Mathematical and Computational Applications

A permanent gravity wave propagating on deep water is a classic mathematical problem. However, the Fourier series approximation (FSA) based on the physical plane was examined to be valid for almost waves at all depths. The accuracy of the FSA for almost-limiting gravity waves remains unevaluated, which is the purpose of this study. We calculate some physical properties of almost-limiting waves on deep water using the FSA and compare them with other studies on the complex plane. The comparison results show that the closer the wave is, the greater the difference. We find that the main reason for this difference is that the wave profile in the FSA retains an original implicit form and is not represented by Fourier series. Therefore, the kinematic and dynamic conditions of the free surface around the wave crest cannot be satisfied at the same time. Full article

Small-scale photovoltaic (PV) systems are essential for the local energy supply. The most commonly known PV cell is configured as a large-area p–n junction made from silicon, but PV systems today include PV cells of various manufactures and origins. The dependence relationship between current and voltage is nonlinear, known as the current–voltage characteristic. The values of the characteristic equation’s parameters define the working regime of the PV cell. In the present work, the parameter values are iteratively obtained by nonlinear regression for an explicit model. The acceleration of the convergence of these values is studied for an approximation simplifying the iterative calculation in the case of perpendicular offsets. The new estimations of parameters allow for a much faster estimate of the maximum power point of the PV system. Full article

It is frequently observed that adult members of prey species sometimes use their predation mechanism on juvenile members of predator species. Ecological literature describes this phenomenon as prey–predator role reversal dynamics.Numerous authors have observed and described the biological development behind this feeding behaviour. However, the dynamics of this role reversal have hardly been illustrated in the literature in a precise way. In this regard, we formulated an ecological model using the standard prey–predator interactions, allowing for a reverse feeding mechanism. The mathematical model consisted of a three-species food-web structure comprising the common prey, intermediate predator, and top predator. Note that a role-reversal mechanism was observed between the intermediate and top predators based on the scarcity of the prey population. However, we observed the most critical parameters had a significant effect on this reverse feeding behaviour. The bifurcation analysis is the primary criterion for this identification. The proposed deterministic model is then extended to its stochastic analogue by allowing for environmental influences on the tri-trophic food web structure. The conditional moment approach is applied to obtain the equilibrium distribution of populations and their conditional moments in the system. The stochastic setup analysis also supports the stability of this food chain structure, with some restricted conditions. Finally, to facilitate the interpretation of our mathematical results, we investigated it using numerical simulations. Full article

In this paper, we develop a finite difference method for solving the wave equation with fractional damping in 1D and 2D cases, where the fractional damping is given based on the Caputo fractional derivative. Firstly, based on the weighted method, we propose a new numerical approximation for the Caputo fractional derivative and apply it for the 1D case to obtain a time-stepping method. We then develop an alternating direction implicit (ADI) scheme for the 2D case. Using the discrete energy method, we prove that the proposed difference schemes are unconditionally stable and convergent in both 1D and 2D cases. Finally, several numerical examples are given to verify the theoretical results. Full article

Simulation and modeling of thermal recuperative incinerators may play an important role in enhancing efficiency and ensuring compliance with environmental regulations. In this context, the primary objective of this study is to simulate and comprehensively understand the operation of a geometrically complex thermal recuperative incinerator with an integrated preheater featuring varying levels of heat recovery. To achieve this objective, a simple yet effective 0D model was developed. This modeling approach allows for a holistic evaluation of the performance of the incinerator, enabling the assessment of key parameters, such as temperatures and heat transfer rates, under varying operating conditions. Successful validation of the model is established by comparing its results with measurements from an industrial thermal recuperative incinerator in operation at a vehicle assembly plant, with maximum relative differences of around 9%. Simulations for different percentages of flue gases bypassing the preheater were conducted, indicating a good compromise between heat transfer and pressure drop and a 22% heat recovery at around 50%. The model presented in this paper provides a robust foundation for comprehensively assessing and optimizing the performance of thermal recuperative incinerators and systems that comprise thermal recuperative incinerators, with implications for waste management and sustainable energy recovery systems. Full article

