Search results for: simultaneous equations

Authors: Gilbert Makanda

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The problem of the teaching of mathematics is studied using differential equations. A mathematical model for knowledge acquisition in mathematics is developed. In this study we adopt the mathematical model that is normally used for disease modelling in the teaching of mathematics. It is assumed that teaching is 'infecting' students with knowledge thereby spreading this knowledge to the students. It is also assumed that students who gain this knowledge spread it to other students making disease model appropriate to adopt for this problem. The results of this study show that increasing recruitment rates, learning contact with teachers and learning materials improves the number of knowledgeable students. High dropout rates and forgetting taught concepts also negatively affect the number of knowledgeable students. The developed model is then solved using Matlab ODE45 and \verb"lsqnonlin" to estimate parameters for the actual data.

Keywords: differential equations, knowledge acquisition, least squares, dynamical systems

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Authors: Bolatbek Rysbaiuly, Aliya S. Azhibekova

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Problems concerning the interpretation of the well testing results belong to the class of inverse problems of subsurface hydromechanics. The distinctive feature of such problems is that additional information is depending on the capabilities of oilfield experiments. Another factor that should not be overlooked is the existence of errors in the test data. To determine reservoir properties, some inverse problems for parabolic equations were investigated. An approach to solving the inverse problems based on the method of regularization is proposed.

Keywords: iterative approach, inverse problem, parabolic equation, reservoir properties

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Authors: Hanan Al-Jabri

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Simultaneous interpreting is deemed to be the most challenging mode of interpreting by many scholars. The special constraints involved in this task including time constraints, different linguistic systems, and stress pose a great challenge to most interpreters. These constraints are likely to maximise when the interpreting task is done live on TV. The TV interpreter is exposed to a wide variety of audiences with different backgrounds and needs and is mostly asked to interpret high profile tasks which raise his/her levels of stress, which further complicate the task. Under these constraints, which require fast and efficient performance, TV interpreters of four TV channels were asked to render Trump's victory speech into Arabic. However, they had also to deal with the burden of rendering English emotive overtones employed by the speaker into a whole different linguistic system. The current study aims at investigating the way TV interpreters, who worked in the simultaneous mode, handled this task; it aims at exploring and evaluating the TV interpreters’ linguistic choices and whether the original emotive effect was maintained, upgraded, downgraded or abandoned in their renditions. It also aims at exploring the possible difficulties and challenges that emerged during this process and might have influenced the interpreters’ linguistic choices. To achieve its aims, the study analysed Trump’s victory speech delivered on November 6, 2016, along with four Arabic simultaneous interpretations produced by four TV channels: Al-Jazeera, RT, CBC News, and France 24. The analysis of the study relied on two frameworks: a macro and a micro framework. The former presents an overview of the wider context of the English speech as well as an overview of the speaker and his political background to help understand the linguistic choices he made in the speech, and the latter framework investigates the linguistic tools which were employed by the speaker to stir people’s emotions. These tools were investigated based on Shamaa’s (1978) classification of emotive meaning according to their linguistic level: phonological, morphological, syntactic, and semantic and lexical levels. Moreover, this level investigates the patterns of rendition which were detected in the Arabic deliveries. The results of the study identified different rendition patterns in the Arabic deliveries, including parallel rendition, approximation, condensation, elaboration, transformation, expansion, generalisation, explicitation, paraphrase, and omission. The emerging patterns, as suggested by the analysis, were influenced by factors such as speedy and continuous delivery of some stretches, and highly-dense segments among other factors. The study aims to contribute to a better understanding of TV simultaneous interpreting between English and Arabic, as well as the practices of TV interpreters when rendering emotiveness especially that little is known about interpreting practices in the field of TV, particularly between Arabic and English.

