Computation, Volume 8, Issue 3 (September 2020) – 24 articles

A modified power-law (MPL) viscosity model of non-Newtonian fluid flow has been used for the multiple-relaxation-time (MRT) lattice Boltzmann methods (LBM) and then validated with the benchmark problems using the graphics process unit (GPU) parallel computing via Compute Unified Device Architecture (CUDA) C platform. The MPL model for characterizing the non-Newtonian behavior is an empirical correlation that considers the Newtonian behavior of a non-Newtonian fluid at a very low and high shear rate. A new time unit parameter ($\lambda$) governing the flow has been identified, and this parameter is the consequence of the induced length scale introduced by the power law. The MPL model is free from any singularities due to the very low or even zero shear-rate. The proposed MPL model was first validated for the benchmark study of the lid-driven cavity and channel flows. The model was then applied for shear-thinning and shear-thickening fluid flows through a backward-facing step with relatively low Reynolds numbers, $Re$ = 100–400. In the case of shear-thinning fluids ($n=0.5$), laminar to transitional flow arises while $Re\ge 300$, and the large vortex breaks into several small vortices. The numerical results are presented regarding the velocity distribution, streamlines, and the lengths of the reattachment points. Full article

In this work, we derive the operational matrix using poly-Bernoulli polynomials. These polynomials generalize the Bernoulli polynomials using a generating function involving a polylogarithm function. We first show some new properties for these poly-Bernoulli polynomials; then we derive new operational matrix based on poly-Bernoulli polynomials for the Atangana–Baleanu derivative. A delay operational matrix based on poly-Bernoulli polynomials is derived. The error bound of this new method is shown. We applied this poly-Bernoulli operational matrix for solving fractional delay differential equations with variable coefficients. The numerical examples show that this method is easy to use and yet able to give accurate results. Full article

The Si/Al ratio and confinement effects of zeolite framework on energetics and vibrational frequencies of pyridine and 4,4′-bipyridine adsorbed on Brønsted acid sites in the straight channel of H-ZSM-5 are investigated by DFT calculations at the B3LYP and M06-2X+D3 levels. The straight channel of H-ZSM-5 is simulated by a cluster of 32 tetrahedral centers covering the intersection between straight and zigzag channels. Pyridine and 4,4′-bipyridine adsorption at two different sites in the intersection (open region) and/or in the narrow region situated between two intersections (closed region) is studied. For two Si/Al ratios (31, 15), the ion pair complexes formed by proton transfer upon pyridine and 4,4′-bipyridine adsorption in the open region and for the first time in the closed region are characterized. Our results indicate: (i) the stability for all adsorption complexes is essentially governed by the dispersive van der Waals interactions and the open region is energetically more favorable than the closed region owing to the predominance of the dispersive interactions over the steric constraints exerted by the confinement effects; (ii) as the Al centers are sufficiently spaced apart, Si/Al ratio does not influence pyridine adsorption energy, but significantly affects the adsorption energies and the relative stability of 4,4′-bipyridine complexes; (iii) neither Si/Al ratio nor confinement significantly influence pyridine and 4,4′-bipyridine vibrational frequencies within their complexes. Full article

One of the most common tasks nowadays in big data environments is the need to classify large amounts of data. There are numerous classification models designed to perform best in different environments and datasets, each with its advantages and disadvantages. However, when dealing with big data, their performance is significantly degraded because they are not designed—or even capable—of handling very large datasets. The current approach is based on a novel proposal of exploiting the dynamics of skyline queries to efficiently identify the decision boundary and classify big data. A comparison against the popular k-nearest neighbor (k-NN), support vector machines (SVM) and naïve Bayes classification algorithms shows that the proposed method is faster than the k-NN and the SVM. The novelty of this method is based on the fact that only a small number of computations are needed in order to make a prediction, while its full potential is revealed in very large datasets. Full article