A method for the analysis of super-resolution microscopy images is presented. This method is based on the analysis of stochastic trajectories of particles moving on the membrane of a cell with the assumption that this motion is determined by the properties of this membrane. Thus, the purpose of this method is to recover the structural properties of the membrane by solving an inverse problem governed by the Fokker–Planck equation related to the stochastic trajectories. Results of numerical experiments demonstrate the ability of the proposed method to reconstruct the potential of a cell membrane by using synthetic data similar those captured by super-resolution microscopy of luminescent activated proteins. Full article

Chemical vapor deposition (CVD) is a common industrial process that incorporates a complex combination of fluid flow, chemical reactions, and surface deposition. Understanding CVD processes requires rigorous and costly experimentation involving multiple spatial scales, from meters to nanometers. The numerical modeling of deposition over macro-scale substrates has been conducted in the literature and results show compliance with experimental data. For smaller-scale substrates, where the corresponding Knudsen number is larger than zero, continuum modeling does not provide accurate results, which calls for the implementation of molecular-level modeling techniques. In the current study, the finite-volume method (FVM) and Direct Simulation Monte Carlo (DSMC) method were combined to model the reactor-scale flow with CVD around micro- and nano-scale fibers. CVD at fibers with round cross-sections was modeled in the reactor, where fibers were oriented perpendicularly with respect to the feedstock gas flow. The DSMC method was applied to modeling flow around the matrix of nano-scale circular individual fibers. Results show that for smaller diameters of individual fibers with the same filling ratio, the residence time of gas particles inside the fibrous media reduces, and, consequently, the amount of material surface deposition decreases. The sticking coefficient on the fibers’ surface plays an important role; for instance, increasing the sticking coefficient from 20% to 80% will double the deposition rate. Full article

In the present paper, the process of estimating the important statistical properties of extreme wind loads on structures is investigated by considering the effect of large variability. In fact, for the safety design and operating conditions of structures such as the ones characterizing tall buildings, wind towers, and offshore structures, it is of interest to obtain the best possible estimates of extreme wind loads on structures, the recurrence frequency, the return periods, and other stochastic properties, given the available statistical data. In this paper, a Bayes estimation of extreme load values is investigated in the framework of structural safety analysis. The evaluation of extreme values of the wind loads on the structures is performed via a combined employment of a Poisson process model for the peak-over-threshold characterization and an adequate characterization of the parent distribution which generates the base wind load values. In particular, the present investigation is based upon a key parameter for assessing the safety of structures, i.e., a proper safety index referred to a given extreme value of wind speed. The attention is focused upon the estimation process, for which the presented procedure proposes an adequate Bayesian approach based upon prior assumptions regarding (1) the Weibull probability that wind speed is higher than a prefixed threshold value, and (2) the frequency of the Poisson process of gusts. In the last part of the investigation, a large set of numerical simulations is analyzed to evaluate the feasibility and efficiency of the above estimation method and with the objective to analyze and compare the presented approach with the classical Maximum Likelihood method. Moreover, the robustness of the proposed Bayes estimation is also investigated with successful results, both with respect to the assumed parameter prior distributions and with respect to the Weibull distribution of the wind speed values. Full article

The extended Fisher–Kolmogorov (EFK) equation is an important model for phase transitions and bistable phenomena. This paper presents some fast explicit numerical schemes based on the integrating factor Runge–Kutta method and the Fourier spectral method to solve the EFK equation. The discrete global convergence of these new schemes is analyzed rigorously. Three numerical examples are presented to verify the theoretical analysis and the efficiency of the proposed schemes. Full article

This article derives approximate formulations for Rayleigh waves on a coated orthorhombic elastic half-space with a prescribed vertical load acting as an elastic Winkler foundation. In addition, perfect continuity conditions are imposed between the coating layer and the substrate, while suitable decaying conditions are slated along the infinite depth of the half-space. The effect of the thin layer is modeled using appropriate effective boundary conditions within the long-wave limit. By applying the Radon transform and using the perturbation method, the derived model successfully captures the physical characteristics of elastic surface waves in coated half-spaces. The model consists of a pesudo-static elliptic equation decaying over the interior of the half-space and a singularly perturbed hyperbolic equation with a pseudo-differential operator. The pseudo-differential equation gives the approximate dispersion of surface waves on the coated half-space structure and is analyzed numerically at the end. Full article