Keywords: emotive overtones, interpreting strategies, political speeches, TV interpreting

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Authors: Phuoc Si Nguyen

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Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables calculation by hand when transforming from one filter to another. This paper will introduce two methods to transform a filter into a digital filter: frequency transformation from the s-domain into the z-domain; and frequency transformation in the z-domain. Further, two Pascal matrix equations are derived: an analogue to digital filter Pascal matrix equation and a digital to digital filter Pascal matrix equation. These are used to design a desired digital filter from a given filter.

Keywords: frequency transformation, bilinear z-transformation, pre-warping frequency, digital filters, analog filters, pascal’s triangle

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Authors: Abhilash Sahu, Amit Priyadarshi

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In this paper, we will discuss the existence of weak solutions of the Kirchhoff type boundary value problem on the Sierpinski gasket. Where S denotes the Sierpinski gasket in R² and S₀ is the intrinsic boundary of the Sierpinski gasket. M: R → R is a positive function and h: S × R → R is a suitable function which is a part of our main equation. ∆p denotes the p-Laplacian, where p > 1. First of all, we will define a weak solution for our problem and then we will show the existence of at least two solutions for the above problem under suitable conditions. There is no well-known concept of a generalized derivative of a function on a fractal domain. Recently, the notion of differential operators such as the Laplacian and the p-Laplacian on fractal domains has been defined. We recall the result first then we will address the above problem. In view of literature, Laplacian and p-Laplacian equations are studied extensively on regular domains (open connected domains) in contrast to fractal domains. In fractal domains, people have studied Laplacian equations more than p-Laplacian probably because in that case, the corresponding function space is reflexive and many minimax theorems which work for regular domains is applicable there which is not the case for the p-Laplacian. This motivates us to study equations involving p-Laplacian on the Sierpinski gasket. Problems on fractal domains lead to nonlinear models such as reaction-diffusion equations on fractals, problems on elastic fractal media and fluid flow through fractal regions etc. We have studied the above p-Laplacian equations on the Sierpinski gasket using fibering map technique on the Nehari manifold. Many authors have studied the Laplacian and p-Laplacian equations on regular domains using this Nehari manifold technique. In general Euler functional associated with such a problem is Frechet or Gateaux differentiable. So, a critical point becomes a solution to the problem. Also, the function space they consider is reflexive and hence we can extract a weakly convergent subsequence from a bounded sequence. But in our case neither the Euler functional is differentiable nor the function space is known to be reflexive. Overcoming these issues we are still able to prove the existence of at least two solutions of the given equation.

Keywords: Euler functional, p-Laplacian, p-energy, Sierpinski gasket, weak solution

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Authors: Abdul Hakim Chikho

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Most international codes allow the use of an equivalent lateral load method for designing practical buildings to withstand earthquake actions. This method requires calculating an approximation to the fundamental mode period of vibrations of these buildings. Several empirical equations have been suggested to calculate approximations to the fundamental periods of different types of structures. Most of these equations are knowing to provide an only crude approximation to the required fundamental periods and repeating the calculation utilizing a more accurate formula is usually required. In this paper, a new formula to calculate a satisfactory approximation of the fundamental period of a practical building is proposed. This formula takes into account the mass and the stiffness of the building therefore, it is more logical than the conventional empirical equations. In order to verify the accuracy of the proposed formula, several examples have been solved. In these examples, calculating the fundamental mode periods of several farmed buildings utilizing the proposed formula and the conventional empirical equations has been accomplished. Comparing the obtained results with those obtained from a dynamic computer has shown that the proposed formula provides a more accurate estimation of the fundamental periods of practical buildings. Since the proposed method is still simple to use and requires only a minimum computing effort, it is believed to be ideally suited for design purposes.

