBE under the FP-guided collision model. This can be interpreted as a new path for the collision process in terms of the relaxation of the various central moments to “equilibria”, which we term as the Markovian central moment attractors that depend on the products of the adjacent lower order moments and a diffusion coefficient tensor, thereby involving of a chain of attractors; effectively, the latter are nonlinear functions of not only the hydrodynamic variables, but also the non-conserved moments; the relaxation rates are based on scaling the drift coefficient by the order of the moment involved. The construction of the method in terms of the relevant central moments rather than via the drift and diffusion of the distribution functions directly in the velocity space facilitates its numerical implementation and analysis. We show its consistency to the Navier-Stokes equations via a Chapman-Enskog analysis and elucidate the choice of the diffusion coefficient based on the second order moments in accurately representing flows at relatively low viscosities or high Reynolds numbers. We will demonstrate the accuracy and robustness of our new central moment FP-LB formulation, termed as the FPC-LBM, using the D3Q27 lattice for simulations of a variety of flows, including wall-bounded turbulent flows. We show that the FPC-LBM is more stable than other existing LB schemes based on central moments, while avoiding numerical hyperviscosity effects in flow simulations at relatively very low physical fluid viscosities through a refinement to a model founded on kinetic theory. Full article