The theory of convexity pertaining to fractional calculus is a well-established concept that has attracted significant attention in mathematics and various scientific disciplines for over a century. In the realm of applied mathematics, convexity, particularly in relation to fractional analysis, finds extensive and remarkable applications. In this manuscript, we establish new fractional identities. Employing these identities, some extensions of the fractional H-H type inequality via generalized preinvexities are explored. Finally, we discuss some applications to the q-digamma and Bessel functions via the established results. We believe that the methodologies and approaches presented in this work will intrigue and spark the researcher’s interest even more. Full article

The preventive measures taken to curb the spread of COVID-19 have emphasized the importance of wearing face masks to prevent potential infection with serious diseases during daily activities or for medical professionals working in hospitals. Due to the mandatory use of face masks, various methods employing artificial intelligence and deep learning have emerged to detect whether individuals are wearing masks. In this paper, we utilized convolutional neural networks (CNNs) to classify the use of face masks into three categories: no mask, incorrect mask, and proper mask. Establishing the appropriate CNN architecture can be a demanding task. This study compares four swarm intelligent metaheuristics: particle swarm optimization (PSO), grey wolf optimizer (GWO), bat algorithm (BA), and whale optimization algorithm (WOA). The CNN architecture design involves determining the essential hyperparameters of the CNNs. The results indicate the effectiveness of the PSO and BA in achieving an accuracy of 100% when using 10% of the images for testing. Meanwhile, when 90% of the images were used for testing, the results were as follows: PSO 97.15%, WOA 97.14%, BA 97.23%, and GWO 97.18%. These statistically significant differences demonstrate that the BA allows better results than the other metaheuristics analyzed in this study. Full article

Non-invasive measurements are important for the development of new treatments for heart failure, which is one of the leading causes of death worldwide. This study aimed to develop realistic subject-specific computational models of human biventricles using clinical data. Three-dimensional finite element models of the human ventricles were created using cardiovascular magnetic resonance images of rheumatic heart disease (RHD) patients and healthy subjects. The material parameter optimization uses inverse modeling based on the finite element method combined with the Levenberg–Marquardt method (LVM) by targeting subject-specific hemodynamics. The study of elastic myocardial parameters between healthy subjects and RHD patients showed an elevated stiffness in diseased hearts. In particular, the anisotropic material behavior of the healthy and diseased cardiac tissue significantly differed from one another. Furthermore, as the LVEF decreased, the stiffness and its orientation-dependent parameters increased. The simulation-derived LV myocardial circumferential and longitudinal stresses were negatively associated with the LVEF. The sensitivity analysis result demonstrated that the observed significant difference between the elastic material parameters of diseased and healthy myocardium was not exclusively attributable to an increased LVEDP in the diseased heart. These results could be applied to future computational studies for developing heart failure treatment. Full article

The aim of this paper is to analyze the determination of interplanetary trajectories from Earth to Mars to evaluate the cost of the required impulse magnitudes for an areostationary orbiter mission design. Such analysis is first conducted by solving the Lambert orbital boundary value problem and studying the launch and arrival conditions for various date combinations. Then, genetic algorithms are applied to investigate the minimum-energy transfer orbit. Afterwards, an iterative procedure is used to determine the heliocentric elliptic transfer orbit that matches at the entry point of Mars’s sphere of influence with an areocentric hyperbolic orbit imposing specific conditions on inclination and periapsis radius. Finally, the maneuvers needed to obtain an areostationary orbit are numerically computed for different objective condition values at the Mars entry point to evaluate an areostationary preliminary mission cost for further study and characterization. Results show that, for the dates of the minimum-energy Earth–Mars transfer trajectory, a low value for the maneuvers to achieve an areostationary orbit is obtained for an arrival hyperbola with the minimum possible inclination and a capture into an elliptical trajectory with a low periapsis radius and an apoapsis at the stationary orbit. For a 2026 mission with a TOF of 304 for the minimum-energy Earth–Mars transfer trajectory, for a capture with a periapsis of 300 km above the Mars surface the value achieved will be 2.083 km/s. Full article