Keywords: earthquake, fundamental mode period, design, building

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Authors: Aurore Cauquis, Philippe Heinrich, Mario Ricchiuto, Audrey Gailler

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In this talk, we look for an accurate time scheme to model the propagation of waves. Several numerical schemes have been developed to solve the extended weakly nonlinear weakly dispersive Boussinesq Equations. The temporal schemes used are two Lax-Wendroff schemes, second or third order accurate, two Runge-Kutta schemes of second and third order and a simplified third order accurate Lax-Wendroff scheme. Spatial derivatives are evaluated with fourth order accuracy. The numerical model is applied to two monodimensional benchmarks on a flat bottom. It is also applied to the simulation of the Algerian tsunami generated by a Mw=6 seism on the 18th March 2021. The tsunami propagation was highly dispersive and propagated across the Mediterranean Sea. We study here the effects of the order of temporal discretization on the accuracy of the results and on the time of computation.

Keywords: numerical analysis, tsunami propagation, water wave, boussinesq equations

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Authors: Ali Kezmane, Said Boukais, Mohand Hamizi

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This paper presents an analytical study on the behavior of reinforced concrete walls with rectangular cross section. Several experiments on such walls have been selected to be studied. Database from various experiments were collected and nominal shear wall strengths have been calculated using formulas, such as those of the ACI (American), NZS (New Zealand), Mexican (NTCC), and Wood and Barda equations. Subsequently, nominal shear wall strengths from the formulas were compared with the ultimate shear wall strengths from the database. These formulas vary substantially in functional form and do not account for all variables that affect the response of walls. There is substantial scatter in the predicted values of ultimate shear strength. Two new semi empirical equations are developed using data from tests of 57 walls for transitions walls and 27 for slender walls with the objective of improving the prediction of peak strength of walls with the most possible accurate.

Keywords: shear strength, reinforced concrete walls, rectangular walls, shear walls, models

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Authors: Yilmaz Simsek

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In this paper, we study the Bernstein-type basis functions with their generating functions. We give various properties of these polynomials with the aid of their generating functions. These polynomials and generating functions have many valuable applications in mathematics, in probability, in statistics and also in mathematical physics. By using the Bernstein-Galerkin and the Bernstein-Petrov-Galerkin methods, we give some applications of the Bernstein-type polynomials for solving high even-order differential equations with their numerical computations. We also give Bezier-type curves related to the Bernstein-type basis functions. We investigate fundamental properties of these curves. These curves have many applications in mathematics, in computer geometric design and other related areas. Moreover, we simulate these polynomials with their plots for some selected numerical values.

Keywords: generating functions, Bernstein basis functions, Bernstein polynomials, Bezier curves, differential equations

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Authors: Boguslaw Schreyer

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In this paper, a general dynamical model is derived using the Lagrange formalism. The two masses: sprang and unsprang are included in a six-degree of freedom model for a sprung mass. The unsprung mass is included and shown only in a simplified model, although its equations have also been derived by an author. The simplified equations, more suitable for the computer model of robot’s dynamics are also shown.

Keywords: dynamics, mobile, robot, wheeled mobile robots

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Authors: Mi-Ju Kim, Hae-Yeong Kim

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Product mislabeling and adulteration have been increasing the concerns in processed meat products. Relatively inexpensive pork meat compared to meat such as beef was adulterated for economic benefit. These food fraud incidents related to pork were concerned due to economic, religious and health reasons. In this study, a rapid on-site detection method using loop-mediated isothermal amplification (LAMP) was developed for the simultaneous identification of beef and pork. Each specific LAMP primer for beef and pork was designed targeting on mitochondrial D-loop region. The LAMP assay reaction was performed at 65 ℃ for 40 min. The specificity of each primer for beef and pork was evaluated using DNAs extracted from 13 animal species including beef and pork. The sensitivity of duplex LAMP assay was examined by serial dilution of beef and pork DNAs, and reference binary mixtures. This assay was applied to processed meat products including beef and pork meat for monitoring. Each set of primers amplified only the targeted species with no cross-reactivity with animal species. The limit of detection of duplex real-time LAMP was 1 pg for each DNA of beef and pork and 1% pork in a beef-meat mixture. Commercial meat products that declared the presence of beef and/or pork meat on the label showed positive results for those species. This method was successfully applied to detect simultaneous beef and pork meats in processed meat products. The optimized duplex LAMP assay can identify simultaneously beef and pork meat within less than 40 min. A portable real-time fluorescence device used in this study is applicable for on-site detection of beef and pork in processed meat products. Thus, this developed assay was considered to be an efficient tool for monitoring meat products.

