Search results for: accelerating numerical solutions

Authors: Pawel Flaszynski, Piotr Doerffer, Jan Holnicki-Szulc, Grzegorz Mikulowski

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Results of numerical simulations for transonic flow in a piezoelectric valve are presented. The valve is the main part of an adaptive pneumatic shock absorber. Flow structure in the valve domain and the influence of the flow non-uniformity in the valve on a mass flow rate is investigated. Numerical simulation results are compared with experimental data.

Keywords: pneumatic valve, transonic flow, numerical simulations, piezoelectric valve

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Authors: Marine Regnier, Pascal Bost, Matthieu Horgnies

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Some of the problems to be solved for the concrete industry are linked to the use of low-reactivity cement, the hardening of concrete under cold-weather and the manufacture of pre-casted concrete without costly heating step. The development of these applications needs to accelerate the hydration kinetics, in order to decrease the setting time and to obtain significant compressive strengths as soon as possible. The mechanisms enhancing the hydration kinetics of alite or Portland cement (e.g. the creation of nucleation sites) were already studied in literature (e.g. by using distinct additions such as titanium dioxide nanoparticles, calcium carbonate fillers, water-soluble polymers, C-S-H, etc.). However, the goal of this study was to establish a clear ranking of the efficiency of several types of additions by using a robust and reproducible methodology based on isothermal calorimetry (performed at 20°C). The cement was a CEM I 52.5N PM-ES (Blaine fineness of 455 m²/kg). To ensure the reproducibility of the experiments and avoid any decrease of the reactivity before use, the cement was stored in waterproof and sealed bags to avoid any contact with moisture and carbon dioxide. The experiments were performed on Portland cement pastes by using a water-to-cement ratio of 0.45, and incorporating different compounds (industrially available or laboratory-synthesized) that were selected according to their main composition and their specific surface area (SSA, calculated using the Brunauer-Emmett-Teller (BET) model and nitrogen adsorption isotherms performed at 77K). The intrinsic effects of (i) dry powders (e.g. fumed silica, activated charcoal, nano-precipitates of calcium carbonate, afwillite germs, nanoparticles of iron and iron oxides , etc.), and (ii) aqueous solutions (e.g. containing calcium chloride, hydrated Portland cement or Master X-SEED 100, etc.) were investigated. The influence of the amount of addition, calculated relatively to the dry extract of each addition compared to cement (and by conserving the same water-to-cement ratio) was also studied. The results demonstrated that the X-SEED®, the hydrated calcium nitrate, the calcium chloride (and, at a minor level, a solution of hydrated Portland cement) were able to accelerate the hydration kinetics of Portland cement, even at low concentration (e.g. 1%wt. of dry extract compared to cement). By using higher rates of additions, the fumed silica, the precipitated calcium carbonate and the titanium dioxide can also accelerate the hydration. In the case of the nano-precipitates of calcium carbonate, a correlation was established between the SSA and the accelerating effect. On the contrary, the nanoparticles of iron or iron oxides, the activated charcoal and the dried crystallised hydrates did not show any accelerating effect. Future experiments will be scheduled to establish the ranking of these additions, in terms of accelerating effect, by using low-reactivity cements and other water to cement ratios.

Keywords: acceleration, hydration kinetics, isothermal calorimetry, Portland cement

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Authors: Beghdadi Lotfi, Belkacem Abdellah

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In this work, a numerical method is proposed in order to solve the thermal performance problems of heat transfer of fins surfaces. The bidimensional temperature distribution on the longitudinal section of the fin is calculated by restoring to the finite volumes method. The heat flux dissipated by a generic profile fin is compared with the heat flux removed by the rectangular profile fin with the same length and volume. In this study, it is shown that a finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation, in order to determine the sinusoidal parameter values which optimize the fin effectiveness. In this scheme, based on the integration around the polygonal control volume, the derivatives of conduction equation must be converted into closed line integrals using same formulation of the Stokes theorem. The numerical results show good agreement with analytical results. To demonstrate the accuracy of the method, the absolute and root-mean square errors versus the grid size are examined quantitatively.