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was found to be a severe threat to global public health in late 2019. Nevertheless, no approved medicines have been found to inhibit the virus effectively. Anti-malarial and antiviral medicines have been reported to target the SARS-CoV-2 virus. This paper chose eight natural eucalyptus compounds to study their binding interactions with the SARS-CoV-2 main protease (Mpro) to assess their potential for becoming herbal drugs for the new SARS-CoV-2 infection virus. In-silico methods such as molecular docking, molecular dynamics (MD) simulations, and Molecular Mechanics Poisson Boltzmann Surface Area (MM/PBSA) analysis were used to examine interactions at the atomistic level. The results of molecular docking indicate that Mpro has good binding energy for all compounds studied. Three docked compounds, α-gurjunene, aromadendrene, and allo-aromadendrene, with highest binding energies of −7.34 kcal/mol (−30.75 kJ/mol), −7.23 kcal/mol (−30.25 kJ/mol), and −7.17 kcal/mol (−29.99 kJ/mol) respectively, were simulated with GROningen MAchine for Chemical Simulations (GROMACS) to measure the molecular interactions between Mpro and inhibitors in detail. Our MD simulation results show that α-gurjunene has the strongest binding energy of −20.37 kcal/mol (−85.21 kJ/mol), followed by aromadendrene with −18.99 kcal/mol (−79.45 kJ/mol), and finally allo-aromadendrene with −17.91 kcal/mol (−74.95 kJ/mol). The findings indicate that eucalyptus may be used to inhibit the Mpro enzyme as a drug candidate. This is the first computational analysis that gives an insight into the potential role of structural flexibility during interactions with eucalyptus compounds. It also sheds light on the structural design of new herbal medicinal products against Mpro. Full article

Mesh-based solution of 3D models defined in plate or shell domains remains a challenging issue nowadays due to the fact that the needed meshes generally involve too many degrees of freedom. When the considered problem involves some parameters aiming at computing its parametric solution the difficulty is twofold. The authors proposed, in some of their former works, strategies for solving both, however they suffer from a deep intrusiveness. This paper proposes a totally novel approach that from any existing discretization is able to reduce the 3D parametric complexity to the one characteristic of a simple 2D calculation. Thus, the 3D complexity is reduced to 2D, the parameters included naturally into the solution, and the procedure applied on a discretization performed with a standard software, which taken together enable real-time engineering. Full article

To date, SARS-CoV-2 infectious disease, named COVID-19 by the World Health Organization (WHO) in February 2020, has caused millions of infections and hundreds of thousands of deaths. Despite the scientific community efforts, there are currently no approved therapies for treating this coronavirus infection. The process of new drug development is expensive and time-consuming, so that drug repurposing may be the ideal solution to fight the pandemic. In this paper, we selected the proteins encoded by SARS-CoV-2 and using homology modeling we identified the high-quality model of proteins. A structure-based pharmacophore modeling study was performed to identify the pharmacophore features for each target. The pharmacophore models were then used to perform a virtual screening against the DrugBank library (investigational, approved and experimental drugs). Potential inhibitors were identified for each target using XP docking and induced fit docking. MM-GBSA was also performed to better prioritize potential inhibitors. This study will provide new important comprehension of the crucial binding hot spots usable for further studies on COVID-19. Our results can be used to guide supervised virtual screening of large commercially available libraries. Full article

In this paper, we study and explore two control strategies to decrease the spread of Zika virus in the human and mosquito populations. The control strategies that we consider in this study are awareness and spraying campaigns. We solve several optimal control problems relying on a mathematical epidemic model of Zika that considers both human and mosquito populations. The first control strategy is broad and includes using information campaigns, encouraging people to use bednetting, wear long-sleeve shirts, or similar protection actions. The second control is more specific and relies on spraying insecticides. The control system relies on a Zika mathematical model with control functions. To develop the optimal control problem, we use Pontryagins’ maximum principle, which is numerically solved as a boundary value problem. For the mathematical model of the Zika epidemic, we use parameter values extracted from real data from an outbreak in Colombia. We study the effect of the costs related to the controls and infected populations. These costs are important in real life since they can change the outcomes and recommendations for health authorities dramatically. Finally, we explore different options regarding which control measures are more cost-efficient for society. Full article

$\mathrm{M}\mathrm{AX}-\mathrm{C}\mathrm{UT}$ is one of the well-studied NP-hard combinatorial optimization problems. It can be formulated as an Integer Quadratic Programming problem and admits a simple relaxation obtained by replacing the integer “spin” variables $x_i$ by unitary vectors ${\overrightarrow{v}}_i$. The Goemans–Williamson rounding algorithm assigns the solution vectors of the relaxed quadratic program to a corresponding integer spin depending on the sign of the scalar product ${\overrightarrow{v}}_i·\overrightarrow{r}$ with a random vector $\overrightarrow{r}$. Here, we investigate whether better graph cuts can be obtained by instead using a more sophisticated clustering algorithm. We answer this question affirmatively. Different initializations of k-means and k-medoids clustering produce better cuts for the graph instances of the most well known benchmark for $\mathrm{M}\mathrm{AX}-\mathrm{C}\mathrm{UT}$. In particular, we found a strong correlation of cluster quality and cut weights during the evolution of the clustering algorithms. Finally, since in general the maximal cut weight of a graph is not known beforehand, we derived instance-specific lower bounds for the approximation ratio, which give information of how close a solution is to the global optima for a particular instance. For the graphs in our benchmark, the instance specific lower bounds significantly exceed the Goemans–Williamson guarantee. Full article