Keywords: beef, duplex real-time LAMP, meat identification, pork

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Authors: Keltoum Bouherine, Olivier Leroy

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The present work is dedicated to study a three–dimensional (3D) self-consistent fluid simulation of microwave discharges of argon plasma in PECVD reactor. The model solves the Maxwell’s equations, continuity equations for charged species and the electron energy balance equation, coupled with Poisson’s equation, and Navier-Stokes equations by finite element method, using COMSOL Multiphysics software. In this study, the simulations yield the profiles of plasma components as well as the charge densities and electron temperature, the electric field, the gas velocity, and gas temperature. The results show that the microwave plasma reactor is outside of local thermodynamic equilibrium.The present work is dedicated to study a three–dimensional (3D) self-consistent fluid simulation of microwave discharges of argon plasma in PECVD reactor. The model solves the Maxwell’s equations, continuity equations for charged species and the electron energy balance equation, coupled with Poisson’s equation, and Navier-Stokes equations by finite element method, using COMSOL Multiphysics software. In this study, the simulations yield the profiles of plasma components as well as the charge densities and electron temperature, the electric field, the gas velocity, and gas temperature. The results show that the microwave plasma reactor is outside of local thermodynamic equilibrium.

Keywords: electron density, electric field, microwave plasma reactor, gas velocity, non-equilibrium plasma

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Authors: Majid Farsadrouh Rashti, Parisa Jahani, Amir Shafiee, Mehrdad Mofidi

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The dihydroxybenzene isomers, hydroquinone (HQ), catechol (CC) and resorcinol (RS) have been widely recognized as important environmental pollutants due to their toxicity and low degradability in the ecological environment. Speciation of HQ, CC and RS is very important for environmental analysis because they co-exist of these isomers in environmental samples and are too difficult to degrade as an environmental contaminant with high toxicity. There are many analytical methods have been reported for detecting these isomers, such as spectrophotometry, fluorescence, High-performance liquid chromatography (HPLC) and electrochemical methods. These methods have attractive advantages such as simple and fast response, low maintenance costs, wide linear analysis range, high efficiency, excellent selectivity and high sensitivity. A novel modified glassy carbon electrode (GCE) with Pd@ Cu/CNTs core−shell nanowires for the simultaneous determination of hydroquinone (HQ), catechol (CC) and resorcinol (RS) is described. A detailed investigation by field emission scanning electron microscopy and electrochemistry was performed in order to elucidate the preparation process and properties of the GCE/ Pd/CuNWs-CNTs. The electrochemical response characteristic of the modified GPE/LFOR toward HQ, CC and RS were investigated by cyclic voltammetry, differential pulse voltammetry (DPV) and Chronoamperometry. Under optimum conditions, the calibrations curves were linear up to 228 µM for each with detection limits of 0.4, 0.6 and 0.8 µM for HQ, CC and RS, respectively. The diffusion coefficient for the oxidation of HQ, CC and RS at the modified electrode was calculated as 6.5×10⁻⁵, 1.6 ×10⁻⁵ and 8.5 ×10⁻⁵ cm² s⁻¹, respectively. DPV was used for the simultaneous determination of HQ, CC and RS at the modified electrode and the relative standard deviations were 2.1%, 1.9% and 1.7% for HQ, CC and RS, respectively. Moreover, GCE/Pd/CuNWs-CNTs was successfully used for determination of HQ, CC and RS in real samples.