Keywords: Stokes theorem, unstructured grid, heat transfer, complex geometry

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Authors: G. De Matteis, L. Martina, V. Turco

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The work is focused on determining and comparing special nonlinear static configurations in cholesteric liquid crystals (CLCs), confined between two parallel plates and in the presence of an external static electric/magnetic field. The solutions are stabilised by topological and non-topological conservation laws since they are described in terms of integrable or partially integrable nonlinear boundary value problems. In cholesteric liquid crystals which are subject to geometric frustration; anchoring conditions at boundaries, i.e., homeotropic conditions, are incompatible with the cholesteric twist. This aspect turns out to be essential in the admissible classes of solutions, allowing also for disclination type singularities. Within the framework of Frank-Oseen theory, we study the static configurations for CLCs. First, we find numerical solutions for isolated axisymmetric states in confined CLCs with weak homeotropic anchoring at the boundaries. These solutions describe 3-dimensional modulations, namely spherulites or cholesteric bubbles, actually observed in these systems, of standard baby skyrmions. Relations with well-known nonlinear integrable systems are found and are used to explore the asymptotic behavior of the solutions. Then we turn our attention to extended periodic static configurations called Helicoids or cholesteric fingers, described by an elliptic sine-Gordon model with appropriate boundary conditions, showing how their period and energies are determined by both the thickness of the cell and the intensity of the external electric/magnetic field. We explicitly show that helicoids with π or 2π of rotations of the molecular director are different in many aspects and are not simply algebraically related. The behaviour of the solutions, their energy and the properties of the associated disclinations are discussed in detail, both analytically and numerically.

Keywords: cholesteric liquid crystals, geometric frustration, helicoids, skyrmions

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Authors: Sadia Arshad

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The new coronavirus disease or COVID-19 still poses an alarming situation around the world. Modeling based on the derivative of fractional order is relatively important to capture real-world problems and to analyze the realistic situation of the proposed model. Weproposed a mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. The new model is formulated in the Caputo sense and employs a nonlinear time-varying transmission rate. The existence and uniqueness solutions of the fractional order derivative have been studied using the fixed-point theory. The associated dynamical behaviors are discussed in terms of equilibrium, stability, and basic reproduction number. For the purpose of numerical implementation, an effcient approximation scheme is also employed to solve the fractional COVID-19 model. Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic. According to the comparative results with real data, we find the best value of fractional orderand justify the use of the fractional concept in the mathematical modelling, for the new fractional modelsimulates the reality more accurately than the other classical frameworks.

Keywords: fractional calculus, modeling, stability, numerical solution

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Authors: Samuel Ahamefula Mba

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Fluid turbulence is a complex and nonlinear phenomenon that occurs in various natural and industrial processes. Understanding turbulence remains a challenging task due to its intricate nature. One approach to gain insights into turbulence is through the study of entropy, which quantifies the disorder or randomness of a system. This research presents a numerical investigation of entropy signatures in fluid turbulence. The work is to develop a numerical framework to describe and analyse fluid turbulence in terms of entropy. This decomposes the turbulent flow field into different scales, ranging from large energy-containing eddies to small dissipative structures, thus establishing a correlation between entropy and other turbulence statistics. This entropy-based framework provides a powerful tool for understanding the underlying mechanisms driving turbulence and its impact on various phenomena. This work necessitates the derivation of the Poisson equation for pressure transformation of Navier-Stokes equation and using Chebyshev-Finite Difference techniques to effectively resolve it. To carry out the mathematical analysis, consider bounded domains with smooth solutions and non-periodic boundary conditions. To address this, a hybrid computational approach combining direct numerical simulation (DNS) and Large Eddy Simulation with Wall Models (LES-WM) is utilized to perform extensive simulations of turbulent flows. The potential impact ranges from industrial process optimization and improved prediction of weather patterns.

