Mathematical and Computational Applications

This article aims to develop a mathematical simulation of the steady mixed convective Darcy–Forchheimer flow of Williamson nanofluid over a linear stretchable surface. In addition, the effects of Cattaneo–Christov heat and mass flux, Brownian motion, activation energy, and thermophoresis are also studied. The novel aspect of this study is that it incorporates thermal radiation to investigate the physical effects of thermal and solutal stratification on mixed convection flow and heat transfer. First, the profiles of velocity and energy equations were transformed toward the ordinary differential equation using the appropriate similarity transformation. Then, the system of equations was modified by first-order ODEs in MATLAB and solved using the bvp4c approach. Graphs and tables imply the impact of physical parameters on concentration, temperature, velocity, skin friction coefficient, mass, and heat transfer rate. The outcomes show that the nanofluid temperature and concentration are reduced with the more significant thermal and mass stratification parameters estimation. Full article

This paper discusses a complex nonlinear fractional model of enzyme inhibitor reaction where reaction memory is taken into account. Analytical expressions of the concentrations of enzyme, substrate, inhibitor, product, and other complex intermediate species are derived using Laplace decomposition and differential transformation methods. Since different rate constants, large initial concentrations, and large time domains are unavoidable in biochemical reactions, different dynamics will result; hence, the convergence of the approximate concentrations may be lost. In this case, the proposed analytical methods will be coupled with Padé approximation. The validity and accuracy of the derived analytical solutions will be established by direct comparison with numerical simulations. Full article

Child undernutrition is one of the 10 most significant public health problems worldwide. There is a rapidly growing demand to produce reliable estimates at the micro administrative level with small sample sizes. In this research, the authors employed small area estimation techniques to estimate the prevalence of malnutrition at the zonal level among children under five in Ethiopia. The small area estimation concept was sought for by linking the most recent possible survey data and census data in Ethiopia. The results show that there is spatial variation of stunting, wasting and being underweight across the zone level, showing different locations facing different challenges or different extents. Full article

In this paper, the applicability of the sine modified Lindley distribution, recently introduced in the statistical literature, is highlighted via the goodness-of-fit approach on biological data. In particular, it is shown to be beneficial in estimating and modeling the life periods of growth hormone guinea pigs given tubercle bacilli, growth hormone treatment for children, and the size of tumors in cancer patients. We anticipate that our model will be effective in modeling the survival times of diseases related to cancer. The R codes for the figures, as well as information on how the data are processed, are provided. Full article

$LSP\left(n\right)$, the largest small polygon with $n$ vertices, is a polygon with a unit diameter that has a maximal of area $A\left(n\right)$. It is known that for all odd values $n\ge 3$, $LSP\left(n\right)$ is a regular $n$-polygon; however, this statement is not valid even for values of $n$. Finding the polygon $LSP\left(n\right)$ and $A\left(n\right)$ for even values $n\ge 6$ has been a long-standing challenge. In this work, we developed high-precision numerical solution estimates of $A\left(n\right)$ for even values $n\ge 4$, using the Mathematica model development environment and the IPOPT local nonlinear optimization solver engine. First, we present a revised (tightened) LSP model that greatly assists in the efficient numerical solution of the model-class considered. This is followed by results for an illustrative sequence of even values of $n$, up to $n\le 1000$. Most of the earlier research addressed special cases up to $n\le 20$, while others obtained numerical optimization results for a range of values from $6\le n\le 100$. The results obtained were used to provide regression model-based estimates of the optimal area sequence $\left\{A\left(n\right)\right\}$, for even values $n$ of interest, thereby essentially solving the LSP model-class numerically, with demonstrably high precision. Full article

The interest in composite materials has increased in the last decades since they have the advantages of combining intrinsic properties of each component and offer better performance with respect to the base constituents. In particular, these kinds of materials can have different electrical characteristics by varying the filling percentage and, therefore, they can be used in diverse applications. Thus, a detailed study of the microwave response of these composite systems is of great practical importance. In fact, the dielectric constant and loss tangent are key factors in the design of microwave components. In this frame, the outstanding properties of graphene-like fillers may be exploited to develop new very interesting materials to study and characterize. In this paper, microwave characterization of compounds, based on nylon 6 containing different percentages of graphene nanoplatelets, is carried out taking the neat matrix sample processed under the same conditions as benchmark. The measurements were carried out using two microwave systems, operating at two different frequency bands, appropriate to characterize solid and compact material samples. The achieved results, in line with limited data from the literature and from material data sheets, highlight the possibility to use the present polymers as an excellent electromagnetic interference shielding, as confirmed by full wave electromagnetic numerical simulations that were conducted with a numerical electromagnetic software. Full article