The Nobel laureate Niels Bohr once said that: “Predictions are very difficult, especially if they are about the future”. Nonetheless, models that can forecast future COVID-19 outbreaks are receiving special attention by policymakers and health authorities, with the aim of putting in place control measures before the infections begin to increase. Nonetheless, two main problems emerge. First, there is no a general agreement on which kind of data should be registered for judging on the resurgence of the virus (e.g., infections, deaths, percentage of hospitalizations, reports from clinicians, signals from social media). Not only this, but all these data also suffer from common defects, linked to their reporting delays and to the uncertainties in the collection process. Second, the complex nature of COVID-19 outbreaks makes it difficult to understand if traditional epidemiological models, such as susceptible, infectious, or recovered (SIR), are more effective for a timely prediction of an outbreak than alternative computational models. Well aware of the complexity of this forecasting problem, we propose here an innovative metric for predicting COVID-19 diffusion based on the hypothesis that a relation exists between the spread of the virus and the presence in the air of particulate pollutants, such as PM_2.5, PM₁₀, and NO₂. Drawing on the recent assumption of 239 experts who claimed that this virus can be airborne, and further considering that particulate matter may favor this airborne route, we developed a machine learning (ML) model that has been instructed with: (i) all the COVID-19 infections that occurred in the Italian region of Emilia-Romagna, one of the most polluted areas in Europe, in the period of February–July 2020, (ii) the daily values of all the particulates taken in the same period and in the same region, and finally (iii) the chronology according to which restrictions were imposed by the Italian Government to human activities. Our ML model was then subjected to a classic ten-fold cross-validation procedure that returned a promising 90% accuracy value. Finally, the model was used to predict a possible resurgence of the virus in all the nine provinces of Emilia-Romagna, in the period of September–December 2020. To make those predictions, input to our ML model were the daily measurements of the aforementioned pollutants registered in the periods of September–December 2017/2018/2019, along with the hypothesis that the mild containment measures taken in Italy in the so-called Phase 3 are obeyed. At the time we write this article, we cannot have a confirmation of the precision of our predictions. Nevertheless, we are projecting a scenario based on an original hypothesis that makes our COVID-19 prediction model unique in the world. Its accuracy will be soon judged by history—and this, too, is science at the service of society. Full article

We investigate the mathematical model of the 2D acoustic waves propagation in a heterogeneous domain. The hyperbolic first order system of partial differential equations is considered and solved by the Godunov method of the first order of approximation. This is a direct problem with appropriate initial and boundary conditions. We solve the coefficient inverse problem (IP) of recovering density. IP is reduced to an optimization problem, which is solved by the gradient descent method. The quality of the IP solution highly depends on the quantity of IP data and positions of receivers. We introduce a new approach for computing a gradient in the descent method in order to use as much IP data as possible on each iteration of descent. Full article

In this paper, we propose a 7th order weakly L-stable time integration scheme. In the process of derivation of the scheme, we use explicit backward Taylor’s polynomial approximation of sixth-order and Hermite interpolation polynomial approximation of fifth order. We apply this formula in the vector form in order to solve Burger’s equation, which is a simplified form of Navier-Stokes equation. The literature survey reveals that several methods fail to capture the solutions in the presence of inconsistency and for small values of viscosity, e.g., ${10}^{-3}$, whereas the present scheme produces highly accurate results. To check the effectiveness of the scheme, we examine it over six test problems and generate several tables and figures. All of the calculations are executed with the help of Mathematica 11.3. The stability and convergence of the scheme are also discussed. Full article

