International Journal of Modeling, Simulation, and Scientific Computing

In recent years, finding precise numerical solutions to nonlinear partial differential equations (NLPDEs) has become a significant research topic. This paper addresses the two well-known nonlinear models, which are $(1+1)$-dimensional Allen–Cahn (AC) and phi-four (PF) equations, and they have applications in various real-world scenarios. These two models are solved by a numerical technique called Hermite wavelet collocation scheme (HWCS). The operational matrices of integration were developed using the Hermite wavelet basis. The proposed method is based on the collocation process. By employing appropriate grid points, this method converts the nonlinear model into a set of nonlinear algebraic equations. We obtain a solution by employing the Newton–Raphson scheme to solve these nonlinear algebraic equations. Tables and figures demonstrate that the proposed method yields superior results. The proposed examples demonstrate the efficacy of the proposed idea, and the results affirm the practicality of the proposed approach. We compared the present method with the non-polynomial spline method and trigonometric B-spline collocation technique to check the potential of the projected method.

This research work presents the numerical solution of the Darcy–Forchheimer flow of Casson nanofluidic model (DFFCNFM) on stretching sheets with Newtonian heating by utilizing a combination of nonlinear input–output neural networks with backpropagation of Levenberg–Marquardt computational approach. The presented study investigates the impact of electroosmosis forces on the boundary layer of the Casson nanofluid, focusing on viscous and Joule dissipations. A dataset for DFFCNFM is generated for the different events with backward differentiation formula (BDF) by varying Casson fluid parameter ($\beta )$, permeability parameter (Da), electric parameter ($E_1)$, Reynolds number (Re) relative to stretching velocity, magnetic field ($M)$, Eckert number (Ec), and Prandtl number (Pr). The artificial intelligence-inspired technique via nonlinear input–output neural networks with backpropagation of Levenberg–Marquardt is utilized from the generated dataset for DFFCNFM to find the approximate solutions. The satisfactory performance levels, as indicated by the mean square error (MSE), have been attained consistently with magnitude around 10${}^{-12}$–10${}^{-14}$ for all scenarios of DFFCNFM. The precision and performance validation is effectively established by the negligible MSE, close proximity to the unit value of regression metric, and the distribution of instances in error-histograms.

Internet worms have received a lot of attention because of their massive hazards to the internet. As the internet worms propagate quickly, therefore, the automatic control on the internet is required. In this paper, we present a new epidemic model called susceptible-breaking out-quarantine-treatment-recovered (SBQTR) model which integrates dynamic quarantine and treatment approaches to control the spread of internet worms. By using the SBQTR model, we can calculate the basic reproduction number $R_0$, which determines the existence of worms. The model has two equilibrium states: virus-free equilibrium (VFE) and viral equilibrium (VE). The stability analysis of both the equilibrium points is carried out and impact of treatment is examined under various parametric values. The sensitivity analysis of model is carried out to determine the impact of model parameters on virus transmission. Furthermore, we established nonstandard finite difference (NSFD) schemes and Runge–Kutta algorithm of order 4 (RK-4) for SBQTR model. The stated NSFD technique retains all of the significant properties of system (1), whereas RK-4 mechanism gives negative solutions and doesn’t converge to the equilibrium points of system (1). Numerical results together with comparison for various values of step size ($h$) are available. Bifurcation value of infection coefficient is also investigated. It is shown that an appropriate treatment is essential to control the spread of worms in computer network.

This paper explores the influence of harvest efforts on a discrete-time prey–predator model. We established the stability criteria for fixed points in the proposed model. We investigate codim-1 and codim-2 bifurcations, exploring a range of multiple and generic bifurcations within the discrete model. The model demonstrates fold, flip, and Neimark–Sacker bifurcations, as well as resonances such as 1:2, 1:3, and 1:4 at distinct fixed points. Through the application of the critical normal form theorem and bifurcation theory, we calculate normal form coefficients for each bifurcation. Our results show that an excessive prey harvest rate can actually destabilize the model dynamics. Numerical simulations validate our findings, shedding light on the intricate dynamics of the system.

The use of statistical techniques has become crucial for detecting and studying emergent behaviors in complex systems. Emergent behavior in complex systems often involves subtle or small changes in system dynamics or patterns. Statistical techniques are sensitive to small effects and can help detect and quantify them. Systems that show emergent behaviors usually involve multiple variables and data sources. Statistical techniques can integrate and analyze data from these diverse sources, allowing the identification of emergent patterns that may be scattered across different data sets. Therefore, this paper proposes the use of principal component analysis (PCA) for visualizing and detecting emergence. PCA is a mature and powerful unsupervised learning algorithm that allows the reduction and visualization of large datasets. The dataset set is obtained from simulations in NetLogo, and interaction metrics are used to represent the data. PCA was able to detect throughout the analysis emergence. In 90% of scenarios, PCA showed clear detection of emergent behavior in the system, the study also gives future directions for this work.