Keywords: dihydroxybenzene isomers, galvanized copper nanowires, electrochemical sensor, Palladium, speciation

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Authors: O. Adjoul, A. Feugier, K. Benfriha, A. Aoussat

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In general, issues related to design and maintenance are considered in an independent manner. However, the decisions made in these two sets influence each other. The design for maintenance is considered an opportunity to optimize the life cycle cost of a product, particularly in the nuclear or aeronautical field, where maintenance expenses represent more than 60% of life cycle costs. The design of large-scale systems starts with product architecture, a choice of components in terms of cost, reliability, weight and other attributes, corresponding to the specifications. On the other hand, the design must take into account maintenance by improving, in particular, real-time monitoring of equipment through the integration of new technologies such as connected sensors and intelligent actuators. We noticed that different approaches used in the Design For Maintenance (DFM) methods are limited to the simultaneous characterization of the reliability and maintainability of a multi-component system. This article proposes a method of DFM that assists designers to propose dynamic maintenance for multi-component industrial systems. The term "dynamic" refers to the ability to integrate available monitoring data to adapt the maintenance decision in real time. The goal is to maximize the availability of the system at a given life cycle cost. This paper presents an approach for simultaneous optimization of the design and maintenance of multi-component systems. Here the design is characterized by four decision variables for each component (reliability level, maintainability level, redundancy level, and level of monitoring data). The maintenance is characterized by two decision variables (the dates of the maintenance stops and the maintenance operations to be performed on the system during these stops). The DFM model helps the designers choose technical solutions for the large-scale industrial products. Large-scale refers to the complex multi-component industrial systems and long life-cycle, such as trains, aircraft, etc. The method is based on a two-level hybrid algorithm for simultaneous optimization of design and maintenance, using genetic algorithms. The first level is to select a design solution for a given system that considers the life cycle cost and the reliability. The second level consists of determining a dynamic and optimal maintenance plan to be deployed for a design solution. This level is based on the Maintenance Free Operating Period (MFOP) concept, which takes into account the decision criteria such as, total reliability, maintenance cost and maintenance time. Depending on the life cycle duration, the desired availability, and the desired business model (sales or rental), this tool provides visibility of overall costs and optimal product architecture.

Keywords: availability, design for maintenance (DFM), dynamic maintenance, life cycle cost (LCC), maintenance free operating period (MFOP), simultaneous optimization

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Authors: M. H. Kazemi, D. Salac

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A semi-implicit phase field method for droplet evolution is proposed. Using the phase field Cahn-Hilliard equation, we are able to track the interface in multiphase flow. The idea of a semi-implicit finite difference scheme is reviewed and employed to solve two nonlinear equations, including the Navier-Stokes and the Cahn-Hilliard equations. The use of a semi-implicit method allows us to have larger time steps compared to explicit schemes. The governing equations are coupled and then solved by a GMRES solver (generalized minimal residual method) using modified Gram-Schmidt orthogonalization. To show the validity of the method, we apply the method to the simulation of a rising droplet, a leaky dielectric drop and the coalescence of drops. The numerical solutions to the phase field model match well with existing solutions over a defined range of variables.

Keywords: coalescence, leaky dielectric, numerical method, phase field, rising droplet, semi-implicit method

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Authors: Eugene Stepanov, Arcady Ponosov

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To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models.

Keywords: hybrid dynamical systems, ill-posed problems, singular perturbation analysis, switching nonlinearities

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Authors: Mujde Turkkan, Nurkan Yagiz

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In this study an active controller is presented for vibration suppression of a full-bus model. The bus is modelled having seven degrees of freedom. Using the achieved model via Lagrange Equations the system equations of motion are derived. The suspensions of the bus model include air springs with two auxiliary chambers are used. Fuzzy logic controller is used to improve the ride comfort. The numerical results, verifies that the presented fuzzy logic controller improves the ride comfort.