Nowadays, in all cities, there is an acute problem of a lack of parking spaces. The number of vehicles is constantly increasing not only in big cities and megacities, but also in small towns of the country, and there are not enough parking places—the pace of solving the problem is several times slower than the growth rate of transport among citizens. The paper is dedicated to the determination of an optimal size of a parking place for design vehicles in a parking space as an element of roads. In the example of passenger cars and trucks, the optimal number of parking places is presented. The results of the research on the dimensioning of parking spaces serve as recommendations and can be used for the design of objects of transportation infrastructure. According to the research, authors introduce the term “design vehicle” and provide its definition. They also figure out optimal parameters for each design vehicle and recommend a special template for designing parking places. Full article

Time series forecasting technology and related applications for stock price forecasting are gradually receiving attention. These approaches can be a great help in making decisions based on historical information to predict possible future situations. This research aims at establishing forecasting models with deep learning technology for share price prediction in the logistics industry. The historical share price data of five logistics companies in Hong Kong were collected and trained with various time series forecasting algorithms. Based on the Mean Absolute Percentage Error (MAPE) results, we adopted Long Short-Term Memory (LSTM) as the methodology to further predict share price. The proposed LSTM model was trained with different hyperparameters and validated by the Root Mean Square Error (RMSE). In this study, we found various optimal parameters for the proposed LSTM model for six different logistics stocks in Hong Kong, and the best RMSE result was 0.43%. Finally, we can forecast economic recessions through the prediction of the stocks, using the LSTM model. Full article

The method of discretization is used to solve nonlinear equations involving Banach space valued operators using Lipschitz or Hölder constants. But these constants cannot always be found. That is why we present results using $\omega -$ continuity conditions on the Fréchet derivative of the operator involved. This way, we extend the applicability of the discretization technique. It turns out that if we specialize $\omega -$ continuity our new results improve those in the literature too in the case of Lipschitz or Hölder continuity. Our analysis includes tighter upper error bounds on the distances involved. Full article

In this paper, we consider the numerical solution of the optimal control problems of the elliptic partial differential equation. Numerically tackling these problems using the finite element method produces a large block coupled algebraic system of equations of saddle point form. These systems are of large dimension, block, sparse, indefinite and ill conditioned. The solution of such systems is a major computational task and poses a greater challenge for iterative techniques. Thus they require specialised methods which involve some preconditioning strategies. The preconditioned solvers must have nice convergence properties independent of the changes in discretisation and problem parameters. Most well known preconditioned solvers converge independently of mesh size but not for the decreasing regularisation parameter. This work proposes and extends the work for the formulation of preconditioners which results in the optimal performances of the iterative solvers independent of both the decreasing mesh size and the regulation parameter. In this paper we solve the indefinite system using the preconditioned minimum residual method. The main task in this work was to analyse the 3 × 3 block diagonal preconditioner that is based on the approximation of the Schur complement form obtained from the matrix system. The eigenvalue distribution of both the proposed Schur complement approximate and the preconditioned system will be investigated since the clustering of eigenvalues points to the effectiveness of the preconditioner in accelerating an iterative solver. This is done in order to create fast, efficient solvers for such problems. Numerical experiments demonstrate the effectiveness and performance of the proposed approximation compared to the other approximations and demonstrate that it can be used in practice. The numerical experiments confirm the effectiveness of the proposed preconditioner. The solver used is robust and optimal with respect to the changes in both mesh size and the regularisation parameter. Full article

Currently, an increasing number of third-party applications exploit the Bitcoin blockchain to store tamper-proof records of their executions, immutably. For this purpose, they leverage the few extra bytes available for encoding custom metadata in Bitcoin transactions. A sequence of records of the same application can thus be abstracted as a stand-alone subchain inside the Bitcoin blockchain. However, several existing approaches do not make any assumptions about the consistency of their subchains, either (i) neglecting the possibility that this sequence of messages can be altered, mainly due to unhandled concurrency, network malfunctions, application bugs, or malicious users, or (ii) giving weak guarantees about their security. To tackle this issue, in this paper, we propose an improved version of a consensus protocol formalized in our previous work, built on top of the Bitcoin protocol, to incentivize third-party nodes to consistently extend their subchains. Besides, we perform an extensive analysis of this protocol, both defining its properties and presenting some real-world attack scenarios, to show how its specific design choices and parameter configurations can be crucial to prevent malicious practices. Full article