Studying and modeling the process of the disease and spread of blast can guide fertilization and reduce the amount of pesticide application. Since most of the existing research focuses on the pathogenesis of the rice blast fungus and the interaction between the plant structure and the fungus, this paper presents a method to simulate the spread of rice blast among rice populations. The method is divided into the following processes. First, based on the cellular automata grid dynamics model, the cell state corresponds to the degree of infection of the rice blast fungus, and its ability to simulate the spatiotemporal evolution of complex systems is used to simulate the spread of disease spots on the surface of rice leaves. Second, according to the biological mechanism of the rice blast fungus and the position of the first infected leaf in a single rice plant, the normal distribution function is used to calculate the infection probability of the remaining leaves, and then the transmission mode of the disease inside a single rice plant is simulated. Then, in view of the natural phenomenon that the blast fungus spores spread with the wind, the wind factor is added to propose a method for the spread of the rice blast fungus among the population of rice plants, and thus a model for the spread of the pathogen among the entire plant population was established. Finally, we set up a simulation system for the spread of rice blasts in rice fields and visualized the spread and spread trend of rice blasts in rice populations. In the simulation experiment, the infection process of rice blast on the surface of the rice leaf was simulated, and the change process of the shape of the diseased spot can be visually seen. This paper not only provides a new idea for the research on pathogen propagation and diffusion between plants in agricultural production but also provides a reference for how to realistically visualize the pathogen propagation model in the virtual agricultural scene.

The Eulerian method of transported PDF is an approach that is considered to be a derivative of the delta function. Among the strengths of this method are its ability to anticipate flame extinction and ignition, as well as its capacity to kinetically control chemical components such as CO and NO${}_x$. The primary objective of this study is to utilize this method to conduct a comparative evaluation of two turbulence models: the $k$-epsilon model and the RSM model. This numerical study aims to deepen our understanding of the combustion dynamics of an H₂/N₂ mixture within a turbulent diffusion flame. To achieve this, the mixture is injected into a co-flow of hot air, allowing for the simulation of real conditions. The selected mixture model is the Interaction by Exchange with the Mean (IEM). For the Eulerian approach, the number of environments is set to (2,0). In this study, the model was solved using the commercial CFD software, ANSYS Fluent, and the chemical reaction mechanism employed for H₂ comprises of 37 reactions involving 13 distinct species. Results are validated with the experimental data and are discussed. The integration of the PDF approach with the RSM turbulence model appears to be a valuable strategy for a better understanding of H₂ flow and combustion.

To improve the uniformity of magnetic flux and increase the stroke of the magnetic levitation system, this paper designs a novel 6-DOF magnetic levitation system and proposes an improved novel Halbach array. First, a repulsive passive magnetic bearing is utilized to provide levitation force, leading to a noticeable reduction in levitation power consumption. Then, a magnetic circuit model for the magnetic levitation system is established, and the improved novel Halbach array is optimized based on this model. Next, the stable levitation model and measurement model for the system are established, and the magnetic field distribution and magnetic bearing stiffness are analyzed. Results indicated an increase of 0.1T in the maximum magnetic flux density, accompanied by an improvement in the uniformity of magnetic flux. Additionally, there is an enhancement of 10% in magnetic bearing stiffness. Finally, a prototype of the system is constructed, and the stable levitation simulation and experiment of the actuator are conducted with this system. The maximum levitation absolute displacement error obtained by simulation is about 655nm, and the experimental results exhibited a maximum levitation absolute displacement error of approximately 750 nm for the system, confirming the effectiveness of the proposed modeling method.

3D reconstruction stands for a method used to generate a three-dimensional (3D) model of a real object using a 3D point cloud or a 3D mesh using computer-aided design(CAD) software or reverse engineering (RE) techniques. The points’ coordinates are acquired by digitizing physical items using specialized instruments such as a three-dimensional measuring machine (CMM), a structured light scanner, or a LASER pulse-based 3D scanner. These scanned objects are notably invested in a panoply of industries, such as mechanics, aeronautics, vehicle manufacturing, medicine, and art. Within this particular framework, achieving a highly accurate reconstruction of the geometric model is a challenging task that requires a significant investment of time and relies heavily on the use of modeling and reverse engineering approaches. In this respect, this work introduces a novel method for reconstructing a CAD model through inserting new points into a given distorted mesh. Walton’s method is employed for accurate rebuilding so as to ensure a high level of accuracy in the fitted surfaces. B-Spline surfaces are estimated relying on the obtained 3D points, and then the geometric model is rebuilt. To assess the performance of the suggested approach, 3D surfaces are reconstructed, applying a 3D reconstruction algorithm to generate an accurate rebuilt model. The accuracy of the elaborated method is manifested through comparing the results of the geometric model reconstruction using the input mesh to those obtained after inserting new points.