Keywords: ride comfort, air spring, bus, fuzzy logic controller

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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: S. B. Mayil Vealan, C. Sekar

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Bisphenol A (BIS A) and 4 Nitrophenol (4N) are the most prevalent environmental endocrine-disrupting chemicals which mimic hormones and have a direct relationship to the development and growth of animal and human reproductive systems. Moreover, intensive exposure to the compound is related to prostate and breast cancer, infertility, obesity, and diabetes. Hence, accurate and reliable determination techniques are crucial for preventing human exposure to these harmful chemicals. Lanthanum Copper Oxide (La₂Cu₂O₅) nanoparticles were synthesized and investigated through various techniques such as scanning electron microscopy, high-resolution transmission electron microscopy, X-ray diffraction, X-ray photoelectron spectroscopy, and electrochemical impedance spectroscopy. Cyclic voltammetry and square wave voltammetry techniques are employed to evaluate the electrochemical behavior of as-synthesized samples toward the electrochemical detection of Bisphenol A and 4-Nitrophenol. Under the optimal conditions, the oxidation current increased linearly with increasing the concentration of BIS A and 4-N in the range of 0.01 to 600 μM with a detection limit of 2.44 nM and 3.8 nM. These are the lowest limits of detection and the widest linear ranges in the literature for this determination. The method was applied to the simultaneous determination of BIS A and 4-N in real samples (food packing materials and river water) with excellent recovery values ranging from 95% to 99%. Better stability, sensitivity, selectivity and reproducibility, fast response, and ease of preparation made the sensor well-suitable for the simultaneous determination of bisphenol and 4 Nitrophenol. To the best of our knowledge, this is the first report in which La₂Cu₂O₅ nano particles were used as efficient electron mediators for the fabrication of endocrine disruptor (BIS A and 4N) chemical sensors.

Keywords: endocrine disruptors, electrochemical sensor, Food contacting materials, lanthanum cuprates, nanomaterials

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Authors: Rawhy Ismail

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Applying fractional calculus in the field of electromagnetics shows significant results. The fractionalization of the conventional curl operator leads to having additional solutions to an electromagnetic problem. This work restudies the concept of the fractional curl operator considering fractional time derivatives in Maxwell’s curl equations. In that sense, a general scheme for the wave loss term is introduced and the degree of freedom of the system is affected through imposing the new fractional parameters. The conventional case is recovered by setting all fractional derivatives to unity.

Keywords: curl operator, fractional calculus, fractional curl operators, Maxwell equations

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Authors: Ainul Haque, Ameeye Kumar Nayak

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Flow enhancement and species transport in a slit hydrophobic microchannel is studied for non-Newtonian fluids with the externally imposed electric field and pressure gradient. The incompressible Poisson-Nernst-Plank equations and the Navier-Stokes equations are approximated by lubrication theory to quantify the flow structure due to hydrophobic and hydrophilic surfaces. The analytical quantification of velocity and pressure of electroosmotic flow (EOF) is made with the numerical results due to the staggered grid based finite volume method for flow governing equations. The resistance force due to fluid friction and shear force along the surface are decreased by the hydrophobicity, enables the faster movement of fluid particles. The resulting flow enhancement factor Ef is increased with the low viscous fluid and provides maximum species transport. Also, the analytical comparison of EOF with pressure driven EOF justifies the flow enhancement due to hydrophobicity and shear impact on flow variation.

Keywords: electroosmotic flow, hydrophobic surface, power-law fluid, shear effect

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Authors: Y. M. Aiyesimi, G. T. Okedayo, O. W. Lawal

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The analysis has been carried out to study unsteady MHD thin film flow of a third grade fluid down an inclined plane with heat transfer when the slippage between the surface of plane and the lower surface of the fluid is valid. The governing nonlinear partial differential equations involved are reduced to linear partial differential equations using regular perturbation method. The resulting equations were solved analytically using method of separation of variable and eigenfunctions expansion. The solutions obtained were examined and discussed graphically. It is interesting to find that the variation of the velocity and temperature profile with the slip and magnetic field parameter depends on time.