We propose two enhancements of quasi-Newton methods used to accelerate coupling iterations for partitioned fluid-structure interaction. Quasi-Newton methods have been established as flexible, yet robust, efficient and accurate coupling methods of multi-physics simulations in general. The coupling library preCICE provides several variants, the so-called IQN-ILS method being the most commonly used. It uses input and output differences of the coupled solvers collected in previous iterations and time steps to approximate Newton iterations. To make quasi-Newton methods both applicable for parallel coupling (where these differences contain data from different physical fields) and to provide a robust approach for re-using information, a combination of information filtering and scaling for the different physical fields is typically required. This leads to good convergence, but increases the cost per iteration. We propose two new approaches—pre-scaling weight monitoring and a new, so-called QR3 filter, to substantially improve runtime while not affecting convergence quality. We evaluate these for a variety of fluid-structure interaction examples. Results show that we achieve drastic speedups for the pure quasi-Newton update steps. In the future, we intend to apply the methods also to volume-coupled scenarios, where these gains can be decisive for the feasibility of the coupling approach. Full article

In the present paper non-convex multi-objective parameter optimization problems are considered which are governed by elliptic parametrized partial differential equations (PDEs). To solve these problems numerically the Pascoletti-Serafini scalarization is applied and the obtained scalar optimization problems are solved by an augmented Lagrangian method. However, due to the PDE constraints, the numerical solution is very expensive so that a model reduction is utilized by using the reduced basis (RB) method. The quality of the RB approximation is ensured by a trust-region strategy which does not require any offline procedure, in which the RB functions are computed in a greedy algorithm. Moreover, convergence of the proposed method is guaranteed and different techniques to prevent the excessive growth of the number of basis functions are explored. Numerical examples illustrate the efficiency of the proposed solution technique. Full article

An interval-based method is presented to evaluate the uncertainty in the computed mechanical properties and the failure assessment of composite unidirectional (UD) laminates. The method was applied to two composite laminates: a carbon/epoxy and a glass/epoxy. The mechanical properties of the UD lamina were derived using simplified micromechanical equations. An uncertainty level of ±5% was assumed for the input properties of the constituents. The global minimum and maximum values of the properties were computed using an interval branch-and-bound algorithm. Interval arithmetic operations were used to evaluate the uncertainty in the Hashin-type failure criteria in a closed form. Using the closed-form uncertainties of intervals and sets of stresses obtained by finite element analysis, the uncertainty in the failure assessment was quantified for the two composite laminates. For the assumed uncertainty level of ±5%, the computed uncertainty for the mechanical properties ranges from 6.64% to 10.63% for the carbon/epoxy material and from 6.72% to 12.28% for the glass/epoxy material. For evaluating the uncertainty effect on the efficiency of failure criteria, a probability of failure function, which employs interval boundaries, was defined and proved capable of evaluating the whole spectrum of stresses. Full article

The purpose of this research is to study the spatial and temporal groupings of 124 meteorological stations in Thailand under ENSO. The multivariate climate variables are rainfall, relative humidity, temperature, max temperature, min temperature, solar downwelling, and horizontal wind from the conformal cubic atmospheric model (CCAM) in years of El Niño (1987, 2004, and 2015) and La Niña (1999, 2000, and 2011). Euclidean distance timed and spaced with average linkage for clustering and silhouette width for cluster validation were employed. Five spatial clusters (SCs) and three temporal clusters (TCs) in each SC with different average precipitation were compared by El Niño and La Niña. The pattern of SCs and TCs was similar for both events except in the case when severe El Niño occurred. This method could be applied using variables forecasted in the future to be used for planning and managing crop cultivation with the climate change in each area. Full article

Musculoskeletal computational models provide a non-invasive approach to investigate human movement biomechanics. These models could be particularly useful for pediatric applications where in vivo and in vitro biomechanical parameters are difficult or impossible to examine using physical experiments alone. The objective was to develop a novel musculoskeletal subject-specific infant model to investigate hip joint biomechanics during cyclic leg movements. Experimental motion-capture marker data of a supine-lying 2-month-old infant were placed on a generic GAIT 2392 OpenSim model. After scaling the model using body segment anthropometric measurements and joint center locations, inverse kinematics and dynamics were used to estimate hip ranges of motion and moments. For the left hip, a maximum moment of 0.975 Nm and a minimum joint moment of 0.031 Nm were estimated at 34.6° and 65.5° of flexion, respectively. For the right hip, a maximum moment of 0.906 Nm and a minimum joint moment of 0.265 Nm were estimated at 23.4° and 66.5° of flexion, respectively. Results showed agreement with reported values from the literature. Further model refinements and validations are needed to develop and establish a normative infant dataset, which will be particularly important when investigating the movement of infants with pathologies such as developmental dysplasia of the hip. This research represents the first step in the longitudinal development of a model that will critically contribute to our understanding of infant growth and development during the first year of life. Full article