The objective of this work is to compare the machining performance of AISI 1040 Carbon Steel and Ti-6Al-4V alloy for a slot cutting operation using a 3-axis vertical milling machine. A set of 16 experiments was conducted, considering four factors: Feed rate, depth of cut, spindle speed, and coolant concentration, to remove material up to a finite depth. Three multi-objective optimization techniques namely, Grey Relational Analysis (GRA), Multi-Response Signal-to-Noise Ratio (MRSN Ratio), and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) were employed to determine the optimal machining conditions by maximizing the material removal rate and minimizing surface roughness and material hardness. It has been observed that the response performance index varies with different optimization techniques as well as different workpiece materials. The most significant contributions of each technique were evaluated through ANOVA analysis. A prediction model was developed using linear regression analysis. Finally, comparing the results of the three objective optimization techniques, GRA gives better performance than both TOPSIS and MRSN by effectively satisfying two objectives (i.e., maximizing material removal rate and minimizing surface roughness) for AISI 1040 Carbon Steel. In contrast, the MRSN technique provides better results than GRA and TOPSIS by effectively satisfying two objectives (i.e., maximizing material removal rate and minimizing material hardness) for Ti-6Al-4V alloy.

To investigate the influence of the friction loss generated by the harmonic drive in the integrated robot joint transmission process on the torque control accuracy, this study analyzed the internal friction loss of the harmonic drive by establishing an integrated joint dynamics model based on multi-factor coupling. According to the nonlinear transmission characteristics of the harmonic drive, the effects of hysteresis characteristics, nonlinear friction, transmission error, and temperature on the friction loss of the harmonic drive were analyzed. With rated and peak torques of 0.4Nm and 1.44Nm, respectively, the theoretical calculations of friction loss inside the harmonic drive and simulations on the co-simulation platform to verify the results were performed. The theoretical analysis yielded friction loss rates of 8.54% and 10.41%, and the co-simulation platform yielded friction loss rates of 9.64% and 12.08%. The simulation results are consistent with the theoretical analysis, and the constructed integrated joint dynamics model is accurate. The scheme used to obtain the joint torque by measuring the deformation of the flexure wheel was found to be feasible; however, the friction loss compensation generated during the transmission process needs to be considered in practical working conditions. By analyzing the friction loss of integrated joints, this study provides the theoretical basis for the torque control of robot joints.

The traditional A-Star algorithm has the problem of performing much invalid traversal work of nodes near concave obstacles when dealing with path planning tasks in the presence of concave obstacles. To solve this problem, a fusion algorithm (called IAPF-A-Star here) based on improved artificial potential field (IAPF) and A-Star is proposed. In IAPF-A-Star, to better measure the distances between the nodes and the target node, the potential energy of the artificial potential field is used to represent the node’s proximity to the target node, and an iterative correction method is used to improve the potential field in order to eliminate the local low-potential energy that may exist in the artificial potential field. The improved potential field effectively avoids the occurrence of local low-potential fields and makes it possible to measure the position of nodes in relation to their target node by means of the potential field. Finally, the obtained path is converted to a curve path by using a cubic spline curve. In addition, to solve the problem that the curve path generated by the cubic spline curve may collide with obstacles, a path optimization strategy based on an adaptive cubic spline curve is proposed to make the final path smooth and collision avoidance, shorter and closer to the actual situation. Simulation experiments show that the proposed IAPF-A-Star algorithm in this paper can effectively avoid the problem of additional local energy consumption caused by concave obstacles when processing path planning tasks, and the traversal of invalid nodes facing different complex concave obstacles is effectively avoided.

To analyze electro-hydrodynamic behavior of low pressure direct-current glow discharge plasma, we propose a numerical model based on the lattice Boltzmann method and the drift-diffusion theory of gas discharge. In our model, three plasma species (excited species, electrons and ions) are considered with eight elementary chemical reactions among them and standard lattice Boltzmann method, finite difference-lattice Boltzmann method and finite difference method are employed for electrons, heavy species (ions and excited species) and electric potential, respectively. The proposed model introduces a unique coupling scheme between electrons and heavy species using a consistent time step and grid, enhancing accuracy and stability of numerical simulations. Our model is applied to one- and two-dimensional analyses of glow discharge, and the results are in good agreement with those from previous works.

In this study, we developed a fractional-order model for polycystic ovarian syndrome issue transmission in women through four compartments with the Mittag-Leffler kernel. For biological feasibility, we discussed the positivity and boundedness of solutions with fixed point mappings in Banach spaces. Sensitivity analysis is performed using different variables as response functions each time, employing Latin Hyper-cube Sampling (LHS) and Partial Rank Correlation Coefficient (PRCC) with 200 iterations. Further, the reproductive number is determined for the model’s biological feasibility with an analysis of parameter impact through Matlab software. The solutions are examined for global stability using the Lyapunov function with a first derivative. Chaos Control will use the regulate for linear responses approach to bring the system to stabilize according to its points of equilibrium. Numerical solutions are derived by using a Newton polynomial in the generalized form of the Mittag-Leffler kernel, which illustrates the effect of the fractional operator and parameters involved in the system. Results are also analyzed with different assumptions of parameter values and initial conditions to observe the different impacts of treatment to overcome the risk of infertility in women. Such type of investigation will be useful to investigate the spread of disease as well as helpful in developing control strategies to overcome the risk of problems and best management care pre-detection of the issue and for treatment.