Keywords: turbulence, Navier-Stokes equation, Poisson pressure equation, numerical investigation, Chebyshev-finite difference, hybrid computational approach, large Eddy simulation with wall models, direct numerical simulation

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Authors: Mohamed Rabhi, Kouider Halim Benrahou

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The rheological properties of the carbonyl-methylcellulose (CMC), of different concentrations (25000, 50000, 60000, 80000 and 100000 ppm) and different temperatures were studied. We found that the rheological behavior of all CMC solutions presents a pseudo-plastic behavior, it follows the model of Ostwald-de Waele. The objective of this work is the modeling of flow by the CMC Cross model. The Cross model gives us the variation of the viscosity according to the shear rate. This model allowed us to adjust more clearly the rheological characteristics of CMC solutions. A comparison between the Cross model and the model of Ostwald was made. Cross the model fitting parameters were determined by a numerical simulation to make an approach between the experimental curve and those given by the two models. Our study has shown that the model of Cross, describes well the flow of "CMC" for low concentrations.

Keywords: CMC, rheological modeling, Ostwald model, cross model, viscosity

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Zuodong Liang, Dong-Sheng Jeng

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Seabed instability around an offshore pipeline is one of key factors that need to be considered in the design of offshore infrastructures. Unlike previous investigations, a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. The numerical model was first validated with 2-D experimental data available in the literature. Then, a parametric study will be carried out to examine the effects of wave, seabed characteristics and confirmation of pipeline. Numerical examples demonstrate significant influence of wave obliquity on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in 2-D numerical simulation.

Keywords: pore pressure, 3D wave model, seabed liquefaction, pipeline

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Authors: Amal Machtalay

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In this survey, we aim to review the rapidly growing literature on numerical methods to solve different forms of mean field problems, namely mean field games (MFG), mean field controls (MFC), potential MFGs, and master equations, as well as their corresponding recent applications. Here, we distinguish two families of numerical methods: iterative methods based on mesh generation and those called mesh-free, normally related to neural networking and learning frameworks.

Keywords: mean-field games, numerical schemes, partial differential equations, complex systems, machine learning

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Authors: A. Ja, J. Belabid, A. Cheddadi

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This paper reports the numerical simulation of double diffusive natural convection flows within a horizontal annular filled with a saturated porous medium. The analysis concerns the influence of the different parameters governing the problem, namely, the Rayleigh number Ra, the Lewis number Le and the buoyancy ratio N, on the heat and mass transfer and on the flow structure, in the case of a fixed radius ratio R = 2. The numerical model used for the discretization of the dimensionless equations governing the problem is based on the finite difference method, using the ADI scheme. The study is focused on steady-state solutions in the cooperation situation.

Keywords: natural convection, double-diffusion, porous medium, annular geometry, finite differences

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Authors: Changiz Valmohammadi

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The main purpose of this study is to explore the perception of Iranian experts and executive managers of sample organizations on the benefits and barriers of Internet of Things (IoT) solutions implementation. Based on the review of the related literature and web sites, benefits and barriers of successful implementation to IoT solutions were identified. Through a self-administered questionnaire which was collected from 67 Iranian organizations the ranking and importance of benefits and barriers of IoT solutions implementation were determined based on the perception of the experts of the surveyed organizations. Analysis of data and the obtained results revealed that “improved customer experience” and “Supply chain optimization and responsiveness” are the most important benefits that the survey organizations expect to reap as a result of IoT solutions implementation. Also,” Integration challenges" and “cannot find right suppliers” were ranked as the most challenging barriers to IoT solutions implementation.

Keywords: internet of things (IoT), exploratory study, benefits, barriers, Iran

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Authors: Tahir Nawaz Cheema, Dumitru Baleanu, Ali Raza

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In this research work, we design intelligent computing through Bayesian Regularization artificial neural networks (BRANNs) introduced to solve the mathematical modeling of infectious diseases (Covid-19). The dynamical transmission is due to the interaction of people and its mathematical representation based on the system's nonlinear differential equations. The generation of the dataset of the Covid-19 model is exploited by the power of the explicit Runge Kutta method for different countries of the world like India, Pakistan, Italy, and many more. The generated dataset is approximately used for training, testing, and validation processes for every frequent update in Bayesian Regularization backpropagation for numerical behavior of the dynamics of the Covid-19 model. The performance and effectiveness of designed methodology BRANNs are checked through mean squared error, error histograms, numerical solutions, absolute error, and regression analysis.