Numerical solutions of heterogeneous Helmholtz problems present various computational challenges, with descriptive theory remaining out of reach for many popular approaches. Robustness and scalability are key for practical and reliable solvers in large-scale applications, especially for large wave number problems. In this work, we explore the use of a GenEO-type coarse space to build a two-level additive Schwarz method applicable to highly indefinite Helmholtz problems. Through a range of numerical tests on a 2D model problem, discretised by finite elements on pollution-free meshes, we observe robust convergence, iteration counts that do not increase with the wave number, and good scalability of our approach. We further provide results showing a favourable comparison with the DtN coarse space. Our numerical study shows promise that our solver methodology can be effective for challenging heterogeneous applications. Full article

Physical systems governed by advection-dominated partial differential equations (PDEs) are found in applications ranging from engineering design to weather forecasting. They are known to pose severe challenges to both projection-based and non-intrusive reduced order modeling, especially when linear subspace approximations are used. In this work, we develop an advection-aware (AA) autoencoder network that can address some of these limitations by learning efficient, physics-informed, nonlinear embeddings of the high-fidelity system snapshots. A fully non-intrusive reduced order model is developed by mapping the high-fidelity snapshots to a latent space defined by an AA autoencoder, followed by learning the latent space dynamics using a long-short-term memory (LSTM) network. This framework is also extended to parametric problems by explicitly incorporating parameter information into both the high-fidelity snapshots and the encoded latent space. Numerical results obtained with parametric linear and nonlinear advection problems indicate that the proposed framework can reproduce the dominant flow features even for unseen parameter values. Full article

Neurodegenerative diseases such as Alzheimer’s (AD) are associated with the propagation and aggregation of toxic proteins. In the case of AD, it was Alzheimer himself who showed the importance of both amyloid beta ($A\beta$) plaques and tau protein neurofibrillary tangles (NFTs) in what he called the “disease of forgetfulness”. The amyloid beta forms extracellular aggregates and plaques, whereas tau proteins are intracellular proteins that stabilize axons by cross-linking microtubules that can form largely messy tangles. On the other hand, astrocytes and microglial cells constantly clear these plaques and NFTs from the brain. Astrocytes transport nutrients from the blood to neurons. Activated astrocytes produce monocyte chemoattractant protein-1 (MCP-1), which attracts anti-inflammatory macrophages and clears $A\beta$. At the same time, the microglia cells are poorly phagocytic for $A\beta$ compared to proinflammatory and anti-inflammatory macrophages. In addition to such distinctive neuropathological features of AD as amyloid beta and tau proteins, neuroinflammation has to be brought into the picture as well. Taking advantage of a coupled mathematical modelling framework, we formulate a network model, accounting for the coupling between neurons and astroglia and integrating all three main neuropathological features with the brain connectome data. We provide details on the coupled dynamics involving cytokines, astrocytes, and microglia. Further, we apply the tumour necrosis factor alpha (TNF-$\alpha$) inhibitor and anti-$A\beta$ drug and analyze their influence on the brain cells, suggesting conditions under which the drug can prevent cell damage. The important role of astrocytes and TNF-$\alpha$ inhibitors in AD pathophysiology is emphasized, along with potentially promising pathways for developing new AD therapies. Full article

Evaporation calculations are important for the proper management of hydrological resources, such as reservoirs, lakes, and rivers. Data-driven approaches, such as adaptive neuro fuzzy inference, are getting popular in many hydrological fields. This paper investigates the effective implementation of artificial intelligence on the prediction of evaporation for agricultural area. In particular, it presents the adaptive neuro fuzzy inference system (ANFIS) and hybridization of ANFIS with three optimizers, which include the genetic algorithm (GA), firefly algorithm (FFA), and particle swarm optimizer (PSO). Six different measured weather variables are taken for the proposed modelling approach, including the maximum, minimum, and average air temperature, sunshine hours, wind speed, and relative humidity of a given location. Models are separately calibrated with a total of 86 data points over an eight-year period, from 2010 to 2017, at the specified station, located in Arizona, United States of America. Farming lands and humid climates are the reason for choosing this location. Ten statistical indices are calculated to find the best fit model. Comparisons shows that ANFIS and ANFIS–PSO are slightly better than ANFIS–FFA and ANFIS–GA. Though the hybrid ANFIS–PSO ($R^2=$ 0.99, VAF = 98.85, RMSE = 9.73, SI = 0.05) is very close to the ANFIS ($R^2$ = 0.99, VAF = 99.04, RMSE = 8.92, SI = 0.05) model, preference can be given to ANFIS, due to its simplicity and easy operation. Full article