The wake dynamics of sharp-edge rigid panels is examined using Overset Grid Assembly (OGA) utilized in OpenFOAM, an open-source platform. The OGA method is an efficient solution technique based on overlap of a single or multiple moving grids on a stationary background grid. Five test cases for a stationary panel at different angle of attack are compared with available computational data, which show a good agreement in predicting global flow variables, such as mean drag. The models also provided accurate results in predicting the main flow features and structures. The flow past a pitching square panel is also investigated at two Reynolds numbers. The study of surface pressure distribution and shear forces acting on the panel suggests that a higher streamwise pressure gradient exists for the high Reynolds number case, which leads to an increase in lift, whereas the highly viscous effects at low Reynolds number lead to an increased drag production. The wake visualizations for the stationary and pitching motion cases show that the vortex shedding and wake characteristics are captured accurately using the OGA method. Full article

Construction of conservation laws of differential equations is an essential part of the mathematical study of differential equations. In this paper we derive, using two approaches, general formulas for finding conservation laws of the Black-Scholes equation. In one approach, we exploit nonlinear self-adjointness and Lie point symmetries of the equation, while in the other approach we use the multiplier method. We present illustrative examples and also show how every solution of the Black-Scholes equation leads to a conservation law of the same equation. Full article

A lot of effort has been devoted to mathematical modelling and simulation of complex systems for a better understanding of their dynamics and control. Modelling and analysis of computer simulations outcomes are also important aspects of studying the behaviour of complex systems. It often involves the use of both traditional and modern statistical approaches, including multiple linear regression, generalized linear model and non-linear regression models such as artificial neural networks. In this work, we first conduct a simulation study of the agents’ decisions learning to cross a cellular automaton based highway and then, we model the simulation data using artificial neural networks. Our research shows that artificial neural networks are capable of capturing the functional relationships between input and output variables of our simulation experiments, and they outperform the classical modelling approaches. The variable importance measure techniques can consistently identify the most dominant factors that affect the response variables, which help us to better understand how the decision-making by the autonomous agents is affected by the input factors. The significance of this work is in extending the investigations of complex systems from mathematical modelling and computer simulations to the analysis and modelling of the data obtained from the simulations using advanced statistical models. Full article

In this work, we consider elastic wave propagation in fractured media. The mathematical model is described by the Helmholtz problem related to wave propagation with specific interface conditions (Linear Slip Model, LSM) on the fracture in the frequency domain. For the numerical solution, we construct a fine grid that resolves all fracture interfaces on the grid level and construct approximation using a finite element method. We use a discontinuous Galerkin method for the approximation by space that helps to weakly impose interface conditions on fractures. Such approximation leads to a large system of equations and is computationally expensive. In this work, we construct a coarse grid approximation for an effective solution using the Generalized Multiscale Finite Element Method (GMsFEM). We construct and compare two types of the multiscale methods—Continuous Galerkin Generalized Multiscale Finite Element Method (CG-GMsFEM) and Discontinuous Galerkin Generalized Multiscale Finite Element Method (DG-GMsFEM). Multiscale basis functions are constructed by solving local spectral problems in each local domains to extract dominant modes of the local solution. In CG-GMsFEM, we construct continuous multiscale basis functions that are defined in the local domains associated with the coarse grid node and contain four coarse grid cells for the structured quadratic coarse grid. The multiscale basis functions in DG-GMsFEM are discontinuous and defined in each coarse grid cell. The results of the numerical solution for the two-dimensional Helmholtz equation are presented for CG-GMsFEM and DG-GMsFEM for different numbers of multiscale basis functions. Full article

Following the corrected chronology of ancient Hindu scientists/mathematicians, in this article, a sincere effort is made to report the origin of Pythagorean triples. We shall account for the development of these triples from the period of their origin and list some known astonishing directions. Although for researchers in this field, there is not much that is new in this article, we genuinely hope students and teachers of mathematics will enjoy this article and search for new directions/patterns. Full article

We introduce a very general class of generalized non-expansive maps. This new class of maps properly includes the class of Suzuki non-expansive maps, Reich–Suzuki type non-expansive maps, and generalized $\alpha$ -non-expansive maps. We establish some basic properties and demiclosed principle for this class of maps. After this, we establish existence and convergence results for this class of maps in the context of uniformly convex Banach spaces and compare several well known iterative algorithms. Full article

The optical equivalence principle is analyzed according to the possibility of describing unbounded states, and the suitable approximations are calculated for highly energetic phenomena. Among these possibilities, the relevance for laser fields, interferometers, and optomehcanical systems are implemented. Their suitableness for research in General Relativity, Cosmology, and High-Energy Physics are outlined. Full article