An innovative cascade predictor is presented in this study to forecast the state of recurrent neural networks (RNNs) with delayed output. This cascade predictor is a chain-structured observer, as opposed to the conventional single observer, and is made up of several sub-observers that individually estimate the state of the neurons at various periods. This new cascade predictor is more useful than the conventional single observer in predicting neural network states when the output delay is arbitrarily large but known. In contrast to examining the stability of error systems solely employing the Lyapunov–Krasovskii functional (LKF), several new global asymptotic stability standards are obtained by combining the application of the Linear Parameter Varying (LPV) approach, LKF and convex principle. Finally, a series of numerical simulations verify the efficacy of the obtained results. Full article

We devised a data-driven framework for uncovering hidden control strategies used by an evolutionary system described by an evolutionary probability distribution. This innovative framework enables deciphering of the concealed mechanisms that contribute to the progression or mitigation of such situations as the spread of COVID-19. Novel algorithms are used to estimate the optimal control in tandem with the parameters for evolution in general dynamical systems, thereby extending the concept of model predictive control. This marks a significant departure from conventional control methods, which require knowledge of the system to manipulate its evolution and of the controller’s strategy or parameters. We use a generalized additive model, supplemented by extensive statistical testing, to identify a set of predictor covariates closely linked to the control. Using real-world COVID-19 data, we delineate the descriptive behaviors of the COVID-19 epidemics in five prefectures in Japan and nine countries. We compare these nine countries and group them on the basis of shared profiles, providing valuable insights into their pandemic responses. Our findings underscore the potential of our framework as a powerful tool for understanding and managing complex evolutionary processes. Full article

In recent years, Physics-Informed Neural Networks (PINNs) have drawn great interest among researchers as a tool to solve computational physics problems. Unlike conventional neural networks, which are black-box models that “blindly” establish a correlation between input and output variables using a large quantity of labeled data, PINNs directly embed physical laws (primarily partial differential equations) within the loss function of neural networks. By minimizing the loss function, this approach allows the output variables to automatically satisfy physical equations without the need for labeled data. The Navier–Stokes equation is one of the most classic governing equations in thermal fluid engineering. This study constructs a PINN to solve the Navier–Stokes equations for a 2D incompressible laminar flow problem. Flows passing around a 2D circular particle are chosen as the benchmark case, and an elliptical particle is also examined to enrich the research. The velocity and pressure fields are predicted by the PINNs, and the results are compared with those derived from Computational Fluid Dynamics (CFD). Additionally, the particle drag force coefficient is calculated to quantify the discrepancy in the results of the PINNs as compared to CFD outcomes. The drag coefficient maintained an error within 10% across all test scenarios. Full article

For positioning and anti-swing control of bridge cranes, the active learning control method can reduce the dependence of controller design on the model and the influence of unmodeled dynamics on the controller’s performance. By only using the real-time online input and output data of the bridge crane system, the active learning control method consists of the finite-dimensional approximation of the Koopman operator and the design of an active learning controller based on the linear quadratic optimal tracking control. The effectiveness of the control strategy for positioning and anti-swing of bridge cranes is verified through numerical simulations. Full article

Various dominance structures have been proposed in the multi-objective optimization literature. However, a systematic procedure to understand their effect in determining the resulting optimal set for generic domination principles, besides the standard Pareto-dominance principle, is lacking. In this paper, we analyze and lay out properties of generalized dominance structures which help provide insights for resulting optimal solutions. We introduce the concept of the anti-dominance structure, derived from the chosen dominance structure, to explain how the resulting non-dominated or optimal set can be identified easily compared to using the dominance structure directly. The concept allows a unified explanation of optimal solutions for both single- and multi-objective optimization problems. The anti-dominance structure is applied to analyze respective optimal solutions for most popularly used static and spatially changing dominance structures. The theoretical and deductive results of this study can be utilized to create more meaningful dominance structures for practical problems, understand and identify resulting optimal solutions, and help develop better test problems and algorithms for multi-objective optimization. Full article