Keywords: mathematical models, beysian regularization, bayesian-regularization backpropagation networks, regression analysis, numerical computing

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Authors: Peng Li, Er-xiang Song

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Numerical analysis of longitudinal tunnel seismic response due to spatial variation of earthquake ground motion is an important issue that cannot be ignored in the design and safety evaluation of tunnel structures. In this paper, numerical methods for analysis of tunnel longitudinal response under asynchronous seismic wave is extensively studied, including the improvement of the 1D time-domain finite element method, three dimensional numerical simulation technique for the site asynchronous earthquake response as well as the 3-D soil-tunnel structure interaction analysis. The study outcome will be beneficial to aid further research on the nonlinear meticulous numerical analysis and seismic response mechanism of tunnel structures under asynchronous earthquake motion.

Keywords: asynchronous input, longitudinal seismic response, tunnel structure, numerical simulation, traveling wave effect

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Authors: Dinara F. Gaynutdinova, Vladimir Ya Modorsky, Nikolay A. Shevelev

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The problem under research is that of unpredictable modes occurring in two-stage centrifugal hydraulic pump as a result of hydraulic processes caused by vibrations of structural components. Numerical, analytical and experimental approaches are considered. A hypothesis was developed that the problem of unpredictable pressure decrease at the second stage of centrifugal pumps is caused by cavitation effects occurring upon vibration. The problem has been studied experimentally and theoretically as of today. The theoretical study was conducted numerically and analytically. Hydroelastic processes in dynamic “liquid – deformed structure” system were numerically modelled and analysed. Using ANSYS CFX program engineering analysis complex and computing capacity of a supercomputer the cavitation parameters were established to depend on vibration parameters. An influence domain of amplitudes and vibration frequencies on concentration of cavitation bubbles was formulated. The obtained numerical solution was verified using CFM program package developed in PNRPU. The package is based on a differential equation system in hyperbolic and elliptic partial derivatives. The system is solved by using one of finite-difference method options – the particle-in-cell method. The method defines the problem solution algorithm. The obtained numerical solution was verified analytically by model problem calculations with the use of known analytical solutions of in-pipe piston movement and cantilever rod end face impact. An infrastructure consisting of an experimental fast hydro-dynamic processes research installation and a supercomputer connected by a high-speed network, was created to verify the obtained numerical solutions. Physical experiments included measurement, record, processing and analysis of data for fast processes research by using National Instrument signals measurement system and Lab View software. The model chamber end face oscillated during physical experiments and, thus, loaded the hydraulic volume. The loading frequency varied from 0 to 5 kHz. The length of the operating chamber varied from 0.4 to 1.0 m. Additional loads weighed from 2 to 10 kg. The liquid column varied from 0.4 to 1 m high. Liquid pressure history was registered. The experiment showed dependence of forced system oscillation amplitude on loading frequency at various values: operating chamber geometrical dimensions, liquid column height and structure weight. Maximum pressure oscillation (in the basic variant) amplitudes were discovered at loading frequencies of approximately 1,5 kHz. These results match the analytical and numerical solutions in ANSYS and CFM.

Keywords: computing experiment, hydroelasticity, physical experiment, vibration

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Authors: Edamana Vasudevan Krishnan

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This paper studies solitons in optical materials with the help of Mapping Method. Two types of nonlinear media have been investigated, namely, the cubic nonlinearity and the quintic nonlinearity. The soliton solutions, shock wave solutions and singular solutions have been derives with certain constraint conditions.

Keywords: solitons, integrability, metamaterials, mapping method

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Authors: Sen Yung Lee, Chih Cheng Huang, Te Wen Tu

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A solution methodology without using integral transformation is proposed to develop analytical solutions for transient heat conduction in nonuniform hollow cylinders with time-dependent boundary condition at the outer surface. It is shown that if the thermal conductivity and the specific heat of the medium are in arbitrary polynomial function forms, the closed solutions of the system can be developed. The influence of physical properties on the temperature distribution of the system is studied. A numerical example is given to illustrate the efficiency and the accuracy of the solution methodology.