Keywords: non-Newtonian fluid, MHD flow, thin film flow, third grade fluid, slip boundary condition, heat transfer, separation of variable, eigenfunction expansion

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Authors: Alex Fedoseyev

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This study explores Generalized Hydrodynamic Equations (GHE) for the simulation of turbulent flows. The GHE was derived from the Generalized Boltzmann Equation (GBE) by Alexeev (1994). GBE was obtained by first principles from the chain of Bogolubov kinetic equations and considered particles of finite dimensions, Alexeev (1994). The GHE has new terms, temporal and spatial fluctuations compared to the Navier-Stokes equations (NSE). These new terms have a timescale multiplier τ, and the GHE becomes the NSE when τ is zero. The nondimensional τ is a product of the Reynolds number and the squared length scale ratio, τ=Re*(l/L)², where l is the apparent Kolmogorov length scale, and L is a hydrodynamic length scale. The turbulence phenomenon is not well understood and is not described by NSE. An additional one or two equations are required for the turbulence model, which may have to be tuned for specific problems. We show that, in the case of the GHE, no additional turbulence model is needed, and the turbulent velocity profile is obtained from the GHE. The 2D turbulent channel and circular pipe flows were investigated using a numerical solution of the GHE for several cases. The solutions are compared with the experimental data in the circular pipes and 2D channels by Nicuradse (1932, Prandtl Lab), Hussain and Reynolds (1975), Wei and Willmarth (1989), Van Doorne (2007), theory by Wosnik, Castillo and George (2000), and the relevant experiments on Superpipe setup at Princeton, data by Zagarola (1996) and Zagarola and Smits (1998), the Reynolds number is from Re=7200 to Re=960000. The numerical solution data compared well with the experimental data, as well as with the approximate analytical solution for turbulent flow in channel Fedoseyev (2023). The obtained results confirm that the Alexeev generalized hydrodynamic theory (GHE) is in good agreement with the experiments for turbulent flows. The proposed approach is limited to 2D and 3D axisymmetric channel geometries. Further work will extend this approach by including channels with square and rectangular cross-sections.

Keywords: comparison with experimental data. generalized hydrodynamic equations, numerical solution, turbulent boundary layer, turbulent flow in channel

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Authors: Mohamed Suleiman, Zarina Bibi Ibrahim, Nor Ain Azeany, Khairil Iskandar Othman

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In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs.

Keywords: block backward differentiation formulas, uniform step size, ordinary differential equations

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Authors: Valiollah Babaeipour, Mahdi Rahaie

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food supplements are rich in specific nutrients and bioactive compounds that eliminate free radicals and improve cellular metabolism. The major bioactive compounds are found in bran and cereal sprouts. Secondary metabolites of these microorganisms have antioxidant properties that can be used alone or in combination with chemotherapy and radiation therapy to treat cancer. Biologically active compounds such as benzoquinone derivatives extracted from fermented wheat germ extract (FWGE) have several positive effects on the overall state of human health and strengthen the immune system. The present work describes the discontinuous fermentation of raw wheat germ for FWGE production through the simultaneous culture process using the probiotic strains of Saccharomyces cerevisiae, Lactobacillus plantarum, and the possibility of using solid waste. To increase production efficiency, first to select important factors in the optimization of each fermentation process, using a factorial statistical scheme of stirring fraction (120 to 200 rpm), dilution of solids to solvent (1 to 8-12), fermentation time (16 to 24 hours) and strain to wheat germ ratio (20% to 50%) were studied and then simultaneous culture was performed to increase the yields of 2 and 6 dimethoxybenzoquinone (2,6-DMBQ). Since 2 and 6 dimethoxy benzoquinone were fermented as the main biologically active compound in wheat germ extract, UV-Vis analysis was performed to confirm the presence of 2 and 6 dimethoxy benzoquinone in the final product. In addition, 2,6-DMBQ of some products was isolated in a non-polar C-18 column and quantified using high performance liquid chromatography (HPLC). Based on our findings, it can be concluded that the increase of 2 and 6 dimethoxybenzoquinone in the simultaneous culture of Saccharomyces cerevisiae - Lactobacillus plantarum compared to pure culture of Saccharomyces cerevisiae (from 1.89 mg / g) to 28.9% (2.66 mg / g) Increased.