Components of Earth system models (ESMs) usually use different numerical grids because of the different environments they represent. Therefore, a coupling field sent by a source model has to be regridded to be used by a target model. The regridding has to be accurate and, in some cases, conservative, in order to ensure the consistency of the coupled model. Here, we present work done to benchmark the quality of four regridding libraries currently used in ESMs, i.e., SCRIP, YAC, ESMF and XIOS. We evaluated five regridding algorithms with four different analytical functions for different combinations of six grids used in real ocean or atmosphere models. Four analytical functions were used to define the coupling fields to be regridded. This benchmark calculated some of the metrics proposed by the CANGA project, including the mean, maximum, RMS misfit, and global conservation. The results show that, besides a few very specific cases that present anomalous values, the regridding functionality in YAC, ESMF and XIOS can be considered of high quality and do not present the specific problems observed for the conservative SCRIP remapping. The evaluation of the computing performance of those libraries is not included in the current work but is planned to be performed in the coming months. This exercise shows that benchmarking can be a great opportunity to favour interactions between users and developers of regridding libraries. Full article

Over the years, several researchers have worked to model phenomena in which the distribution of data presents more or less heavy tails. With this aim, several generalizations or extensions of the Lomax distribution have been proposed. In this paper, an attempt is made to create a hybrid distribution mixing the functionalities of the Nadarajah–Haghighi and Lomax distributions, namely the Nadarajah–Haghighi Lomax (NHLx) distribution. It can also be thought of as an extension of the exponential Lomax distribution. The NHLx distribution has the features of having four parameters, a lower bounded support, and very flexible distributional functions, including a decreasing or unimodal probability density function and an increasing, decreasing, or upside-down bathtub hazard rate function. In addition, it benefits from the treatable statistical properties of moments and quantiles. The statistical applicability of the NHLx model is highlighted, with simulations carried out. Four real data sets are also used to illustrate the practical applications. In particular, results are compared with Lomax-based models of importance, such as the Lomax, Weibull Lomax, and exponential Lomax models, and it is observed that the NHLx model fits better. Full article

ANFIS-type algorithms have been used in various modeling and simulation problems. With the help of algorithms with more accuracy and adaptability, it is possible to obtain better real-life emulating models. A critical environmental problem is the discharge of saline industrial effluents in the form of buoyant jets into water bodies. Given the potentially harmful effects of the discharge effluents from desalination plants on the marine environment and the coastal ecosystem, minimizing such an effect is crucial. Hence, it is important to design the outfall system properly to reduce these impacts. To the best of the authors’ knowledge, a study that formulates the effluent discharge to find an optimum numerical model under the conditions considered here using AI methods has not been completed before. In this study, submerged discharges, specifically, negatively buoyant jets are modeled. The objective of this study is to compare various artificial intelligence algorithms along with multivariate regression models to find the best fit model emulating effluent discharge and determine the model with less computational time. This is achieved by training and testing the Adaptive Neuro-Fuzzy Inference System (ANFIS), ANFIS-Genetic Algorithm (GA), ANFIS-Particle Swarm Optimization (PSO) and ANFIS-Firefly Algorithm (FFA) models with input parameters, which are obtained by using the realizable k-ε turbulence model, and simulated parameters, which are obtained after modeling the turbulent jet using the OpenFOAM simulation platform. A comparison of the realizable k-ε turbulence model outputs and AI algorithms’ outputs is conducted in this study. Statistical parameters such as least error, coefficient of determination (R²), Mean Absolute Error (MAE), and Average Absolute Deviation (AED) are measured to evaluate the performance of the models. In this work, it is found that ANFIS-PSO performs better compared to the other four models and the multivariate regression model. It is shown that this model provides better R², MAE, and AED, however, the non-hybrid ANFIS model provides reasonably acceptable results with lower computational costs. The results of the study demonstrate an error of 6.908% as the best-case scenario in the AI models. Full article

Many computer simulation models of the cardiovascular system, of varying complexity and objectives, have been proposed in physiological science. Every model needs to be parameterized and evaluated individually. We conducted a porcine animal model to parameterize and evaluate a computer simulation model, recently proposed by our group. The results of an animal model, on thirteen healthy pigs, were used to generate consistent parameterization data for the full heart computer simulation model. To evaluate the simulation model, differences between the resulting simulation output and original animal data were analysed. The input parameters of the animal model, used to individualize the computer simulation, showed high interindividual variability (range of coefficient of variation: 10.1–84.5%), which was well-reflected by the resulting haemodynamic output parameters of the simulation (range of coefficient of variation: 12.6–45.7%). The overall bias between the animal and simulation model was low (mean: −3.24%, range: from −26.5 to 20.1%). The simulation model used in this study was able to adapt to the high physiological variability in the animal model. Possible reasons for the remaining differences between the animal and simulation model might be a static measurement error, unconsidered inaccuracies within the model, or unconsidered physiological interactions. Full article