Keywords: analytical solution, nonuniform hollow cylinder, time-dependent boundary condition, transient heat conduction

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: A. Giniatoulline

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A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid

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Authors: Panagiotis Tsarchopoulos, Nicos Komninos, Christina Kakderi

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Smart cities are high on the political agenda around the globe. However, planning smart cities and deploying applications dealing with the complex problems of the urban environment is a very challenging task that is difficult to be undertaken solely by the cities. We argue that the uptake of smart city strategies is facilitated, first, through the development of smart city application repositories allowing re-use of already developed and tested software, and, second, through cloud computing which disengages city authorities from any resource constraints, technical or financial, and has a higher impact and greater effect at the city level The combination of these two solutions allows city governments and municipalities to select and deploy a large number of applications dedicated to different city functions, which collectively could create a multiplier effect with a greater impact on the urban environment.

Keywords: smart cities, applications, cloud computing, migration to the cloud, application repositories

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Authors: Mohamed Driouich, Kamal Gueraoui, Mohamed Sammouda

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The main objective of this work is to establish a numerical code for studying the flow of molten polymers in deformable pipes. Using an iterative numerical method based on finite differences, we determine the profiles of the fluid velocity, the temperature and the apparent viscosity of the fluid. The numerical code presented can also be applied to other industrial applications.

Keywords: numerical code, molten polymers, deformable pipes, finite differences

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Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: Ebrahim Alamatian, Seyed Mehdi Afzalnia

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One of the most vital hydraulic structures is the dam. Regarding the unrecoverable damages which may occur after a dam break phenomenon, analyzing dams’ break is absolutely essential. GOLESTAN dam is located in the western South of Mashhad city in Iran. GOLESTAN dam break might lead to severe problems due to adjacent tourist and entertainment areas. In this paper, a numerical code based on the finite volume method was applied for assessing the risk of GOLESTAN dam break. As to this issue, first, a canal with a triangular barrier was modeled so as to verify the capability of the concerned code. Comparing analytical, experimental and numerical results showed that water level in the model results is in a good agreement with the similar water level in the analytical solutions and experimental data. The results of dam break modeling are revealed that two of the bridges, that are PARTOIE and NAMAYESHGAH, located downstream in the flow direction, are at risk following the potential GOLESTAN dam break. Therefore, the required times to conduct the precautionary measures at bridges were calculated at about 12 and 21 minutes, respectively. Thus, it is crucial to announce people about the possible risks of the dam break in order to decrease likely losses.

Keywords: numerical model, shallow water equations, GOLESTAN dam break, dry and wet beds modeling

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Authors: Duygu Kan, Mehmet Cayoren

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Sommerfeld-integrals (SIs) are commonly encountered in electromagnetics problems involving analysis of antennas and scatterers embedded in planar multilayered media. Generally speaking, the analytical solution of SIs is unavailable, and it is well known that numerical evaluation of SIs is very time consuming and computationally expensive due to the highly oscillating and slowly decaying nature of the integrands. Therefore, fast computation of SIs has a paramount importance. In this paper, a parallel code has been developed to speed up the computation of SI in the framework of calculation of dyadic Green’s function in multilayered media. OpenMP shared memory approach is used to parallelize the SI algorithm and resulted in significant time savings. Moreover accelerating the computation of dyadic Green’s function is discussed based on the parallel SI algorithm developed.

Keywords: Sommerfeld-integrals, multilayer dyadic Green’s function, OpenMP, shared memory parallel programming

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Authors: Rishabh Ambavanekar

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Expressive Aphasia (EA) is an oral disability, common among stroke victims, in which the Broca’s area of the brain is damaged, interfering with verbal communication abilities. EA currently has no technological solutions and its only current viable solutions are inefficient or only available to the affluent. This prompts the need for an affordable, innovative solution to facilitate recovery and assist in speech generation. This project proposes a novel concept: using a wearable low-cost electroencephalography (EEG) device-based brain-computer interface (BCI) to translate a user’s inner dialogue into words. A low-cost EEG device was developed and found to be 10 to 100 times less expensive than any current EEG device on the market. As part of the BCI, a machine learning (ML) model was developed and trained using the EEG data. Two stages of testing were conducted to analyze the effectiveness of the device: a proof-of-concept and a final solution test. The proof-of-concept test demonstrated an average accuracy of above 90% and the final solution test demonstrated an average accuracy of above 75%. These two successful tests were used as a basis to demonstrate the viability of BCI research in developing lower-cost verbal communication devices. Additionally, the device proved to not only enable users to verbally communicate but has the potential to also assist in accelerated recovery from the disorder.