Keywords: wheat germ, FWGE, saccharomyces cerevisiae, lactobacillus plantarum, co-culture, 2, 6-DMBQ

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Authors: Said Algarni

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The purpose of this study was to investigate selected numerical methods that demonstrate good performance in solving PDEs. We adapted alternative method that involve rational polynomials. Padé time stepping (PTS) method, which is highly stable for the purposes of the present application and is associated with lower computational costs, was applied. Furthermore, PTS was modified for our study which focused on diffusion equations. Numerical runs were conducted to obtain the optimal local error control threshold.

Keywords: Padé time stepping, finite difference, reaction diffusion equation, PDEs

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Authors: Minas Balyan

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In the third-order nonlinear Takagi’s equations for monochromatic waves and in the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses for forbidden reflections the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero. The dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well known Renninger effect takes place. In this work, the ‘third order nonlinear Renninger effect’ is considered theoretically and numerically. If the reflection exactly is forbidden the diffracted wave’s amplitude is zero both in Laue and Bragg cases since the boundary conditions and dynamical diffraction equations are compatible with zero solution. But in real crystals due to some percent of dislocations and other localized defects, the atoms are displaced with respect to their equilibrium positions. Thus in real crystals susceptibilities of forbidden reflection are by some order small than for usual not forbidden reflections but are not exactly equal to zero. The numerical calculations for susceptibilities two order less than for not forbidden reflection show that in Bragg geometry case the nonlinear reflection curve’s behavior is the same as for not forbidden reflection, but for forbidden reflection the rocking curves’ width, center and boundaries are two order sensitive on the input intensity value. This gives an opportunity to investigate third order nonlinear X-ray dynamical diffraction for not intense beams – 0.001 in the units of critical intensity.

Keywords: third order nonlinearity, Bragg diffraction, nonlinear Renninger effect, rocking curves

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Authors: Youb Said, Fourar Ali

Abstract:

To describe the influence of bottom roughness on the free surface flows by numerical modeling, a two-dimensional model was developed. The equations of continuity and momentum (Naviers Stokes equations) are solved by the finite volume method. We considered a turbulent flow in an open channel with a bottom roughness. For our simulations, the K-ε model was used. After setting the initial and boundary conditions and solve the equations set, we were able to achieve the following results: vortex forming in the hollow causing substantial energy dissipation in the obstacle areas that form the bottom roughness. The comparison of our results with experimental ones shows a good agreement in terms of the results in the rough area. However, in other areas, differences were more or less important. These differences are in areas far from the bottom, especially the free surface area just after the bottom. These disagreements are probably due to experimental constants used by the k-ε model.

Keywords: modeling, free surface flow, turbulence, bottom roughness, finite volume, K-ε model, energy dissipation

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Authors: A. Abbasi Moshaii, M. Soltan Rezaee, M. Mohammadi Moghaddam

Abstract:

Control of some mechanisms is hard because of their complex dynamic equations. If part of the complexity is resulting from uncertainties, an efficient way for solving that is robust control. By this way, the control procedure could be simple and fast and finally, a simple controller can be designed. One kind of these mechanisms is 3-RRR which is a parallel mechanism and has three revolute joints. This paper aims to robust control a 3-RRR planner mechanism and it presents that this could be used for other mechanisms. So, a significant problem in mechanisms control could be solved. The relevant diagrams are drawn and they show the correctness of control process.

Keywords: 3-RRR, dynamic equations, mechanisms control, structural uncertainty

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Authors: Youssef Abdelli, Rachid Nasri

Abstract:

The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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