Keywords: neurotechnology, brain-computer interface, neuroscience, human-machine interface, BCI, HMI, aphasia, verbal disability, stroke, low-cost, machine learning, ML, image recognition, EEG, signal analysis

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Authors: Roslinda Nazar, Amin Noor, Khamisah Jafar, Ioan Pop

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In this paper, the steady laminar three-dimensional boundary layer flow and heat transfer of a copper (Cu)-water nanofluid in the vicinity of a permeable shrinking flat surface in an otherwise quiescent fluid is studied. The nanofluid mathematical model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Dual solutions (upper and lower branch solutions) are found for the similarity boundary layer equations for a certain range of the suction parameter. A stability analysis has been performed to show which branch solutions are stable and physically realizable. The numerical results for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are obtained, presented and discussed in detail for a range of various governing parameters.

Keywords: heat transfer, nanofluid, shrinking surface, stability analysis, three-dimensional flow

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Authors: Yu Liang, Wei Wei

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Spatial representation of numbers and numerical magnitude are important for preschoolers’ mathematical ability. Mental number line, a typical index to measure numbers spatial representation, and numerical comparison are both related to arithmetic obviously. However, they seem to rely on different mechanisms and probably influence arithmetic through different mechanisms. In line with this idea, preschool children were trained with two tasks to investigate which one is more important for approximate arithmetic. The training of numerical processing and number line estimation were proved to be effective. They both improved the ability of approximate arithmetic. When the difficulty of approximate arithmetic was taken into account, the performance in number line training group was not significantly different among three levels. However, two harder levels achieved significance in numerical comparison training group. Thus, comparing spatial representation ability, symbolic approximation arithmetic relies more on numerical magnitude. Educational implications of the study were discussed.

Keywords: approximate arithmetic, mental number line, numerical magnitude, preschooler

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Authors: Ovais U. Khan, G. M. Arshed, S. A. Raza, H. Ali

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A numerical model based on the computational fluid dynamics (CFD) approach is developed to investigate heat transfer across a longitudinal row of six circular cylinders. The momentum and energy equations are solved using the finite volume discretization technique. The convective terms are discretized using a second-order upwind methodology, whereas diffusion terms are discretized using a central differencing scheme. The second-order implicit technique is utilized to integrate time. Numerical simulations have been carried out for three different values of free stream Reynolds number (ReD) 100, 200, 300 and two different values of dimensionless longitudinal pitch ratio (SL/D) 1.5, 2.5 to demonstrate the fluid flow and heat transfer behavior. Numerical results are validated with the analytical findings reported in the literature and have been found to be in good agreement. The maximum percentage error in values of the average Nusselt number obtained from the numerical and analytical solutions is in the range of 10% for the free stream Reynolds number up to 300. It is demonstrated that the average Nusselt number for the array of cylinders increases with increasing the free stream Reynolds number and dimensionless longitudinal pitch ratio. The information generated would be useful in the design of more efficient heat exchangers or other fluid systems involving arrays of cylinders.

Keywords: computational fluid dynamics, array of cylinders, longitudinal pitch ratio, finite volume method, incompressible navier-stokes equations

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Authors: Khairil I. Othman, Nur N. Kamal, Zarina B. Ibrahim

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In this paper, we present modified Newton method as a new strategy for improving the efficiency of Two Point Block Backward Differentiation Formulas (BBDF) when solving stiff systems of ordinary differential equations (ODEs). These methods are constructed to produce two approximate solutions simultaneously at each iteration The detailed implementation of the predictor corrector BBDF with PE(CE)2 with modified Newton are discussed. The proposed modification of BBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing Block Backward Differentiation Formula. Numerical results show the advantage of using the new strategy for solving stiff ODEs in improving the accuracy of the solution.

Keywords: newton method, two point, block, accuracy

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Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis

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Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation.

Keywords: Hodgkin-Huxley equation, solitary solution, existence condition, operator method

Procedia PDF Downloads 347